Essays on Wage Determination

Kenneth Lykke Sørensen

A PhD thesis submitted to Business and Social Sciences, Aarhus University, in partial fulfilment of the requirements of the PhD degree in Economics and Business

Contents Preface

v

Summary

vii

Summary in Danish (dansk resum´e)

xi

1

Worker and Firm Heterogeneity in Wage Growth: An AKM Approach

1

2

Wage Sorting Trends

33

3

Return To Experience and Initial Wages: Do Low Wage Workers Catch Up?

51

4

Effects of Intensifying Labor Market Programs on Post-Unemployment Wages: Evidence From a Controlled Experiment

iii

85

Preface This thesis was written in the period from September 2009 to August 2012 while I was enrolled as a PhD student at the Department of Economics and Business, Aarhus University. I would like to thank the Department for giving me the opportunity to write this dissertation and for providing an excellent research environment. In addition, I thank the Department for letting me attend numerous courses and conferences, both abroad and in Denmark. I would like to thank my main advisor, Michael Svarer, for being available and giving comments whenever necessary and for understanding I was not a PhD student in need of weekly meetings. The always relaxed tone has suited me very well. I would also like to thank my secondary supervisor and co-author on chapters one, two and three in this dissertation (plus yet another paper describing wage applications on Danish data, forthcoming in book on Danish data, edited by Dale T. Mortensen) Rune Vejlin for all his efforts on these chapters. I have learned a lot by working so closely alongside Rune and am grateful for all those many hours both of us have put into the chapters. Also my other co-author on chapter two, Jesper Bagger, deserves thanks. Especially for showing me the value of always pursuing an even better paper. Thanks to Kirsten Stentoft for very competently proofreading my manuscripts. Furthermore, I am, as almost all researchers (staff and visitors) at the Department working on Danish data, indebted to my other secondary supervisor, Henning Bunzel. Thanks for always being willing to put in uncountable hours in helping prepare data, communicating with Statistics Denmark, debugging fortran code and for the always exiting talks about Linux servers, Fortran code, numerical optimization, etc. From January - June 2011 I visited the Department of Economics at the University of Wisconsin-Madison. I would like to thank the Department for its hospitality. Especially, I thank Rasmus Lentz for arranging and sponsoring my stay at the Department and Chris Taber for being willing to discuss my papers. It was definitely an experience for life staying those six months in Madison. Of course, thanks also have to go to all my fellow PhD students at the Department. All of v

vi you guys have made some very long days behind the yellow walls much more interesting. I have enjoyed sharing an office with Tine and Ritwik and special thanks go to Mark and Mikkel for all those fantastic coffee breaks and great discussions, both the intellectual and the not-sointellectual ones. Finally, thanks to Ellen and my family for coping with lots of talks about data problems, annoying server conditions, labor economics, worker effects, etc., etc. Kenneth Lykke Sørensen Aarhus, August 2012

Updated Preface I would like to thank the members of the assessment committee, Lars Skipper (chair, Aarhus University), Jakob Roland Munch (University of Copenhagen) and Francis Kramarz (CRESTENSAE, Paris) for carefully reading my thesis and for all their comments and suggestions for improvements. I appreciate the time and effort the committee has put into delivering thoughtful and usable comments, and firmly believe they have added value to the revised version of this thesis.

Kenneth Lykke Sørensen Odense, January 2013

Summary This thesis consists of four independent chapters insofar that all four chapters empirically estimate determination of wages using Danish data. However, the chapters do so in three very different ways. Chapter one specifies a linear wage growth equation including unobserved worker and firm heterogeneity. Chapter two is a note dealing with an indirect outcome of linear wage equations with worker and firm fixed effects (like in chapter one). In chapter three we use nonparametric methods to estimate the relationship between the wage in the first job and the individual expected return to experience profile six to ten years after labor market entry. Finally, chapter four uses duration analysis to estimate a post-unemployment wage hazard for newly unemployed workers who participated in a field experiment where roughly half of them was put into an intensified active labor market policy program. In the first chapter, Worker and Firm Heterogeneity in Wage Growth: An AKM Approach (published in LABOUR, 2011, vol. 25, 4, pp. 485-507, co-authored by Rune Vejlin), we exploit the statistical methods developed by Abowd, Kramarz and Margolis (1999) (the socalled AKM approach), later refined and extended by Abowd, Creecy and Kramarz (2002), to estimate worker fixed effects and firm fixed effects in a linear wage growth specification. A specific outcome of this method is the decomposition of the variance of wage growth. The AKM decomposition has been used for analysis on a number of different datasets, but almost all are estimating worker and firm effects on wages in levels. We contribute to the literature by focusing on wage growth (although, in the chapter, we also estimate the traditional wage level equation). From a policy perspective, it is important to know how the variance of wage growth is distributed across firms. Imagine there is no variance in wage growth across firms. Then, placing a worker in any firm will lead to higher wages independent of the worker-firm match. If the variation in wage growth on the other hand primarily is caused by firm effects, it becomes important for the worker to be placed in the best firms in order to receive higher wages. We find that unobserved worker effects are more important for the variance in wage growth than observables and unobserved firm effects. However, there is still a considerable amount of the vii

viii variance of wage growth left unexplained. Chapter two, Wage Sorting Trends (co-authored by Jesper Bagger and Rune Vejlin) is a note that documents a trend in the correlation between worker fixed effects and firm fixed effects estimated from an AKM wage equation. Studies using the AKM specification often report the correlation between worker and firm effects as one number (Abowd et al. (2002), correlation -0.28, France and -0.03, the US. Gruetter and Lalive (2004), correlation -0.22, Austria. Andrews, Gill, Schank and Upward (2008), correlation -0.21 to -0.15, Germany and Sørensen and Vejlin (2012), correlation -0.06 to 0.11, Denmark). We find a correlation of 0.05 and show that it masks a systematic non-stationarity and the cross-section specific correlations show an increasing trend over time. In the chapter, we decompose correlations and show that most of this trend can be attributed to workers in the top quartile of worker effects. The increasing wage sorting trend in the top quartile of worker effects could be related to high wage workers employed in high wage firms being increasingly likely to transit to another high wage firm, or to high wage workers employed in low wage firms being increasingly likely to transit to a high wage firm. Our analysis supports the former relation. In Chapter three, Return to Experience and Initial Wages: Do Low Wage Workers Catch Up? (under Revision for Resubmision to the Journal of Applied Econometrics, co-authored by Rune Vejlin) we use nonparametric methods to estimate the relationship between an individual permanent component of wages and an individual return to experience in the early stages of a worker’s labor market career. From chapter one and two we see that individual permanent components matter for the explanation of wages. Another literature going all the way back to Mincer (1958) has shown human capital (such as experience and education) to be important for wage determination. Putting this together, we thus suspect that return to experience could change with unobservable skills. We use and extend the identification of this relationship by Gladden and Taber (2009) and estimate the expected return to experience for an individual worker given his initial wages. We find an overall negative relationship between initial wages and return to experience, but a positive relationship between return to experience and educational level (an observable individual characteristic). Especially for vocational educated workers, the catching up effect for low initial wage workers is relatively large. We relate these findings to three theoretical models: search theory, unobserved productivity and learning, and human capital theory. Finally, chapter four, Effects of Intensifying Labor Market Programs on Post-Unemployment Wages: Evidence From a Controlled Experiment analyzes how treatment of intensified active

ix labor market policies (ALMP) (in this case frequent meetings with a case worker and early entry into activation) affected average wages in jobs after leaving unemployment. An extensive literature on ALMP (both experimental and non-experimental) has shown that intensifying ALMP generally increases the exit rate out of unemployment and to some extend decreases the re-entering rate into unemployment (see Card, Kluve and Weber (2010) for a meta analysis of 97 different studies on ALMP). However, Card et al. (2010) show that analyses with insignificant or negative short term effects have positive medium or long term effects and vice versa. In this chapter, I use an ALMP experiment conducted in two Danish counties, Storstroem (St.) and Southern Jutland (S.J.) during the winter of 2005-2006 and estimate short, medium and long term effects of treatment on wages. I find that men in St. experience a significant increase in the wage hazard in the short term but no significant effects in the medium term and negative effects in the long term (These are effects on the wage hazard, i.e. a positive estimate means you become more likely to “exit” earlier out of the wage distribution. In other words, you are more likely to receive a lower wage). Men in S.J. have significant negative average treatment effects on the wage hazard both in the medium and long term. Women in S.J. have a significant negative effect of treatment on the wage hazard in the short term and positive otherwise, while the wage hazard of women in St. is affected negatively in the medium term and positive otherwise.

References Abowd, J. M., R. H. Creecy and F. Kramarz (2002), Computing Person and Firm Effects Using Linked Longitudinal Employer-Employee Data, Technical Paper 2002-06, U.S. Census Bureau. Abowd, J. M., F. Kramarz and D. N. Margolis (1999), High Wage Workers and High Wage Firms, Econometrica, 67(2): 251–333. Andrews, M. J., L. Gill, T. Schank and R. Upward (2008), High wage workers and low wage firms: negative assortative matching or limited mobility bias?, Journal of the Royal Statistical Society, A(2008) 171(Part 3): 673–697. Card, D., J. Kluve and A. Weber (2010), Active Labour Market Policy Evaluations: A MetaAnalysis, The Economic Journal, 120(November): F452–F477. Gladden, T. and C. Taber (2009), The Relationship Between Wage Growth and Wage Levels, Journal of Applied Econometrics, 24: 914–932.

x Gruetter, M. and R. Lalive (2004), The Importance of Firms in Wage Determination, IEW Working Papers 207, Institute for Empirical Research in Economics - IEW. Mincer, J. (1958), Investment in Human Capital and Personal Income Distribution, The Journal of Political Economy, 66(4): 281–302. Sørensen, T. and R. Vejlin (2012), The importance of worker, firm and match fixed effects in wage regressions, Forthcoming in Empirical Economics.

Summary in Danish (dansk resum´e) Denne ph.d.-afhandling best˚ar af fire uafhængige kapitler med løndannelsen som fælles tema. Alle fire kapitler estimerer individuelle lønninger p˚a danske data, men med tre vidt forskellige metoder. Første kapitel estimerer individuel lønvækst som en lineær funktion af individuelle observerbare karakteristika og uobserverbare arbejder- og virksomhedsspecifik heterogenitet. Kapitel to er en note, der ser p˚a et indirekte resultat fra AKM specifikationer (den type ligning der bruges i første kapitel). Tredje kapitel benytter sig af ikke-parametriske metoder til at estimere en sammenhæng mellem den løn, en arbejder tjener i sit første job, og det afkast han/hun kan forvente seks til ti a˚ r frem, betinget p˚a den løn han/hun startede ud med. Til sidst estimerer kapitel fire ved brug af forløbsstatistike metoder, hvordan lønhazarden p˚avirkes for arbejdere, der har været igennem et intensivt arbejdsmarkedspolitisk tiltag. Første kapitel, Worker and Firm Heterogeneity in Wage Growth: An AKM Approach (udgivet i LABOUR, 2011, vol. 25, 4, pp. 485-507, skrevet med Rune Vejlin), benytter statistiske metoder udviklet af Abowd et al. (1999) (den s˚akaldte AKM metode), siden rettet og udvidet af Abowd et al. (2002), til at estimere individuelle arbejder- og virksomhedsspecifikke effekter i en lineær lønvækstspecification. Et specifikt udfald af AKM modellen er en dekomponering af variansen p˚a venstresidevariablen. Derved findes et estimat p˚a forklaringsgraden af arbejderog virksomhedsspecifikke effekter af variansen p˚a lønninger. Denne metode har i litteraturen været brugt p˚a adskillige datasæt, hvoraf hovedparten estimeres p˚a basis af lønninger i niveau. I stedet fokuserer vi p˚a lønvæksten (for at kunne sammenligne med litteraturen estimerer vi ogs˚a p˚a lønninger i niveau). Ud fra et politisk synspunkt er det vigtigt at vide, om der er varians af lønvæksten p˚a tværs af virksomheder. Hvis ikke der er betydelig varians p˚a tværs af virksomheder, vil en tilfældig placering af arbejdere betyde, at de kan forvente den samme virksomhedsspecifikke lønvækst. Hvis der derimod er betydelig varians af lønvæksten mellem virksomheder, vil det for arbejdere være essentielt at komme ind i den rigtige virksomhed for at kunne forvente en større lønvækst. Vi finder i kapitlet, at uobserverbare arbejdereffekter er vigtigere for at beskrive variansen af lønvæksten end uobserverbare virksomhedseffekter og obxi

xii serverbare arbejderkarakteristika. Der er dog stadig en stor del af variansen af lønvæksten, som ikke kan forklares ved denne dekomponering. Kapitel to, Wage Sorting Trends (skrevet med Jesper Bagger og Rune Vejlin) er en note, der dokumenterer og specificerer en tendens i korrelationen med uobserverbare arbejder- og virksomhedseffekter estimeret ud fra en AKM model som i første kapitel. Studier p˚a AKM dekomponeringen rapporterer som oftest korrelationen ved et enkelt punkt, Abowd et al. (2002) (-0,28 for Frankrig og -0,03 for USA), Gruetter and Lalive (2004) (-0,22 for Østrig), Andrews et al. (2008) (-0,21 til -0,15 for Tyskland) og Sørensen and Vejlin (2012) (-0,06 til 0,11 for Danmark). Vi finder en korrelation p˚a 0,05 og viser, at den dækker over en systematisk ikke-stationaritet. P˚a tværs af a˚ rene 1980-2006 viser korrelationen en stigende tendens. Vi dekomponerer korrelationen og viser, at hovedparten af denne ikke-stationaritet kan forklares af arbejdere i den øverste kvartil blandt individuelle arbejderspecifikke effekter. Den stigende tendens for denne gruppe af arbejdere kan relateres til flere a˚ rsager. Tendensen kan f.eks. skyldes, at high wage arbejdere ansat i high wage virksomheder er mere tilbøjelige til at flytte til andre high wage virksomheder, eller at high wage arbejdere ansat i low wage virksomheder bliver mere tilbøjelige over tid til at skifte til high wage virksomheder. Vores resultater peger i retning af det første. I kapitel tre, Return to Experience and Initial Wages: Do Low Wage Workers Catch Up? (under revision for resubmision til Journal of Applied Econometrics, skrevet med Rune Vejlin) benytter vi ikke-parametriske metoder til at estimere en sammenhæng mellem en individuel permanent komponent af lønninger og et individuelt afkast af erfaring i de tidlige a˚ r af en arbejders karriere. Kapitel et og to viste, at individuelle permanente komponenter er vigtige for at beskrive en arbejders løn. En anden del af litteraturen helt tilbage til Mincer (1958) har vist, at human kapital (som erfaring og uddannelse) er vigtige elementer i lønforklaringen. Sættes dette sammen kunne vi derfor forvente at afkastet af human kapital (her erfaring) kan være forskellig betinget af uobserverbare individuelle evner. Vi bruger og udvider identifikationsstrategien fra Gladden and Taber (2009) til at estimere det forventede afkast til erfaring for en individuel arbejder betinget af hans/hendes første løn. Resultaterne peger p˚a et negativt forhold mellem initial løn og afkast af erfaring, men samtidigt et positivt forhold mellem afkast af erfaring og uddannelsesniveau (en observerbar individuel karakteristik). Især for erhvervsuddannede arbejdere finder vi en relativt stor catching-up effekt. Vi relaterer vores resultater til tre teoretiske modeller: search theory, unobserved productivity and learning, og human capital theory.

xiii Det fjerde og sidste kapitel, Effects of Intensifying Labor Market Programs on Post-Unemployment Wages: Evidence From a Controlled Experiment analyserer, hvordan et intensivt arbejdsmarkedspolitisk forløb under arbejdsløshed har p˚avirket lønninger op til tre a˚ r efter arbejdsløsheden. Der findes allerede en mængde litteratur p˚a omr˚adet omkring arbejdsmarkedspolitikker, der har vist, at en intensivering af forløbet giver en hurtigere afgang fra arbejdsløshed, og for visse grupper nedsætter det raten tilbage i arbejdsløshed (Card et al. (2010) har en stor metaanalyse af 97 forskellige studier omkring arbejdsmarkedspolitikker). Card et al. (2010) viser, at analyser med insignifikante eller negative effekter p˚a kort sigt kan have positive effekter p˚a mellem og langt sigt og omvendt. I dette kapitel benytter jeg et arbejdsmarkedpolitisk eksperiment udført i Storstrøm (St.) og Sønderjyllands (S.J.) amter over vinteren 2005/2006 til at estimere kort-, mellem- og langsigtseffekter af intensiveringen p˚a lønninger. Jeg finder, at mænd i St. rammes af en signifikant stigning i lønhazarden p˚a kort sigt, men ingen signifikante effekter p˚a mellemlangt sigt og negative effekter p˚a langt sigt (dette er effekter p˚a en lønhazard, og en positiv effekt p˚a lønhazarden betyder, at sandsynligheden for at, en arbejder tjener en lavere løn, stiger). Mænd i S.J., har derimod en signifikant negativ effekt p˚a lønhazarden p˚a b˚ade mellemlangt og langt sigt. For kvinder i S.J. har eksperimentet ligeledes haft en negativ effekt p˚a lønhazarden p˚a kort sigt men positiv p˚a langt sigt, mens lønhazarden for kvinder i St. er p˚avirket positivt af eksperimentet p˚a kort og langt sigt.

Referencer Se referencer sidst i Summary sektionen (det engelske resum´e).

Chapter 1 Worker and Firm Heterogeneity in Wage Growth: An AKM Approach

Worker and Firm Heterogeneity in Wage Growth: An AKM Approach∗ Kenneth Lykke Sørensen†

Rune Vejlin‡

Aarhus University and LMDG

Aarhus University and LMDG

Abstract This paper estimates a wage growth equation containing human capital variables known from the traditional Mincerian wage equation with year, worker and firm fixed effects included as well. The paper thus contributes further to the large empirical literature on unobserved heterogeneity following the work of Abowd, Kramarz and Margolis (1999). Our main contribution is to extend the analysis from wage levels to wage growth. The specification enables us to estimate the individual specific and firm specific fixed effects and their degree of explanation on wage growth. The analysis is conducted using Danish longitudinal matched employer-employee data from 1980 to 2006. We find that the worker fixed effects dominate both the firm fixed effects and the effect of the observed covariates. Worker effects are estimated to explain seven to twelve percent of the variance in wage growth while firm effects are estimated to explain four to ten percent. We furthermore find a negative correlation between the worker and firm effects, as do nearly all authors examining wage level equations. Keywords: MEE data, fixed effects, wage growth. JEL codes: J21, J31 This paper has been published as: Worker and Firm Heterogeneity in Wage Growth: An AKM Approach, LABOUR, 2011, vol. 25, 4, pp. 485-507. We thank Michael Svarer, Henning Bunzel, one anonymous referee and participants at the European Society for Population Economics Conference in Essen, Germany (June 2010) and DGPE, Denmark (November 2009) for comments and the Labour Market Dynamics and Growth research unit, LMDG, Department of Economics and Business, Aarhus University for providing the data. Any remaining errors are our. Vejlin greatly acknowledge financial support from the Danish Social Sciences Research Council (grant no. FSE 09-066745). † Department of Economics and Business, Aarhus University, Fuglesangs All´e 4, DK-8210 Aarhus V, Denmark. Correspondence to; Kenneth Lykke Sørensen, email: [email protected]. ‡ Department of Economics and Business, Aarhus University, Fuglesangs All´e 4, DK-8210 Aarhus V, Denmark. ∗

3

Chapter 1

4

1

Introduction

A well known fact about the labor market is that there exists a large degree of wage dispersion in the levels of wages. The same fact can be said about wage growth, but this has not yet been exploited to its full extent. Wage growth and wage levels are, of course, closely connected as wage growth is the first difference of wage levels, but the explanation of wage growth is different from the explanation of wage levels. Typically, observable characteristics are estimated to explain around 30 percent of the variation in wage levels while they are able to explain much less of the variation in wage growth.1 This leads to other differences in the explanation given by the unobserved effects as well, and it is especially interesting that Abowd, Kramarz and Margolis (1999) (henceforth denoted AKM), who introduced how to statistically analyze simultaneous observed and unobserved individual- and firm-level heterogeneity, show that when controlling for unobserved heterogeneity they can explain nearly all of the variation of wages. The methods have ever since been broadly explored by authors like Abowd and Kramarz (1999), Abowd, Finer and Kramarz (1999) (American data), Abowd, Creecy and Kramarz (2002) (American and French data), Barth and Dale-Olsen (2003) (Norwegian data), Gruetter and Lalive (2004) (Austrian data), Andrews, Gill, Schank and Upward (2008) (German data), and Sørensen and Vejlin (2009) (Danish data). Often, the main focus has been on the question of whether high wage workers are sorting into high wage firms.2 Almost all studies done to date find small negative or zero sorting in wages. AKM show that the worker effects strongly dominate the firm effects in explaining the wage determination. The worker effect together with the correlation between the worker and the firm effects have been given most attention in the literature. In the literature following AKM the common approach so far has been to focus on the wage level, while very little effort has been spent on explaining the wage growth distribution using these methods. The levels of wages have been the natural starting point of research for several reasons. Firstly, wage levels have been the natural dependent variable in any human capital wage equation ever since Mincer (1958) developed the so-called Mincerian wage equation. Secondly, much earlier research has been forced to use annual wage income making a credible wage growth practically difficult to calculate as the direct wages will be troublesome to extract 1

See e.g. Abowd, Kramarz and Margolis (1999, Table II), Barth and Dale-Olsen (2003, Table 2) and Mortensen (2005) for analysis of wage level equations. In section 5 Robustness we find a degree of explanation of 2.24 percent in an OLS regression on wage growth. 2 A high wage worker is in the terminology by AKM a worker receiving above what he is expected to, given his level of observable characteristics. A high wage firm is a firm paying wages higher than expected given these same characteristics.

Worker and Firm Heterogeneity in Wage Growth

5

and compare with the corresponding wage one year before, since it might be contaminated by different hours worked and changing bonus schemes, thus containing lots of measurement error. The goal of this paper is to estimate an empirical model of wage growth allowing for both worker and firm fixed effects. We argue that this is interesting from a policy perspective, since if there is no variation in wage growth across firms then all workers need to do, is to find a job in order to get higher wages. However, if most of the variation in wage growth comes from firm effects then it will matter a lot for the worker which job he takes. Baker (1997), Gladden and Taber (2009) and Sørensen and Vejlin (2011) show differences in wage growth given initial wages. They particularly show that it matters for the worker which job he enters into as the wage structure is different for different initial jobs. In other words, should labor market policy be directed at simply allocating workers into any job or should it more try to find the “correct” job for the specific worker. The more important firm specific effects are for variance in wage growth, the more important for the worker it is to find the “correct” job. In much the same way, were all workers born identically (i.e. zero worker specific effects) then guiding workers into any job increasing overall physical experience the most would be optimal. With worker specific effects (Sørensen and Vejlin (2011) refer to worker effects as worker specific return to experience) the wage profile will be different for different jobs. We show that much less of the variation of wage growth can be explained by observables, worker and firm effects compared to the degree of explanation in the levels of wages. The common result that unobserved worker heterogeneity is more important than unobserved firm heterogeneity and observable covariates is found to be the case for the variance in wage growth as well. Furthermore, we find a negative correlation between the estimated worker specific effects and the estimated firm specific effects of a much stronger magnitude than typically found in wage level analysis. A more theoretical literature inspired by the empirical findings of AKM argues that the fixed effects in the wage equation do not necessarily correlate very well with the underlying productivity of the firm and worker, respectively. When motivating the AKM specification as a structural representation of the wage equation, it is generally assumed that the outside options of workers and firms are independent of the prevailing match. Recently, several studies have illustrated the implications of relaxing this assumption. Eeckhout and Kircher (2009) and Lopes de Melo (2008) both generate a non-monotonicity in the wage equation due to high productivity firms facing better outside options than their counterparts when they match with a

Chapter 1

6

low productivity worker. A low productivity worker has to compensate a high productivity firm for giving up the opportunity to match with a more productive worker. Eeckhout and Kircher (2009) illustrate the insufficiency of wage data alone to identify sorting in the labor market: for every production function that induces positive sorting they can find a production function inducing negative sorting whilst generating identical wages. In Postel-Vinay and Robin (2002) the dynamic nature of the wage bargaining process implies that although workers always move up in the productivity distribution upon a job-to-job transition, a move may be associated with a drop in wages. Bagger and Lentz (2008) adopt this wage setting in an on-the-job search model with endogenous search effort and show that positive sorting can be consistent with a negative correlation between the fixed effects in the wage equation. Shimer (2005) makes the same point within an assignment model. This recent strand of the literature shows that one should be very careful when interpreting AKM type wage decompositions and, hence, we do not push our results in the direction of revealing the underlying productivity structure of the labor market. Given the theoretical interest alluded to above, one of the contributions of this paper is also to investigate whether or not the structural models need to take into account that the growth rate of wages can be different for different workers. An implication of the human capital model by Mincer (1974) is parallel log earnings profiles across schooling levels. Heckman, Lochner and Todd (2003) test whether data support this parallel implication and find that only 1940s and 1950s US Census data support parallel log earnings profiles across schooling levels, while formal econometric tests reject any support for such parallelism for newer data (1960 to 1990). Connolly and Gottschalk (2006) show that log earnings profiles are not even parallel when controlling for workers making job-to-job transitions and workers experiencing a non-employment spell between jobs with high educated workers experiencing higher wage growth than lower educated workers. Postel-Vinay and Robin (2002) and Bagger, Fontaine, Postel-Vinay and Robin (2007) produce wage equations in which the wage change does not depend on the worker, but only on the current and the last firm that the worker was in. E.g., if it is a high productivity firm then wage changes are large, since the initial wage is low, because the worker is willing to accept an initial low wage at a high productivity firm in order to get higher wage raises in the future, and then high wage firm matches all wage offers. The paper is organized as follows: Section 2 presents our empirical model, discusses identification and summarizes the implementation procedure. We describe the Danish IDA data

Worker and Firm Heterogeneity in Wage Growth

7

in Section 3 and, in particular, the realized mobility patterns that are of high importance for both identification and precision of the parameters. In Section 4 we present the results of the wage decomposition and the analysis taking the estimated parameters as input. In section 5 we analyze the robustness of our model. Section 6 concludes.

2

The Two-Way Fixed Effects Model

We will be using a wage specification inspired by Abowd et al. (1999) and Abowd et al. (2002) with wage growth decomposed into a linear relationship between observed covariates, an unobserved worker fixed effect, an unobserved firm fixed effect and an error term. Let i ∈ I = {1, . . . , I} index workers and let worker i be represented by Ni observations P indexed by n ∈ Ni = {1, . . . , Ni } totaling N ∗ = i∈I Ni observations in the data. The set of firms is J = {1, . . . , J}. We assume that worker i’s log wage growth from time t − 1 to time t when employed at firm J(i, t) arises from the linear model given by3 ∆wit = x0it β + θi + ψJ(i,t) + εit ,

(1)

where ∆wit = wit − wit−1 , xit is a 1 × K vector of observed time-varying covariates, β is a conformable vector of slope parameters, θi and ψJ(i,t) are worker specific and firm specific

components of the variation of log wage growth, respectively. εit is the residual wage growth. Our specification is different from the original AKM specification as the error structure allows for time varying unobservables to have long term consequences on wage growth. Kramarz, Machin and Ouazad (2009) have a specification much like ours. They analyze a value added model in which they decompose the progress of children in the English primary education system into a child fixed effect (corresponding to our worker effect), a school-grade-year effect (corresponding to our firm effect) and an error term. A crucial difference between our analysis and the one by Kramarz, Machin and Oazad is that we have up to 26 time periods per person while they analyze the change in test scores for English primary school pupils over two periods; period one at age 6/7 and period two at age 10/11. We shall treat the residual εit in (1) as a genuine statistical residual. We thus impose the 3

Note that for the comparison regressions of wages in levels, we use the same specification, but with wage levels as left hand side variables instead of wage growth.

Chapter 1

8 identifying assumptions E[εit |xit , i, t, J(i, t)] = 0, Cov[εit , εhs |xit , xhs , i, h, t, s, J(i, t), J(h, s)] =

∀ n ∈ Ni and ∀ i ∈ I   σ 2 < ∞ ∀ i = h, t = s  0

(2) (3)

otherwise.

Equation (2) ensures strict exogeneity, i.e. it rules out endogenous mobility.

2.1

Identification of the Person and Firm Fixed Effects

We need to make sure that both person and firm effects are identified. This is no trivial problem though, since the usual techniques by sweeping out the singular row and column combinations from the normal equations of the system cannot be done as the normal equations are solved without actually computing the generalized inverse. Instead, person and firm effects can be identified by forming groups of connected workers and firms using the grouping algorithm developed by Abowd et al. (2002). To do this, one must use the movers to tie workers and firms together such that each group consists of all the workers who have ever worked for any of the firms within the group and all the firms at which any of the workers has ever been employed at.4 This implies that a group is a connection of workers and firms in a graph theoretical sense. The algorithm results are displayed in Table 1. As none of the firms in group k is connected to any of the firms in group h for all k 6= h

we cannot compare firm and worker effects between groups. This leaves us with the option of performing the analysis on each group separately or focusing on one group only within which worker and firm specific effects can be identified using conventional methods from analysis of covariance. Table 1 shows that after doing the graph theoretical grouping algorithm by Abowd et al. (2002) the largest group contains almost all observations (99 percent), workers (98 percent) and firms (91 percent) so we will focus on the largest group only and discard all observations belonging to any other group than the largest. This is also the normal procedure in the literature. It is useful to write equation (1) in matrix notation w = Zβ + Dθ + Fψ + , 4

See ACK for a more detailed description of the grouping algorithm.

(4)

Worker and Firm Heterogeneity in Wage Growth

9

Table 1: Descriptive statistics merging from the grouping algorithm.

Full sample Men High educ. Medium educ. Low educ. Total Women High educ. Medium educ. Low educ. Total

Number of observations

Number of workers

Number of firms

Number of groups

Number of estimable effects

20,881,823 (20,703,609)

2,116,094 (2,083,391)

322,802 (295,034)

24,793 (1)

2,414,103 (2,378,424)

1,750,247 (1,682,834) 8,912,263 (8,823,828) 4,074,495 (3,996,477) 14,737,005 (14,619,789)

179,108 (166,827) 798,308 (780,009) 401,943 (385,574) 1,379,359 (1,354,251)

59,733 (47,019) 217,298 (198,844) 147,853 (129,944) 268,088 (244,242)

9,270 (1) 15,671 (1) 14,171 (1) 20,578 (1)

229,571 (213,845) 999,935 (978,852) 535,625 (515,517) 1,626,869 (1,298,492)

515,512 (450,948) 3,555,893 (3,443,791) 2,028,413 (1,914,928) 6,099,818 (5,949,155)

87,387 (71,760) 404,602 (382,385) 244,746 (222,350) 736,735 (704,109)

33,262 (20,277) 139,539 (116,365) 95,732 (71,028) 179,832 (149,086)

9,715 (1) 18,360 (1) 18,693 (1) 25,569 (1)

110,934 (92,036) 525,781 (498,749) 321,785 (293,377) 890,998 (853,194)

Note: The figures from the largest group of each sample are in parenthesis.

where w and  are N ∗ × 1 vectors, D is an N ∗ × N matrix of worker dummy variables, F is an

N ∗ × J matrix of firm dummy variables and Z is N ∗ × K matrix of covariates. θ is an N × 1 parameter vector, ψ is a J × 1 parameter vector and β is a K × 1 parameter vector.5

Equation (4) is known as the Least Squares Dummy Variable method (LSDV), which is a two-way high dimensional fixed effects model. There are several ways to estimate such a model. AKM note that the LSDV estimation of (4) requires the estimation of N worker effects and J firm effects. Since N is often in millions and J is often in thousands, such an estimation is unfeasible with standard approaches. We use the conjugate gradient (CG) algorithm also used by Abowd et al. (2002) and Kramarz et al. (2009) to solve the problem. The CG algorithm deals with the high dimensionality of the data by using sparse matrices and iterates the solution according to a convergence criteria which we have set to 10−14 .

3

Data

The data source used in this paper is the Integrated Database for Labor Market Research (IDA) kept by Statistics Denmark (SD). The data are confidential but our access is not exclusive. IDA 5

Note that (4) is actually a generalization of the model used by Abowd et al. (1999). Instead of using wages in level we use wage growth and have furthermore assumed that the firm effects are all constant over time, hence m = 1 in AKM’s model.

Chapter 1

10 Table 2: Costs in terms of observations when narrowing down the sample. Correction

Observation cost

Sample size

Population Missing education information Labor market entry Private sector Students Experience outliers Full-time employment Non-positive hourly wages Non-credible hours Wages below P1 Wages above P99 Final corrections

1,256,538 11,064,910 18,207,737 938,862 15,168 2,402,026 65,571 1,115,560 248,899 254,555 4,395,944

60,847,593 59,591,055 48,526,145 30,318,408 29,379,546 29,364,378 26,962,352 26,896,781 25,781,221 25,532,322 25,277,767 20,881,823

is a matched employer-employee longitudinal database containing socio-economic information on the entire Danish population, the population’s attachment to the labor market, and at which firms the worker is employed. Both persons and firms can be monitored from 1980 onwards. The reference period in IDA is given as follows; The linkage of persons and firms refers to the end of November, ensuring that seasonal changes (such as e.g. shutdown of establishments around Christmas) do not affect the registration, meaning that the creation of jobs in the individual firms refers to the end of November. On the other hand, the background information on individuals mainly refers to the end of the year.6 Our gross sample contains all workers having their main employment at a private firm in the period of 1980 − 2006.7

3.1

The Sample

The raw data consists of 60,847,593 yearly wage observations. We have detrended wages according to the Danish 2006 consumer price index. The data is then narrowed down to the sample of estimation by the following corrections according to Table 2. First, since we divide the sample into educational groups, the observations with missing educational information are deleted (1,256,538 observations deleted). Second, we only include observations after the completion of the highest education (11,064,910 observations deleted). I.e. if a worker has a job with some lower education and then achieves a new (mainly higher) education, we only include the observations belonging to his last education and are thus deleting all observations prior to the completion of his highest education. This is done such that we are ensured not to compare e.g. an economist when working as an economist with when 6

See a more detailed documentation on IDA constructed by SD: http://www.dst.dk/HomeUK/Guide/documentation/Varedeklarationer/emnegruppe/emne.aspx?sysrid=1013 7 Since we will be using the first difference of wages the estimation period will be 1981 − 2006.

Worker and Firm Heterogeneity in Wage Growth

11

he was working as a clerk in a department store before finishing his studies. The private and public sector labor markets are very different, and we will only be looking at the private sector, thus deleting all public sector observations (18,207,737 observations deleted). Furthermore, if a worker is currently undertaking education he is deleted as well (938,862 observations deleted). If the experience measure of a worker is negative or above his age less his years of education the observation is deleted (15,168 observations deleted). All non-full-time employment observations are deleted (2,402,026 observations) and so are observations with negative or noncredible hourly wages (65,571 + 1,115,560 observations deleted).8 To deal with outliers, we delete all observations with wages in the top and bottom percentile of the wage distribution (248,899 + 254,555 observations), and finally, as we use yearly wage growth, we have deleted all the observations in which we observe a worker for the first time. If, for some reason, we miss any intervening observations for a worker we also delete the first subsequent observation we have on him such that all wage growth observations are yearly (4,395,944 observations). I.e. when analyzing wage growth the growth is always between consecutive years. The final sample consists of 20,836,823 observations which then is divided into three educational groups, which are low, medium and high for both men and women. These groups are thoroughly described in the next section.

3.2

Observable Characteristics

The IDA data contains actual labor market experience but only measured from 1964 and onwards. Hence, for workers entering the labor market prior to 1964 this experience measure is left-censored. Therefore, we construct our own measure of experience as potential experience (age less the total length of education less schooling starting age) at the first observation for a given worker and then add actual increments in experience. Woodcock (2008) uses a similar measure except that he only knows whether or not a worker was employed sometime during a quarter, whereas we have more precise information on actual experience accumulated during each year. Sørensen and Vejlin (2009) also use this measure. Table 3 presents summary statistics of our measure of experience. In our sample men are relatively more experienced than women and low educated are more experienced than high educated. The latter partly reflects that high educated enter the labor market later. 8

The hourly wage measure is calculated on the basis of payments to the Danish mandatory pension scheme, ATP which is a step-function of hours worked. If Statistics Denmark report this hourly measure as non-credible, we delete the associated observation.

Chapter 1

12 Table 3: Descriptive Statistics of Labor Market Experience Mean

Median

Std. dev.

P10

P90

Total observations

Full sample

16.65

16.00

8.54

5.87

28.56

20,836,823

Men High edu. Medium edu. Low edu. Total

16.21 17.52 17.74 17.43

15.50 17.00 17.89 17.00

8.68 8.48 8.84 8.61

5.24 6.75 5.81 6.32

28.33 29.20 29.80 29.23

1,750,247 8,912,263 4,074,495 14,737,005

Women High edu. Medium edu. Low edu. Total

12.8 15.01 14.91 14.79

11.00 13.89 14.18 13.77

7.96 8.14 7.85 8.05

3.88 5.25 4.97 5.00

24.55 26.67 25.85 26.07

515,512 3,555,893 2,028,413 6,099,818

The time varying observables, x0it , consist of calendar time and labor market experience.9 In the implementation we include a full set of year dummies and parameterize the experience profile by including experience and experience squared. Time-invariant characteristics are gender and length of education. We construct an education measure which divides the sample into three mutually exclusive groups: less than 12 years of education, 12-14 years and more than 14 years. The first group contains high-school drop-outs, the second contains high-school graduates, individuals with a vocational education, and individuals with a short cycle tertiary education, and the third contains those with medium and long cycle tertiary educations. We will denote these educational groups as low, medium and high educated workers, respectively. The IDA data does contain considerable further information on workers. However, this paper focuses on disentangling worker and firm effects and not on which particular characteristics on either the worker or firm side that drive wage growth differentials. Hence, the time-invariant worker characteristics included in the analysis are chosen such that well-defined subsamples can be formed on which separate analysis can be performed. Since the firm effect in the AKM model is identified from workers moving between different firms it is important to have long panels and a lot of job changes per worker. Table 4 shows the distribution of number of observations for each worker. Each worker appears in the sample on average 9.85 times with men being on average more frequently than women. We have more than ten observations for almost 40 percent of the entire sample divided on 44 percent of the male sample and 31 percent of the female sample. It is only 18 percent of the total number of workers that appears less than three times in our total sample. Table 5 reports the distribution of number of employers per worker. Approximately two 9

In the robustness section we include dummies for marital status, parenthood and size of the firm current and one period before to check whether year dummies and experience profiles fully capture observable heterogeneity.

Worker and Firm Heterogeneity in Wage Growth

13

Table 4: Number of Observations per Worker Average

1

2

3-5

6 - 10

11 - 20

21+

Full sample

9.85

221,977 (0.1049)

167,198 (0.0790)

386,807 (0.1828)

499,124 (0.2359)

584,950 (0.2764)

256,038 (0.1210)

2,116,094

Men High edu.

9.77

17,585 (0.0982) 61,566 (0.0771) 41,977 (0.1044) 121,128 (0.0878)

13,741 (0.0767) 50,807 (0.0636) 31,275 (0.0778) 95,823 (0.0695)

32,480 (0.1813) 126,284 (0.1582) 70,589 (0.1756) 229,353 (0.1663)

44,762 (0.2499) 183,109 (0.2294) 93,081 (0.2316) 320,952 (0.2327)

50,926 (0.2843) 248,180 (0.3109) 109,897 (0.2734) 409,003 (0.2965)

19,614 (0.1095) 128,362 (0.1608) 55,124 (0.1371) 203,100 (0.1472)

179,108

16,977 (0.1943) 48,775 (0.1206) 35,097 (0.1434) 100,849 (0.1369)

11,562 (0.1323) 35,616 (0.0880) 24,197 (0.0989) 71,375 (0.0969)

22,557 (0.2581) 83,420 (0.2062) 51,477 (0.2103) 157,454 (0.2137)

22,204 (0.2541) 98,159 (0.2426) 57,809 (0.2362) 178,172 (0.2418)

12,345 (0.1413) 106,227 (0.2625) 57,375 (0.2344) 175,947 (0.2388)

1,742 (0.0199) 32,405 (0.0801) 18,791 (0.0768) 52,938 (0.0719)

Medium edu.

11.16

Low edu.

10.14

Total Women High edu.

5.90

Medium edu.

8.79

Low edu.

8.29

Total

Total workers

798,308 401,943 1,379,359

87,387 404,602 244,746 736,735

Note: Numbers in parenthesizes denote percentages of subsamples.

thirds of all workers are in multiple firms and 40 percent of the workers in the entire sample have three or more different employers. On average, each worker has 2.52 different employers. 45 percent of all men and 32 percent of all women have three or more employers. To compare these figures, Abowd et al. (1999) have a maximum of ten years of observations, but only 10 percent of their workers are observed ten times and only one half of the workers in their sample changes employers, i.e. we have more observations per worker and more frequent job changes in our sample compared to the original sample used to estimate the AKM model. The main interest in this paper is to estimate the effect of firm and worker heterogeneity on wage growth. Figure 1 shows the cross-section distribution of wage growth over all years. The wage growth distribution is almost symmetrical around a mean value of three percent and there are considerable variations.

Chapter 1

14 Table 5: Number of Employers per Worker Average

1

2

3

4

5 - 10

11+

Full sample

2.52

772,003 (0.3648)

501,601 (0.2370)

345,654 (0.1634)

231,683 (0.1095)

262,153 (0.1239)

3,000 (0.0014)

2,116,094

Men High edu.

2.44

67,199 (0.3752) 238,394 (0.2986) 144,643 (0.3599) 450,236 (0.3264)

43,441 (0.2425) 186,110 (0.2332) 89,662 (0.2230) 319,213 (0.2314)

29,463 (0.1645) 142,408 (0.1784) 63,678 (0.1584) 235,549 (0.1708)

18,573 (0.1037) 101,481 (0.1271) 45,311 (0.1127) 165,365 (0.1199)

20,313 (0.1134) 128,142 (0.1605) 57,739 (0.1437) 206,194 (0.1495)

119 (0.0007) 1,773 (0.0022) 910 (0.0023) 2,802 (0.0020)

179,108

50,603 (0.5790) 157,558 (0.3894) 113,606 (0.4642) 321,767 (0.4367)

19,494 (0.2231) 103,714 (0.2563) 59,180 (0.2418) 182,388 (0.2475)

9,459 (0.1082) 66,414 (0.1642) 34,232 (0.1399) 110,105 (0.1495)

4,491 (0.0514) 40,898 (0.1011) 20,929 (0.0854) 66,318 (0.0900)

3,336 (0.0382) 35,889 (0.0887) 16,734 (0.0684) 55,959 (0.0760)

4 (0.0001) 129 (0.0003) 65 (0.0003) 198 (0.0003)

Medium edu.

2.80

Low edu.

2.63

Total Women High edu.

1.77

Medium edu.

2.31

Low edu.

2.10

Total

Total workers

798,308 401,943 1,379,359

87,387 404,602 244,746 736,735

Note: Numbers in parenthesizes denote percentages of subsamples.

0

2

Percent

4

6

Figure 1: The distribution of wage growth for the entire sample 1980-2006.

−1 −.9 −.8 −.7 −.6 −.5 −.4 −.3 −.2 −.1 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 Wage growth, percent

4

Results

In this section we present results for model (4). The model is estimated both in terms of wage growth and wage levels, i.e. the original AKM model. This is done in order to compare the two models. Model (4) is also estimated on subgroups, which allow for the firm effect, the year effect and the experience profile to differ between subgroups, although the structure of the identification process prevents us from comparing subgroups directly.

Worker and Firm Heterogeneity in Wage Growth

4.1

15

Contributions of Fixed Effects to the Variance of Wage Growth

Notice that the variance of either wage growth or levels can be decomposed into pairwise covariances between the dependent variable and independent variables. This is shown in equation (5) by inserting for the wage growth equation V ar(∆wit ) = Cov(∆wit , ∆wit ) = Cov(∆wit , x0it βˆ + θˆi + ψˆJ(i,t) + εˆit ) ˆ + Cov(∆wit , θˆi ) + Cov(∆wit , ψˆJ(i,t) ) + Cov(∆wit , εˆit ). = Cov(∆wit , x0it β) (5) Dividing through by the variance of the dependent variable lets us interpret each component as the relative contribution to the explanation of the variance of the dependent variable. I.e. the degree of explanation by each component arising from the decomposition is given by10 ˆ Cov(∆wit , x0it β) Cov(∆wit , θˆi ) Cov(∆wit , ψˆJ(i,t) ) Cov(∆wit , εˆit ) + + + = 1. V ar(∆wit ) V ar(∆wit ) V ar(∆wit ) V ar(∆wit )

(6)

This decomposition constitutes a nice measure of how ’important’ each component can be said to be for the description of the variance of wage growth. Abowd et al. (1999) (and subsequently Abowd et al. (2002)) make a decomposition much like this and find that the worker effect is by far the most important component in determining the variance in wage levels leaving only very little explanation to firm effects. Sørensen and Vejlin (2009) also decompose the variance of wage levels following the method of Woodcock (2008) who shows how to decompose the variance of wages when including worker fixed effects, firm fixed effects and a match specific effect. Sørensen and Vejlin use the same raw data as us but with a slightly different subgroup selection, and they include a match fixed effect besides worker and firm fixed effects. Their paper also only uses the years from 1980 to 2003. They find that depending on skill levels, the firm effect can be said to explain from 10 to 25 percent of the variation in wages. Furthermore, they find that the degree of explanation given by firm effects is declining when the skill level increases. Sørensen and Vejlin find the contributions to the explanation of the variance in wages given by worker effects to range from 35 percent for low skilled workers to 45 percent for high skilled workers. 10

Note that for a normal OLS regression with regular covariates included only, ∆wit = x0it β + εit the following holds ˆ Cov(∆wit ,x0it β) ε) it ,ˆ 2 = 1 − Cov(∆w V ar(∆wit ) V ar(∆wit ) = R .

Chapter 1

16

Table 6 shows summary statistics from the AKM model estimated on wage growth and wage levels and the variance decomposition as shown above. First, turning to the model for wage levels, i.e. the standard AKM model, we find that the worker fixed effects dominate the explanation of the variance of wages explaining around 58 percent of wage variation in the estimation on the full sample. The firm fixed effects contribute with 14 percent, while experience and year fixed effects (put together into Xβ) contribute with 9 percent. However, turning to the subgroup analysis we find that the worker fixed effects mostly dominate for high educated, while for low educated the worker and firm fixed effects are almost equally important. It seems that the heterogeneity in the explanatory power of each is completely based on education and not on gender, even though, of course, there are small differences between men and women. Sørensen and Vejlin (2009) also find nearly the same contributions from firm fixed effects while our worker effects contribute with more to the explanation of the variance in wages. Our covariates (experience and year effects) contribute with much less than what Sørensen and Vejlin find. This difference can be explained by their inclusion of a match effect and a slightly different sample selection. Sørensen and Vejlin (2009) also find the same pattern in the subgroup analysis. Thus, our sample seems to be able to produce results in the same range as known in the literature.

Worker and Firm Heterogeneity in Wage Growth

17

Table 6: Regression results. Wage growth

Wage levels Cov(w,Z)

Z

Mean

Std. Dev.

Cov(w,Z)

Cov(w,Z)

/ Var(w)

Mean

Std. Dev.

Cov(w,Z)

/ Var(w)

0.1486

0.0221

1.0000

5.2372

0.3072

0.0944

1.0000

Full sample (20,703,609 observations) w

0.0196

θ

-0.0780

0.0578

0.0019

0.0868

4.8103

0.2319

0.0543

0.5752

ψ

0.1110

0.0470

0.0009

0.0415

0.2547

0.1107

0.0132

0.1399

Xβ

-0.0134

0.0248

0.0005

0.0218

0.1723

0.0940

0.0088

0.0927

ε

0.0000

0.1370

0.0188

0.8499

0.0000

0.1347

0.0181

0.1922

High educated Men (1,682,834 observations) w

0.0279

0.1537

0.0236

1.0000

5.6571

0.3354

0.1125

1.0000

θ

-0.3121

0.0687

0.0017

0.0739

5.5965

0.2945

0.0645

0.5732

ψ

0.3370

0.0673

0.0018

0.0753

0.1186

0.1392

0.0119

0.1059

Xβ

0.0031

0.0259

0.0005

0.0216

-0.0581

0.1838

0.0141

0.1255

ε

0.0000

0.1400

0.0196

0.8292

0.0000

0.1483

0.0220

0.1954

0.0297

0.1482

0.0220

1.0000

5.4231

0.3104

0.0963

1.0000

θ

0.0960

0.1130

0.0026

0.1161

5.5190

0.2689

0.0598

0.6208

ψ

-0.0581

0.1106

0.0021

0.0961

-0.0851

0.1451

0.0124

0.1289

Xβ

-0.0083

0.0217

0.0005

0.0208

-0.0108

0.1315

0.0099

0.1031

ε

0.0000

0.1298

0.0169

0.7670

0.0000

0.1191

0.0142

0.1472

0.1488

0.0222

1.0000

5.2778

0.2633

0.0693

1.0000

Women (450,948 observations) w

Medium educated Men (8,823,828 observations) w

0.0181

θ

-0.0533

0.0582

0.0016

0.0712

4.8230

0.1817

0.0313

0.4513

ψ

0.0931

0.0546

0.0012

0.0558

0.2670

0.1199

0.0134

0.1935

Xβ

-0.0218

0.0238

0.0005

0.0220

0.1878

0.0882

0.0071

0.1025

ε

0.0000

0.1373

0.0189

0.8509

0.0000

0.1324

0.0175

0.2527

0.1406

0.0198

1.0000

5.0995

0.2546

0.0648

1.0000

Women (3,443,791 observations) w

0.0259

θ

-0.2304

0.0720

0.0020

0.1024

4.5700

0.1774

0.0277

0.4271

ψ

0.2595

0.0650

0.0013

0.0661

0.3321

0.1104

0.0103

0.1591

Xβ

-0.0032

0.0276

0.0006

0.0280

0.1974

0.1181

0.0127

0.1955

ε

0.0000

0.1260

0.0159

0.8036

0.0000

0.1190

0.0141

0.2183

Low educated Men (3,996,477 observations) w

0.0151

0.1554

0.0241

1.0000

5.1837

0.2447

0.0599

1.0000

θ

0.0051

0.0720

0.0020

0.0841

4.6726

0.1620

0.0211

0.3531

ψ

0.0359

0.0704

0.0019

0.0781

0.3344

0.1432

0.0175

0.2915

Xβ

-0.0258

0.0275

0.0006

0.0267

0.1767

0.0783

0.0058

0.0976

ε

0.0000

0.1400

0.0196

0.8111

0.0000

0.1242

0.0154

0.2577

This table continues on the next page. Note: Z in columns 4, 5, 9 and 10 denotes w, θ, ψ, Xβ or ε depending on the row in question.

Chapter 1

18 Table 6 – continued from previous page. Wage growth

Wage levels Cov(w,Z)

Z

Mean

Std. Dev.

Cov(w,Z)

Cov(w,Z)

/ Var(w)

Mean

Std. Dev.

Cov(w,Z)

/ Var(w)

Women (1,914,928 observations) w

0.0160

0.1376

0.0189

1.0000

5.0194

0.2277

0.0518

1.0000

θ

0.0526

0.0785

0.0020

0.1063

4.7302

0.1593

0.0178

0.3429

ψ

-0.0577

0.0738

0.0016

0.0825

0.1063

0.1420

0.0154

0.2972

Xβ

0.0212

0.0279

0.0005

0.0277

0.1830

0.0853

0.0064

0.1244

ε

0.0000

0.1218

0.0148

0.7836

0.0000

0.1105

0.0122

0.2355

Note: Z in columns 4, 5, 9 and 10 denotes w, θ, ψ, Xβ or ε depending on the row in question.

Our results of the variance decomposition yield much lower estimates of the degree of explanation of the variance in wage levels than those given by most former literature. One explanation of this can be that we use much longer panels than e.g. Abowd et al. (1999) (panel covering 1976-1987, excluding 1981 and 1983), Abowd et al. (2002) (same panel length as AKM) and Barth and Dale-Olsen (2003) (panel covering 1989-1997). Figures 2 to 4 show the variance decomposition (equation (6)) plotted for each subgroup against the number of times we have observed the individual worker. The development in contribution to the variance of wages is almost the same for all three subgroups where the worker effects seem to be mostly negatively affected by the length of the panels while the contributions from firm effects are relatively constant and the covariates experience increasing contribution to the variance of wages for all subgroups. AKM, Abowd et. al, and Barth and Dale-Olsen all use unbalanced panels as we do, and they could thus possibly have an upward biased worker effect. It is a subject for further research whether the estimated worker and firm effects are dependent on the panel lengths at hand. Now turning to the main analysis of the wage growth equation. For the full sample the variation in the worker effect explains 8.7 percent, the firm effect explains 4.2 percent, and experience and year effects explain 2.2 percent. I.e., as in the regressions on wage levels, the most important component is the worker fixed effect. When we estimate the model on the six subgroups of gender and educational level an interesting pattern emerges. It seems that especially the worker effect, but to some extent also the firm effect, is more important in explaining women’s wage growth. In all subgroups with an equal amount of education the explanatory power of both the worker and the firm effect is higher for women than for men.

Worker and Firm Heterogeneity in Wage Growth

19

Figure 2: Degree of explanation given by worker effects, firm effects and covariates according to the variance decomposition plotted against number of person-years observed.

.8 Degree of explanation .4 .6 .2 0

0

.2

Degree of explanation .4 .6

.8

1

High educated women

1

High educated men

1

5

9 13 17 21 Number of years observed

Worker effects Covariates

25

1

Firm effects Residuals

5

9 13 17 21 Number of years observed

Worker effects Covariates

25

Firm effects Residuals

Figure 3: Degree of explanation given by worker effects, firm effects and covariates according to the variance decomposition plotted against number of person-years observed.

.8 Degree of explanation .4 .6 .2 0

0

.2

Degree of explanation .4 .6

.8

1

Medium educated women

1

Medium educated men

1

5

9 13 17 21 Number of years observed

Worker effects Covariates

25

Firm effects Residuals

1

5

9 13 17 21 Number of years observed

Worker effects Covariates

25

Firm effects Residuals

Chapter 1

20

Figure 4: Degree of explanation given by worker effects, firm effects and covariates according to the variance decomposition plotted against number of person-years observed.

.8 Degree of explanation .4 .6 .2 0

0

.2

Degree of explanation .4 .6

.8

1

Low educated women

1

Low educated men

1

5

9 13 17 21 Number of years observed

Worker effects Covariates

25

Firm effects Residuals

1

5

9 13 17 21 Number of years observed

Worker effects Covariates

25

Firm effects Residuals

The clear pattern from the wage level estimation, where worker effects were most important for high educated, is nearly not present in wage growth. In general, worker effects explain around 8 to 12 percent, firm effects explain around 4 to 10 percent, and experience and the year dummies together explain 2 to 3 percent. That is, the most important component of wage growth is worker specific differences, but it also seems that firm heterogeneity plays a relatively important role in determining wage growth compared to determining variance in wage levels. We also see that experience and year dummies explain a very small fraction of the variation in wage growth. This is not a surprising result though, since (in the Robustness section below (table A1 column (1))) we find R2 = 0.024 when running a simple OLS regression without including any fixed effects. Compared to the model for wage levels the degree of explanation is dramatically smaller for wage growth. I.e. we cannot explain the variation in wage growth as precisely as we can explain the variation in the level of wages. Also for wage levels the most important component is the worker fixed effect, while the firm fixed effect and experience and year dummies seem to explain an almost equal share. The latter part is in contrast to the model for wage growth where the covariates constantly contribute with around half the share of the contribution given by firm fixed effects. A possible explanation of this can simply be that there is a relatively higher variance in the error term when analyzing wage growth than wage levels. Given the relatively

Worker and Firm Heterogeneity in Wage Growth

21

low contribution by firm effects compared to the worker effects and the residual, one could doubt the significance of the firm effects. We have tested this for each subgroup using a simple F-test with the hypothesis that the model with firm effects included does not provide a significant better fit of wage growth (and levels) than a model without firm fixed effects included. The test gives a p-value of zero for all subgroups for both wage growth and wage levels.11 Table 7 shows the correlation structure of the two models for wage growth and wage levels. In levels we see that there is a small but positive correlation between the firm effect and the worker effect in the full sample, but when we turn to the subsamples we find a negative correlation. This is also found by Sørensen and Vejlin (2009). In the wage growth equation we find a strong negative correlation between the firm effect and the worker effect. I.e. workers with high wage growth are on average in firms with low wage growth. One reason could be the negative bias between worker and firm effects, see e.g. Bagger and Lentz (2008). Furthermore, Andrews et al. (2008) show that the magnitude of this bias is increasing in the size of the error term variance which explains our much stronger correlation than earlier studies such as e. g. Abowd et al. (2002) and Gruetter and Lalive (2004). The negative correlation between worker and firm effects is consistently stronger for women than for men throughout the educational subgroups, and does not differ much for men whether they are high, medium or low educated, whereas the correlation is much higher (in absolute terms) for high educated women than for low and medium educated women. The difference in the magnitude of the correlation between worker and firm effects when analyzing wage growth and wage levels can to a large extent be explained by a much lower standard deviation of worker and firm effects in the wage growth estimations compared to wage levels.

11

The test with the lowest F-statistic is high educated women, wage growth at F = 52, 393. The corresponding critical value on a significance level of five percent is F (92, 036 − 20, 277; 450, 948 − 20, 277) = 1.009 and the firm effects are thus highly significant.

Chapter 1

22 Table 7: Correlation structure, full AKM model, wage growth and wage levels. Wage growth w

θ

ψ

Wage levels Xβ

ε

w

θ

ψ

Xβ

ε

Full sample w

1.0000

0.2232

0.1313

0.1306

0.9219

1.0000

0.7619

0.3883

0.3029

0.4384

θ

0.2232

1.0000

-0.4749

-0.0931

0.0000

0.7619

1.0000

0.0302

-0.0124

0.0000

ψ

0.1313

-0.4749

1.0000

-0.0008

0.0000

0.3883

0.0302

1.0000

0.0169

0.0000

Xβ

0.1306

-0.0931

-0.0008

1.0000

0.0000

0.3029

-0.0124

0.0169

1.0000

0.0000

ε

0.9219

0.0000

0.0000

0.0000

1.0000

0.4384

0.0000

0.0000

0.0000

1.0000

w

1.0000

0.1652

0.1720

0.1285

0.9106

1.0000

0.6528

0.2551

0.2290

0.4420

θ

0.1652

1.0000

-0.6020

-0.1089

0.0000

0.6528

1.0000

-0.1225

-0.3182

0.0000

ψ

0.1720

-0.6020

1.0000

0.0198

0.0000

0.2551

-0.1225

1.0000

-0.0955

0.0000

Xβ

0.1285

-0.1089

0.0198

1.0000

0.0000

0.2290

-0.3182

-0.0955

1.0000

0.0000

ε

0.9106

0.0000

0.0000

0.0000

1.0000

0.4420

0.0000

0.0000

0.0000

1.0000

w

1.0000

0.1523

0.1288

0.1422

0.8758

1.0000

0.7165

0.2756

0.2434

0.3837

θ

0.1523

1.0000

-0.8131

-0.0229

0.0000

0.7165

1.0000

-0.1768

-0.1589

0.0000

ψ

0.1288

-0.8131

1.0000

0.0178

0.0000

0.2756

-0.1768

1.0000

-0.0911

0.0000

Xβ

0.1422

-0.0229

0.0178

1.0000

0.0000

0.2434

-0.1589

-0.0911

1.0000

0.0000

ε

0.8758

0.0000

0.0000

0.0000

1.0000

0.3837

0.0000

0.0000

0.0000

1.0000

w

1.0000

0.1821

0.1523

0.1379

0.9225

1.0000

0.6540

0.4249

0.3061

0.5027

θ

0.1821

1.0000

-0.5467

-0.0523

0.0000

0.6540

1.0000

-0.0463

-0.0449

0.0000

ψ

0.1523

-0.5467

1.0000

-0.0039

0.0000

0.4249

-0.0463

1.0000

0.0048

0.0000

Xβ

0.1379

-0.0523

-0.0039

1.0000

0.0000

0.3061

-0.0449

0.0048

1.0000

0.0000

ε

0.9225

0.0000

0.0000

0.0000

1.0000

0.5027

0.0000

0.0000

0.0000

1.0000

w

1.0000

0.1999

0.1429

0.1428

0.8964

1.0000

0.6130

0.3668

0.4215

0.4672

θ

0.1999

1.0000

-0.6275

-0.1128

0.0000

0.6130

1.0000

-0.1121

-0.0759

0.0000

ψ

0.1429

-0.6275

1.0000

0.0098

0.0000

0.3668

-0.1121

1.0000

0.0243

0.0000

Xβ

0.1428

-0.1128

0.0098

1.0000

0.0000

0.4215

-0.0759

0.0243

1.0000

0.0000

ε

0.8964

0.0000

0.0000

0.0000

1.0000

0.4672

0.0000

0.0000

0.0000

1.0000

w

1.0000

0.1816

0.1723

0.1512

0.9006

1.0000

0.5333

0.4983

0.3048

0.5077

θ

0.1816

1.0000

-0.6030

-0.0478

0.0000

0.5333

1.0000

-0.1693

-0.0927

0.0000

ψ

0.1723

-0.6030

1.0000

-0.0077

0.0000

0.4983

-0.1693

1.0000

0.0786

0.0000

Xβ

0.1512

-0.0478

-0.0077

1.0000

0.0000

0.3048

-0.0927

0.0786

1.0000

0.0000

ε

0.9006

0.0000

0.0000

0.0000

1.0000

0.5077

0.0000

0.0000

0.0000

1.0000

High educated Men

Women

Medium educated Men

Women

Low educated Men

This table continues on the next page.

Worker and Firm Heterogeneity in Wage Growth

23

Table 7 – continued from previous page. Wage growth

Wage levels

w

θ

ψ

Xβ

ε

w

θ

ψ

Xβ

ε

w

1.0000

0.1862

0.1537

0.1366

0.8852

1.0000

0.4901

0.4764

0.3319

0.4853

θ

0.1862

1.0000

-0.6717

-0.1175

0.0000

0.4901

1.0000

-0.2549

-0.1348

0.0000

ψ

0.1537

-0.6717

1.0000

0.0015

0.0000

0.4764

-0.2549

1.0000

0.0826

0.0000

Xβ

0.1366

-0.1175

0.0015

1.0000

0.0000

0.3319

-0.1348

0.0826

1.0000

0.0000

ε

0.8852

0.0000

0.0000

0.0000

1.0000

0.4853

0.0000

0.0000

0.0000

1.0000

Women

4.2

Within- and Between-Firm Wage Growth

So far, all results have been solely focusing on wage growth. Here we distinguish between within- and between-firm wage growth. We have divided our samples of the full sample, men and women, into those who have made a transition into a new job and those who have not. Table 8 shows the results of within- and between-firm wage growth. First, we have included transition as a dummy in the covariates of the basis regression to see whether transition itself can help explain wage growth variation. The first five rows of Table 8 contain results from this exercise. Comparison with Table 6 reveals that inclusion of this transition dummy contributes no extra explanatory power to the model. Second, we regress the standard model for men and women together as well as for men and women separately for both the sample of workers staying at the same employer (within-firm wage growth) and workers making a transition into a new job (between-firm wage growth). Two very interesting results leap out of Table 8; first, the overall explanatory power of the model rises for both samples. We are able to explain 20 percent of the variance in within-firm wage growth and as much as 46 percent of the full sample and male between-firm wage growth variation and even 58 percent of female between-firm wage growth variation. Second, the relative firm specific importance in wage growth variation rises dramatically when analyzing between-firm wage growth. Table 9 shows the correlation structure of the within- and between-firm wage growth analysis. Comparing with the baseline model, we see that the correlation structure of worker and firm specific effects changes only very little and it retains its overall structure with worker specific effects being highly negatively correlated with firm specific effects, although the correlation is slight lesser in the between-firm wage growth sample than it is in the within-firm sample.

1.0000 0.2889 0.1590 0.0207 0.5314

1.0000 0.1392 0.0294 0.0264 0.8050

1.0000 0.0866 0.0415 0.0221 0.8499

Cov(w, Z)/ V ar(w) Std. Dev Cov(w, Z)

Transition = 1 (2,469,392 obs) 0.0211 0.2168 0.0470 0.0304 0.1376 0.0125 0.0578 0.1221 0.0084 -0.0671 0.0340 0.0010 0.0000 0.1587 0.0252

Transition = 0 (12,074,930 obs) 0.0178 0.1337 0.0179 0.0688 0.0592 0.0023 -0.0398 0.0412 0.0006 -0.0112 0.0237 0.0004 0.0000 0.1206 0.0145

Full Sample (14,619,789 obs) 0.0184 0.1514 0.0229 -0.0755 0.0581 0.0018 0.1104 0.0507 0.0011 -0.0165 0.0249 0.0005 0.0000 0.1399 0.0196

Mean

Men

? Transition

sample; Covariates include: experience, experience squared, year effects and a transition dummy. samples; Covariates include: experience, experience squared and year effects.

0.0443 0.0128 0.0070 0.0009 0.0235

Transition = 1 (3,374,561 obs) w 0.0208 0.2104 θ 0.0046 0.1367 ψ 0.0731 0.1140 Xβ ? -0.0569 0.0337 ε 0.0000 0.1534

∗ Full

0.0176 0.0025 0.0005 0.0005 0.0142

Cov(w, Z)

Transition = 0 (17,227,144 obs) w 0.0194 0.1327 θ 0.0413 0.0599 ψ -0.0077 0.0396 Xβ ? -0.0141 0.0235 ε 0.0000 0.1191

Std. Dev

0.0221 0.0019 0.0009 0.0005 0.0188

Mean

Full Sample (20,703,609 obs) w 0.0196 0.1486 θ -0.0750 0.0576 ψ 0.1094 0.0470 Xβ ∗ -0.0148 0.0248 ε 0.0000 0.1370

Z

All

1.0000 0.2652 0.1784 0.0207 0.5356

1.0000 0.1286 0.0335 0.0250 0.8129

1.0000 0.0777 0.0481 0.0213 0.8530

Cov(w, Z)/ V ar(w) Std. Dev

Transition = 1 (882,627 obs) 0.0201 0.1908 -0.9155 0.1510 0.9575 0.1334 -0.0219 0.0346 0.0000 0.1227

0.0364 0.0128 0.0077 0.0008 0.0151

Transition = 0 (4,976,707 obs) 0.0235 0.1289 0.0166 -0.0741 0.0706 0.0027 0.1123 0.0540 0.0007 -0.0148 0.0241 0.0005 0.0000 0.1129 0.0127

0.0198 0.0021 0.0011 0.0005 0.0160

Cov(w, Z)

Women

Full Sample (5,949,155 obs) 0.0229 0.1407 -0.2248 0.0687 0.2537 0.0594 -0.0060 0.0260 0.0000 0.1267

Mean

Table 8: Robustness checks for wage growth; Regression Results.

1.0000 0.3512 0.2126 0.0226 0.4135

1.0000 0.1614 0.0405 0.0312 0.7669

1.0000 0.1082 0.0555 0.0259 0.8104

Cov(w, Z)/ V ar(w)

24 Chapter 1

0.1323 -0.0147 -0.0268 1.0000 0.0000

0.1406 -0.0811 -0.0033 1.0000 0.0000

0.1296 -0.0876 -0.0034 1.0000 0.0000

Xβ

0.7319 0.0000 0.0000 0.0000 1.0000

0.9016 0.0000 0.0000 0.0000 1.0000

0.9236 0.0000 0.0000 0.0000 1.0000

ε

θ

Men ψ

Transition = 1 (2,469,392 obs) 1.0000 0.4178 0.3169 0.4178 1.0000 -0.3813 0.3169 -0.3813 1.0000 0.1323 -0.0147 -0.0268 0.7319 0.0000 0.0000

Transition = 0 (12,074,930 obs) 1.0000 0.2905 0.1089 0.2905 1.0000 -0.4478 0.1089 -0.4478 1.0000 0.1406 -0.0811 -0.0033 0.9016 0.0000 0.0000

Full Sample (14,619,789 obs) 1.0000 0.2025 0.1435 0.2025 1.0000 -0.4978 0.1435 -0.4978 1.0000 0.1296 -0.0876 -0.0034 0.9236 0.0000 0.0000

w

? Transition

sample; Covariates include: experience, experience squared, year effects and a transition dummy. samples; Covariates include: experience, experience squared and year effects.

0.3169 -0.3813 1.0000 -0.0268 0.0000

Transition = 1 (3,374,561 obs) w 1.0000 0.4178 θ 0.4178 1.0000 ψ 0.3169 -0.3813 Xβ ? 0.1323 -0.0147 ε 0.7319 0.0000

∗ Full

0.1089 -0.4478 1.0000 -0.0033 0.0000

All ψ

Transition = 0 (17,227,144 obs) w 1.0000 0.2905 θ 0.2905 1.0000 ψ 0.1089 -0.4478 Xβ ? 0.1406 -0.0811 ε 0.9016 0.0000

θ

0.1435 -0.4978 1.0000 -0.0034 0.0000

w

Full Sample (20,703,609 obs) w 1.0000 0.2025 θ 0.2025 1.0000 ψ 0.1435 -0.4978 Xβ ∗ 0.1296 -0.0876 ε 0.9236 0.0000

Z

0.1323 -0.0147 -0.0268 1.0000 0.0000

0.1406 -0.0811 -0.0033 1.0000 0.0000

0.1296 -0.0876 -0.0034 1.0000 0.0000

Xβ

0.7319 0.0000 0.0000 0.0000 1.0000

0.9016 0.0000 0.0000 0.0000 1.0000

0.9236 0.0000 0.0000 0.0000 1.0000

ε

θ

Women ψ

Transition = 1 (882,627 obs) 1.0000 0.4440 0.3043 0.4440 1.0000 -0.4884 0.3043 -0.4884 1.0000 0.1246 -0.0313 -0.0459 0.6431 0.0000 0.0000

Transition = 0 (4,976,707 obs) 1.0000 0.2946 0.0968 0.2946 1.0000 -0.5883 0.0968 -0.5883 1.0000 0.1670 -0.0363 0.0006 0.8757 0.0000 0.0000

Full Sample (5,949,155 obs) 1.0000 0.2216 0.1315 0.2216 1.0000 -0.5935 0.1315 -0.5935 1.0000 0.1401 -0.0883 -0.0038 0.9002 0.0000 0.0000

w

Table 9: Robustness checks for wage growth; Correlation Structure.

0.1246 -0.0313 -0.0459 1.0000 0.0000

0.1670 -0.0363 0.0006 1.0000 0.0000

0.1401 -0.0883 -0.0038 1.0000 0.0000

Xβ

0.6431 0.0000 0.0000 0.0000 1.0000

0.8757 0.0000 0.0000 0.0000 1.0000

0.9002 0.0000 0.0000 0.0000 1.0000

ε

Worker and Firm Heterogeneity in Wage Growth 25

Chapter 1

26

5

Robustness

To analyze the robustness of our results we have run several different specifications of the model. First, to check if the low contribution in the wage growth variance decomposition by covariates results from too few variables added, we have included information on marital status, children, the size of the firm this period and one period before to the covariates. Second, we regress seven different variations of the model to see if the results change between them. Table A1 (in the appendix) shows these robustness checks. Column (3) is the baseline model where the only difference compared to the full sample part of Table 6 (row 2 - 6) is that a very small fraction of the worker effect and the residuals has been absorbed by the covariates with the inclusion of the extra variables. The difference between column (3) and the full sample part of Table 6 is not significant on any conventional levels, though, and we have thus no reason to think that excluding the extra covariates alters our results.12 Column (1) is the original OLS regression and the covariates themselves are seen to explain 2.24 percent of the variance in wage growth; The same contribution up to four decimals as in the baseline model with both worker and firm fixed effects added. We thus seem to be able to extract truly unobserved heterogeneity by including the fixed effects. The importance of the covariates does not alter much if we include either firm effects (column (2)) or worker effects (column (6)) to the model only, and lies between 2.1 and 2.9 percent. The contribution from the unobserved worker heterogeneity on the variance of wage growth is relatively robust over columns (3) to (6) but the importance of the unobserved firm heterogeneity seems to increase for models with worker fixed effects included (columns (3) and (5)) than without worker specific effects (columns (2) and (7)). In the end, our model specification seems to be relatively robust.13 Table A2 and A3 list the same robustness checks as Table A1 but for growth in wages over two and three periods, respectively. Comparing the baseline model (column (3)) in Table A2 and A3 with Table 6 shows that the interrelationship between the worker fixed effects, the firm fixed effects and the covariates remains relatively constant with the firm effects being twice as important as the covariates and the worker effects again twice as important as the firm effects. When analyzing higher period wage growth one would expect the different components to absorb some of the residual explanation compared to one-period wage growth; the covariates 12

F-test not shown, but available upon request. One could argue a more important experience measure were firm or industry tenure instead of overall experience. We have tried several different specifications, letting firm or industry tenure be an extra covariate or replace experience and experience squared with tenure and tenure squared. None of these operations led to any significant changes in regression results or the correlation structure. 13

Worker and Firm Heterogeneity in Wage Growth

27

because experience increases. the firm effect because firms paying consistently higher than average period-to-period wage growth will be paying even higher two-period wage growth. Finally, the worker effect will follow a similar pattern and be more important for describing the variance in wage growth over two periods than in only one period. Likewise, these effects would be expected to be even more clear when analyzing wage growth over three periods. Table A2 and A3 indeed show that the contribution to the variance in wage growth rises when moving from one-period to two- and three-period wage growth as we would expect. However, it is important to note that the relative contribution does not change much. Furthermore, Table A2 and A3 support our conjecture that the part of the lack in wage growth variance explanatory power compared to analysis of wage level variation can be contributed to a higher variance in the error term as we are able to extract more and more explanatory power from the error term when using longer period wage growth. As a final robustness check, one could argue that using size of the firm as the only firm specific control would not capture wage policies within firms. We have thus regressed the baseline model with average firm wage growth within each year as covariate together with worker experience and experience squared to see if this changes the results dramatically. Table A4 shows the regression results and following correlation structure. Comparing the results with those of the baseline model (table 6) reveals that including average firm wage growth in the regression lowers the contribution to the variance of wage growth by firm effects to 2.6 percent while covariates become much more important. Including average firm wage growth thus raise the explanatory power of observables from 2.2 percent to 9.6 percent. There is no significant change in the contribution of worker specific effects to the variance of wage growth. However, it is not surprising that including average firm wage growth in the regression lowers the importance of firm effects and rises the effect of the covariates. A positive firm effect firm is characterized by being one that pays higher than average wage growth given the observables so including exactly the characterization into the observables will automatically bias the results towards the covariates. The correlation structure does not change much by this inclusion, and especially the correlation between worker and firm effects remains the same as for the baseline model.

Chapter 1

28

6

Conclusions

This paper estimates a regression model for individual wage growth incorporating fixed worker and firm effects. We find that these worker and firm fixed effects influence wage growth very differently from the way they influence wages in levels. We have decomposed the variance of wage growth and wage levels into contributions from fixed worker effects, fixed firm effects, observable experience and year effects and what is left unexplained. We found that while worker effects could contribute with around 60 percent for high educated workers, around 42 percent for medium educated workers and around 35 percent for low educated workers of the variance in wage levels we are only able to attribute around 7 to 12 percent to worker effects for all three educational groups of the variance in wage growth to fixed worker effects. The same pattern seems to be the case for firm effects, for which we can attribute from 10 to 30 percent of the contribution to the variance in wage levels, while they are estimated to explain 4 to 10 percent of the variance in wage growth. Finally, the amount of variance left unexplained is much higher for wage growth than it is for wage levels ranging from 76 percent to 85 percent for subgroups and 85 percent for the full sample in wage growth versus 14 to 25 percent for subgroups and 19 percent for the full sample in wage levels. However, the amount of variance that we can explain increases from 15 percent to 30 percent, when we use three-period wage growth instead of one-period growth. Importantly, the interrelationship between the components does not alter considerably when moving from using one-period wage growth to either two- or three-period wage growth, as the worker effect keeps having around twice the explanatory power as firm effects which then have almost twice the explanatory power as observable covariates. We also find a very strong negative correlation between fixed worker and fixed firm effects in wage growth, much stronger than usually found for AKM wage level models. Some of this difference can be attributed to our estimated worker and firm effects having much lower standard deviation than worker and firm effects in wage levels. However, the major explanation lies in the high residual variance which Andrews et al. (2008) have shown to be important for the size of the correlation in worker and firm effects.

Worker and Firm Heterogeneity in Wage Growth

29

References Abowd, J., H. Finer and F. Kramarz (1999), Individual and Firm Heterogeneity in Compensation: An Analysis of Matched Longitudinal Employer and Employee Data for the State of Washington, in J. Haltiwanger, J. Lane, J. Spletzer and K. Troske (eds.), The Creation and Analysis of Employer-Employee Matched Data, North-Holland, 3–24. Abowd, J. M., R. H. Creecy and F. Kramarz (2002), Computing Person and Firm Effects Using Linked Longitudinal Employer-Employee Data, Technical Paper 2002-06, U.S. Census Bureau. Abowd, J. M. and F. Kramarz (1999), The Analysis of Labor Markets using Matched EmployerEmployee Data , vol. 3 of Handbook of Labor Economics, chap. 40, Elsevier Science B.V., 2629–2710. Abowd, J. M., F. Kramarz and D. N. Margolis (1999), High Wage Workers and High Wage Firms, Econometrica, 67(2): 251–333. Andrews, M. J., L. Gill, T. Schank and R. Upward (2008), High wage workers and low wage firms: negative assortative matching or limited mobility bias?, Journal of the Royal Statistical Society, A(2008) 171(Part 3): 673–697. Bagger, J., F. Fontaine, F. Postel-Vinay and J.-M. Robin (2007), A Tractable Equilibrium Search Model with Experience Accumulation, Working Paper. Bagger, J. and R. Lentz (2008), An Empirical Model of Wage Dispersion with Sorting, Working Paper. Baker, M. (1997), Growth-Rate Heterogeneity and the Covariance Structure of Life-Cycle Earnings, Journal of Labor Economics, 15(2): 338–375. Barth, E. and H. Dale-Olsen (2003), Assortative matching in the labor market? Stylized facts about workers and plants, Institute for Social Research, Oslo, Norway. Connolly, H. and P. Gottschalk (2006), Differences in Wage Growth by Education Level: Do Less-Educated Workers Gain Less from Work Experience?, IZA Discussion Papers 2331, Institute for the Study of Labor (IZA). Eeckhout, J. and P. Kircher (2009), Identifying Sorting - In Theory, Working Paper. Gladden, T. and C. Taber (2009), The Relationship Between Wage Growth and Wage Levels, Journal of Applied Econometrics, 24: 914–932. Gruetter, M. and R. Lalive (2004), The Importance of Firms in Wage Determination, IEW Working Papers 207, Institute for Empirical Research in Economics - IEW. Heckman, J. J., L. J. Lochner and P. E. Todd (2003), Fifty Years of Mincer Earnings Regressions, NBER Working Papers 9732, National Bureau of Economic Research, Inc. Kramarz, F., S. Machin and A. Ouazad (2009), What Makes a Test Score? The Respective Contributions of Pupils, Schools and Peers in Achievement in English Primary Education, CEE Discussion Papers CEEDP0102, CEE. Lopes de Melo, R. (2008), Sorting In the Labor Market: Theory and Measurement, Working Paper, Yale. Mincer, J. (1958), Investment in Human Capital and Personal Income Distribution, The Journal of Political Economy, 66(4): 281–302. Mincer, J. A. (1974), Schooling, Experience, and Earnings, New York: Columbia University Press.

30

Chapter 1

Mortensen, D. T. (2005), Wage Dispersion - Why are similar workers paid differently, First MIT Press paperback edition. Postel-Vinay, F. and J.-M. Robin (2002), Equilibrium Wage Dispersion with Worker and Employer Heterogeneity, Econometrica, 70(6): 2295–2350. Shimer, R. (2005), The Assignment of Workers in an Economy with Coordination Frictions, Journal of Political Economy, 113(5): 996–1025. Sørensen, K. L. and R. M. Vejlin (2011), Return to Experience and Initial Wage Level: Do Low Wage Workers Catch Up?, Working Paper; School of Economics and Management, Aarhus University. Sørensen, T. and R. Vejlin (2009), The Importance of Worker, Firm and Match Fixed Effects in the Formation of Wages, Working Paper; School of Economics and Management, Aarhus University. Woodcock, S. (2008), Match Effects, Discussion Papers. Department of Economics, Simon Fraser University.

Worker and Firm Heterogeneity in Wage Growth

31

Appendices A

Tables Table A1: Results from the wage growth variance decomposition for different models. Degree of contribution to the variance of wage growth

θ ψ Xβ ε

(1)

(2)

(3)

(4)

(5)

(6)

(7)

0.0224 0.9776

0.0352 0.0292 0.9356

0.0864 0.0415 0.0224 0.8497

0.0890 0.9110

0.0872 0.0436 0.8692

0.0905 0.0212 0.8883

0.0377 0.9623

yes yes no 20,703,609 2,083,391 295,034 0

yes no yes 20,703,609 2,083,391 295,034 7

no yes no 20,703,609 2,083,391 295,034 0

Components included θ ψ Xβ Observations Workers Firms Covariates

no no yes 20,703,609 2,083,391 295,034 7

no yes yes 20,703,609 2,083,391 295,034 7

yes yes yes 20,703,609 2,083,391 295,034 7

yes no no 20,703,609 2,083,391 295,034 0

Note: Covariates included are; Experience, experience squared, married, children, firm size, lagged firm size and year dummies.

Table A2: Results from the two-period wage growth variance decomposition for different models. Degree of contribution to the variance of two-period wage growth

θ ψ Xβ ε

(1)

(2)

(3)

(4)

(5)

(6)

(7)

0.0269 0.9731

0.0554 0.0416 0.9030

0.1231 0.0645 0.0317 0.7807

0.1245 0.8755

0.1221 0.0706 0.8073

0.1327 0.0297 0.8376

0.0601 0.9399

yes yes no 19,583,137 1,865,333 276,391 0

yes no yes 19,583,137 1,865,333 276,391 3

no yes no 19,583,137 1,865,333 276,391 0

Components included θ ψ Xβ Observations Workers Firms Covariates

no no yes 19,583,137 1,865,333 276,391 3

no yes yes 19,583,137 1,865,333 276,391 3

yes yes yes 19,583,137 1,865,333 276,391 3

yes no no 19,583,137 1,865,333 276,391 0

Note: Covariates included are; Experience, experience squared and year dummies.

Chapter 1

32

Table A3: Results from the three-period wage growth variance decomposition for different models. Degree of contribution to the variance of three-period wage growth

θ ψ Xβ ε

(1)

(2)

(3)

(4)

(5)

(6)

(7)

0.0397 0.9603

0.0698 0.0528 0.8774

0.1712 0.0765 0.0407 0.7116

0.1742 0.8258

0.1667 0.0879 0.7454

0.1868 0.0382 0.7750

0.0774 0.9226

no no yes 17,680,262 1,724,736 254,920 3

no yes yes 17,680,262 1,724,736 254,920 3

yes yes yes 17,680,262 1,724,736 254,920 3

yes yes no 17,680,262 1,724,736 254,920 0

yes no yes 17,680,262 1,724,736 254,920 3

no yes no 17,680,262 1,724,736 254,920 0

Components included θ ψ Xβ Observations Workers Firms Covariates

yes no no 17,680,262 1,724,736 254,920 0

Note: Covariates included are; Experience, experience squared and year dummies.

Table A4: Wage growth regression results with average firm wage growth included in the covariates. Z

Mean

Std. Dev.

Full sample (19,758,785 obs) w 0.0193 0.1465 θ 0.0310 0.0567 ψ -0.0135 0.0422 Xβ 0.0017 0.0474 ε 0.0000 0.1301

Cov(w, Z)

Cov(w, Z) /V ar(w)

0.0215 0.0019 0.0006 0.0021 0.0169

1.0000 0.0893 0.0259 0.0964 0.7884

Corr.

w

θ

ψ

Xβ

ε

w θ ψ Xβ ε

1.0000 0.2307 0.0898 0.2979 0.8879

0.2307 1.0000 -0.4903 -0.0467 0.0000

0.0898 -0.4903 1.0000 -0.0261 0.0000

0.2979 -0.0467 -0.0261 1.0000 0.0000

0.8879 0.0000 0.0000 0.0000 1.0000

Chapter 2 Wage Sorting Trends

Wage Sorting Trends∗ Jesper Bagger†

Rune Vejlin‡

Royal Holloway College

Aarhus University

Kenneth L. Sørensen§ Aarhus University

Abstract Using a population-wide Danish Matched Employer-Employee panel from 1980-2006, we document a strong trend towards more positive assortative wage sorting. The correlation between worker and firm fixed effects estimated from a log wage regression increases from −.07 in 1981 to .14 in 2001. The nonstationary wage sorting pattern is not due to com-

positional changes in the labor market, primarily occurs among high wage workers, and comprises 41 percent of the increase in the standard deviation of log real wages between

1980 and 2006. We show that the wage sorting trend is associated with worker reallocation via voluntary quits. Keywords: Matched Employer-Employee Data, Firm fixed effects, Worker fixed effects, Wage sorting, Wage inequality, Voluntary quits. JEL codes: J30, J31, J62

This chapter has been published in a shorter version as: Wage Sorting Trends, Economics Letters, 2013, vol. 118(1), pp. 63-67. We would like to thank Juan Pablo Rud, Dan Hamermesh, Michael Svarer, and Francis Kramarz for helpful comments and suggestions, and The Cycles, Adjustment, and Policy research unit, CAP, Department of Economics and Business, Aarhus University, for support and for making the data available. Vejlin greatly acknowledges financial support from the Danish Social Sciences Research Council (grant no. FSE 09-066745). † Department of Economics, Royal Holloway College, University of London, Egham, Surrey TW20 0EX, United Kingdom; E-mail: [email protected] ‡ Department of Economics and Business, Aarhus University, Fuglesangs All´e 4, DK-8210 Aarhus V, Denmark; E-mail: [email protected]. § Department of Economics and Business, Aarhus University, Fuglesangs All´e 4, DK-8210 Aarhus V, Denmark; E-mail: [email protected]. ∗

35

Chapter 2

36

1

Introduction

The seminal paper of Abowd et al. (1999), refined and extended in Abowd et al. (2002), investigates whether “high wage firms” employ “high wage workers”. The empirical analysis builds on a log wage regression with fixed worker and firm effects. In this context, a high wage worker is a worker with a relatively high worker fixed effect. A high wage firm is defined analogously. Subsequent to estimation on French and US Matched Employer-Employee (MEE) panels, the authors compute the empirical correlation between worker and firm fixed effects, pooling annual cross sections, and find that it is negative in France (correlation −.28 using data from

1976-1987) and in the US (correlation −.03 using data from 1984-1993).1 Similar studies have

since been conducted on a number of different datasets.2 We refer to the correlation between worker and firm fixed effects, as estimated from a log linear wage regression, as wage sorting.3 The purpose of this paper is to document and examine trends in wage sorting. We use a Danish full population MEE panel for 1980-2006. Pooling across annual cross sections, the correlation between worker and firm fixed effects is .05. We show that this estimate masks a systematic nonstationarity. By computing cross section specific correlations we find that the correlation between worker and firm effects increases from a low −.07 in 1981 to a high

.14 in 2001. The trend towards positive assortative wage sorting occurs almost exclusively in the top quartile of the distribution of worker effects, i.e. among high wage workers, and is economically important: it comprises 41 percent of the increase in the standard deviation of log wages between 1980 and 2006. We ascertain that the nonstationary wage sorting pattern is due to nonstationarity in the covariance between firm and worker effects, and that it is not driven by compositional changes in the labor force in terms of education, age, and gender. Further evidence suggests that the trend towards more positive assortative wage sorting is driven in part by entry and exit of workers, although this channel is likely to be weak, and in part by voluntary quits.4 The increasing wage sorting trend in the top quartile of worker effects could be related to high wage workers 1

These results are reported in Abowd et al. (2002). See e.g. Gruetter and Lalive (2004) (1990-1997, correlation −.22, Austria), Andrews et al. (2008) (1993-1997, correlation −.21 to −.15, Germany), Sørensen and Vejlin (2012) (1980-2006, correlation −.06 to .11, Denmark). 3 This notion of wage sorting is not linked to economic theory, and is distinct from that of productivity sorting, i.e. sorting on worker and firm productivity. A number of recent studies of productivity sorting (see e.g. Eeckhout and Kircher (2011), Bagger and Lentz (2012), and Bartolucci and Devicienti (2012)) find that it is difficult to identify productivity sorting from wage data alone. 4 In our terminology, a worker who is employed in different firms at date t − 1 and t has made a voluntary quit between t − 1 and t. 2

Wage Sorting Trends

37

employed in high wage firms being increasingly likely to transit to another high wage firm, or to high wage workers employed in low wage firms being increasingly likely to transit to a high wage firm. Our analysis supports the former relation.

2

Data

Our empirical analysis is based on IDA, a Danish register-based annual MEE panel covering 1980-2006. This data set is unique in an international comparison since it covers 27 years full labor force population and is perfectly suited for this study. The unit of observation is a given individual in a given year with measurements generally referring to the last week of November. Measures of actual labor market experience are available from 1964. For workers entering the labor market prior to 1964 (born before 1948) we add the potential pre-1964 experience net of education.5 The raw data consists of 60,847,593 observations. We inflate wages to 2006 levels. We discard (i) public sector jobs and individuals under education (19,191,599 observations), (ii) observations with missing data (6,103,607 observations), (iii) observations preceding observed labor market entry or if the individual enters later than age 35 (13,804,815 observations). We trim the within-experience-education group wage distribution (top and bottom 1 percent deleted, 503,454 observations) and select the maximal set of connected workers and firms (99,953 observations deleted).6 The analysis data contains 21,144,165 observations. Table 1 documents that average (real) log wages and their dispersion are increasing over our data period. Moreover, average education increases by around 1.5 years over the data period, the labor force ages due to the general demographic development, average experience is stable, and female (private sector) labor force participation is increasing.7

5

In this specification older workers are assigned too much experience. We have experimented with different forms of pre-1964 experience, including specifications that assign too little experience to older workers. Our results are very robust to these changes. 6 See Abowd et al. (2002) for an explanation of the necessity of conditioning on workers and firms being connected. 7 Potential experience is trending upwards while our actual experience measure is stationary. We ascribe this to older cohorts being assigned too much experience, and an increased prevalence of sabbaticals from education during 1980-2006.

Chapter 2

38 Table 1: Summary Statistics

3

Year

Obs.

Avg. ln w

S.d. ln w

Share women

Avg. age

Avg. years of education

Avg. experience

1980 1985 1990 1995 2000 2005

767,088 787,526 777,097 778,641 816,112 799,643

5.069 5.103 5.246 5.257 5.291 5.299

.304 .293 .296 .303 .326 .335

.24 .24 .26 .28 .31 .32

36.43 36.47 37.09 38.82 41.44 43.06

10.45 10.81 11.19 11.49 11.67 11.78

21.50 20.14 19.59 19.91 21.11 21.86

Econometric Framework

Let i index individuals, j index employers, and let t index annual cross sections. The function J(i, t) maps individual observations into employer IDs. Consider a log-linear two-way error component wage equation ln wit = x0it β + θi + ψJ(i,t) + εit ,

(1)

where ln wit is the log-wage, x0it contains time-varying regressors: experience, experience squared and a set of year dummies, θi is a time-invariant worker effect, ψJ(i,t) is a time-invariant firm effect, and εit is the residual log-wage. Throughout we maintain the assumption that E[εit |x0it , J(·, ·), i, t] = 0.8 Conditioning on workers and firms being connected ensures that

the matrix of regressors in (1) has full column rank.

Abowd and Kramarz (1999) argue that many existing models of wage determination under two-sided heterogeneity fail to deliver a log-linear wage equation with worker and firm effects. Estimated worker and firm effects from an OLS regression are therefore complicated functions of the underlying true (i.e. economically well-defined) worker and firm effects, and in general do not admit a structural interpretation.9 Nonetheless, for descriptive purposes, (1) is a useful and widely used representation of log wages. Wage sorting is measured by Pearson’s correlation coefficient between the estimated worker and firm effects. As is usual, the correlation is computed by pooling all available cross sections, and it is here denoted ρb. We are interested in the evolution of wage sorting over time and report

cross section specific estimates of Pearson’s correlation coefficient, a time-varying measure of 8

See Abowd et al. (1999) and Postel-Vinay and Robin (2006) for discussions of the economic content of this assumption. 9 Abowd et al. (2012) show how a version of the model developed in Shimer (2005) conditions the structure of worker and firm effects as estimated from a log linear wage equation, and use this structure to test for assortative matching in the labor market.

Wage Sorting Trends

39

wage sorting, which we denote ρbt . Formally, let θeit = (θbi − µ bθ,t )/b σθ,t and ψeJ(i,t)t = (ψbJ(i,t) −

µ bψ,t )/b σψ,t be worker and firm effects standardized with respect to cross section t averages and

standard errors, denoted µ bθ,t and σ bθ,t , and µ bψ,t and σ bψ,t for worker and firm effects, respectively. Let N be the total number of observations and let It be the index set of workers present in cross

section t. Then,

N

1 X ρbt = 1(i ∈ It )θeit ψeJ(i,t)t , |It | i=1

(2)

where 1(·) is an indicator function.

Part of our analysis involves partitioning each cross section into K groups to investigate possible sources of trends in ρbt . In these cases it will be useful to employ the following decomposition of ρbt ,

ρbt =

K X k=1

π bkt ρbkt ,

(3)

where π bkt = |Ikt |/|It | is the empirical share of cross section t workers belonging to group PN k (Ikt is the index set of workers in group k in cross-section t), and ρbkt = i=1 1(i ∈

Ikt )θeit ψeJ(i,t)t /|Ikt | measures the strength of the statistical dependence between θeit and ψeJ(i,t)t

in group k in cross section t. Note that ρbt is not a within-group Pearson’s correlation coefficient

as the worker and firm effects are standardized using cross section specific means and standard deviations.10 Expression (3) is useful in that it allows us to assert the extent to which changes to ρbt stem from compositional changes, i.e. changes to π bkt , and from group changes in wage

sorting, i.e. changes to ρbkt .

4

Results

The correlation over pooled cross-sections between the estimated worker and firm fixed effects is found to be ρb = .05. Figure 1 plots the ρbt -profile (solid line) which exhibits a strong upward trend. This phenomenon has not been documented in previous studies. Overall, the correlation

increases from a low −.07 in 1981 to a high .14 in 2001 at which point the correlation declines slightly. Conducting the analysis separately for two subperiods, 1980-1993 and 1994-2006, we obtain estimates of the pooled correlation of −.03 in 1980-1993 and .07 in 1994-2006.

A correlation between two variables may change because the covariance changes or because

10

Using Pearson’s correlation coefficient within groups in each cross section has the severe drawback that, if the marginal distributions of worker and firm effects differ across groups, the notions of high wage workers and high wage firms differ across groups, invalidating inter-group comparisons of wage sorting.

Chapter 2

40 Figure 1: Wage Sorting Trends

of changes to the marginal distributions. The dashed line in Figure 1 plots the time profile of ρb∗t ,

which is computed similarly to ρbt (cf. (2)), except that worker and firm effects are standardized using the means and standard errors in the pooled cross-sections. If the marginal distributions

of worker and firm effects are constant over time we have ρb∗t = ρbt . Comparing the solid and dashed lines in Figure 1, we note they are almost coinciding; the rising ρbt -profile is driven exclusively by changes in the covariance between worker and firm effects.

It is well-known that the empirical covariance between estimated worker and firm effects

underestimates the true covariance (cf. Andrews et al. (2008)). The intuition is simple: if a firm effect is under-estimated, workers at that firm will have over-estimated worker effects, and vice versa. This could drive the rising ρt -profile if the bias is more pronounced in earlier years. This could happen if, for example, the number of job movers, firms, worker observations, or firm size distribution are not stable over the time period considered. To ascertain that this is not the case we retain the allocation of workers to firms as found in the data, but simulate counterfactual individual wages by independently and randomly sampling the empirical marginal distributions of firm and worker effects, and residual wages. This generates a “true” zero correlation between worker and firm effects, with a flat ρt -profile. The dotted line in Figure 1 shows the ρbt -profile

from re-estimating (1) on this simulated data. There is a small negative bias in the estimated covariance, but the counterfactual ρbt -profile is flat.

Partitioning each annual cross section into quartiles of the distribution of worker effects,

we can compute quartile-specific ρbkt -profiles according to (3). These are plotted in Figure

2. Wage sorting in the first and third quartile of the worker effect distribution is stationary, whereas it is weakly increasing in the second and strongly trending among the highest worker

Wage Sorting Trends

41 Figure 2: Wage Sorting Trends in Worker Quartiles

effects, increasing from a low −.20 to a high .37. Hence, the economic forces that generated the nonstationary wage sorting pattern appear to have impacted almost exclusively on high wage workers. As many other countries, Denmark has experienced an increase in wage inequality (cf. Krueger et al. (2010) and Table 1). Ceteris paribus, a rising ρbt -profile contributes to this in-

crease. To relate the documented wage sorting trend to wage inequality trends, we compute the standard deviation of log wages and a counterfactual standard deviation under stationary wage sorting. Using (1), the (cross section t) counterfactual standard deviation is constructed as p [Var(ln wit ) + 2Cov(θbi , ψbJ(i,t) |t = 1980) − 2Cov(θbi , ψbJ(i,t) )]. The adjustment to Var(ln wit ) ensures that wage sorting, Cov(θbi , ψbJ(i,t) ), is fixed at the 1980 level for all t, and thus stationary.

The standard deviation of log wages increases from .30 to .34 between 1980 and 2006. Nonstationary wage sorting comprises 41 percent of this increase. We make no attempt at identifying the direction of causality, but conclude that nonstationary wage sorting is an economically important phenomenon.

4.1

Compositional Changes in Education, Age, and Gender

Table 1 documented three compositional shifts in the (private sector) labor market: rising education, aging, and rising female labor force participation. These offer potential explanations for the wage sorting trend. If, for example, the market for highly educated workers exhibits higher wage sorting than that of workers with low education, a shift towards a more educated labor force will induce an increase in overall wage sorting, even if wage sorting is stationary in each education group. We assess these explanations by partitioning the data according to

Chapter 2

42

workers’ education, age, and gender, and decompose the ρbt according to (3). The decomposition in (3) also allows us to construct two alternative ρt -profiles, by holding in turn labor market composition (the πkt s) and group wage sorting (the ρkt s) constant at their 1980 level.11

We define three education groups (7-11, 12-14 and 15-20 years of education),12 and four age groups (≤ 30, 31-40, 41-50, ≥ 51 years). We also split the data according to gender. The

top panel of Figure 3 traces the time profiles of the shares of each of the groups in our data (i.e. the π bkt ’s in (3)) related to education (top-left), age (top-middle) and gender (top-right),

respectively. The middle panel of Figure 3 plots the corresponding ρbkt -profiles. And finally, the

bottom panel depicts the alternative ρt -profiles.

With respect to education, the share of workers with 7-11 years of education is in decline

while those of workers with 12-14 and 15-20 years of education are on the rise. Turning to the ρbkt -profiles, they are all nonstationary, with the ρbkt -profile for high educated workers increasing

more than the rest. This is reminiscent of the result obtained from Figure 2, since highly educated workers are more likely to have high worker effects. Putting these two results together, the alternative ρt -profiles in the bottom panel confirms that the increasing wage sorting profile is not associated with compositional changes in educational attainment. A similar pattern emerges when partitioning the data according to workers’ age (middle panel) or gender (right panel). Thus, subgroup wage sorting exhibits nonstationarity similar to the overall trend: the rising ρbt -profile does not appear to be associated with compositional changes in education, age and gender. Notice that for young workers, our group sorting measure ρbkt drops sharply from around year 2000. Workers who are young towards the end of the data

period are only observed for a short period. This exacerbates the negative bias in the estimated covariance discussed earlier (cf. Andrews et al. (2008)). Hence, ρbkt is likely to be significantly underestimated for late t’s among young workers. Results not reported also rule out shifts in industry-level employment as the main driver of the nonstationary wage sorting pattern.

4.2

Worker Reallocation, Entry, and Exit

Having documented a robust nonstationary wage sorting pattern we now consider how this pattern is related to worker entry and exit over the data period, as well as worker reallocation. 11

We deliberately refrain from denoting the alternative profiles counterfactual profiles. They are not counterfactual since one cannot, in general, manipulate π bkt independent of ρbkt , or vice versa. 12 These groups correspond roughly to workers with primary school education, workers with high school or vocational education, and workers with some college education.

Figure 3: Wage Sorting and Compositional Trends in Education, Age, and Gender

Wage Sorting Trends 43

Chapter 2

44 Consider the following two partitions of workers in cross section t:

• Entry worker partition: An entering worker is not present in t − k for k ≥ 1, but

present in t. A staying worker remains employed in the same employer in t − 1 and t. A

voluntarily quitting worker changes employer between t and t − 1, while an involuntarily quitting worker is not present in t − 1, but is present in the data at some date t − k, k ≥ 2.

• Exit worker partition: An exiting worker is present in t, but not present at any date t + k

for k ≥ 1. A staying worker remains employed by the same employer in t and t + 1. A

voluntarily quitting worker changes employer between t and t + 1, while an involuntarily quitting worker is not present in t + 1, but is present in the data at some date t + k, k ≥ 2. If a worker has a gap (e.g. is present at t − 2, not at t − 1, but again present at t) s/he

most likely experienced a nonemployment or a public sector employment spell. However, with

annual data, being present in two consecutive cross sections does not ensure that the worker did not undergo an unemployment period. Hence, the terms voluntary and involuntary quits are imprecise, but reflect the fact that workers who undergo an involuntary quit are more likely to have experienced an unemployment period in between jobs than workers who undergo a voluntary quit. Notice also that in the Entry worker partition, a voluntary (involuntary) quitting worker, is a worker who has just undergone a voluntary (involuntary) quit. In the Exit worker partition, a voluntary (involuntary) quitting worker, is a worker who is about to undergo a voluntary (involuntary) quit. For each of the two partitions we plot, in Figure 4, the share of each group of workers (top panel), the subgroup wage sorting profile, ρbkt (middle panel), and the two alternative profiles (bottom panel). The shares of the groups are roughly constant over the period we consider in both partitions (cf. top panel in Figure 4). Hence, composition effects along the worker entry

and exit dimensions are not likely drivers of the increasing ρbt -profile. This is confirmed in the bottom panel. The middle panel in Figure 4 reveals nonstationary subgroup wage sorting patterns similar to the overall pattern in Figure 1.

Comparing the ρbkt -profile of entering workers (middle-left) and exiting workers (middle-

right) we see that the correlation is higher for entering workers in most years except from 2000 onwards where the correlation profile for entering workers is in decline (as is the overall ρbt -

profile in Figure 1). Similar to young workers in Figure 3, workers who enter late or exit early in the data period are only observed for short periods, and ρbkt is likely to be downward biased

Wage Sorting Trends

45 Figure 4: Wage Sorting Trends and Worker Reallocation

for late t’s among entering workers and for early t’s among exiting workers. Thus, the negative bias among the entering workers might be part of the explanation of the downward sloping ρbt -profile in the early 2000s. Keeping this potential caveat in mind, entering workers exhibit

stronger wage sorting than exiting workers over most of the data period. This selection process contributes to the increasing ρbt -profile in Figure 1, although the share of workers entering and exiting every year is too low to generate the wage sorting trend in Figure 1.13

Next we focus on the role of worker reallocations in generating an increasing wage sorting

trend. Considering the Entry worker partition, ρbkt is higher for workers who have just undergone a quit (voluntary or involuntary), than it is for staying (and entering) workers. It also seems that

workers who have undergone a voluntary quit exhibit higher wage sorting than workers who quit involuntarily, except in a few years in the 1990s.14 In the Exit worker partition, voluntarily

quitting, involuntarily quitting, and staying workers appear similar in terms of ρbkt -profiles. That 13

Results not reported show that the increasing wage sorting trend is also weakly related to the entry and exit of firms. 14 As mentioned earlier, our categorization of quits into voluntary and involuntary is imperfect. This leads to an underestimation of the difference between the two types of transitions in terms of wage sorting.

Chapter 2

46

is, job outflow seems to be a random sample in terms of wage sorting. Moreover, comparing the ρbkt -profiles of voluntary quitting workers in the Entry and Exit partitions, we see that workers undergoing a voluntary quit move towards firms where the correlation between worker and firm

effect is higher. In summary: (a) new matches initiated by a voluntary quit exhibit higher wage sorting than existing matches. In other words, wage sorting is more pronounced in the match inflow than in the stock. (b) Matches that break up are not different from matches that survive in terms of wage sorting. In other words, wage sorting in the match outflow and in the stock are

similar. From (a) and (b), the correlation between worker and firm effects in the new match is higher than in the old match. These facts imply that wage sorting becomes increasingly positive assortative over time.

4.3

Voluntary Quits

We have shown that wage sorting is trending, that the trend appears mostly in the top quartile of the distribution of worker effects, and that the trend is associated with voluntary quits. We now further investigate the association between voluntary quits and the observed wage sorting pattern. o Let Dθ,t be the decile of the worker effect in an annual cross section t, let Dψ,t be the decile

of the origin firm effect (the firm effect of the firm from which the worker made the transition), d and let Dψ,t be the decile of the destination firm effect (the firm effect of the worker’s current

firm). Finally, let Vt be an indicator for a voluntary quit in cross section t as defined in the Entry worker partition above. We now consider the probability of making a voluntary quit that involves a given worker type moving to a similar firm type.15 That is, we consider Pr[Dψd = Dθ , Vt = 1|Dθ , Dψo ] = Pr[Dψd = Dθ |Dθ , Dψo , Vt = 1] × Pr[Vt = 1|Dθ , Dψo ].

(4)

Equation (4) decomposes the object of interest, Pr[Dψd = Dθ , Vt = 1|Dθ , Dψo ], into the probability of Dψd = Dθ conditional on Dθ , Dψo and a voluntary quit, and the probability of a voluntary quit, conditional on Dθ and Dψo . Without an explicit model of the labor market there is no formal relationship between wage sorting and Pr[Dψd = Dθ , Vt = 1|Dθ , Dψo ], but it seems plausible that an increase in Pr[Dψd = Dθ , Vt = 1|Dθ , Dψo ] is associated with an increase in wage sorting.16 15

Using the definitions of voluntary and involuntary quits from the Exit worker partition leads to identical conclusions. 16 d o It is of course possible to envisage situations where Pr[Dψ = Dθ , Vt = 1|Dθ , Dψ ] and wage sorting move in

Wage Sorting Trends

47

We are interested in the evolution of Pr[Dψd = Dθ , Vt = 1|Dθ , Dψo ] over time. As it turns out, Pr[Vt = 1|Dθ , Dψo ], does not change systematically over our data period, and its contribution towards generating increased assortative wage sorting is therefore negligible, and we focus attention on Pr[Dψd = Dθ |Dθ , Dψo , Vt = 1].17

Unconditionally on ranking in the distributions of worker and origin firm effects, Pr[Dψd =

Dθ |Vt = 1] is increasing over time from .09 in 1980 to .13 in 2002, a 44 percent increase.

This pattern is consistent with an increasing wage sorting trend. Figure 5 shows contour plots of Pr[Dψd = Dθ |Dθ , Dψo , Vt = 1] for nine three-year subperiods. Darker areas indicate higher

probabilities and are predominantly located in the south-west and north-east corners in each subperiod. Interestingly, the north-east areas (high worker effect, high origin firm effect) appear to darken further and expand from 1980 to 2000. Hence, during this period, voluntary quits among high wage workers employed in high wage firms are increasingly likely to involve a transition to another high wage firm. We cannot detect any other systematic changes over time in Figure 5. Considering involuntary quits, results not shown, but available upon request, document that Pr[Dψd = Dθ |Dθ , Dψo , It = 1],where It is an indicator for involuntary quits, does not exhibit systematic changes over the data period.

The increasing wage sorting trend in the top quartile of worker effects could be explained by two processes: (a) high wage workers employed in high wage firms are increasingly likely to transit to another high wage firm or (b) high wage workers employed in low wage firms are increasingly likely to transit to a high wage firm. The above analysis shows that the increased wage sorting arises (at least in part) because of (a). Ceteris paribus, both explanations result in increased wage sorting and cross section wage inequality. However, the two processes have different implications in terms of lifetime wage inequality. (a) is likely to lead to a higher increase in lifetime wage inequality than (b) as it stifles the transitions between deciles in the cross sectional wage distribution (simply because Pr[Dψd = Dθ |Dθ , Dψo , Vt = 1] increases).18

Notice also that the increase in lifetime inequality generated by (a) is one in which the workers in the high deciles of the wage distribution benefits, whereas those in the bottom are not adversely affected.

opposite directions because changes in within-decile wage sorting, or because other decile transition probabilities also change. 17 d o Contour plots of Pr[Dψ = Dθ , Vt = 1|Dθ , Dψ ] for nine different subperiods are available upon request. 18 Flinn (2002) and Bowlus and Robin (2004) study lifetime wage inequality in Italy and the U.S. (Flinn) and in the U.S. (Bowlus and Robin), but do not use MEE data, and so, do not consider wage sorting.

1980−1982

Worker effect decile 1989−1991

10th 9th 8th 7th 6th 5th 4th 3rd 2nd 1st

Worker effect decile 1992−1994

Worker effect decile 2001−2003

Worker effect decile

0.00

0.05

0.10

0.15

0.20

10th 9th 8th 7th 6th 5th 4th 3rd 2nd 1st

10th 9th 8th 7th 6th 5th 4th 3rd 2nd 1st

Worker effect decile

Worker effect decile 1998−2000

0.00

0.05

0.10

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1983−1985

0.00

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0.00

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Figure 5: Wage Sorting Trends and Voluntary Quits

10th 9th 8th 7th 6th 5th 4th 3rd 2nd 1st

10th 9th 8th 7th 6th 5th 4th 3rd 2nd 1st

10th 9th 8th 7th 6th 5th 4th 3rd 2nd 1st

1986−1988

Worker effect decile 1995−1997

Worker effect decile 2004−2006

Worker effect decile

0.00

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0.00

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0.00

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d o d o Note: The contours indicate Pr[Dψ = Dθ |Dθ , Dψ , Vt = 1], where Dψ is the decile of the destination firm effect, Dψ is the decile of the origin firm effect, Dθ is the d o decile of the worker effect, and a voluntary quit is defined as in the Entry worker partition. Pr[Dψ = Dθ |Dθ , Dψ , Vt = 1] is truncated at .20.

10th 9th 8th 7th 6th 5th 4th 3rd 2nd 1st

10th 9th 8th 7th 6th 5th 4th 3rd 2nd 1st

10th 9th 8th 7th 6th 5th 4th 3rd 2nd 1st

Origin firm effect decile

Origin firm effect decile

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th

Origin firm effect decile

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th

Origin firm effect decile Origin firm effect decile Origin firm effect decile

Origin firm effect decile Origin firm effect decile Origin firm effect decile

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th

48 Chapter 2

Wage Sorting Trends

5

49

Conclusions

Wage sorting is measured by the correlation between worker fixed effects and firm fixed effects, as estimated from a log-linear wage regression. Using a Danish MEE panel for 1980-2006, this paper documents a strong trend towards more positive assortative wage sorting. The correlation between worker and firm fixed effects computed from pooled annual cross sections is .05, but masks a systematic nonstationarity over the data period. Quantitatively, the correlation ranges from −.07 in 1981 to .14 in 2001. The nonstationarity is not explained by compositional shifts

in the labor force in terms of education, age, and gender. We provide evidence that is consistent with the wage sorting trend being associated with entry and exit of workers, although this channel is likely to be weak, as well as worker reallocation. The latter is consistent with the observed wage sorting trend because, over the period we consider, wage sorting is more pronounced in the match inflow than in the stock, while wage sorting in the match outflow and in the stock are similar. The contribution to the wage sorting trend from the reallocation process is driven primarily by high wage workers employed in high wage firms. Finally, while it is beyond the scope of this paper to give a structural interpretation to the documented wage sorting trend, it is economically important in that it comprises 41 percent of the increase in the standard deviation of log wages between 1980 and 2006.

References Abowd, J. M., R. H. Creecy and F. Kramarz (2002), Computing Person and Firm Effects Using Linked Longitudinal Employer-Employee Data, Technical Paper 2002-06, U.S. Census Bureau. Abowd, J. M. and F. Kramarz (1999), The Analysis of Labor Markets using Matched EmployerEmployee Data, vol. 3, chap. 40, Handbook of Labor Economics, Elsevier Science B.V., 2629– 2710. Abowd, J. M., F. Kramarz and D. N. Margolis (1999), High Wage Workers and High Wage Firms, Econometrica, 67(2): 251–333. Abowd, J. M., F. Kramarz, S. Perez-Duarte and I. M. Schmutte (2012), A Formal Test of Assortative Matching in the Labor Market, Working Paper. Andrews, M. J., L. Gill, T. Schank and R. Upward (2008), High wage workers and low wage firms: negative assortative matching or limited mobility bias?, Journal of the Royal Statistical Society, A(2008) 171(Part 3): 673–697.

50

Chapter 2

Bagger, J. and R. Lentz (2012), An Empirical Model of Wage Dispersion with Sorting, Working Paper. Bartolucci, C. and F. Devicienti (2012), Better Workers Move to Better Firms: A Simple Test to Identify Sorting, Working Paper. Bowlus, A. and J.-M. Robin (2004), Twenty Years of Rising Inequality in US Lifetime Labor Income Values, The Review of Economic Studies, 71(7): 709–774. Eeckhout, J. and P. Kircher (2011), Identifying Sorting - In Theory, The Review of Economic Studies, 78(3): 872–906. Flinn, C. (2002), Labour Market Structure and Inequality: A Comparison of Italy and the U.S., The Review of Economic Studies, 69(3): 611–645. Gruetter, M. and R. Lalive (2004), The Importance of Firms in Wage Determination, IEW Working Papers 207, Institute for Empirical Research in Economics - IEW. Krueger, D., F. Perri, L. Pistaferri and G. Violante (2010), Cross-Sectional Facts for Macroeconomists, Review of Economic Dynamics, 13(1): 1–14. Postel-Vinay, F. and J.-M. Robin (2006), Microeconometric Search-Matching Models and Matched Employer-Employee Data, chap. 11, in: Blundell, R., Newey, W., Persson, T. (Eds), The Proceedings of the 9th World Congress of the Econometric Society, Cambridge University Press: Cambridge, UK, 279–310. Shimer, R. (2005), The Assignment of Workers in an Economy with Coordination Frictions, Journal of Political Economy, 113(5). Sørensen, T. and R. Vejlin (2012), The importance of worker, firm and match fixed effects in wage regressions, Forthcoming in Empirical Economics.

Chapter 3 Return To Experience and Initial Wages: Do Low Wage Workers Catch Up?

Return to Experience and Initial Wage Level: Do Low Wage Workers Catch Up?∗ Kenneth L. Sørensen†

Rune Vejlin†

Aarhus University

Aarhus University and CAP

Abstract This paper estimates the relationship between initial wage and return to experience. We use a Mincerlike wage model to nonparametrically estimate this relationship allowing for an unobservable individual permanent effect in wages and unobservable individual return to experience. The relationship between return to experience and unobservable individual ability is negative when conditioning on educational attainment while the relationship between return to experience and educational attainment is positive. We link our finding to three main theories of wage growth, namely search, unobserved productivity and learning, and human capital. We devise several empirical tests in order to separate the theories. We find evidence in favor of the learning model and mixed evidence regarding the search model. We find no evidence in support of the human capital model. Keywords: Wage growth, initial wage, return to experience, nonparametric estimation JEL codes: J3, J24

We thank Michael Svarer, Christopher Taber, Greg Veramendi, participants at the DGPE conference 2010, the Xiamen-Aarhus Labor workshop, Xiamen 2010, CEF 2011, San Francisco, BI-LMDG annual meeting, 2011, Brownbag lunch seminar Aarhus University 2011 and at the annual workshop of the NBER group on micro and macro perspectives, 2011. We would like to thank The Cycles, Adjustment, and Policy research unit, CAP, Department of Economics and Business, Aarhus University, for support and for making the data available. Vejlin greatly acknowledges financial support from the Danish Social Sciences Research Council (grant no. FSE 09-066745). † Department of Economics and Business, Aarhus University, Building 1322, Bartholins All´e 10, DK-8000 Aarhus C, Denmark. Correspondence to: Kenneth Lykke Sørensen, email: [email protected]. ∗

53

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54

1

Introduction

Since Mincer (1958, 1974) it has been commonly acknowledged that earnings rise with the accumulation of experience. Furthermore, one of the most established facts in the literature is that wage profiles can be ranked by education. The wage-experience profile for workers with a higher educational level dominates that of workers with a lower educational level. E.g. Sørensen and Vejlin (2013) show that the return to experience depends on observable measures of permanent ability such as education, while Bagger, Fontaine, Postel-Vinay and Robin (2011) show the same in a structural search model with experience accumulation. It is also widely recognized that workers have permanent abilities that go beyond for instance education. Thus, including education in wage regressions might bias the estimates because both education and wages are affected by by permanent abilities, and therefore the inclusion of an individual worker fixed effect in wage regressions is by now standard. Using for instance the Abowd, Kramarz and Margolis (1999) decomposition, which decomposes wages into observed and unobserved fixed effects for workers and firms, one usually finds that observable measures for skills such as detailed educational information only explain a smaller part of the variation in the estimated worker fixed effect, see e.g. Sørensen and Vejlin (2013) and Woodcock (2011). Combining these two empirical regularities, we might suspect that the return to experience also change with unobservable skills. However, the relationship between unobserved individual permanent ability and the individual experience profile is greatly understudied in the literature. One of the contributions of this paper is to nonparametrically estimate the relationship between an individual permanent component of wages and an individual return to experience. We thus extend the identification argument developed by Gladden and Taber (2009), who show that the covariance between the permanent component of wages and a random coefficient on experience can be estimated from initial wages and later wage growth. We extend this argument in order to nonparametrically estimate this relationship. Like Gladden and Taber (2009) we find that workers with high permanent abilities have low individual returns to experience for all educational groups. Gladden and Taber (2009) use a sample of the NLSY79 data set to estimate the covariance between initial wages and later wage growth for low skilled workers. They estimate the relationship using observations that are sufficiently far apart in time such that they avoid potential problems with autocorrelation in the error term, which would generate a negative bias in the

Return to Experience and Initial Wage Level

55

estimate. They find only a small and insignificant effect between initial wages (interpreted as skill level) and future wage growth. Specifically they find that a one standard deviation increase in permanent skill level reduces future wage growth (interpreted as return to experience) by 0.87 per cent. Gladden and Taber (2009) conduct their analysis using mainly covariances because of lack of data. Almost all their estimates are only borderline significant, which is a problem since the limited amount of observations only allows them to estimate a covariance giving them an estimate of the slope between wage growth and initial wages. Although not the focus of his paper, Baker (1997) also estimates a similar model and finds a negative covariance between wage growth and wage level in the PSID data. However, Baker does not emphasize the potential problem with autocorrelation in the error term. Connolly and Gottschalk (2006) analyze whether returns to education and experience are lower for the less educated using the 1986-1993 panels of the Survey of Income and Program Participation (SIPP) which are comparable to the PSID although its time frame is considerably shorter than that of the PSID. SIPP’s advantage lies in more frequent interviews and thus more precise information on income and employer tenure. Connolly and Gottschalk argue that the number of former successful job matches is more important for job match quality than the number of former draws from the wage distribution. They analyze all age groups, both men and women, and find that higher educated do have higher returns to both experience and tenure. French, Mazumder and Taber (2006) also use the SIPP, but confine themselves to using workers between the ages of 18-28, in order to analyze the dependence of early career wage growth from accumulated work experience and job match quality for three different groups of education levels. Formally, they would like to test whether labor market policies encouraging job market experience help low educated workers out of poverty. They find that simple experience accumulation is important for early career wage growth whereas they on average do not find support for the importance of job changes in wage growth. Since we use a much larger data set than both Baker (1997) and Gladden and Taber (2009) we are able to divide our sample into finer educational groups. For all educational subgroups (primary/high school, vocational, bachelor, and master) there seems to be a negative relationship between initial wage and later wage growth. The negative relationship is most pronounced for those with a vocational education. Both Baker (1997) and Gladden and Taber (2009) only estimate the covariance. A potential problem is that the relationship between wage growth and wage level is non-linear. This paper

Chapter 3

56

thus takes the analysis one step further and nonparametrically estimates the return to experience given permanent skills. We find that the relationship is non-linear for those with only a primary/high school education and those with a master degree and thus the covariance might not be a particular good measure to describe the distribution. Using our rich data set we explore some of the theoretical channels of the negative relationship. One explanation is provided by human capital theory. Human capital theory is based on the seminal work of Becker (1962), Mincer (1962), and Ben-Porath (1967) and emphasizes the role of human capital acquirement in school and on the job. While on the job, workers face a trade-off between earning wages and investing in their human capital in order to earn higher wages in the future. Thus, human capital theory will predict a negative relationship between initial wages and return to experience. The second explanation is one of frictions. Standard search models like Burdett and Mortensen (1998) or Postel-Vinay and Robin (2002) also predict a negative relationship. In a wage posting model like Burdett and Mortensen workers will gradually move up the wage ladder. This implies that those who are initially lucky and find a firm with a high wage will later have lower wage growth, simply because there are fewer firms which are offering higher wages. Postel-Vinay and Robin (2002) use Bertrand competition among firms to determine wages. This mechanism actually enhances the negative relationship, since high productivity firms will be able to pressure workers to start out with a very low wage in order to later have the potential of very high wage growth as they find outside offers to pressure the incumbent firm. Like in the human capital theory this will generate a negative relationship between initial wages and later wage growth. The third explanation is based on unobserved productivity and learning. The model that we have in mind is inspired by Jovanovic (1979). The central idea behind this explanation is that workers slowly gets sorted out of the job. The employer pays the worker his expected productivity and gets noisy signals on the worker’s ability. As the option value of keeping low productive workers get smaller over time the workers are fired. Hence, the concave wage profile is driven by low productive workers getting fired. We concive several empirical tests in order to separate the three competing explanations. We find suggestive evidence that the learning model might be part of the explanation (especially for low educated). We find no evidence in the favor of the human capital explanation and mixed evidence for the search explanation. Finally, we investigate if the negative relationship between permanent ability and return to experience is driven by any specific group. We look closer at occupations, industries, time of

Return to Experience and Initial Wage Level

57

labor market entry and finally labor market transitions. We find that none of these observable features explain the negative relationship. The rest of this paper is organized as follows. Section 2 goes through our wage model and the nonparametric estimation approach. In section 3 we discuss the data used for the estimation and sections 4 and 5 present results and robustness checks. Finally, in section 6, we conclude.

2

Econometric Approach

We use a correlated random effects model inspired by Baker (1997) and Gladden and Taber (2009). Our goal is to analyze the relationship between initial wages and future wage growth within the first ten years of a worker’s labor market life. This relationship holds important information on wage profiles for workers with different skill levels. We assume that the wage structure is a linear function of worker specific permanent ability and human capital, measured as experience. Wages have been detrended by a simple OLS regression of year dummies on log wages such that all year specific effects have been removed. Let detrended log wages be defined as wit = θi + γi Eit + εit ,

(1)

where θi and γi are worker specific random effects, Eit is the experience of worker i at time t and εit is an error term. The linear relationship in (1) necessitates us to be very restrictive with how many years to include in the sample. The typical experience-wage profile is concave on its full support, but will be very nearly linear during the first 10 years on the labor market.1 We thus include observations up until t = 9 only (labor market entry at t = 0 makes it 10 years). θi and γi represent unobserved individual permanent abilities and the unobserved individual ability to make use of experience interpreted as the return to experience. The overall goal of this paper is to gain insights in the relationship between θi and γi from model (1). We allow workers into our sample only after they have completed their highest education. The identifying assumption is that no worker has any experience when entering the labor market or that the experience that he has is not useful, i.e. Ei0 = 0. This assumption is crucial for the 1

Gladden and Taber (2009) also use a linear model in experience. They justify this by referring to experience profiles in Gladden and Taber (2000), which are very close to linear. Sørensen and Vejlin (2011) estimate experience profiles using the same Danish data as used in this paper and find that the experience profiles are also close to linear.

Chapter 3

58

identification of the random effects. With the wage specification (1) the initial wage is wi0 = θi + εi0 ,

(2)

and the wage growth from period t − τ to t becomes ∆τ wit = γi ∆τ Eit + ∆τ εit ,

(3)

where ∆τ xit = xit − xit−τ . To ensure that we do not measure serial correlation, we discard

all wage growth observations before year 6 on the labor market. A simple transformation of (3) gives the more convenient representation of wage growth normalized by the growth in experience as a function of the unobservable individual return to experience and an altered error term ∆τ wit ∆τ εit = γi + . ∆τ Eit ∆τ Eit

(4)

As intuition would suggest equations (2) and (4) tell us that the initial wage might be a good estimate of unobserved permanent ability, while wage growth might be a good estimate for unobserved ability to learn. We thus use these to estimate the relationship between θ and γ . Notice, that we do not need to make any assumptions regarding the relationship between (θi , γi ) and Eit for the estimator to work. This is important since any reasonable model would imply that actual experience is correlated with (θi , γi ). However, loosely speaking we need the error terms in equations (2) and (4) to be uncorrelated. Baker (1997) estimates a model very close to ours and fits the error term by an ARMA(1,2) process. Gladden and Taber (2009) use Baker’s estimates to show that the covariance between the error term in equations (2) and (4) is tiny compared to the estimate and thus the potential bias is very small. Using the data in this paper we have estimated a corresponding model.2 The results confirm the previous findings by Gladden and Taber (2009) and Baker (1997) in that the potential bias is negligible compared to the estimates. Before we turn to our nonparametric approach we start out analyzing a more simple vari2

Table 5 contains covariations between initial errors and later changes in errors estimated by assuming the residuals of equation (1) following an ARMA(1,2) process as assumed by Baker (1997) and Gladden and Taber (2009). All correlations fall dramatically after year three and compared to the estimated covariance between θ and γ we find very low covariances between initial errors and later error growth. We thus feel confident using the conservative choice of year six as our first yearly wage growth in our regression analysis.

Return to Experience and Initial Wage Level

59

ant of the relationship between individual permanent abilities (θi ) and the individual return to experience (γi ), the covariance. Since θi and γi , by definition, are unobserved, we make use of the model specification (2) and (4). A simple OLS regression of wage growth normalized by growth in experience on initial wages gives us a slope coefficient that converges to   ∆wit Cov wi0 , ∆E it V ar(wi0 )

.

By the structure of (2) and (4), the slope coefficient will converge to Cov(θi , γi ) , V ar(wi0 ) so the covariance between permanent individual ability and the individual return to experience can thus fairly easy be estimated using OLS. We distinguish between two types of experience; potential and actual. Potential experience is initially set equal to zero and then simply grows one unit per year. Actual experience is an exact measure of experience accumulation each year, but is also set to zero at labor market entry. If the worker has worked full time all year, actual experience accumulation is equal to one unit. To eliminate the serial correlation in the error term, we use yearly wage growth only from period 6 to 9 after entering the labor market. We are not able to bring in later observations because of the linearity in the experience measure in (1).

2.1

Nonparametric Estimation Model

Given the structure of our model and the richness of our data we are able to nonparametrically estimate the joint distribution of γi and θi using initial wages and future wage growth. First, to estimate the expected level of wage growth for different levels of unobserved worker specific abilities (i.e. E[γi | θi ]) we consider the nonparametric regression model ∆τ wit = g(wi0 ) + ui , ∆τ Eit

i = 1, . . . , N,

t = 6, 7, 8, 9,

τ = 1,

(5)

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where the functional form of g is unknown. g can, however, be interpreted as the conditional h i ∆wit ∆wit 3 mean of ∆E given W = w . E | w i0 i0 i0 = g(wi0 ) is estimated nonparametrically as ∆Eit it gˆ(wi0 ) =

N X ∆wit i=1

∆Eit

Xi (wi0 ),

(6)

with Xi (wi0 ) =




wi0 −w ˜0 h .  PN wj0 −w ˜0 K j=1 h

K

h is the bandwidth smoothing parameter for initial wages. w˜0 is the grid point for which we evaluate the kernel. Optimally h would be chosen to minimize the asymptotic mean integrated squared error of the kernel estimates, which is the integration of the sum of the approximate variance and squared bias. Unfortunately, this includes unknown terms such as the second derivative of the unknown true density function. Instead of the theoretical optimal bandwidth, we use Silverman’s Rule-of-Thumb bandwidth determined as h = 2.34ˆ σwi0 n−1/5 .

(7)

Alternatively, we could implement a cross-validation method to estimate the bandwidth. Instead, we have tested the robustness of the Silverman rule of thumb bandwidth and found the estimates to be very robust to changes in the bandwidth. Indeed, if the true density is normal, then the rule-of-thumb bandwidth will give the optimal bandwidth, and for g close to normal, h will be close to optimal.4 K(·) is the second order Epanechnikov kernel given by5

K



wi0 − w˜0 h



=

   3 1 − 4

 0


wi0 −w ˜0 2 h



for wi0h−w˜0 ≤ 1 . w −w˜ 0 i0 for >1 h

(8)

The fact that we have chosen an Epanechnikov kernel instead of e.g. a Gaussian, Uniform or Triangular kernel is of minor importance. Instead, the important factor for the performance of any nonparametric kernel density estimation is not so much the choice of kernel itself, but rather the bandwidth smoothing selection (Zhang et al. (2006)). However, the Epanechnikov kernel 3

See Li and Racine (2007, Chapter 2 and especially Theorem 2.1). See e.g. Hansen (2010, Chapter 16). 5 See Li and Racine (2007, Chapter 1) and Zhang, King and Hyndman (2006) 4

Return to Experience and Initial Wage Level

61

has the advantage of being relatively fast to compute and it is the most efficient in minimizing the asymptotic mean squared error (Silverman (1986)). Second, we take the estimation one step further and nonparametrically estimate the full joint distribution between initial wages and future wage growth. The estimate of the full joint density of initial wages and wage growth is given by       n ∆w it X − ∆w˜ ∆wit 1 wi0 − w˜0 , fˆ wi0 , = K K  ∆Eit ∆Eit nhwi0 h ∆wit i=1 hwi0 h ∆wit ∆Eit

(9)

∆Eit

where hwi0 and h ∆wit are the bandwidth smoothing parameters for initial wages and wage ∆Eit

growth respectively while K(·) remains to be the Epanechnikov kernel from equation (8).6 When turning from a nonparametric regression model to a nonparametric two-variate joint density model, Silverman’s rule of thumb smoothing bandwidth parameter changes to −1/5

hj = 2.20ˆ σj n

3

for

  ∆wit j ∈ wi0 , . ∆Eit

(10)

Data

This paper uses Danish data to estimate the models specified above. We utilize two different kinds of data; (1) we use yearly data from the Integrated Database for Labor Market Research (IDA) and (2) we use weekly spell data. Both data sets are kept by Statistics Denmark. The data are confidential but our access is not exclusive. IDA is a matched employer-employee longitudinal database containing socio-economic information on the entire Danish population, the population’s attachment to the labor market, and at which firms workers are employed. Both persons and firms can be monitored from 1980 onwards. The reference period in IDA is given as follows; the linkage of persons and firms refers to the end of November, ensuring that seasonal changes (such as e.g. shutdown of establishments around Christmas) do not affect the registration. The creation of jobs within individual firms thus refers to the end of November. Background information on individuals mainly refers to the end of the year.7 Our gross sample contains all male workers having their main employment at a private firm in the period of 1987 − 2006 and having entered the labor market after 1980. 6

Li and Racine (2007) show that this is a MSE consistent estimate of the true joint density. See a more detailed documentation on IDA: http://www.dst.dk/HomeUK/Guide/documentation/Varedeklarationer/emnegruppe/emne.aspx?sysrid=1013 7

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62

The weekly spell data set is a longitudinal data set containing information of labor market transitions for each individual in the Danish population. The spell data is constructed by merging several Danish register data sets. All individuals are at first assigned to one of sixteen mutually exclusive labor market states in each week over the years 1985-2003 using the different register data sets. These states are then narrowed down to two states; non-employment and employment. We use the spell data to split the sample into three mutually exclusive subsamples. The first sample are those making a Job-to-Job transition within the year where we measure wage growth. The second sample is those making a Job-to-Nonemployment-to-Job transition likewise in the year where wage growth is measured. The final sample are those who have not changed jobs (henceforth denoted stayers). The advantage of IDA is the detailed socio-economic information on each individual from year to year while spell data delivers important information on how each individual acts on the labor market between the last week of November one year to the following last week of November next year. This information is very important since all we can see from IDA is whether or not an individual has changed employer or not, not whether he has switched directly from one job to another or if there has been a spell of un- or nonemployment in between, which is potentially very important for wage growth. The time period of our analysis is 1987-2006 except when we analyze transitions where spell data forces us to narrow down the sample to 1987-2003.

3.1

Sample Selection

In this section we present how we have chosen to narrow down the sample. The raw data consist of the entire Danish male labor force. First of all, we look only at full-time employment within the private sector. Second, we are interested only in labor market participation after the completion of education, so we delete all observations referring to periods before completion of the highest education as well as observations during education. Furthermore, to eliminate educational outliers we delete all observations belonging to individuals finishing their highest education after turning 35. As we are interested in examining the wage structure for the first ten years on the labor market, this ensures that all individuals will be relatively young workers. Also, one of the identifying assumptions was that rewardable experience at labor market entry was zero. This is unlikely to be a valid assumption if labor market entry happens when the worker is relatively old. We have split the sample into groups of education crossed with expe-

Return to Experience and Initial Wage Level

63

Table 1: Individuals in the sample.

1 obs 2 obs 3 obs 4 obs Total

Full sample

Primary/ High school

Vocational

Bachelor

Master

Vocational educated Stayers JtJ† JtNtJ∗

38,028 29,794 25,712 146,337 239,871

10,331 7,254 5,893 22,999 46,477

18,980 14,971 12,918 82,786 129,655

5,685 4,929 4,517 28,697 43,828

3,032 2,640 2,384 11,855 19,911

22,609 22,432 28,353 43,863 117,257

† Job-to-Job

transitions.

∗ Job-to-Nonemployment-to-Job

34,570 10,375 2,299 287 47,531

5,836 399 51 10 6,296

transitions.

rience, and then trimmed the top and bottom percentile of the wage distribution within each of these groups for each year separately. This results in a total of 239,871 male workers. Of these, 20 percent have at most a primary or high school diploma, 54 percent are educated at a vocational level, 18 percent hold a bachelor and 8 percent carry a master’s degree. 16 percent of all workers are present only once in our sample, 12 percent are in the sample twice, 11 percent enter three times and 61 percent of all workers are present four times. This comprises our sample to 760,100 worker observations.8 Tables 1 and 2 describe the sample used. Table 1 shows the number of individuals by education and by transitions within the vocational educated sample. The reason we have such a low number of Job-to-Nonemployment-to-Job transitions is that the requirement for being in this sample is that we observe two consecutive November cross-section job spells. I.e. in order for the worker to be in the Job-to-Nonemployment-to-Job sample he will need to be employed at one firm in a given November cross-section, become nonemployed during the year, and then finally find a job before the next November cross-section. This leaves out a lot of transitions that do not fulfill these requirements. Table 2 shows descriptive statistics for initial wage and wage growth by education and type of transition. Those making a Job-to-Job transition has a little higher initial experience and much higher wage growth. Workers that experience a Job-to-Nonemployment-to-Job transition on average have a negative wage growth. There is also a clear pattern across educational groups. The higher the educational level the higher is the initial wage and the wage growth.

8

Note that since we do not use wage growth between the entry on the labor market and year 6 as well as wage growth earned later than year 9, we can include a maximum of four observations per individual.

Chapter 3

64 Table 2: Descriptive statistics on initial wages and future wage growth. w0 Obs. Mean Std. dev. P5 P25 Median P75 P95

Obs. Mean Std. dev. P5 P25 Median P75 P95

4

Primary/High school ∆w ∆w ∆E

w0

Vocational ∆w

∆w ∆E

134,514 4.8170 0.3799 4.1751 4.5282 4.8587 5.1012 5.3992

134,514 0.0131 0.1587 -0.2406 -0.0625 0.0113 0.0858 0.2776

134,514 0.0145 0.2058 -0.2572 -0.0657 0.0118 0.0907 0.2990

418,820 5.0592 0.2711 4.6028 4.8669 5.0642 5.2487 5.5034

418,820 0.0075 0.1529 -0.2488 -0.0633 0.0077 0.0789 0.2649

418,820 0.0079 0.1985 -0.2607 -0.0652 0.0079 0.0816 0.2792

w0

Full sample ∆w

∆w ∆E

w0

Stayers ∆w

∆w ∆E

760,100 5.0858 0.3296 4.4936 4.8824 5.1140 5.3175 5.5702

760,100 0.0148 0.1524 -0.2370 -0.0536 0.0142 0.0841 0.2691

760,100 0.0157 0.1968 -0.2478 -0.0551 0.0145 0.0866 0.2828

327,984 5.0570 0.2709 4.6004 4.8663 5.0636 5.2454 5.4998

327,984 0.0059 0.1287 -0.2148 -0.0545 0.0065 0.0668 0.2254

327,984 0.0067 0.1398 -0.2189 -0.0559 0.0067 0.0685 0.2343

w0

Master ∆w

∆w ∆E

143,882 143,882 143,882 5.2769 0.0262 0.0276 0.2357 0.1430 0.1814 4.8809 -0.2064 -0.2101 5.1326 -0.0318 -0.0321 5.2900 0.0233 0.0234 5.4335 0.0863 0.0871 5.6383 0.2655 0.2730 Vocational educated Job-to-Job ∆w w0 ∆w ∆E

62,884 5.4007 0.2127 5.0396 5.2676 5.4015 5.5316 5.7496

62,884 0.0413 0.1516 -0.1890 -0.0203 0.0356 0.1045 0.2889

62,884 0.0433 0.1959 -0.1919 -0.0204 0.0357 0.1051 0.2963

63,365 5.0631 0.2742 4.5993 4.8681 5.0661 5.2529 5.5106

6,827 5.0934 0.2673 4.6407 4.9095 5.0943 5.2772 5.5296

w0

Bachelor ∆w

63,365 0.0182 0.2260 -0.3629 -0.1166 0.0226 0.1577 0.3815

∆w ∆E

63,365 0.0174 0.2578 -0.3992 -0.1240 0.0236 0.1656 0.4115

Job-to-Nonemployment-to-Job ∆w w0 ∆w ∆E 6,827 -0.0001 0.2199 -0.3595 -0.1270 -0.0008 0.1243 0.3635

6,827 -0.0040 0.3544 -0.5301 -0.1689 -0.0009 0.1628 0.5102

The Results

In this section we present the results. We first estimate the covariance of θi and γi in equation (1) also estimated in Gladden and Taber (2009). Secondly, we move to the nonparametric estimation. And finally, we present evidence on the degree of wage catch up.

4.1

The Covariance of Initial Wage Level and Return to Experience

In this section we present results similar to those of Gladden and Taber (2009). Table 3 presents the regression results for both potential and actual experience for each of the four educational groups. Column (1) contains unweighted estimates of the slope. Column (2) contains weighted versions such that each individual gets equal weight regardless if they appear one, two, three or four times in the sample. All groups display significant negative slopes except the weighted bachelor regressions. There are no significant differences in the weighted vs. unweighted regressions. A result of the descriptive fact that most of our workers are represented by four observations. Vocational educations see the steepest negative covariances between wage growth and initial wages followed by workers holding a master’s degree and workers with at most a primary or high school diploma. Gladden and Taber (2009) calculate similar numbers for low educated (corresponding to our primary/high school group) and find results of an insignificant magnitude of -0.005. We estimate a significant covariance for primary/high school workers of -0.0139. There is a tendency that the coefficients get more negative when using actual experience, although there is no significant difference. The important coefficient is the significant negative slope coefficient on initial wage which reveals that e.g. a worker with a vocational education earning one percent higher initial wage

Return to Experience and Initial Wage Level

65

Table 3: Regression of log wage growth years 6 to 7, 7 to 8, 8 to 9 and 9 to 10 on initial log wages, subsamples. Primary/High school (1) (2)

Model ∆wit = α + βwi0 + εit ∆wit ∆AEit

= α+βwi0 +εit

Observations Individuals

-0.0105*** -0.0110*** (0.0012) (0.0015) -0.0123*** -0.0139*** (0.0015) (0.0021) 134,514 46,477

134,514 46,477

(1)

Vocational (2)

(1)

Bachelor (2)

(1)

Master

(2)

-0.0318*** -0.0322*** -0.0047*** -0.0025 -0.0169*** -0.0156*** (0.0009) (0.0011) (0.0017) (0.0021) (0.0030) (0.0039) -0.0337*** -0.0353*** -0.0043** -0.0010 -0.0191*** -0.0193*** (0.0011) (0.0019) (0.0020) (0.0030) (0.0035) (0.0049) 418,820 129,655

418,820 129,655

143,882 43,828

143,882 43,828

62,884 19,911

62,884 19,911

The standard errors in parentheses are robust. (1) Unweighted regressions. (2) The regressions are weighted such that each individual have equal weights. ***, **, * indicates significance at levels 1, 5 and 10 percent respectively.

will on average have 0.032 percentage point less wage growth than the normalized worker and 0.034 percentage point lower wage growth per actual experience year. Gladden and Taber (2009) report that a worker with a one standard deviation higher level of permanent ability have around 0.61 to 0.87 percentage point lower return to experience. If we calculate the similar number given our sample we find that a primary/high school worker with a one standard deviation higher level of permanent ability have a 0.40 to 0.53 lower return to experience. These are very similar results.

4.2

Nonparametric estimation

One might suspect that the relationship between return to experience and initial wage levels is non-linear. If this is the case, then the covariance will not capture the true relationship. We here present evidence that the relationship may not be linear on the entire support. We estimate equation (6), the expected wage growth conditional on initial wages using the actual experience measure. As shown above, this relationship contains information on the return to experience we would expect of a worker conditional on his individual permanent ability level. Figure 1 plots the estimated expected wage growth conditional on initial wage levels with bootstrapped confidence intervals for the four subsamples. The four figures confirm the results from the OLS regressions. Vocational educated workers see a steep negative relationship, primary/high school workers have an overall negative slope, but for lower ability workers the relationship is insignificant. Workers with a bachelor degree exhibit an almost constant initial wage - wage growth relationship and master’s degree workers have an overall negative slope. The figure highlights slope differences within especially the groups of primary/high school workers and master’s degree holders. The covariance analysis thus only gives an overview over the true relationship while the nonparametric approach is able to give a more thorough picture.

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66

.03 .01 ï.01

Expected wage growth

.05

Figure 1: Expected wage growth over initial wages for educational subgroups.

4.1

4.3

4.5

4.7

4.9 5.1 Initial log wage

Primary/High school Bachelor

5.3

5.5

5.7

Vocational Master

Note how a large fraction of primary/high school workers start out lower than vocational educated, but for workers starting at the same level between the two groups, primary/high school workers can expect a higher wage growth than vocational educated workers. All workers with a bachelor and a master’s degree can, on the other hand, expect even higher wage growth for all permanent worker types. Another very important conclusion from Figure 1 is that if we had estimated the model on the entire sample we would get a U-shape of growth by initial wages. This is done in figure 2 However, the U-shape is simply a composition effect from estimating the model on all educational groups at the same time. In general, both initial wages and wage growth is increasing in educational attainment. This leads to the U-shape which was observed in Figure 2. Wage growth is thus increasing in observed permanent ability (education), while it is decreasing in unobserved permanent ability (initial wage).

4.3

Catching Up or Not?

Given the non-parametric estimations presented above we are able to calculate the expected log wage levels any permanent ability type worker can on average expect at any point in time during his early labor market career. The calculations are based on the results presented in figure 1. From this figure we can find the average wage growth for each group in the initial wage distribution. However, though we can calculate the expected wage increase for each year of extra experience, it is harder to find out how the level should be. We have chosen to use the

Return to Experience and Initial Wage Level

67

.025 .02 .015 .01

Expected wage growth

.03

Figure 2: Expected wage growth over initial wages for the full sample.

4.4

4.6

4.8

5.0 Initial log wage

5.2

5.4

fifth year wage. E.g. for the fifth percentile (P5) the level is set to the average fifth year wage for all workers within a 0.1 log wage distance of the fifth percentile initial wage and likewise for the other percentiles. Figure 3 depicts the graphical estimated wage paths for five initial wage distributional groups in each of our educational subgroups. These graphs are interesting in at least two ways; (1) they show how the wage paths are expected to evolve for each subgroup and (2) they give a better picture of the robustness of our estimations. Imagine that the DGP is equation (1) and that all workers have the same permanent ability (θi = θ), and when entering the labor market they each draw an error term, εi0 . Some workers draw a high value of εi0 and therefore a high initial wage while some workers draw a low εi0 and receive a low initial wage. Given that all are the same and the errors are iid, these random draws should be neutralized by time and all workers should see wage paths converging to the same level.9 Primary/high school workers below the 75th percentile initial wage in fact do seem to follow a pattern like the example of homogeneous workers. The average fifth year wage is the same for the 5th, 25th and 50th percentile while higher initial wage workers with a primary/high school degree still have a higher wage after five years on the labor market. Because of the steep negative slope in the nonparametric analysis, wee see that the lower wage workers are not only catching up to the higher wage workers, but are overtaking them. Workers with a vocational education see some of the same pattern, only not as clear. As both the covariance and nonparametric analysis indicated, workers with a bachelor degree do not show any kind 9

This is confirmed by our ARMA estimations presented in table 5.

Chapter 3

68

Figure 3: Estimated mean log wages per year after entry. Percentiles P5 to P95 refer to the respective initial wage distributions.

5.6 5.4

Expected wage level

5

5.2

5.5 5.4 5.3 5.2 5.1

Expected wage level

5.8

Vocational

5.6

Primary/High school

5

6

7 Years after entry P5 P75

8

P25 P95

9

5

6

P50

7 Years after entry P5 P75

9 P50

Master

5.2

6.5 6 5.5

5.4

5.6

5.8

Expected wage level

6

6.2

7

Bachelor

Expected wage level

8

P25 P95

5

6

7 Years after entry P5 P75

P25 P95

8

9 P50

5

6

7 Years after entry P5 P75

P25 P95

8

9 P50

of catching up for any of the distributional groups, although the median initial wage percentile does have a higher wage growth rate than the 75th percentile. Low initial wage workers holding a master’s degree stay at the bottom while the 25th percentile and median workers overtake the top initial wage workers after year seven. One might be suspicious that these results are an artifact of the estimation procedure, which puts some restrictions on the functional form. Figure 4 shows experience profiles for different groups of the initial wage distribution estimated by log wages on experience and experience squared. Looking at figure 4 the qualitative results regarding catching up seems to be related to the data and not just be spurious. Especially for those with either primary/high school or a vocational education it seems that the 5th percentile almost catches up to the 95th percentile. For those with a bachelor or a master’s degree there seems to be very little catch up. This is true in particular for the bachelor group. However, there are also differences. Note that there are differences on the scale of the x-axis between Figure 3 and 4. In particular, since Figure 3 is based on a linear model we can never replicate the inverted U-shape that Figure 4 has. Therefore it also only makes sense to compare the first 10 years of the graphs.

Return to Experience and Initial Wage Level

69

Figure 4: OLS estimates of log wage-experience profiles for different initial wages groups.

4

4.8

5

Log wages 5.2

Log wages 4.5 5

5.4

5.6

Vocational

5.5

Primary/High school

0

5

10 15 20 Experience years after labor market entry P0ïP5 P50ïP75

P5ïP25 P75ïP95

25

0

5

P25ïP50 P95ïP100

10 15 20 Experience years after labor market entry P0ïP5 P50ïP75

25

P25ïP50 P95ïP100

Master

5

4.8

5

5.2

Log wages 5.2 5.4

Log wages 5.4 5.6 5.8

5.6

6

5.8

Bachelor

P5ïP25 P75ïP95

0

5

10 15 20 Experience years after labor market entry P0ïP5 P50ïP75

5

P5ïP25 P75ïP95

P25ïP50 P95ïP100

25

0

5

10 15 20 Experience y ears after labor market entry P0ïP5 P50ïP75

P5ïP25 P75ïP95

25

P25ïP50 P95ïP100

Relation to Theory

Our main finding is that initial wages and later wage growth have a negative relationship. In this section we will relate this finding to the three main theories relating initial wages to later wage growth, namely search theory, unobserved productivity and learning, and finally human capital theory. All three theories predict the negative relationship, so in order to try to shed light on which of the theories are consistent with the data we will devise empirical implications that hold only for a subset of theories and then test these implications. Since many versions of these theories exist we start by presenting our view of the fundamental theories.

5.1

Search Theory

One of the theories that explain the negative correlation between individual return to experience and initial wages is job search theory. The models that we have in mind are search models like Burdett and Mortensen (1998) or Postel-Vinay and Robin (2002). However, the implications of how wage posting models and second price auctions model wages are different in a number of ways as we will show later. In a wage posting model like Burdett-Mortensen workers will gradually move up the wage/productivity ladder. This implies that those who are initially lucky and find a firm with a high wage will later have lower wage growth. This happens because

Chapter 3

70

there are simply fewer firms offering higher wages. In Postel-Vinay and Robin (2002) this mechanism is actually enhanced. In the Postel-Vinay and Robin model wages are set in Bertrand competition between firms. High productivity firms will be able to pressure workers to start out with a very low wage in order to later have the potential of very high wage growth as they find outside offers. However, the one to one correspondence between wages and productivity, as was present in the wage posting model, is now broken.

5.2

Unobserved Productivity, Job Matching, and Learning

The theory of unobserved productivity and learning is centered around the assumption of imperfect information within the job match. In job search theory transitions and wage changes happen because of arrival of new information about alternative matches. In the theory of job matching new information arrives in the form of information about the current job match. One of the seminal papers in the literature regarding unobserved productivity, job matching, and learning is Jovanovic (1979). In this model workers and firms have match specific unobserved productivity. True match specific productivity is an experience good and is slowly recovered from noisy signals. Workers receive a wage equal to their expected output. One of the key predictions is that it delivers a concave wage-tenure profile. This is loosely speaking caused by selection, since workers with a low match quality slowly separate and thus only high match workers are left. The separated workers move to another firm and start the process again. One implication of this is a negative relationship between initial wages and later wage growth in general. The reason for this negative relationship is that workers who initially receive a high wage are more likely to be of a high match quality and therefore more likely to stay at the same firm. Since this profile is concave it gives on average higher wage growth at low tenure values. The main difference between the job search theory and the theory of job matching is that in the search theory the main determinants of wage growth are outside offers while in job matching it is based on new information of the match. Thus, one way to try to separate the theories is to look at wage growth within and between the original job match.

5.3

Human Capital Theory

The final theory that we want to relate our results to is human capital theory. This is based on the seminal work of Becker (1962), Mincer (1962), and Ben-Porath (1967) and emphasizes the role of human capital acquirement in school and on the job. What we have in mind here

Return to Experience and Initial Wage Level

71

is a Ben-Porath type model where workers face a trade-off on the job between earning higher wages and investing in their human capital, thereby increasing their earnings potential in the future. In order to invest in human capital the worker will have to take a job with a lower wage. Thus, human capital theory will predict a negative relationship between the initial wages and individual wage growth (return to experience). For a survey on this literature see Weiss (1986). The model can be extended to incorporate workers with scholastic abilities, see e.g. Rubinstein and Weiss (2006). If we allow for individuals to have different abilities to learn (scholastic ability) one of the predictions is that those with high ability will stay longer in school. However, they will then do less investment on the job. The driving force behind the negative relationship between initial wages and later wage growth according to human capital theory is different investment strategies by otherwise identical workers. This is contrary to both of the two previous explanations that focused on informational frictions.

5.4

Key Predictions and Testable Outcomes

In order to try to differentiate between the three theories we have two possible paths. The first is to write down a fully structural model encompassing all three explanations. However, this is well beyond the scope of this paper. Thus, our approach is to devise different testable outcomes of the three theories presented. The goal is to try to find suggestive evidence for or against each for them. Unemployment A feature of almost all search models is that unemployment acts as a resetting device. If a worker becomes unemployed, search models like those mentioned above, dictate that he will be searching on the grounds of his unemployment benefit and not his former wage, eliminating the link between his former (initial) wage and later wage growth. We can thus test if search is the main explanation by looking at workers who have been unemployed between entry on the labor market and year six and workers who have not.10 In order to do this we make use of the weekly spell data previously described. An insignificant relationship between initial wages and future wage growth for those who have been unemployed would thus confirm the search theory explanation, while a significant slope contradicts it. 10

We categorize unemployed to be only those with more than 12 weeks of unemployment to get rid of possible bias from workers with only short-term unemployment in between jobs. The results do not depend on this assumption.

Chapter 3

72

Figure 5: Expected wage growth divided on workers experiencing at least one 12 weeks unemployment spell between entry on the labor market and his 6th year. Vocational .03 .02 .01

Expected wage growth

ï.01

0

.02 .01 0 ï.01

Expected wage growth

.03

Primary/high school

4.1

4.3

4.5

4.7 4.9 Initial log wage

Some U spells > 12 weeks

5.1

5.3

5.5

4.5

No U spells > 12 weeks

4.7

4.9 5.1 Initial log wage

Some U spells > 12 weeks

No U spells > 12 weeks

.07 .06 .05 .04

Expected wage growth

.02

.03

.04 .035 .03 .025 .02

Expected wage growth

5.5

Master

.045

Bachelor

5.3

4.8

5

5.2 Initial log wage

Some U spells > 12 weeks

5.4

5.6

5

No U spells > 12 weeks

5.2

5.4 Initial log wage

Some U spells > 12 weeks

5.6

5.8

No U spells > 12 weeks

Figure 5 indicates that in general, there seems to be very little difference between the groups that experienced an unemployment spell and those that did not. Note, that for the Primary/high school group we find some indicative evidence that search theory might be an explanation, since workers that have experienced an unemployment spell have a flatter relationship. We take this to indicate that the search model might explain some of the negative relationship for low educated but not for high and medium educated. Job to Job transitions

Both Learning models and Burdett and Mortensen (1998) imply a

negative relationship between initial wages and the number of job to job transitions. However, Postel-Vinay and Robin (2002) implies a positive relationship. Figure 6 shows the yearly average number of job to job transitions by educational group and initial wage. The pattern is quite different for the four educational groups. For primary/high school and vocational educations the relationship is negative, while it is clearly positive for master degree holders. For workers with a bachelor degree it is hard to say anything, but the mass of the data seems to be on the upward sloping part. Note, that this mixed pattern is consistent with the results in Postel-Vinay and Robin (2004). They show that in an environment, where workers choose search intensity and firms have the possibility to commit to never match an outside offer, a plausible labor market pattern is one

Return to Experience and Initial Wage Level

73

0

.05

.2

.4 .6 CDF (grey lines)

.8

Avg. # of Job−to−Job transitions .1 .15 .2 .25 .3

1

Figure 6: Average Yearly Job to Job transitions by educational group and initial wages.

4.6

4.8

5.0

5.2 5.4 Initial log wage Primary Bachelor

5.6

5.8

6.0

Vocational Master

where bad jobs exist at low-productivity, non-matching firms and good jobs exist at highproductivity, matching firms. Thus, the Postel-Vinay and Robin (2002) offer matching game is mostly likely to arise in high-productive jobs, whereas ’ordinary’ wage search is most likely to arise in low productive jobs. Since education is a very good proxy for productivity, this is in accordance with the results in figure 6. E.g. the negative slope for low educated as predicted by the wage search and the positive slope for high educated as predicted by the Postel-Vinay and Robin (2002) model. We take this as suggestive evidence that the Learning model is not the main driver behind the negative relationship for high educated, but it might be a part of the explanation for low educated. Cyclical variation In search models, wage growth is due to the arrival of outside offers. Thus, if the search model is the primary driving force we would expect to see a less negative slope in recessions, since job offers in recessions are fewer. The learning explanation is essentially an argument about recovering unobserved productivity from noisy signals. It is hard to imagine that this has much to do with cyclical variation. Figure 7 shows the profile separated into years of high and low GDP growth.11 In general we observe lower growth in times of low GDP growth which is not surprising. For bachelor degree holders it seems that the relationship is more flat, but the differences are only marginally significant. For the three other educational groups the estimated negative rela11

We divide growth by the median.

Chapter 3

74

Figure 7: Expected wage growth given initial wages. Divided into high and low GDP growth years.

.03 −.01

.01

Expected wage growth

.03 .01 −.01

Expected wage growth

.05

Vocational

.05

Primary/high school

4

4.2

4.4

4.6

4.8 5 5.2 Initial log wage

Low GDP growth years

5.4

5.6

5.8

6

4

4.2

High GDP growth years

4.4

4.6

Low GDP growth years

5.4

5.6

5.8

6

High GDP growth years

.03 .01 −.01

−.01

.01

.03

Expected wage growth

.05

Master

.05

Bachelor

Expected wage growth

4.8 5 5.2 Initial log wage

4

4.2

4.4

4.6

4.8 5 5.2 Initial log wage

Low GDP growth years

5.4

5.6

5.8

High GDP growth years

6

4

4.2

4.4

4.6

4.8 5 5.2 Initial log wage

Low GDP growth years

5.4

5.6

5.8

6

High GDP growth years

tionship seems to have almost the same slope. We conclude that there is little evidence here to support the search explanation.

Separations and shocks All reasonable theories would predict that if a firm is hit by a productivity shock it should lay-off workers. However, theories differ in which workers the firm should lay-off. The learning model predicts that if a firm is hit by a shock it should lay-off relatively more high tenure workers compared to a firm that has not been hit by a shock. The mechanism is that older workers have no option value, so it matter more for those workers. However, the human capital model would predict that if human capital investments are to some extent firm-specific then the firm should lay-off younger workers since these workers have little firm-specific human capital. The argument is more formally presented in Nagypal (2007), where a structural model is estimated using this identification argument. It is hard to define firm shocks, but we define it as a firm losing more than 50 % of its employees during a year.12 Figure 8 presents the job destruction hazard rate for different tenure levels in firms that are hit by a shock and firms that are not. We see that for all educational groups high tenure workers are laid off relatively more when the firm is hit by a shock. We take this as suggestive evidence in favor of the learning explanation 12

We limit this analysis for firms with more than 10 employees and workers aged less than 55

Return to Experience and Initial Wage Level

75

Figure 8: Job termination hazard rate for workers below the age of 55 and working in firms with more than 10 employees by years of tenure.

Hazard rate 0 .05 .1 .15 .2 .25 .3 .35 .4 .45 .5

Vocational

Hazard rate 0 .05 .1 .15 .2 .25 .3 .35 .4 .45 .5

Primary/high school

1

3

5

7

9

11 13 15 Tenure (years)

Low separation rate

17

19

21

23

25

1

3

High separation rate

5

7

9

11 13 15 Tenure (years)

Low separation rate

19

21

23

25

High separation rate

Hazard rate 0 .05 .1 .15 .2 .25 .3 .35 .4 .45 .5

Master

Hazard rate 0 .05 .1 .15 .2 .25 .3 .35 .4 .45 .5

Bachelor

17

1

3

5

7

9

11 13 15 Tenure (years)

Low separation rate

17

19

21

23

25

High separation rate

1

3

5

7

9

11 13 15 Tenure (years)

Low separation rate

17

19

21

23

25

High separation rate

and in disfavor of the human capital explanation. Training We add to our data on individuals data on intensity of government co-sponsored training for the Danish adult population. On average each worker in our sample gets around one week of government co-sponsored training per year of employment.13 The training courses consist both of basic courses (literacy and basic skills training), vocational and technical courses (cooperation courses and industry-specific courses), and post-secondary courses (college courses). Admittedly this training is only the part that is co-sponsered by the government. However, we suspect that a very large fraction of total training is government co-sponsored. Figure 9 show the non-parametric estimates of the average number of yearly course weeks for years 0 to 5 since entry. The different educational groups display very different patterns. For those with primary/high school and vocational educations we see that those taking more courses are those with a low to medium initial wages (except for those with primary/high school education with really low initial wages). For bachelor degree holders there are no clear pattern, but for those in the master group it is those with high initial wages that takes more training. Hence, it seems that the human capital explanation might have some merit for those with a low level of education, while it has 13

For a more thorough description of the institutional features consult Simonsen and Skipper (2008).

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Figure 9: Average number of course weeks in years 0 to 5 after entering the labor market.

1.2 1 .8 .4

.6

Expected # of course weeks

1.2 1 .8 .6 .4

Expected # of course weeks

1.4

Vocational

1.4

Primary

4.1

4.3

4.5

4.7

4.9 5.1 5.3 Initial log wage

5.5

5.7

4.1

4.3

4.5

expected # of course weeks

4.7

5.5

5.7

5.5

5.7

expected # of course weeks

1.2 1 .8 .6 .4

.4

.6

.8

1

1.2

Expected # of course weeks

1.4

Master

1.4

Bachelor

Expected # of course weeks

4.9 5.1 5.3 Initial log wage

4.1

4.3

4.5

4.7

4.9 5.1 5.3 Initial log wage

expected # of course weeks

5.5

5.7

4.1

4.3

4.5

4.7

4.9 5.1 5.3 Initial log wage

expected # of course weeks

less for those with higher levels. Figure 10 shows average wage growth by initial wages for each of the four educational subgroups divided into the categories ’No Courses’ (which means no government co-sponsored training) and ’Some Courses’ (which means they have taken some government co-sponsored training).14 Even though we in Figure 9 found differences in the amount of training that different groups received, we find in Figure 10 that there are no significant differences between those taking courses and those taking no courses. This is consistent with previous estimates, see Kristensen and Skipper (2009). However, it might be that we do not have the correct measure for human capital accumulation. Even though we believe that we have a good measure of more formal training activities these might not be the most important ones. If human capital accumulation is more of a learning-by-doing mechanism then formal training might be a bad way of measuring this.15 In total the evidence using training data is at best mixed. We find some evidence that individuals with lower levels of education and low initial wages get more training. However, these 14

Training is measured in years 0 to 5 after labor market entry. We have experimented with many different measures such as courses measured in year t and wage growth from t to t + 1 for different years since labor market entry. All results indicate that training does not affect wage growth. 15

Return to Experience and Initial Wage Level

77

Figure 10: Expected wage growth per initial wage by acquiring job training or not.

Expected wage growth .01 .03 −.01

−.01

Expected wage growth .01 .03

.05

Vocational

.05

Primary/high school

4.1

4.3

4.5

4.7

4.9 5.1 Initial log wage

No courses

5.3

5.5

5.7

4.1

4.3

4.5

Some courses

4.7

4.9 5.1 Initial log wage

No courses

5.5

5.7

Some courses

Master

−.01

−.01

Expected wage growth .01 .03

Expected wage growth .01 .03 .05

.05

Bachelor

5.3

4.1

4.3

4.5

4.7

4.9 5.1 Initial log wage

No courses

5.3

Some courses

5.5

5.7

4.1

4.3

4.5

4.7

4.9 5.1 Initial log wage

No courses

5.3

5.5

5.7

Some courses

individuals do not have higher wage growth compared to those with similar initial wages and education.

Summary of Tests The empirical tests above show little evidence to support the human capital explanation. Both the indirect test via the job hazard and the more direct test using training data found no support. The learning model did relatively better. The test using separations found in favor of the learning model, since high tenure workers were fired relatively more when the firm experienced a negative shock. Also, the negative relationship between job-to-job transitions and initial wages for low educated support the learning explanation, while the positive relationship between job-to-job transitions and initial wages for high educated goes against it. Regarding the search explanation, we find mixed evidence. Using unemployment spells we find some evidence that support the search explanation for low educated. Also, the test using job to job transitions give some, but limited, support to the search explanation.

6

Robustness

Imagine that the labor market consists of two groups. The first group has a positive covariance between initial wage and return to experience, while the second has a negative covariance.

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Table 4: Regression of log wage growth years 6 to 7, 7 to 8, 8 to 9 and 9 to 10 on initial log wages for vocational educated, labor market transitions. Model

(1)

∆wit = α + wi0 + εit ∆wit ∆AEit

= α + wi0 + εit

Observations Individuals

Stayers

(2)

(1)

-0.0261*** (0.0008) -0.0259*** (0.0009)

-0.0259*** (0.0010) -0.0261*** (0.0012)

327,984 117,257

327,984 117,257

JtJ†

JtNtJ∗

(2)

(1)

-0.0551*** (0.0033) -0.0586*** (0.0038)

-0.0543*** (0.0040) -0.0578*** (0.0049)

-0.0255** (0.0100) -0.0352** (0.0155)

-0.0265** (0.0124) -0.0384** (0.0186)

(2)

63,365 47,531

63,365 47,531

6,827 6,296

6,827 6,296

The standard errors in parentheses are robust. (1) Unweighted regressions. (2) The regressions are weighted such that each individual have equal weights. ***, **, * indicates significance at levels 1, 5 and 10 percent respectively. † Job-to-Job transitions. ∗ Job-to-Nonemployment-to-Job transitions.

Estimating the joint covariance using both groups could potentially result in a zero covariance estimate. This highlights the importance of estimating on a homogeneous group of workers. This was one of the reasons to separate by educational groups in the above analysis as we saw that we estimated a U-shape when using the entire sample. In this section we look for other possible explanations for the negative relationship. We restrict the analysis to those with a vocational education, since this is the largest group and the one with the clearest negative relationship. We look at labor market transitions, differences in industries, differences in occupation, time of labor market entry, and minimum wages. In general we find that none of these explain the negative relationship.

Labor Market Transitions It is a common result that much wage growth can be attributed to job change (see e.g. Altonji and Williams (1992), Topel and Ward (1992), Neal (1995), and Dustmann and Meghir (2005)). Table 4 and figure 11 show the covariance analysis and the non-parametric estimates for the vocational educated divided into stayers, Job-to-Job and Job-to-Nonemployment-to-Job transitions.16 Generally, those with Job-to-Job transitions have a much stronger negative covariance between return to experience and initial wages than the stayer sample. This result carries through no matter which measure of experience we use. Workers making a Job-toNonemployment-to-Job have a more negative covariance if we use real experience, but not if we use potential experience. Comparing to the main results in table 3 the stayer sample has a less negative covariance of about three quarters of what it was before, but it is still very significant. From this it is clear that the negative relationship is not driven by differences in labor 16

The transitions refer to the year where wage growth is measured.

Return to Experience and Initial Wage Level

79

.03 .01 ï.01 ï.05

ï.03

Expected wage growth

.05

Figure 11: Expected wage growth over initial wages for stayers, job-to-job switchers, and job-tononemployment-to-job switchers, vocational education.

4.6

4.8 Stayers

5.0 5.2 Initial log wage JobïtoïJob

5.4

5.6

JobïtoïNonïtoïJob

market transitions in the year where wage growth is measured. Industry One could imagine that different industries have different relationships between initial wages and return to experience. Figure 12 shows the results for the four largest industries for vocational educated workers; the financial sector, wholesale, construction and manufacturing.17 There are level differences as one would expect. The financial sector enjoys higher wage growth than the others. Wholesale come next, and then the manufacturing industry while construction sees the lowest levels of wage growth for fixed permanent ability types, but all four industries maintain the downward sloping relationship for the vocational educated group as a whole. Occupations Figure 12 also shows results where we have split the vocational workers into occupations. Once more, there are level differences corresponding to what one would expect, but again the overall pattern of the downward sloping relationship does not seem to be explained by differences between occupations.18 Labor Market Entry; 80’ies vs. 90’ies Finally, although wages have been controlled for year effects, one could imagine that entry in different periods of time could play a role in the 17

We measure industry at the time of wage growth. We have also tried to measure it at labor market entry. This makes little difference. 18 We measure occupation at the time of wage growth. We have also tried to measure it at labor market entry. This makes little difference.

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80

.03 .01 ï.01

Expected wage growth

.05

Figure 12: Expected wage growth over initial wages. Vocational educated workers divided into industries (upper panel), occupations (lower left panel) and entry (lower right panel).

4.6

4.8

5.0 5.2 Initial log wage

.04 .02

.03 4.6

4.8 Manager Salaried worker

5 5.2 Initial log wage Executive Skilled

5.4

5.6

ï.01

ï.01

0

.01

Expected wage growth

.03 .01

Expected wage growth

5.6

Construction Manufacturing

.05

Wholesale Finance

5.4

4.6 Some management Unskilled

4.8

5 5.2 Initial log wage Entry 1980ï1989

5.4

5.6

Entry 1990ï2000

relationship between permanent observable ability and the return to experience. The lower right panel of figure 12 divides the vocational educated workers into whether they entered the labor market in the eighties or in the nineties. There seems to be a slight difference in the magnitude of the slopes as the relationship for eighties-enters displays a steeper negative slope, but their overall pattern does not reveal much difference. Minimum Wages

One potential problem with the above specifications is that e.g. minimum

wages could enforce a negative relationship. Denmark does not have an official fixed minimum wage level but nevertheless, there are unofficial lower thresholds for wages within occupations negotiated by the trade unions and the employer association. Think of a very low permanent ability type worker (i.e. a worker with a very low initial wage). He would gain wage increases simply because his wage could only go up. If this sign went through over the entire initial wage support we would see a negative sloping relationship as the ones above. However, we would also see a much lower variance in wage growth for low permanent ability types than for high permanent ability types as there is no such thing as an upper ceiling of wages. In order to address such an issue we have nonparametrically calculated the variance of wage growth conditional on initial wages. Figure 13 shows the estimated conditional variance. The variance for low permanent ability types is actually higher than for high permanent

Return to Experience and Initial Wage Level

81

.03

Variance of normalized wage growth conditional on initial log wage .04 .05

.06

Figure 13: Nonparametrically estimated variance of normalized wage growth conditional on initial log wages, vocational educated workers.

4.4

4.6

4.8

5 Initial log wage

5.2

5.4

5.6

ability types and the suspicion that minimum wages were driving the result does not seem to hold.

7

Conclusion

The main goal of this paper was to estimate the relationship between wage levels and wage growth. We have estimated a Mincer type wage equation allowing for an individual unobserved permanent effect and an individual unobserved return to experience. We have extended previous analysis of this relationship to cover the entire sample of male workers. We have also extended it to go beyond a covariance analysis. We find an overall negative relationship between initial wages and return to experience, but a positive relationship between return to experience and educational level (observable individual characteristics). We have done the analysis on several educational subgroups, and find that the negative relationship between unobserved individual permanent ability and individual unobserved return to experience is most clear for lower levels of education (primary/high school and vocational) while higher levels of education (bachelor and master’s degrees) see an only borderline significant relationship. In general, and especially for the group of vocational educated individuals, the catching up effect in wages is relatively large. We have connected the empirical findings with three main theories; search, unobserved productivity and learning, and human capital. Using several empirical tests we find evidence in

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favor of the learning model, but no evidence in support of the human capital model. We find mixed evidence for the search explanation. Finally, we tested if we could find any observable characteristics that would explain the negative relationship. We found that neither job transitions, industry, occupation, labor market entry time or minimum wages could explain the pattern.

References Abowd, J. M., F. Kramarz and D. N. Margolis (1999), High Wage Workers and High Wage Firms, Econometrica, 67(2): 251–333. Altonji, J. G. and N. Williams (1992), The Effects of Labor Market Experience, Job Seniority, and Job Mobility on Wage Growth, NBER Working Papers 4133, National Bureau of Economic Research, Inc. Bagger, J., F. Fontaine, F. Postel-Vinay and J.-M. Robin (2011), A Tractable Equilibrium Search Model of Individual Wage Dynamics With Experience Accumulation, Working Paper. Baker, M. (1997), Growth-Rate Heterogeneity and the Covariance Structure of Life-Cycle Earnings, Journal of Labor Economics, 15(2): 338–75. Becker, G. S. (1962), Investment in Human Capital: A Theoretical Analysis, Journal of Political Economy, 70(5): 9–49. Ben-Porath, Y. (1967), The Production of Human Capital and the Life Cycle of Earnings, Journal of Political Economy, 75(4): 352–365. Burdett, K. and D. T. Mortensen (1998), Wage Differentials, Employer Size, and Unemployment, International Economic Review, 39(2): 257–273. Connolly, H. and P. Gottschalk (2006), Differences in Wage Growth by Education Level: Do Less Educated Workers Gain Less from Work Experience?, Working Paper, Economics Department, Boston College. Dustmann, C. and C. Meghir (2005), Wages, Experience and Seniority, Review of Economic Studies, 72(1): 77–108. French, E., B. Mazumder and C. Taber (2006), “The changing pattern of wage growth for low skilled workers” In: Working and Poor: How Economic and Policy Changes are Affecting Low-Wage Workers, Russell Sage Foundation: New York, NY; Blank R., S. Danziger, and R. Shoeni (eds), 141–172. Gladden, T. and C. Taber (2000), “Wage Progression Among Less Skilled Workers” In: Finding Jobs: Work and Welfare Reforms, Russell Sage Foundation: New York, NY; Blank, R. M. and D. Card (eds), 160–192. ——— (2009), The Relationship Between Wage Growth and Wage Levels, Journal of Applied Econometrics, 24: 914–932. Hansen, B. E. (2010), Econometrics, University of Wisconsin. Jovanovic, B. (1979), Job Matching and the Theory of Turnover, Journal of Political Economy, 87(5): pp. 972–990.

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Kristensen, N. and L. Skipper (2009), Effektanalyser af voksenefteruddannelse. Li, Q. and J. S. Racine (2007), Nonparametric Econometrics : theory and practice, Princeton University Press. Mincer, J. (1958), Investment in Human Capital and Personal Income Distribution, The Journal of Political Economy, 66(4): 281–302. ——— (1962), On-the-Job Training: Costs, Returns, and Some Implications, Journal of Political Economy, 70(5): 50–79. ——— (1974), Schooling, Experience, and Earnings, National Bureau of Economic Research. Nagypal, E. (2007), Learning by Doing vs. Learning about Match Quality: Can We Tell Them Apart?, The Review of Economic Studies, 74(2): pp. 537–566. Neal, D. (1995), Industry-Specific Human Capital: Evidence from Displaced Workers, Journal of Labor Economics, 13(4): 653–77. Postel-Vinay, F. and J.-M. Robin (2002), Equilibrium Wage Dispersion with Worker and Employer Heterogeneity, Econometrica, 70(6): 2295–2350. ——— (2004), To match or not to match?: Optimal wage policy with endogenous worker search intensity, Review of Economic Dynamics, 7(2): 297 – 330. Rubinstein, Y. and Y. Weiss (2006), “Chapter 1 Post Schooling Wage Growth: Investment, Search and Learning,” vol. 1 of Handbook of the Economics of Education, , Elsevier, 1–67. Silverman, B. (1986), Density Estimation for Statistics and Data Analysis, London: Chapman and Hall. Simonsen, M. and L. Skipper (2008), The Incidence and Intensity of Formal Lifelong Learning, Working paper, School of Economics and Management, Aarhus Universitet. Sørensen, K. L. and R. Vejlin (2011), From Mincer to AKM: Lessons from Danish Matched Employer-Employee Data, Working Paper. Sørensen, T. and R. Vejlin (2013), The Importance of Worker, Firm and Match Fixed Effects in Wage Regressions, Empirical Economics: To appear. Topel, R. H. and M. P. Ward (1992), Job Mobility and the Careers of Young Men, The Quarterly Journal of Economics, 107(2): 439–479. Weiss, Y. (1986), The Determination of Life Cycle Earnings, vol. Ashenfelter, Orley and Layard, Richard eds., chap. 11, Handbook of Labor Economics vol. 1, Oxfordl, 603–640. Woodcock, S. (2011), Match Effects, Discussion Papers. Department of Economics, Simon Fraser University. Zhang, X., M. L. King and R. J. Hyndman (2006), A Bayesian approach to bandwidth selection for multivariate kernel density estimation, Computational Statistics & Data Analysis, 50: 3009–3031.

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A

Tables Table 5: Covariations between initial errors and future error growth from an ARMA(1,2) model. Primary / High school

Vocational

Bachelor

Master

µ ρ1 ρ2 σν2

0.7308 -0.6994 -0.0393 0.0127

0.6865 -0.7801 -0.3128 0.0102

0.6835 -0.7759 -0.3202 0.0086

-0.4017 0.6354 0.1314 0.0120

Cov(ε0 , ∆ε1 ) Cov(ε0 , ∆ε2 ) Cov(ε0 , ∆ε3 ) Cov(ε0 , ∆ε4 ) Cov(ε0 , ∆ε5 ) Cov(ε0 , ∆ε6 )

-0.01229 -0.00061 0.00006 0.00004 0.00003 0.00002

-0.01120 -0.00290 0.00121 0.00083 0.00057 0.00039

-0.00944 -0.00251 0.00105 0.00072 0.00049 0.00033

-0.00923 -0.00236 -0.00063 0.00025 -0.00010 0.00004

Cov(θ, γ)∗

-0.00201

-0.00248

-0.00006

-0.00087

Coefficients

ε is the error term estimated from equation (1). Model: εt = µεt−1 + νt + ρ1 νt−1 + ρ2 νt−2 . ∗ Calculated from the estimates in table 3.

Chapter 4 Effects of Intensifying Labor Market Programs on Post-Unemployment Wages: Evidence From a Controlled Experiment

Effects of Intensifying Labor Market Programs on Post-Unemployment Wages: Evidence From a Controlled Experiment Kenneth L. Sørensen∗ KORA and Aarhus University, CAP and CAFE´

Abstract This paper investigates effects on wages from a Danish field experiment intensifying Active Labor Market Policies (ALMP). We link unemployed workers who participated in an ALMP experiment called “Quickly Back” carried out by the Danish Ministry of Employment 2005-2006 in two counties to matched employer-employee and public transfer register data up to 2008 enabling us to analyze exact labor market transitions and jobs of the participants. Men in one of the counties experienced significant higher probability of earning higher medium and long term wages after treatment. Treated men in the other county encountered a higher probability of earning lower wages in the short term and higher wages in the long term than non-treated. Women in one county saw positive short term and negative long term treatment effects and in the other county negative treatment effects both in the short and long term. Keywords: Active Labor Market Policies, controlled experiment, wages, Mixed Proportional Hazard model. JEL codes: C41, J31, J64, I wish to thank Michael Svarer, Henning Bunzel, Rune Vejlin and Mark Kristoffersen for valuable comments. Additionally, I thank participants at the DGPE conference 2011, seminar participants at Aarhus University, the annual meeting of the Danish Econometric Society, Sandbjerg, participants at the annual BI-CAP meeting, Oslo and at the CAFE´ workshop, Børkop 2012 for comments. I wish to thank the Cycles, Adjustment, and Policy research unit, CAP, Department of Economics and Business, Aarhus University sponsored by the Danish National Research Foundation for support and for providing the data. Correspondence to; Kenneth Lykke Sørensen, email: [email protected]. KORA, Danish Institute for Local and Regional Government Research, Købmagergade 22, DK1150 København K, Denmark. ∗

87

Chapter 4

88

1

Introduction

Many welfare states are characterized by a flexible labor market for firms and a generous social safety net for workers made redundant. For a system with a large public sector, high social benefits and easy access to lay off workers to be sustainable, a necessary condition is to maintain a low unemployment rate and a high participation rate. However, frictions (caused by e.g. incomplete information of supply and demand) and human capital depreciation in the labor market induce difficulties for unemployed workers to find jobs. Therefore, most western countries have a wide range of Active Labor Market Policies (ALMP) consisting of, among other things, training, activation, wage subsidies, monitoring and sanctions. Active labor market policies are meant to reduce these frictions and rebuild human capital of the unemployed worker by adding skills and knowledge, and by offering job search assistance, resume guidance, etc. to the unemployed as well as inducing him/her to actively search for a new job. This exercise is very expensive, though, and a natural question arises: does it provide value for the money?1 The direct and short term outcome of ALMP is quite simple: Does it increase the exit-rate out of unemployment and/or decrease the re-entering rate into unemployment? The long term outcome of ALMP is less clear. First, ideally, after participating in ALMP, the unemployed worker should have gained new or updated skills securing a good and sustainable worker-firm match. Second, if, on the other hand, ALMP send unemployed workers into unsustainable or bad worker-firm matches, policy makers should rethink the setting of the ALMP system. Third, by guidance from a case worker or by participating in activation, the unemployed worker can be updated with the state of the labor market and might choose to lower his/her reservation wage in order to accept a job. If so, we would see workers entering lower paid jobs than if s/he had not been treated by ALMP. In this paper, we analyze short, medium and long term post-unemployment outcomes (wages one, two and three years after leaving unemployment) from participating in an intensive active labor market policy program using a mixed proportional hazard framework (see Abbring and van den Berg (2003)).2 We explore a field experiment carried out in two Danish counties, Storstroem and Southern Jutland, during the winter of 2005/2006. The experiment randomly assigned a fraction of all newly unemployed individuals to a treatment group with an intensive 1

Denmark spends more than 1.5% of GDP every year on active measures of ALMP. Germany spends 0.9%, France 0.9%, The Netherlands 1.2%, Sweden 1.1%, Switzerland 0.7%, United Kingdom 0.4% and the United States spends 0.1% of GDP on active measures of labor market policies (2005 numbers, OECD.StatExtracts). 2 Following the definition of Card, Kluve and Weber (2010), wages one, two and three years after leaving unemployment relate to short, medium and long term outcomes, respectively.

Effects on Post-Unemployment Wages

89

ALMP scheme compared to the current system.3 The purpose of the experiment was to test whether an early effort could help treated newly unemployed back to work faster than nontreated. The intensification mainly consisted of increasing the frequency of meetings between the unemployed worker and a case worker and by advancing the time of activation. We use unique Danish administrative register data that allow us to measure labor market histories of the unemployed workers, both before they entered the experiment and up to three years after in a duration model setting. From these registers, we construct average hourly wages by following each of their post-unemployment employment spells. This is the first paper to our knowledge that link intensification of ALMP and post-unemployment wages using Danish data. Our findings in terms of wage outcomes from treatment are ambiguous. We find significant negative long term outcomes for women in both counties and find treated men in Southern Jutland to have a significantly higher probability of earning higher long term wages than nontreated. Treated men in Storstroem county experience a higher probability of earning lower short term wages than non-treated. Treated women in Southern Jutland have a higher probability of earning higher short term wages than non-treated while treated women in Storstroem have a higher probability of earning lower wages than non-treated women. This indicates that the intensification of ALMP may have had an impact on (short term) reservation wages as well as on long term wages. Following the seminal works of Heckman and Singer (1984a,b) and Ham and Lalonde (1996) many studies have looked into various effects of Active Labor Market Policies. Often, in the duration model setting, data restrict the focus to the effectiveness of ALMP on the exit rate out of unemployment into different labor market states such as other public transfers (inactivity) or self-support (mainly interpreted as employment) (see Heckman, Lalonde and Smith (1999), Lalive, Zweim¨uller and van Ours (2005), Rosholm and Svarer (2008), and Kluve (2010)), or the return rate into unemployment (e.g. Crepon, Dejemeppe and Gurgand (2005), Doiron and Gørgens (2008), and Blasco and Rosholm (2011)).4 Most of these studies look at the labor market spell after leaving the unemployment pool when participating in an ALMP program ignoring long term effects. Authors looking into long term effects often evaluate these on the basis of length of employment or self support. In a meta analysis of 97 ALMP studies (totaling 199 program estimates) Card et al. (2010) show that 3

The assignment to treatment was conducted by day of birth. See section 2 for a more thorough description. See Kluve (2010) for a meta analysis of European ALMP studies and Card et al. (2010) for an extensive meta analysis of ALMP evaluations in general. 4

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many programs with insignificant or negative short term impacts (within a year) have significant positive medium and long term impacts (after 2 to 3 years), and we thus argue that analyzing the short term as well as medium and long term impacts is important. The field experiment used in this paper has previously been used to analyze ALMP in a Danish context. Graversen and van Ours (2008a,b) find that treated individuals experience shorter unemployment durations. They use a mixed proportional hazard model and find a 30% higher job finding rate for treated participants compared to control group members. Rosholm (2008) finds a similar estimate on the exit rate out of unemployment, but also shows that when controlling for time-varying indicators of treatment all positive effects vanish and some even become negative, the so-called lock-in effect. He finds that the estimated risks of meetings and being activated drive the difference in the job finding rates between treated and non-treated individuals. Vikstr¨om, Rosholm and Svarer (2011) use non-parametric methods to separate the sub-treatment effects on the exit rate out of unemployment. They find that job search assistance, frequent meetings and activation threats have positive impacts on the exit rate. Gautier, Muller, van der Klaauw, Rosholm and Svarer (2012) examine the outcomes for non-treated unemployed workers and compare these with unemployed workers in different counties of Denmark unaffected by the experiment to measure general equilibrium effects on the job finding rates. They find evidence of negative spillovers from treatment. Specifically, they find that estimating effects of treatment without accounting for externalities will result in an upward biased estimate. Finally, Blasco and Rosholm (2011) analyze long term effects on post-unemployment employment stability in terms of duration on self support after leaving the unemployment pool. They find that treatment increases the post-unemployment self support duration by ten percent for men while treated women show no post-unemployment stability effects. Decomposing the effect, they show that 20-25 percent is due to lagged duration dependence. Still, we know very little about post-unemployment labor market participation other than the duration of self support. To further elaborate on the knowledge of long term ALMP effects on post-unemployment employment, this paper contributes by adding another and very important dimension of outcomes, namely wages. ALMP schemes are designed to both increase the exit rate out of unemployment and to equip the unemployed better for a return to employment and thus enhance the quality of the workerfirm match. Studies of ALMP should not only evaluate exit and return rates but also take into account post-unemployment labor market outcomes such as wages and employment stability

Effects on Post-Unemployment Wages

91

(see Crepon et al. (2005)). Analysis in these dimensions is important to tell the full story of potential successes or failures of ALMP programs. This paper contributes to the literature with research in post-unemployment wages. Other studies have examined wage gains/losses from participating in labor market schemes. Most authors analyzing labor market programs use either a duration or a matching framework to handle problems of selection into different programs. In the matching model literature, a number of studies have analyzed the impact of labor market programs on post-unemployment wages.5 Using propensity score matching, Jespersen et al. (2008) analyse cost and benefits of labor market programs in Denmark. They find both public and especially private job training to have positive earnings effects, even after correcting for costs of training. For two Swedish labor market programs on practice and labor market training targeting young unemployed, Larsson (2003) finds zero or negative short term effects and zero or slight positive long term effects of participation in the programs. Within the duration framework, Gaure, Røed and Westlie (2012) examine effects of unemployment benefits and ALMP participation on unemployment duration together with short term post-unemployment employment stability and earnings in Norway. They find that participation in ALMP lengthens the unemployment duration, i.e. the time until finding a job. However, they estimate ALMP to induce a higher probability of finding a job, and once the job is found, expected earnings have increased as well. Examining young workers being unemployed for more than nine months after finishing school, Cockx and Picchio (2012) find that prolonging the unemployment lowers the chance of getting a job but has no effect on starting wages earned once a job is found. Recently, literature has studied the effect of sanctions on the quality of post-program employment. In a study of sanctions on Swedish data, van den Berg and Vikstr¨om (2009) measure the effect on post-unemployment wages and hours worked. They find sanctioned workers to experience a 23 percent increase in the exit rate to employment, but with lower wages and fewer hours worked than non-sanctioned. On top of this, they find sanctioned workers to incur a higher level of human capital loss than non-sanctioned. Using rich Swiss unemployment and employment register data, Arni, Lalive and van Ours (2012) analyze the effect of monitoring and sanctions (full benefit reduction) on post-unemployment duration and earnings. They find that increasing monitoring increases the exit rate to employment with reduced earnings while durations are unaffected. Arni et al. (2012) show that sanctions also 5

See e.g. Jespersen, Munch and Skipper (2008), Sianesi (2004), Larsson (2003), Raaum, Torp and Zhang (2002) using nordic data and Lechner (1999) using swiss data. See Heckman, Ichimura and Todd (1997) on the method of matching.

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increase the exit rate, but with both lower earnings and lower post-unemployment employment durations as the result. For a US ALMP experiment, targeting unemployed believed to have a low probability of re-entering employment before benefit exhaustion, Berger, Black, Noel and Smith (2003) find that program participation decreases expected unemployment by 2.2 weeks, but more importantly, it increases subsequent earnings by $1,000. The rest of this paper is laid out as follows: Section 2 sketches the social experiment “Quickly Back”, section 3 presents the data we utilize, section 4 review the econometric framework, and in section 5 we present our empirical results. Finally, section 6 concludes.

2

The Experiment

The controlled field experiment “Quickly Back” (henceforth denoted QB) was conducted by The National Labor Market Authority under the Danish Ministry of Labor in two Danish counties: Southern Jutland and Storstroem. QB was the first in a series of experiments conducted by the National Labor Market Authority testing the effects of intensifying ALMP in several dimensions. We use QB, partly because of a good setup related to measuring precise treatment and, partly because adequate time has passed since the beginning of the experiment such that we now are able to link post-unemployment employment spells to the participants. The experiment consisted of an intensification in multiple dimensions of the 2005 ALMP system. The experiment setting was constructed by randomly assigning a fraction of newly unemployed (UI benefit eligible) individuals to a treatment group. If a newly unemployed worker was born between the 1st and the 15th of any given month, he or she was assigned to the treatment group. Importantly, there were no publicly announced description of the experiment before it was implemented. The participants in the control group were not told they were put into a control group of an experiment and individuals in the treatment group were only notified that they participated in a “pilot study”, not in an experiment, a week and a half after registering as unemployed. Individuals in both groups were sent to a CV/basic registration meeting within the first four weeks of their unemployment spell. In the period of the experiment (first week of November 2005 to the last week of February 2006), the labor market program (i.e. for the control group) further consisted of:6 6

C is for Control group.

Effects on Post-Unemployment Wages

93

C-1 After four and twelve weeks of unemployment (receiving benefits), the unemployed should attend a meeting with a case worker. C-2 Hereafter, the unemployed had to attend a meeting with a case worker every 13 weeks. C-3 After a year of unemployment, the unemployed should participate in an unspecified program of at least one week duration. C-4 For the rest of the unemployment spell, the unemployed worker had to participate in programs at least once every six month. The intensification of the existing labor market program consisted of exposing the treatment group to:7 T-1 1.5 weeks after entering unemployment (receiving benefits) a letter informing the participant that s/he has been drawn as a member of a “labor market pilot study” and the entire course of the intense study was sent to the individual in the treatment group. T-2 A two-week Job Search Assistance (JSA) program was mandatory after five or six weeks of unemployment. T-3 During week 9 to 15 of unemployment, the treatment participant should (ideally) meet frequently with a case worker to ensure active job search and to provide JSA. The frequency was once a week in Storstroem and once every other week in Southern Jutland. T-4 After week 18, an unspecified mandatory program lasting at a minimum of 13 weeks would start. There were four different possible programs of different lengths. (i) Private sector temporary job (subsidized by the authorities, lasting up to 6 months). (ii) Public sector temporary job (6-12 months). (iii) Classroom training (often less than 13 weeks each) and (iv) vocational training programs within firms (a couple of months). T-5 The experiment ended and individuals still unemployed were transferred into the ordinary labor market program. Note that the although the experiment was conducted at the same time in the two counties, it was not identical between them. The meeting frequency differed between the two counties (cf. T-3). In Storstroem county the treatment participant were to meet with a case worker once every week between week 9 and 15 of receiving benefits while the treatment participants from 7

T is for Treatment group. See Table B1 (in the appendix) for an overview of the time schedule of treated versus non-treated individuals.

Chapter 4

94

Southern Jutland should only met with their case worker once every other week between week 9 and 15. This difference between the counties de-facto means that QB was not one but two experiments, and the analysis in this paper is carried out for each of the counties separately. This particular experiment setting constitutes a good background for the analysis in this paper as the setting of random assignment by birthdays eliminates selection into treatment groups and justifies the ex-ante assumptions on unobserved heterogeneity of our mixed proportional hazard model (see Abbring and van den Berg (2003)). Further, it allows us to follow the individual worker throughout the experiment and, by linkage to register data, through his or her labor market transitions up to three years after leaving the experiment. Lastly, the treatment group member was imposed to a much more intense search scheme during his/her unemployment spell than the control group member. Other studies have already shown QB to have mixed positive and negative short term effects for men and women in terms of the exit rate out of unemployment and lowering the probability of re-entering unemployment (see Graversen and van Ours (2008a,b), Blasco and Rosholm (2011), Vikstr¨om et al. (2011)). In continuation of Card et al. (2010), who find that studies of labor market policies with zero or negative short term effects can have positive long term effects, it would be very interesting to analyze the long term effects of such an intensification of ALMP. The down side of QB is the impossibility of distinguishing between the three dimensions of intensified treatment, (i) the two-week JSA program, (ii) the intensive meeting schedule, (iii) the faster entry into an activation scheme. The treatments came sequentially and we can thus not identify whether e.g. it was the meetings with a case worker having an impact or it simply was that the JSA program had a delayed effect. However, we argue, analyzing whether a general intensification of treatments has long term labor market outcome effects constitute important knowledge and insight into the full impacts of ALMP schemes. The division of individual effects of treatment is an important topic of further research but is beyond the scope of this paper.8

8

In a later experiment named QB II, the National Labor Market Authority assigned each of the treatment dimensions to different counties such that explicit analysis of types of treatment in time could be conducted. We are thus in some years (when the participants of QB II have had the opportunity to experience post-unemployment outcomes) able to take the analysis from this paper further into dividing up the treatment effects.

Effects on Post-Unemployment Wages

3

95

Data

We use three administrative register databases in this paper; (i) Quickly Back collected by the National Labor Market Board, (ii) weekly Spell data containing all labor market transitions and (iii) yearly data from the Integrated Database for Labor Market Research (IDA). All databases are maintained by Statistics Denmark. The QB data contain information on individuals participating in the field experiment carried out in two Danish counties, Storstroem and Southern Jutland, during the winter of 2005 − 2006. The information covers participation in the treatment

or control group, spells of unemployment (in terms of which week it started and which week it ended) prior, during and after the experiment, type of activation if the unemployed experienced any such and several socio-economic variables on the individual. The weekly Spell data is a longitudinal data set containing information of labor market transitions for each individual in the Danish population including wages from employment spells. IDA is a matched employeremployee longitudinal database containing socio-economic information on the entire Danish population, the population’s attachment to the labor market, and at which firms the worker is employed. Both workers and firms can be monitored from 1980 − 2008. The reference period

in IDA is given as follows: the linkage of workers and firms refers to the end of November, ensuring that seasonal changes (such as e.g. shutdown of establishments around Christmas) do not affect the registration. Background information on individuals mainly refers to the end of the year.9 The key feature of these three databases is the unique link between them given by individual id and firm id that are common across QB, Spell and IDA. We construct hourly wages by accumulating wages net of public transfers from all employment spells during a year and normalizing by hours worked. Hours worked are measured by payments to the Danish mandatory public pension scheme. Payments to the pension scheme are determined by a step-function of hours worked.

3.1

Descriptive Summary

Here we present descriptives on the counties, QB, the Spell data and on IDA. 9

See a more detailed documentation on IDA: http://www.dst.dk/HomeUK/Guide/documentation/Varedeklarationer/emnegruppe/emne.aspx?sysrid=1013.

Chapter 4

96 Figure 1: Map of Denmark with Storstroem and Southern Jutland shaded in black.

3.1.1

The Two Counties

QB was conducted in the two Danish counties, Storstroem and Southern Jutland. They are both counties without larger cities.10 Both Storstroem and Southern Jutland lie in the geographically outer regions of Denmark as a whole and should thus not be considered representative of Denmark as a whole (Figure 1 shows Storstroem and Southern Jutland shaded in black). However, as Table 1 shows, West and South Zealand (which contain Storstroem county) saw similar unemployment rates as the Danish average after 2004. Southern Jutland had lower unemployment rates than Denmark on average from 2001 to 2008. In both counties as for Denmark, men had a lower unemployment rate than women. Notice, Table 1 shows that pooling the counties together should be done carefully, as they face two different labor markets. Southern Jutland participants face a lower local unemployment rate than their Storstroem counterparts and an assumption that treated and non-treated in one county have the same employment possibilities as in the other could very easily be violated. These facts, on top of the difference in the experimental nature with more frequent meetings in Storstroem than in Southern Jutland, are the reason that we will not be pooling the counties together, but instead do the full analysis on each county separately as well as for men and women.

10

The largest cities (2006) in Storstroem and Southern Jutland were Næstved (41,158 residents) and Sønderborg (27,391 residents) ranked 15th and 23rd in Denmark, respectively, in terms of residents.

Effects on Post-Unemployment Wages

97

Table 1: Net unemployment rates in percent.

Denmark West and South Zeeland∗ Southern Jutland Men Denmark West and South Zeeland∗ Southern Jutland Women Denmark West and South Zeeland∗ Southern Jutland

2001

2002

2003

2004

2005

2006

2007

2008

4.7 5.1 4.5

4.8 5.2 4.5

5.8 6.1 5.5

5.8 6.0 5.3

5.1 5.2 4.6

3.9 3.9 3.1

2.7 2.9 2.0

1.9 2.0 1.3

4.1 4.4 3.7

4.4 4.6 3.8

5.4 5.6 4.8

5.4 5.4 4.5

4.5 4.5 3.7

3.3 3.2 2.4

2.3 2.3 1.6

1.8 1.9 1.2

5.2 6.0 5.5

5.2 5.8 5.3

6.1 6.7 6.4

6.3 6.6 6.4

5.7 5.9 5.6

4.5 4.7 4.0

3.2 3.5 2.6

2.0 2.1 1.5

∗ Covers

Storstroem county and more. Source: Statistics Denmark (statistikbanken.dk/AUL06).

3.1.2

The Treatment Group vs. the Control Group

Table 2 shows descriptive statistics on the estimation samples. Storstroem county contains 1,169 observations in the treatment group and 1,217 in the control group. Southern Jutland county consists of 1,060 observations in the treatment group and 1,064 observations in the control group. The fraction of women in the Storstroem control group is slightly, but insignificantly, larger than in the treatment group. In Southern Jutland there is no difference. There are no major differences between treatment and control groups in the two counties with respect to week of entering the experiment. The only significant difference is entry in weeks 49-50 with a larger fraction of newly unemployed individuals being allocated to the treatment groups. There are only small educational differences between treatment and control groups in Storstroem county and none in Southern Jutland. Storstroem has a slightly larger fraction of vocational and smaller fraction of primary/high school graduates in the treatment than in the control group. Both counties have a higher fraction of nonwestern immigrants being treated than non-treated. There are only very few nonwestern immigrants, however, and the significant difference is very unlikely to cause major selection issues between the groups, if any. Treatment and control groups do not display any major differences with respect to age, experience, marital status, lagged unemployment duration or post-unemployment transition to employment. Treated individuals in Southern Jutland seem to be heading into slightly more stable employment spells than non-treated in the sense that in 2007 a larger fraction of treated holds only one job than non-treated. The opposite is the case in Storstroem in 2006 and 2008. There are only small insignificant differences in the fraction seeing one or more un- or non-employment spells after leaving QB.

Chapter 4

98 Table 2: Summary statistics. Storstroem county Treatment

Control

Women

0.381

Married

0.466

Age Experience

Southern Jutland Diff.

Treatment

Control

0.404

0.464

0.453

0.474

0.499

0.477

40.93

40.65

39.59

39.75

14.47

14.51

12.92

13.19

Danish

0.928

0.952

0.911

0.925

Western immigrant

0.021

0.015

0.047

0.044

Nonwestern immigrant

0.052

0.034

0.042

0.031

Primary and high school

0.397

0.429

0.419

0.428

Vocational

0.491

0.463

Bachelor

0.093

0.097

Master and above

0.020

0.012

Diff.

Pre-experiment characteristics Individual Characteristics

**

*

Level of education, 2005 * *

0.456

0.446

0.111

0.109

0.014

0.017

Occupation in the last week of November 2005 Management level

0.031

0.041

0.027

0.026

Skilled level

0.470

0.467

0.450

0.453

Unskilled level

0.304

0.293

0.305

0.303

Unemployed

0.121

0.121

0.133

0.137

Non-employed

0.074

0.077

0.083

0.077

Accumulated unemployment duration 3 years before entering QB ≤ 6 weeks

0.477

0.505

0.517

0.508

7-8 weeks

0.015

0.012

0.015

0.024

9-16 weeks

0.073

0.072

0.068

0.071

17-28 weeks

0.079

0.076

0.068

0.069

29-52 weeks

0.122

0.118

0.125

0.122

> 52 weeks

0.234

0.219

0.208

0.207

43-44, 2005

0.123

0.118

0.148

0.149

45-46, 2005

0.062

0.054

0.053

0.061

47-48, 2005

0.082

0.107

0.127

0.121

49-50, 2005

0.119

0.082

0.097

0.069

51-52, 2005

0.111

0.110

0.108

0.111

01-02, 2006

0.199

0.210

0.190

0.207

03-04, 2006

0.122

0.107

0.093

0.100

05-06, 2006

0.125

0.151

0.143

0.126

07-08, 2006

0.058

0.061

0.041

0.057

Earned during 2004

179.0

181.4

172.8

173.3

Earned during 2005

186.4

192.0

180.0

181.5

Earned during 2004

157.0

157.5

151.8

153.3

Earned during 2005

165.7

166.9

161.3

164.9

Week of entry into QB

***

Average hourly wages (DKK), men **

Average hourly wages (DKK), women

*: Indicates statistical significant difference at the 10% level. **: At the 5% level. ***: At the 1% level. This table continues on the next page.

***

Effects on Post-Unemployment Wages

99

Table 2: Continued from previous page. Storstroem county

Southern Jutland

Treatment

Control

Diff.

Treatment

Control

Diff.

Treated ≤ 30 weeks

0.888

0.000

***

0.861

0.000

***

Treated > 30 weeks

0.112

0.000

***

0.139

0.000

***

Transition QB, U → E

0.895

0.886

0.876

0.879

2006, zero employers

0.074

0.092

0.077

0.116

2006, 1 employer

0.416

0.441

0.419

0.406

2006, 2 employers

0.283

0.288

0.287

0.288

2006, 3 or more employers

0.228

0.179

0.217

0.191

2007, zero employers

0.125

0.126

0.105

0.123

2007, 1 employer

0.511

0.518

0.571

0.513

2007, 2 employers

0.241

0.241

0.204

0.243

2007, 3 or more employers

0.123

0.116

0.121

0.120

2008, zero employers

0.169

0.167

0.145

0.160

2008, 1 employer

0.483

0.536

0.536

0.522

2008, 2 employers

0.222

0.198

*

0.211

0.205

2008, 3 or more employers

0.126

0.099

**

0.108

0.114

Post-experiment characteristics QB characteristics

Number of different employers after QB

***

* ***

Experiences unemployment spells after QB During 2006

0.329

0.303

0.326

0.322

During 2007

0.367

0.377

0.339

0.372

During 2008

0.295

0.310

0.259

0.279

Experiences non-employment spells after QB During 2006

0.418

0.397

0.450

0.429

During 2007

0.519

0.533

0.556

0.593

During 2008

0.537

0.563

0.583

0.607

Earned during 2006

185.2

191.1

179.7

181.4

Earned during 2007

189.3

190.3

185.3

180.0

**

Earned during 2008

194.5

191.1

191.5

185.4

**

Earned during 2006

160.0

170.1

165.2

166.0

Earned during 2007

163.1

164.0

161.0

161.9

Earned during 2008

164.8

167.6

164.9

172.6

1,169

1,217

1,060

1,064

Average hourly wages (DKK), men **

Average hourly wages (DKK), women

Individuals

***

**

*: Indicates statistical significant difference at the 10% level. **: At the 5% level. ***: At the 1% level.

For average hourly wages we see no significant differences before QB in all samples but men in Storstroem county in 2005. They display a 5 percent significantly higher average hourly

Chapter 4

100

Figure 2: Evolution of average earnings (2008 prices) and average employment rate for the male treatment and control group members 2004-2008. Storstroem, men

.65

200,000

Avg. earnings 220,000 240,000

Avg. employment rate .7 .75 .8

.85

260,000

Storstroem, men

2004

2005

2006 Year

2008

2004

2005

Control

2006 Year Treatment

2008

Control

Southern Jutland, men

Avg. employment rate .7 .75

.8

Southern Jutland, men

2007

.65

Avg. earnings 180,000 200,000 220,000 240,000 260,000

Treatment

2007

2004

2005

2006 Year Treatment

2007 Control

2008

2004

2005

2006 Year Treatment

2007

2008

Control

wage rate. Treated men in Southern Jutland have significantly higher average hourly wages in 2007 and 2008, while no significant differences after the experiment are present in Storstroem county. Southern Jutland treated women see a significant lower average wage level in 2008 than non-treated. The outcome of interest in this paper is average hourly wages earned in the years after participating in the experiment QB. Of course average hourly wages is a measure of wages earned by the amount of hours worked. If one individual earns 150,000 Dkk in 2007 working 1,000 hours (just below 2/3 of a full time work-year) he will see the same average hourly wage as another individual earning 200,000 Dkk in 2007 working at a higher paying job putting in 1,333 hours. They are in reality not equal off however. To examine the evolution of both total wages earned and hours worked, Figure 2 and 3 show the descriptives of these over the years 2004 to 2008. There are clearly differences between the treated and non-treated in both counties and especially so for men. Comparing average earnings and employment rates within groups reveal, however, that it does not seem that it is only the employment rate or the earnings that change after participating in QB. Both seem to be affected in a comparable manner.

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101

Figure 3: Evolution of average earnings (2008 prices) and average employment rate for the female treatment and control group members 2004-2008. Storstroem, women

.55

140,000

Avg. earnings 160,000 180,000

Avg. employment rate .6 .65 .7

.75

200,000

Storstroem, women

2004

2005

2006 Year Treatment

2007

2008

2004

Control

2006 Year Treatment

Southern Jutland, women

2007

2008

Control

Southern Jutland, women

.5

140,000

Avg. employment rate .55 .6 .65

Avg. earnings 160,000 180,000

.7

200,000

2005

2004

2005

2006 Year Treatment

2007 Control

2008

2004

2005

2006 Year Treatment

2007

2008

Control

Table B2 (in the appendix) shows the fraction of individuals in different occupational levels recorded by the last week of November in the years 2004 to 2008. None of the employment occupational groups differ significantly between treatment and control groups in either county in any of the years 2004 and 2005. Only workers employed at unskilled level in Storstroem county in 2005 that have a 10% level significantly larger fraction in the control than in the treatment group. In 2006 we see, not surprisingly, that a significantly larger fraction of control group members are unemployed. More interestingly, a larger fraction within the treatment groups is now employed at the unskilled level than in the two control groups. The other employment groups do not display any significant differences. Thus, it seems that it is lower occupational jobs that differ between the treatment groups and the control groups in 2006. In 2007 this difference has vanished in Storstroem county while it remains the same in Southern Jutland with a larger part of individuals from the treatment group employed at unskilled level than from the control group. The fraction of unemployed in Storstroem by 2007 has grown larger within the treated versus non-treated and equal by 2008. In Southern Jutland it remains to be a smaller fraction of treated than non-treated being unemployed during the last week of November 2007 and 2008 (at the 10 percent significance level).

Chapter 4

102 Table 3: Number of QB participants in different unemployment duration categories. Unemployment duration (weeks)

Storstroem Treatment Control

1-4 5-8 9 - 15 16 - 30 31 + Individuals

0.232 0.203 0.244 0.209 0.112 1,169

0.200 0.170 0.222 0.239 0.169 1,217

Diff. ∗

∗∗ ∗

∗∗∗

Southern Jutland Treatment Control Diff. 0.205 0.194 0.249 0.213 0.139 1,060

0.194 0.160 0.209 0.248 0.189 1,064

∗∗ ∗∗ ∗

∗∗∗

*: Indicates statistical significance at the 10% level. **: At the 5% level. ***: At the 1% level.

3.1.3 QB Durations Several papers have shown that QB increased the exit rate out of unemployment (Graversen and van Ours (2008a,b), Rosholm (2008)). Table 3 contains the fraction of individuals leaving the benefit system within each of the experiment schemes (cf. Table B1). As expected, a higher fraction of treated individuals leaves unemployment before week 16 than non-treated. During the activation program scheme, this is circumvented and a larger fraction of non-treated individuals leaves unemployment.

3.1.4 Post-Unemployment Wages Table B3 holds summary statistics of average hourly wages for men and women. Over all samples, the is no clear picture from the median and different percentiles of hourly wage. Note, however, that treated men in Southern Jutland 2008 dominates non-treated in terms of hourly wages at all percentiles. Figure 4 shows the cumulative average hourly wage distribution function (CDF) for treated individuals subtracted the CDF for non-treated at given wage levels.11 A difference of zero at wage level w∗ indicates an equal fraction of individuals earning w∗ or less between treated and non-treated. If the difference is positive at wage level w∗ , a higher fraction of treated individuals earns w∗ or less than non-treated and vice versa. A common feature of all samples is that the 2004 and 2005 differences are close to zero for all wage levels. 2005, Storstroem men being an outlier. For 2006 wages (triangles), Storstroem women display positive CDF differences for all wage levels and Storstroem men for all wages higher than 150 Dkk. Men and women in Southern Jutland see negative or zero differences. The CDF differences for average 2007 wages (circles) of men in Southern Jutland lie below zero with a minimum of 4 percentage 11

Note that, by construction, Ftreated (w) − Gnon-treated (w) → 0 for w → ∞ where F and G are the CDF’s of treated and non-treated respectively.

Effects on Post-Unemployment Wages

103

300

.02 0 −.02

CDF treatment − CDF control 350+

2004 2006 2008

100

150

200 250 Hourly wage (DKK)

100

150

200 250 Hourly wage (DKK)

2005 2007

300

350+

.04 .02 0 −.02

CDF treatment − CDF control

2005 2007

Southern Jutland, women 2004 2006 2008

−.06

2004 2006 2008

−.04

.04 .02 0 −.02 −.04

Storstroem, women

−.06

CDF treatment − CDF control

.04

.06 200 250 Hourly wage (DKK)

Southern Jutland, men

.06

150

.06

100

2005 2007

−.06

2004 2006 2008

−.04

.04 .02 0 −.02 −.04

Storstroem, men

−.06

CDF treatment − CDF control

.06

Figure 4: Plots of treatment group CDF subtracted the control group CDF for given hourly wage levels.

300

350+

100

150

200 250 Hourly wage (DKK)

2005 2007

300

350+

points lower fraction of treated paid an hourly wage of 150 Dkk than non-treated.12 Women in Southern Jutland also see an overall negative difference in 2007 wages, but not as strong as men. Neither men or women have any differences in the CDF of 2007 wages in Storstroem. Finally, for 2008 wages (diamonds) men in both counties have a negative difference in CDFs of roughly 1.5 percentage points in Storstroem and as high as 5 percentage point in Southern Jutland. Figure A1 and A2 hold the levels of all the CDFs. Most masses are located below 200 DKK for men and 150 Dkk for women. None of the samples has single mass points and the distributions all seem to be nice and smooth. We have performed Kolmogorov-Smirnov tests for equal hourly wage distributions between treated and non-treated. Table 4 presents both one- and two-sided p-values from these tests.13 Using one-sided tests, we cannot reject the null hypothesis of different underlying wage distributions on a 5 percent significance level for men in Southern Jutland 2006-2008 and borderline 12

Figure A1 (in the appendix) shows that roughly 50 percent in the control group have a wage less than 150 DKK. 13 In the one-sided test, if at the point of the largest difference, the CDF of treated is greater than the CDF of non-treated, the null is H0 : Ftreated (w) ≤ Gnon-treated (w) versus H1 : Ftreated (w) > Gnon-treated (w), and vice versa if the CDF of treated is smaller than the CDF of non-treated. The null in the two-sided test is H0 : Ftreated (w) = Gnon-treated (w) versus H1 : Ftreated (w) 6= Gnon-treated (w). F and G are the cumulative wage distributions that treated and non-treated draw their wages from respectively.

Chapter 4

104

Table 4: p-values from Kolmogorov-Smirnov tests for equal hourly wage distributions between treated and nontreated individuals. Storstroem (1) (2)

Year 2004 2005 2006 2007 2008

0.449 0.256 0.178 0.480 0.580

Men Southern Jutland (1) (2)

0.818 0.504 0.355 0.857 0.948

0.632 0.555 0.022 0.006 0.039

0.976 0.930 0.044 0.012 0.078

Storstroem (1) (2) 0.334 0.522 0.057 0.343 0.122

Women Southern Jutland (1) (2)

0.644 0.902 0.114 0.659 0.244

0.542 0.649 0.368 0.140 0.102

0.919 0.982 0.700 0.279 0.204

(1) One-sided tests. (2) Two-sided tests. Bold numbers are those ≤ 0.05.

for women in Storstroem 2006. The two-sided test also rejects equal hourly wage distributions between treated and non-treated in the male Southern Jutland sample for the years 2006 and 2007. In 2008 the two-sided test rejects equal distribution on a 10 percent significance level. None of the samples (including men, 2005 in Storstroem county) rejects the null of equal pre-experiment wage distributions.

3.2

Observables included

In the model estimation, we include a number of observables. These observables cover individual characteristics perceived to influence the transition out of unemployment and the explanation of wages. They are personal variables (married, origin, education and age), labor market variables (experience, occupation, all measured last week of November 2005 and lagged unemployment duration) and experiment-specific variables (treatment and week of entry into unemployment). In the wage specification we have dropped time of entry into the experiment and lagged unemployment duration. Instead we control for the level of average log hourly wages earned in 2004 and 2005 prior to the experiment. The observables chosen for the transition out of unemployment are almost identical to those used by Blasco and Rosholm (2011), although they also control for UI fund, but not for experience and education. In our wage specification, we have chosen to include prior wages as well as the other observables partly because it is by now common knowledge that former wages are important for future wages and partly to follow in the footsteps of Arni et al. (2012). Ideally, we would have liked to include the precise wage earned in the very last job before entering QB, but unfortunately the data is not rich enough to give us this information. The estimation is carried out using a mixed proportional hazard model (see section 4 below), and one of the identifying assumptions is that the baseline hazards are piecewise-constant and that the effect of the covariates affect them in a linear manner. This has been frequently used

Effects on Post-Unemployment Wages

105

in the transition out of unemployment, but treating wages as a hazard is not that common. However, given the outlook of the hazard specification, if wages are perfectly log normal (which is assumed in e.g. Mincer type log wage equations) then MPH wage estimates will boil down to those of a linear log wage equation.

4

Econometric Framework

Analyzing treatment from active labor market programs in general requires that one controls for the fact, that in general, it is not random who is allocated to which labor market program. This can be done in several ways, but as we have access to a controlled experiment with randomized allocation to treatment, the identification of treatment effects on our outcomes is secured under some mild identifying restrictions. We use a Mixed Proportional Hazard (MPH) framework to capture the effect of treatment on post-unemployment wages. The first two key identifying assumptions are that participants could not anticipate to be included in the experiment and that there are no general equilibrium effects, i.e. that the potential outcome of any worker is independent of the treatment status of any other worker. The third key assumption is that both hazards of leaving unemployment and wage hazards follow a mixed proportional hazard structure. In section 4.1 below, we discuss potential problems with the first identifying assumption. Concerning the no general equilibrium assumption, there could be reasons to suspect it would be violated. E.g. if control group members were neglected by the case workers during the experiment simply because they had to spend more time on the treatment group. Fortunately, the counties participating in the experiment were given extra man-hours to cover the extra workload, minimizing this potential threat. However, Gautier et al. (2012) examine potential general equilibrium effects of the QB experiment by using comparison counties not in the experiment. They find that the job finding rate for the control group was affected negatively because of the experiment. Wages are measured by use of the same MPH structure as transitions from unemployment to either employment or non-employment and will thus be capturing a treatment effect on the probability of receiving a wage w∗ conditional on receiving at least a wage w∗ . In this section, we will discuss selection problems and go through the econometric methods used to address these issues and estimate the average treatment effects on post-unemployment wages.

Chapter 4

106

4.1

Selection Bias

Even though the experiment analyzed here has a treatment and control group formed on the basis of birthday (i.e. almost as random and exogenous treatment placement as we can get) it is only random until after the first week and a half of the experiment. Hereafter, the treatment group members have received the letter sketching out the entire “pilot study” course. It would be a very strict assumption to assume that awareness of the program would not affect the behavior of the treatment group members. Thus, if we do not control for this fact, there will be a selection bias in the observed transition rates out of unemployment and into different jobs or other spells. In other words, when the experiment starts and no individuals know anything about the experiment, the hazard rate out of unemployment θ(t | x, ν, d), where x is observable covariates, d ∈ {0, 1} denotes membership of the treatment group and ν is unobserved heterogeneity, will be the same for both groups in weeks t = {0, 1}. I.e. θ(t = 0 | x, ν, d = 0) = θ(t = 0 | x, ν, d = 1) and θ(t = 1 | x, ν, d = 0) = θ(t = 1 | x, ν, d = 1). However, when treatment group members receive the information letter, dynamic selection kicks in as the observed duration now depends on whether or not the individual was a member of the treatment or control group. This is because the treatment group members now hold better, or at least more, timing information on their future labor market program. It would be too harsh an assumption not to allow for different types of individuals to select themselves into different states. Since we only observe individuals leaving the experiment at a specific point in time if they actually stayed in the experiment up until that point in time, the observed hazard rate out of unemployment at time t ≥ 2 will be dependent on the unobserved heterogeneity and conditional on staying at least until t. So

ˆ | x, d) = Eν [θ(t | x, ν, d) | T ≥ t], θ(t will be the observed hazard out of unemployment at time t with T measuring realized unemployment duration. In other words, without explicitly controlling for dynamic selection, it is not possible to evaluate the effect of the experiment by comparing transition rates for the treatment group and for the control group as this would capture both the direct effect and the dynamic

Effects on Post-Unemployment Wages

107

selection effects so we would have trouble identifying true effects. An appealing strategy to account for dynamic selection is to model the selection out of unemployment simultaneously with the hazard into post-unemployment outcomes.

4.2

The Mixed Proportional Hazard Model

4.2.1 Baseline Model The MPH framework is attractable for this analysis for several reasons. First, the approach has already been extensively used in the field experiment literature.14 Secondly, the MPH model specifically captures the dynamic selection effects by controlling for the fact that observed duration depends on participation (See Abbring and van den Berg (2003) for proof of identification). Let tue and tun denote duration in the experiment until leaving unemployment for employment and non-employment, respectively. The instantaneous hazard for an individual out of unemployment into employment or non-employment at time t is then given by θh (th | xh , d, νh ) = λh (th ) exp(x0h βh + d0 δh ) exp(νh ),

h ∈ {ue, un},

(1)

where xh is observed individual characteristics used in the instantaneous hazard of h, the baseline hazard λh (th ) is duration dependence, d = (1(treated ≤ 30 weeks), 1(treated > 30 weeks)) is a vector of two treatment dummies and νh is unobserved heterogeneity.15

Following the literature on duration analysis, the duration dependence parameter, λh , is modeled as a step function to allow for a more flexible duration dependence,

λh (th ) = exp

"

X k

#

λh,k 1(th ∈ k) ,

(2)

with k a subscript for time intervals. 1(th ∈ k) is the index function indexing time intervals.

We normalize the duration dependence around one week of unemployment and allow for seven levels of duration dependence in weeks, k ∈ {2 − 3, 4 − 5, 6 − 8, 9 − 16, 17 − 30, 31 − 52, 53+}. Our baseline model jointly estimates the parameters in a maximum likelihood setting as 14

See e.g. van den Berg and van der Klaauw (2006), Rosholm (2008) and Blasco and Rosholm (2011). In practice, the treatment for an individual i is di = (1, 0) during the first 30 week-observations. If individual i is still unemployed after week 30, the dummy switches to di = (0, 1) for the rest of his week-observations. 15

Chapter 4

108 (indexing by individuals instead of writing out the conditioning on x, d and ν)

L =

I Z Y i=1

ν

c

c

ue,i un,i θue,i (tue )Sue,i (tue )θun,i (tun )Sun,i (tun )dG(ν),

(3)

with ch,i ’s are censoring variables indicating whether individual i goes to spell h or not, i.e. cue,i = 1(individual i moves to employment). In this way we account for both right-censoring of the unemployment spell and the employment/non-employment competing risks. ν = (νue , νun ) is a vector of unobserved heterogeneity with G(ν) its cumulative joint distribution. We include two mass points in the distribution of each transition out of unemployment and in the wage specification. This means we allow for eight different types in total. Optimally, Gaure, Røed and Zhang (2007) lay out a recipe of looking for the best number of mass points in a model setting like the one used in this paper. However, this is a fairly tedious process and with two mass points in each transition and wages we end up having very few significant types, not suggesting that we lack mass points, but rather indicating that the observables describe our samples rather well.  Z Sh,i (th ) = exp −

0

th



θh,i (z | xh , d, νh )dz ,

(4)

is the time-to-event specific survivor function. In the baseline model, we let ν have two support points in each transition totaling four mass points (αj for j = 1, 2, . . . , J) that are allowed to be freely correlated across transitions. For identification purposes, we normalize one mass point to zero (here αJ ≡ 0). The mass point probabilities are given by exp(αj ) P r(αj ) = P . i exp(αi )

(5)

Below, this model will be extended to capture post-unemployment wage dynamics. 4.2.2 Post-Unemployment Wages Wages enter the model in the same mixed proportional hazard framework as duration in unemployment, i.e. as a continuous wage hazard. The method of modeling wages as a hazard goes back to Donald, Green and Paarsch (2000) while Cockx and Picchio (2012) and Arni et al. (2012) extend it to a setting like the one used in this paper. Since wages are modeled by a hazard approach, we are estimating the average treatment effect on the probability of earning

Effects on Post-Unemployment Wages

109

exactly w∗ conditional on earning at least w∗ . I.e. the interpretation of treatment effects on wages is upward. There are several advantages of including wages in the mixed proportional hazard setting. First, the dynamic selection problem is incorporated in the MPH model. Second, in this setting we do not have to impose any parametric distribution on wages. Notice, however, if hourly wages are exponentially distributed, this setting would imply log wages to be linear in observables and unobservables. If hourly wages are not exponential, we will through the MPH structure be modeling proportionate shifts in the integrated hourly wage hazards (see Arni et al. (2012)). Third, short term results have an upper estimate reservation wage interpretation which we will elaborate on below.

We estimate the model for average hourly wages within the first, second and third year after entering the QB experiment, wi,2006 , wi,2007 and wi,2008 . The instantaneous hazard into a given wage level is composed as θwm (wm | xwm , d, νwm ) = λwm (wm ) exp(x0wm βwm + d0wm δwm ) exp(νwm ),

(6)

for m ∈ {2006, 2007, 2008}. dwm is a dummy variable indicating treatment. Unlike in the

hazard out of unemployment where treatment were divided into treatment in the first 30 weeks or later, the dummy for treatment in the wage hazard is simply treatment or not. λwm is the baseline wage hazard, modeled piecewise constant (normalized around average hourly wages below 100 Dkk.) to allow for a more flexible wage setting as

λwm (wm ) = exp

"

X l

#

λwm ,l 1(wm ∈ l) ,

(7)

with l being wage intervals, l ∈ {100 − 140, 140 − 180, 180 − 220, 220 − 240, 240 − 280, 280 − 350, 350+}. When specifying wages in terms of a piecewise constant hazard, the wage distri-

bution will only be identified up the levels of these hazard terms. Obviously this restricts the wage distribution considerably and is a strict assumption. One way to overcome the strictness of the piecewise constant assumption is to include a large number of hazard intervals measuring a histogram over wages (see e.g. Donald et al. (2000)). However, to do this, your need a lot of observations since each interval is only identified if there are actually realized wages within the interval. Given the size of the samples used in this paper, we have been forced to restrict the wage intervals to the above mentioned.

Chapter 4

110 The wage “survivor” function is composed by16  Z Swm (wi,m ) = exp −



wi,m

0

θwm (z | xwi,m , dwi,m , νwi,m )dz ,

(8)

which leads to three models with likelihoods given by

Lw2006 =

I Z Y

ue,i un,i i,2006 θue,i (tue )Sue,i (tue )θun,i (wi,2006 )Sw2006 (wi,2006 )dG(ν), (tun )Sun,i (tun )θw2006

I Z Y

ue,i un,i i,2007 θue,i (tue )Sue,i (tue )θun,i (wi,2007 )Sw2007 (wi,2007 )dG(ν), (tun )Sun,i (tun )θw2007

I Z Y

ue,i un,i i,2008 (wi,2008 )Sw2008 (wi,2008 )dG(ν), θue,i (tue )Sue,i (tue )θun,i (tun )Sun,i (tun )θw2008

i=1

Lw2007 =

i=1

Lw2008 =

i=1

ν

ν

ν

c

c

cw

(9) c

c

cw

(10) c

c

cw

(11)

where ν = (νue , νun , νwm ). Again, each entry in νh , h ∈ {ue, un, wm }, has two points of

support so the total number of mass points in the unobserved heterogeneity distribution is eight with α8 ≡ 0, and cwm = 1(wm > 0) is the average hourly wage censoring variable. xwm include

information on wages 2004 and 2005, experience, marriage, occupation and educational level pre-QB, origin and age. The observable heterogeneity in the transition out of unemployment is in the shape of experience, marriage, occupation and educational level pre-QB, week of entry into QB, origin, age and lagged unemployment duration.

5

Results

In this section we present our findings of average treatment effects by participating in the intensified ALMP scheme on post-unemployment wages.

5.1

Post-Unemployment Wages

Table 5 contains the estimated δwm parameters for m ∈ {2006, 2007, 2008} from equations

(9) to (11) on the male samples while Table 6 holds the female sample estimates (Table B4 to 16

For the wage transition, the survivor function S(wm ) measures individuals who have not exited into a wage level lower than wm . I.e. those who have not accepted (if offered) a job with a wage w∗∗ < wm .

Effects on Post-Unemployment Wages

111

Table 5: Wage specification estimation results for men (treatment effects singled out). Men Average treatment effects Treatment Percentage effect Observable heterogeneity Unobservable heterogeneity Avg. log likelihood Individuals

2006 wages St. S.J. 0.090*** (0.004) 0.094 yes yes -9,283 1,446

0.001** (0.001) 0.001 yes yes -7,434 1,150

St.

2007 wages S.J.

0.000 (0.004) 0.000 yes yes -9,085 1,446

-0.106*** (0.002) -0.101 yes yes -7,345 1,150

St.

2008 wages S.J.

-0.036*** (0.003) -0.035 yes yes -8,892 1,446

-0.091*** (0.002) -0.087 yes yes -7,254 1,150

*: Indicates statistical significance at the 10% level. **: At the 5% level. ***: At the 1% level. Percentage change is calculated as ∆ = exp(δ) − 1. All parameter estimates can be found in Table B4 and B5 in the appendix. St.: Storstroem county. S. J. Southern Jutland county. Note: The numbers presented here are average treatment effects on the wage hazard. I.e. a positive estimate cause an increase in the wage hazard which means that the probability of “exiting” earlier in the wage distribution increases. A positive estimate on the wage hazard thus causes a lower expected wage level.

B7 present all parameter estimates). Remember, these estimates are effects on wage hazards. A positive estimate increases the probability of “exiting” the wage distribution early, i.e. you are more likely to receive a lower average hourly wage rate. For male individuals in Storstroem county, treatment has significantly increased the probability of earning lower wages in 2006 than non-treated. Participation in the experiment increased the 2006 wage hazard by 9.4 percent. For Southern Jutland men, treatment has only slightly increased the 2006 wage hazard. In the short term, men in both counties have thus seen negative or almost zero effects on their wage levels. For women, the short term effects are more clear. Treated women in Southern Jutland have a strong negative average treatment effect on the wage hazard of 1.3 percent. I.e. treatment have increased their probability of earning higher wages than non-treated. Storstroem county treated women, on the other hand, are affected by an increase of 12 percent in the 2006 wage hazard. Treatment has increased their probability of earning lower wages than non-treated. In the medium term, the 9 percent increase of the Storstroem male wage hazard from treatment has vanished and has become insignificant. Treated men from Southern Jutland have also gained in terms of a 10 percent decrease in the wage hazard in the medium term. The exact opposite is the case for women. In storstroem, treatment has lowered the wage hazard by 3.7 percent and has had no effect on the Southern Jutland female wage hazard. Moving to long term impacts of the intensified labor market program, for both Storstroem and Southern Jutland men, treatment has significantly increased the probability of receiving higher wages in 2008 than if there had been no treatment. The size of the gains from treatment is a factor of more than double between the counties, with Southern Jutland men gaining most from treatment both in the short, medium and long term. Women, on the other hand, reveal

112

Chapter 4

significant increases in the wage hazard in both counties, indicating that the long term wage effects of treatment are negative. In storstroem, treatment increase the wage hazard by just below two percent while the wage hazard in Southern Jutland is increased by 8.6 percent. The long term wage effects for women are thus negative, and most so in Southern Jutland. Estimating short term treatment effects of ALMP on wages by a hazard delivers an interesting economic interpretation caused by its upward looking characteristic. Imagine an unemployed worker searching for a job, receives an offer with a wage w∗ . S/he will then, according to standard search theory, accept the offer if and only if the wage offered is higher than his/her reservation wage (see e.g. Burdett and Mortensen (1998)). For the pool of QB participants who hold a job in year Y , the wage hazard delivers the probability that the average wage earned during year Y is w∗ given that it is at least w∗ . In other words, the wage hazard describes the fraction of workers who are willing to work for wage w∗ but not necessarily for any wages w∗∗ < w∗ . Thus, we are also contributing with an upper estimate of revealed reservation wages for those who actually accept a job offer. The short term average treatment effect reveals if treatment conditional on everything else being equal has had an impact on the upper level of reservation wages or not. Donald et al. (2000) discuss how one has to be careful interpreting estimates of the hazard function for wages since it is not straightforward to say that a 200 Dkk hourly wage job was at risk of being only a 150 Dkk hourly wage job. What we can conclude, however, is that when we observe a 200 Dkk hourly wage job the worker has revealed to be willing to accept at least an offer of a wage of 200 Dkk. Turning back to Table 5 and 6, we see that especially Storstroem male short term estimates reveal large positive significant average treatment effects on the wage hazard. Southern Jutland female estimates are significantly negative. Treated men and women in Storstroem county have thus lowered the upper estimate of their reservation wages by increasing the wage hazard by 9.4 and 12.3 percent respectively. Using the same field experiment as this paper, Gautier et al. (2012) analyze general equilibrium effects by comparing the control group of the experiment to other newly unemployed individuals living in other counties of Denmark. They find negative spill-overs from treatment on the control group and show that outcomes from the experiment will be upward biased if not accounting for externalities. They look at the exit rate out of unemployment, but it is very likely their result of negative spill-overs transfers to wage outcomes as well. If so, then the significant negative parameter estimates in the Southern Jutland samples are even stronger results. To sum up, we find male post-unemployment wages to be overall more affected than female

Effects on Post-Unemployment Wages

113

Table 6: Wage specification estimation results for women (treatment effects singled out). Women Average treatment effects Treatment Percentage effect Observable heterogeneity Unobservable heterogeneity Avg. log likelihood Individuals

St.

2006 wages S.J.

0.116*** (0.003) 0.123 yes yes -6,410 936

-0.013*** (0.004) -0.013 yes yes -6,634 974

2007 wages St. S.J. -0.038*** (0.004) -0.037 yes yes -6,263 936

0.000 (0.002) 0.000 yes yes -6,540 974

St.

2008 wages S.J.

0.020*** (0.004) 0.021 yes yes -6,142 936

0.083*** (0.003) 0.086 yes yes -6,419 974

*: Indicates statistical significance at the 10% level. **: At the 5% level. ***: At the 1% level. Percentage change is calculated as ∆ = exp(δ) − 1. All parameter estimates can be found in Table B6 and B7 in the appendix. St.: Storstroem county. S. J. Southern Jutland county. Note: The numbers presented here are average treatment effects on the wage hazard. I.e. a positive estimate cause an increase in the wage hazard which means that the probability of “exiting” earlier in the wage distribution increases. A positive estimate on the wage hazard thus causes a lower expected wage level.

wages. Within the male samples, Storstroem treated workers experience a short term negative effect on wages which hereafter dies out in the medium term and becomes significant positive in the long term. Treatment causes the Southern Jutland wage hazard to increase slightly in the short term, and the decline rapidly in the medium term and stays on decreasing the wage hazard in the long term. For females, Storstroem workers have a sharp short term increase in the wage hazard, a decrease in the medium term wage hazard and a slight increase in the long term hazard followed from treatment. In Southern Jutland, treatment caused a decrease in the short term wage hazard, had no effect in the medium term and increased the long term wage hazard. These results should be considered with Table 1 displaying regional unemployment rates in mind. Storstroem workers face a higher local unemployment rate than Southern Jutland workers do. In fact, the unemployment rate of Southern Jutland falls as low as to 1.3 percent in 2008 while Storstroem has unemployment rates of 3.9 in 2006 and 2.0 in 2008. These figures will ceteris paribus put less pressure on wages in Southern Jutland than in Storstroem county or if e.g. the unemployment rates had been at 2003 level of 6.1 percent.

5.1.1 Relating to the Literature Our findings of men being more affected than women are consistent with those of Blasco and Rosholm (2011) analyzing post-unemployment employment (self support) stability effects by participating in QB. They find no significant treatment effects for women but find treated men to experience a reduction of 9 percent in the transition rate back into unemployment. They do not estimate their model on counties separately but include a dummy identifying Southern Jutland. This approach does not give any significant effect on self support stability. Rosholm

114

Chapter 4

(2008) shows differences in the treatment effect on exit rates for the two counties (pooling men and women together) with Southern Jutland increasing the exit rate out of unemployment more than Storstroem, consistent with the 2006 unemployment rates (cf. Table 1) and our Southern Jutland short term estimates of wages being less affected than Storstroem short term wages. In relation to the international literature on the effects of labor market programs on postunemployment wages our findings are in line with Gaure et al. (2012) examining impacts of (among other things) ALMP on earnings associated with the first job after unemployment. They find participation in ALMP to raise the expected post-unemployment earnings level (i.e. in the short term). Specifically, they find that for a typical worker, participation in very short ALMP programs (one month) have an effect of -5 percent on post-unemployment wages while participation in long programs (nine) months increase wages by up to 10 percent. The findings in this paper is thus comparable with those found in Norway despite the differences in the data settings. As this paper, they model ALMP as one treatment independent of which type of program the individual is being assigned to. They deviate from this paper in the measurement however. They measure participation in ALMP or not, whereas this paper measures an intensification of ALMP versus normal ALMP. Cockx and Picchio (2012) find that prolonging unemployment for young school-leavers who have already been unemployed for nine months lowers the probability of them finding a job, but have no effect on the subsequent starting wages. In the literature analyzing the effect of sanctions on post-unemployment wages, the typical finding is a reduction in reservation wages and earnings in the short term (see Arni et al. (2012) and van den Berg and Vikstr¨om (2009)). The primary goal of setting up the QB experiment by the National Labor Market Authority was to help newly unemployed individuals back to work faster through guidance and early activation than would otherwise be achieved. Graversen and van Ours (2008a,b) and Rosholm (2008) showed that the experiment did lead to a higher exit rate for treated than non-treated. It is therefore interesting to analyze how the treatment has affected the post-unemployment outcomes for these participants. We have now shown that for individuals participating in the experiment, the average treatment effects on post-unemployment wages are ambiguous. In Southern Jutland women see a positive treatment effect on short term wage levels and negative treatment effects on their long term wage levels. Men have a small negative short term average treatment effect and a large positive long term treatment effect on wages. In Storstroem county, however, both men and women experience a negative short term treatment effect on wages.

Effects on Post-Unemployment Wages

115

Men have had no treatment effect on medium term wages, while women gained from treatment in the medium term but lost in the long term. Men in Storstroem had a gain of around three percent decrease in the wage hazard in the long term. The main difference in the setting of the experiment between the counties was the meeting schedule. A newly unemployed worker in Storstroem was supposed to meet with a case worker every week while the schedule was only every other week in Southern Jutland. This can most likely explain some of the differences in the results between the counties. In 2006, the local labor market tightness in Storstroem and Southern Jutland was 0.23 and 0.26 respectively (cf. Table 7), and one could imagine, that if Storstroem participants every week in contrast to Southern Jutland participants only every other week, was told by the case worker that it is a tough labor market right now, he should be more prone to lower his reservation wage, which would case the wage hazard to increase more in Storstroem than in Southern Jutland.

5.1.2 State of the Labor Market A primary difference between the economical setting during the experiment, however, was the local unemployment rates (cf. Table 1). Nonetheless, unemployment in both counties was still at historically low rates during the experiment, and it is plausible that they have not been the driving force behind our results, and at the least both the treatment and control groups within counties faced the same local labor market. Of course, the unemployment rate is only showing one side of the state of the labor market the unemployed workers are situated in. If e.g. there are no open jobs for the unemployed to apply for, then a low unemployment rate will not indicate easy access to employment. The term of labor market tightness (the ratio of vacant jobs and unemployed workers) reveals how many open positions per unemployed are available and give a broader picture of the state of the labor market. Table 7 holds labor market tightness for the two counties. In 2006 there are 0.23 and 0.26 vacant jobs per unemployed in Storstroem and Southern Jutland, respectively, a difference of 14 percent. However, the tightness is still very low in both counties and we would not expect the difference in the labor market tightness to solely explain the difference between short term treatment effects in Storstroem versus Southern Jutland. We do, on the other hand, think that the labor market tightness difference together with the difference in the experiment setting across the counties can explain much of the difference in the treatment effect (cf. the discussion in section 5.1.1). In the long term, however, there is a stronger difference in the labor market

Chapter 4

116 Table 7: Labor market summary. County

Average # of vacancies 2006 2007 2008

Average # of unemployed 2006 2007 2008

Labor market tightness∗ 2006 2007 2008

Storstroem Southern Jutland

1,394 1,458

6,208 5,680

0.225 0.257

1,356 1,361

1,195 1,339

4,306 3,748

3,107 2,352

0.315 0.363

0.385 0.569

∗ Labor

market tightness calculated as the average number of vacancies divided by the average number of unemployed. Note: The number of vacant jobs is collected by the National Labor Market Board by gathering information from the local job centers.

tightness between the two counties with 0.39 vacant jobs per unemployed worker in Storstroem and 0.57 vacant jobs per unemployed worker in Southern Jutland (a difference of 47 percent). In other words, there are thus, all else equal, easier access to vacant jobs in Southern Jutland than in Storstroem county in 2008. Given these market tightnesses, we would expect workers in Southern Jutland, generally, to have better outside options than workers in Storstroem, and if treatment has either increased the human capital of the treated individuals or taught them the true state of the labor market, treated workers should be able to extract more rent, resulting in higher treatment effects, in Southern Jutland than in Storstroem. This is also what we find, at least for men (cf. Table 5).

5.2

Robustness – Log Wages

Modeling hourly wages by an MPH structure is appealing because of the dispensable assumption of a specific distribution on wages. If, on the other hand, we assume hourly wages to be log-normal the individual likelihood contribution of log hourly wages is φ



ln wi,m − x0i,wm βwm − d0i,wm δwm − νi,wm σwm

ci,wm

,

(12)

with φ(·) being the p.d.f. of the standard normal distribution and σwm is the standard deviation of log wages in year m. By incorporating this likelihood contribution in the baseline model instead of the average hourly wage MPH structure above, we can estimate the effect of treatment on the log hourly wage. If hourly wages are exactly exponentially distributed then this specification should yield the exact same estimates as in the MPH structure model. We have incorporated (12) and estimated it simultaneously with the baseline likelihood function. Table 8 shows selected parameter estimates from this exercise. We only present parameter estimates on wages in the short and long term for men (the samples with the most clear results above). Comparison of average treatment effects on wage hazards and log wages in Table 8 shows that, as expected, a negative effect on the hazard is followed by a positive effect on log wages and vice versa.

Effects on Post-Unemployment Wages

117

Table 8: Hourly wage and log hourly wage specification average treatment effects. Men Storstroem Treatment Southern Jutland Treatment

2006 wages Hourly wages Log hourly wages

2008 wages Hourly wages Log hourly wages

0.090*** (0.004)

-0.005*** (0.000)

-0.036*** (0.003)

0.003*** (0.001)

0.001** (0.001)

-0.004*** (0.000)

-0.091*** (0.002)

0.011*** (0.001)

*: Indicates statistical significance at the 10% level. **: At the 5% level. ***: At the 1% level. Note: Hourly wage estimates are average treatment effects on the hourly wage hazard. Log hourly wage estimates are average treatment effects on the log hourly wage rate. Parameter estimates from log wages equations are not shown. Can be delivered upon request.

In terms of significance, the two approaches seem to deliver the same results. Assuming log normal hourly wages also results in the conclusion that treated men in Storstroem county are hit by significantly lower short term wages wages than non-treated, while treatment affects wages positively in the long term. Likewise, for men in Southern Jutland treatment lowers the short term wages and increases long term wages. If average hourly wages were perfectly log normal distributed, we should have seen the exact same parameter estimates (with opposite signs). Differences between hourly and log hourly wage estimates indicate that average hourly wages are not exactly log normal, and we thus prefer using our wage hazard specification without the assumption of a specific wage distribution.17

6

Conclusions

This paper uses a controlled field experiment of intensifying active labor market policies in Denmark to analyze post-unemployment wages. The experiment was carried out to test whether an early effort could help treated newly unemployed back to work faster than non-treated. The primary treatments were frequent meetings with a case worker and faster entry into activation. Previous studies analyzing the experiment have shown treatment to have positive effects on the exit rate out of unemployment and to have lowered the re-entry rate into unemployment for men. To take the analysis on post-unemployment outcomes further, we link the experiment to Danish employment register data and construct hourly wages pre- and post-unemployment. Using a mixed proportional hazard framework we control for dynamic selection and estimate the average treatment effect on the wage hazard. We find male post-unemployment wages to be overall more affected by treatment than female post-unemployment wages. Within the male 17

Kolmogorov-Smirnov, Anderson-Darling and Shapiro-Wilk tests for normality (not shown, but available upon request) rejects the null hypothesis of normally distributed log wages for all samples.

118

Chapter 4

samples there are significant differences between the two counties Storstroem and Southern Jutland. Men in Storstroem have a negative short term effect of treatment on wages resulting in a 9 percent higher expected hourly wage hazard in 2006 but no significant medium effects and a 3.7 percent lower expected wage hazard than non-treated in the long term. In Southern Jutland, men have zero to moderate negative short term and large positive medium and long term average treatment effects on wage levels, decreasing their expected 2008 hourly wage hazard by 9.5 percent. Treated Southern Jutland women display a decrease in the wage hazard in the short term but have no effects in the medium term and negative wage level effects in the long term. Finally, treated women in Storstroem have a large increase in the expected hazard in the short term, a decrease in the medium term and a slight increase of the wage hazard in the long term. ALMPs are meant to update or teach skills of the unemployed worker and to help him/her realize the state of the labor market. The outcome on wages from these measures is not straightforward. If ALMP build on the human capital of the worker the resulting worker-firm match should reflect the updated skills and the wage could very well be higher than if no treatment were conducted. If the treatment effect on the other hand goes through guidance of the state of the labor market resulting in advice to accept lower paying jobs than the worker would be willing to without such guidance we would see lower wages as the outcome of ALMP. Our results point to the latter in the Storstroem samples. Relating to standard search theory, unemployed workers will accept a job if and only if the offer is better than their reservation wage. In this framework, short term wages can be thought of as a revealed upper estimate of the worker’s reservation wage. We thus find evidence towards that treatment has lowered the upper estimate of the reservation wage of especially men in Storstroem county.

References Abbring, J. H. and G. J. van den Berg (2003), The Identifiability of the Mixed Proportional Hazards Competing Risks Model, Journal of the Royal Statistical Society Series B, 65(Part 3): 701–710. Arni, P., R. Lalive and J. C. van Ours (2012), How Effective Are Unemployment Benefit Sanctions? Looking Beyond Unemployment Exit, Forthcoming in Journal of Applied Econometrics. Berger, M. C., D. A. Black, B. J. Noel and J. A. Smith (2003), Is the Threat of Reemployment Services More Effective Than the Services Themselves? Evidence from Random Assignment in the UI System, American Economic Review, 93(4): 1313–1327.

Effects on Post-Unemployment Wages

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Blasco, S. and M. Rosholm (2011), The Impact of Active Labour Market Policy on PostUnemployment Outcomes: Evidence from a Social Experiment in Denmark, Working Paper. Burdett, K. and D. T. Mortensen (1998), Wage Differentials, Employer Size, and Unemployment, International Economic Review, 39(2): 257–273. Card, D., J. Kluve and A. Weber (2010), Active Labour Market Policy Evaluations: A MetaAnalysis, The Economic Journal, 120(November): F452–F477. Cockx, B. and M. Picchio (2012), Scarring Effects of Remaining Unemployed for Long-Term Unemployed School-Leavers, Working Paper. Crepon, B., M. Dejemeppe and M. Gurgand (2005), Counseling the unemployed: does it lower unemployment duration and recurrence?, Discussion Papers (ECON - D´epartement des Sciences Economiques). Doiron, D. and T. Gørgens (2008), State dependence in youth labor market experiences, and the evaluation of policy interventions, Journal of Econometrics, 145: 81–97. Donald, S. G., D. A. Green and H. J. Paarsch (2000), Differences in Wage Distributions between Canada and the United States: An Application of a Flexible Estimator of Distribution Functions in the Presence of Covariates, The Review of Economic Studies, 67(4): 609–633. Gaure, S., K. Røed and L. Westlie (2012), Job search incentives and job match quality, Labour Economics, 19(3): 438–450. Gaure, S., K. Røed and T. Zhang (2007), Time and Causality: A Monte Carlo Assessment of the Timing-of-Events Approach, Journal of Econometrics, 141: 1159–1195. Gautier, P., P. Muller, B. van der Klaauw, M. Rosholm and M. Svarer (2012), Estimating Equilibrium Effects of Job Search Assistance, Working Paper. Graversen, B. and J. van Ours (2008a), Activating Unemployed Workers Work: Experimental Evidence from Denmark, Economic Letters, 100: 308–310. ——— (2008b), How to Help Unemployed Find Jobs Jobs Quickly: Evidence from a Mandatory Activation Programme, Journal of Public Economics, 92: 2020–2035. Ham, J. C. and R. J. Lalonde (1996), The Effect of Sample Selection and Initial Conditions in Duration Models: Evidence from Experimental Data on Training, Econometrica, 64(1): 175–205. Heckman, J. J., H. Ichimura and P. Todd (1997), Matching As An Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme, The Review of Economic Studies, 64: 605–654. Heckman, J. J., R. Lalonde and J. Smith (1999), The Economics and Econometrics of ALMP, vol. 3 of Handbook of Labor Economics, North-Holland, Amsterdam. Heckman, J. J. and B. Singer (1984a), Econometric Duration Analysis, Journal of Econometrics, 24: 63–132. ——— (1984b), The Identifiability of the Proportional Hazard Model, Review of Economic Studies, 51(2): 231–241. Jespersen, S. T., J. R. Munch and L. Skipper (2008), Costs and benefits of Danish active labour market programmes, Labour Economics, 15: 859–884. Kluve, J. (2010), The Effectiveness of European Active Labor Market Programs, Labor Economics, 17: 904–918.

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Lalive, R., J. Zweim¨uller and J. C. van Ours (2005), The Effect of Benefit Sanctions on the Duration of Unemployment, Journal of the European Economic Association, 3(6): 1386– 1417. Larsson, L. (2003), Evaluation of Swedish Youth Labor Market Programs, The Journal of Human Resources, 38(4): 891–927. Lechner, M. (1999), Earnings and employment effects of continuous of-the-job training in East Germany after unification, Journal of Business and Economic Statistics, 17: 74–90. Raaum, O., H. Torp and T. Zhang (2002), Do individual programme effects exceed the costs? Norwegian evidence on long run Do individual programme effects exceed the costs? Norwegian evidence on long run effects of labour market training, Memorandum, vol. 15. University of Oslo, Department of Economics. Rosholm, M. (2008), Experimental Evidence on the Nature of the Danish Employment Miracle, IZA Discussion Paper No. 3620. Rosholm, M. and M. Svarer (2008), The Threat Effect of Active Labour Market Programmes, The Scandinavian Journal of Economics, 110(2): 385–401. Sianesi, B. (2004), An Evaluation of the Swedish System of Active Labor Market Programs in the 1990s, The Review of Economics and Statistics, 86(1): 133–155. van den Berg, G. and B. van der Klaauw (2006), Counseling and Monitoring of Unemployed Workers: Theory and Evidence From A Controlled Social Experiment, International Economic Review, 47(3): 895–936. van den Berg, G. J. and J. Vikstr¨om (2009), Monitoring Job Offer Decisions, Punishments, Exit to Work, and Job Quality, IFAU Working Paper 2009:18. Vikstr¨om, J., M. Rosholm and M. Svarer (2011), The Relative Efficiency of Active Labour Market Policies: Evidence From a Social Experiment and Non-Parametric Methods, IZA Discussion Paper No. 5596.

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121

Appendices A

Figures

100

150

100

150

200 Hourly wage

1 .6 .4 150

100

150

200 Hourly wage

2005 Southern Jutland, men 300

200 Hourly wage

150

100

150

200 Hourly wage

Control group

250

300

.8 CDF .4 .2

2007 Storstroem, men Treatment group

0

Control group

250

100

.6

.8 .2

.4

CDF

.6

.8 CDF .4 .2

Treatment group

0

300

Treatment group

0

Control group

250

300

200 Hourly wage

2007 Southern Jutland, men

Control group

250

300

Treatment group

200 Hourly wage

Control group

250

300

.8 .6 CDF .4 .2

.2

.4

CDF

.6

.8

1

0

Treatment group

100

2006 Southern Jutland, men

Control group

250

1

200 Hourly wage

CDF

300

.6

.8 .6 CDF .4 .2

2006 Storstroem, men Treatment group

.2

2005 Storstroem, men

Control group

250

1

150

0

150

Treatment group

100

1

100

300

1 150

2004 Southern Jutland, men

Control group

250

0

0 100

200 Hourly wage

1

150

0

2004 Storstroem, men Treatment group

100

.8

1 .2

.4

CDF

.6

.8

1 .8 .6 CDF .4 .2

.2

.4

CDF

.6

.8

1

Figure A1: Cumulative distribution graphs of average hourly wages, men.

2008 Storstroem, men 200 Hourly wage

2008 Southern Jutland, men

Control group

250

Treatment group

0

0

Treatment group

300

200 Hourly wage

Control group

250

300

150

100

150

200 Hourly wage

.8 .6 CDF .4

Treatment group

200 Hourly wage

Control group

250

300

.8 .6

CDF

.4 100

150

100

150

200 Hourly wage

Control group

250

300

.8 .2

.4

CDF

.6

.8 300

.2 300

0

0

150

Treatment group

300

CDF Control group

250

2005 Southern Jutland, women

Control group

250

.4 200 Hourly wage

2008 Southern Jutland, women

Control group

250

100

200 Hourly wage

.2

0

Treatment group

1

0 .8 .6 CDF .4 .2

200 Hourly wage

150

.6

.8 .2

.4

CDF

.6

.8 .6 CDF .4 .2

300

2008 Storstroem, women Treatment group

100

.2

.2

Treatment group

300

2006 Southern Jutland, women

Control group

250

1

200 Hourly wage

2005 Storstroem, women

Control group

250

1

100

2006 Storstroem, women Treatment group

.6

CDF

.4 Treatment group

150

2007 Storstroem, women Treatment group

200 Hourly wage

2007 Southern Jutland, women

Control group

250

300

Treatment group

0

150

2004 Southern Jutland, women 100

1

100

300

1 150

Control group

250

1 100

200 Hourly wage

0

Treatment group

150

.2

.2

2004 Storstroem, women 100

1

1 .8

1 .6

CDF

.4

.6 .4

CDF

.8

.8

1

Figure A2: Cumulative distribution graphs of average hourly wages, women.

200 Hourly wage

Control group

250

300

Chapter 4

122

B

Tables Table B1: Outline of the treatments. Weeks after registering for unemployment benefits 1.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Treatment group

Control group

Letter of ’pilot study’ notification received CV/basic registration meeting with case worker

CV/basic registration meeting with case worker Meeting with case worker

Two-week JSA programme

Frequent meetings with case worker

Meeting with case worker

Between programs

Activation program

Meeting with case worker

Post-treatment, transferred to normal scheme after week 39 Meeting with case worker

Dashed lines separate treatment group programs. Solid lines separate control group programs.

Effects on Post-Unemployment Wages

123

Table B2: Occupational level in the last week of November each year. Occupation 2004 Management level Skilled level Unskilled level Unemployed Outside the labour force 2005 Management level Skilled level Unskilled level Unemployed Outside the labour force 2006 Management level Skilled level Unskilled level Unemployed Outside the labour force 2007 Management level Skilled level Unskilled level Unemployed Outside the labour force 2008 Management level Skilled level Unskilled level Unemployed Outside the labour force Individuals

Storstroem Treatment Control

Diff.

Southern Jutland Treatment Control Diff.

0.064 0.070 0.740 0.092 0.033

0.065 0.082 0.730 0.085 0.038

0.076 0.068 0.740 0.075 0.042

0.063 0.063 0.735 0.084 0.055

0.050 0.059 0.712 0.144 0.035

0.056 0.070 0.690 0.145 0.039

0.052 0.061 0.692 0.153 0.042

0.043 0.064 0.695 0.154 0.044

0.044 0.089 0.728 0.092 0.048

0.052 0.086 0.690 0.123 0.048

0.049 0.079 0.737 0.099 0.036

0.050 0.077 0.682 0.146 0.045

*** *** *

0.054 0.084 0.667 0.099 0.096

0.065 0.085 0.689 0.079 0.082

0.057 0.075 0.728 0.067 0.074

0.062 0.088 0.679 0.082 0.089

** * *

0.072 0.078 0.591 0.098 0.162

0.086 0.083 0.577 0.103 0.151

0.060 0.101 0.637 0.075 0.127

0.075 0.092 0.601 0.095 0.137

1,169

1,217

1,060

1,064

*

** **

*

*: Indicates statistical significance at the 10% level. **: At the 5% level. ***: At the 1% level.

*

* * *

Obs

683 698 683 646 606

Obs

529 533 536 526 502

Obs

407 410 396 373 362

Obs

446 448 442 423 404

Men Storstroem

2004 2005 2006 2007 2008

Southern Jutland

2004 2005 2006 2007 2008

Women Storstroem

2004 2005 2006 2007 2008

Southern Jutland

2004 2005 2006 2007 2008

151.8 161.3 165.2 161.0 164.9

Average

157.0 165.7 160.0 163.1 164.8

Average

172.8 180.0 179.7 185.3 191.5

Average

179.0 186.4 185.2 189.3 194.5

Average

50.1 56.7 68.4 50.5 48.4

S.D.

61.0 56.4 50.7 48.3 45.9

S.D.

53.0 52.2 50.6 52.1 57.6

S.D.

53.7 51.9 57.0 54.8 57.8

S.D. 147.5 154.4 152.3 158.1 159.8

143.8 150.5 151.0 154.2 155.9

129.2 131.8 133.7 135.9 135.4

98.1 102.3 112.5 114.0 119.2

124.8 130.2 133.4 133.9 137.7

Treatment P10 P25

85.7 97.0 109.8 118.5 121.0

Treatment P10 P25

121.6 128.9 133.7 137.7 140.2

Treatment P10 P25

128.1 135.1 136.6 140.5 142.0

Treatment P10 P25

146.1 155.5 151.1 152.4 156.0

P50

148.8 157.9 152.0 153.9 159.7

P50

164.2 170.5 169.9 175.0 177.3

P50

170.2 177.6 173.3 178.6 181.6

P50

169.4 180.6 177.6 179.9 185.2

P75

174.1 190.4 176.8 183.1 186.1

P75

193.5 200.5 196.3 207.2 214.4

P75

198.8 206.6 200.2 209.8 213.5

P75

206.9 218.9 224.4 218.1 216.7

P90

214.9 233.8 208.7 229.6 219.5

P90

234.5 239.2 238.9 248.7 259.3

P90

245.4 249.2 248.1 258.2 265.1

P90

440 428 408 420 399

Obs

448 450 436 425 404

Obs

545 552 533 513 495

Obs

691 694 669 639 610

Obs

153.3 164.9 166.0 161.9 172.6

Average

157.5 166.9 170.1 164.0 167.6

Average

173.3 181.5 181.4 180.0 185.4

Average

181.4 192.0 191.1 190.3 191.1

Average

51.7 57.7 61.5 48.0 60.1

S.D.

62 58.6 64.1 50.9 47.5

S.D.

58.1 55.1 63.9 45.6 51.5

S.D.

57.1 56.7 63.6 51.8 54.0

S.D. 149.7 157.2 155.4 158.1 159.2

145.1 150.4 146.0 153.5 154.3

127.9 132.2 138.6 137.0 140.3

98.9 103.8 120.4 119.0 123.7

125.5 132.5 135.0 134.3 138.7

Control P10 P25

102.9 109.4 120.6 116.3 125.1

Control P10 P25

118.8 131.4 133.8 136.9 136.9

Control P10 P25

131.6 139.5 138.1 138.8 139.8

Control P10 P25

146.9 154.5 152.1 155.5 159.2

P50

148.5 158.0 158.9 154.6 158.1

P50

163.0 170.3 169.3 172.2 173.6

P50

168.9 180.4 176.6 181.1 181.7

P50

Table B3: Descriptives on average hourly wages, men in the top panel and women in the bottom panel.

171.8 184.2 174.7 177.9 185.9

P75

173.7 189.1 181.4 179.4 183.3

P75

193.0 198.9 197.2 200.4 206.8

P75

199.2 213.3 210.5 210.5 211.1

P75

204.1 229.5 227.0 207.7 227.0

P90

213.2 230.8 222.4 219.0 225.3

P90

232.9 241.0 227.8 233.8 250.0

P90

247.2 259.3 256.9 259.4 253.9

P90

124 Chapter 4

Effects on Post-Unemployment Wages

125

Table B4: Men, Storstroem county. 2006 wages Estimate S.D.

2007 wages Estimate S.D.

2008 wages Estimate S.D.

Transition U → E Experience Experience squared/100 Treatment (U ≤ 30 weeks) Treatment (U > 30 weeks) Married Occupation, top 2005 Occupation, middle 2005 Occupation, base 2005 Occupation, unempl. 2005 Education, vocational 2006 Education, bachelor 2006 Education, master 2006 Entry week, 45 - 46, 2005 Entry week, 47 - 48, 2005 Entry week, 49 - 50, 2005 Entry week, 51 - 52, 2005 Entry week, 01 - 02, 2006 Entry week, 03 - 04, 2006 Entry week, 05 - 06, 2006 Entry week, 07 - 08, 2006 Western immigrant Non-western immigrant Age 25 - 29 Age 30 - 39 Age 40 - 49 Age 50 + Lagged Uempl. duration, 7 - 8 weeks Lagged Uempl. duration, 9 - 16 weeks Lagged Uempl. duration, 17 - 28 weeks Lagged Uempl. duration, 29 - 52 weeks Lagged Uempl. duration, 52 + weeks Baseline hazard 2 - 3 weeks Baseline hazard 4 - 5 weeks Baseline hazard 6 - 8 weeks Baseline hazard 9 - 16 weeks Baseline hazard 17 - 30 weeks Baseline hazard 31 - 52 weeks Baseline hazard 53 + weeks νe1 νe2

0.030 -0.068 0.269 0.377 0.059 -0.171 0.536 0.359 -0.338 0.127 -0.191 -0.112 -0.035 -0.321 -0.271 -0.071 -0.165 0.528 -0.189 0.242 0.146 -0.370 -0.235 -0.351 -0.474 -0.525 0.382 0.279 0.148 0.072 -0.319 0.914 1.117 0.997 1.310 1.631 1.554 1.325 -3.919 -5.339

0.000 0.000 0.002 0.016 0.004 0.012 0.002 0.002 0.007 0.002 0.008 0.016 0.008 0.004 0.008 0.004 0.004 0.004 0.006 0.008 0.002 0.006 0.002 0.004 0.004 0.004 0.016 0.007 0.004 0.004 0.003 0.008 0.004 0.008 0.004 0.004 0.002 0.012 0.000 0.003

0.037 -0.086 0.283 0.408 0.049 -0.168 0.609 0.404 -0.269 0.117 -0.247 -0.231 0.035 -0.261 -0.199 -0.012 -0.075 0.612 -0.057 0.314 0.031 -0.512 -0.165 -0.325 -0.436 -0.468 0.314 0.232 0.080 0.025 -0.378 0.955 1.161 1.050 1.377 1.817 1.953 1.961 -4.040 -5.908

0.000 0.001 0.000 0.008 0.001 0.016 0.004 0.004 0.008 0.004 0.003 0.008 0.008 0.007 0.004 0.003 0.008 0.008 0.004 0.008 0.002 0.016 0.005 0.004 0.004 0.002 0.016 0.008 0.008 0.004 0.004 0.004 0.004 0.008 0.000 0.007 0.008 0.008 0.004 0.016

0.041 -0.102 0.284 0.383 0.052 -0.112 0.624 0.425 -0.269 0.113 -0.240 -0.244 0.039 -0.262 -0.203 -0.022 -0.094 0.607 -0.042 0.329 0.052 -0.495 -0.173 -0.318 -0.441 -0.469 0.327 0.233 0.080 0.018 -0.373 0.967 1.177 1.068 1.404 1.853 2.008 1.942 -4.101 -5.914

0.000 0.002 0.003 0.014 0.003 0.014 0.003 0.002 0.007 0.003 0.010 0.021 0.015 0.007 0.006 0.005 0.005 0.005 0.007 0.012 0.002 0.014 0.006 0.005 0.003 0.005 0.013 0.011 0.007 0.006 0.005 0.006 0.001 0.006 0.003 0.003 0.012 0.014 0.002 0.014

Transition U → N Experience Experience squared/100 Treatment (U ≤ 30 weeks) Treatment (U > 30 weeks) Married Occupation, top 2005 Occupation, middle 2005 Occupation, base 2005 Occupation, unempl. 2005 Education, vocational 2006 Education, bachelor 2006 Education, master 2006 Entry week, 45 - 46, 2005 Entry week, 47 - 48, 2005 Entry week, 49 - 50, 2005 Entry week, 51 - 52, 2005 Entry week, 01 - 02, 2006 Entry week, 03 - 04, 2006 Entry week, 05 - 06, 2006 Entry week, 07 - 08, 2006 Western immigrant Non-western immigrant Age 25 - 29

0.118 -0.513 -0.079 0.200 0.396 -0.923 -0.190 0.038 -1.605 0.686 0.975 -0.181 -0.813 -0.749 0.013 -0.771 -1.383 -0.762 -1.312 -1.449 0.993 0.692 0.673

0.001 0.002 0.008 0.032 0.008 0.026 0.008 0.003 0.032 0.006 0.032 0.032 0.032 0.012 0.016 0.016 0.006 0.032 0.032 0.032 0.002 0.064 0.016

0.124 -0.541 -0.072 0.218 0.403 -0.909 -0.175 0.054 -1.576 0.686 0.977 -0.061 -0.797 -0.730 0.045 -0.762 -1.378 -0.756 -1.279 -1.425 1.122 0.835 0.710

0.000 0.001 0.008 0.016 0.008 0.016 0.008 0.008 0.028 0.008 0.016 0.032 0.032 0.016 0.016 0.016 0.004 0.016 0.016 0.020 0.002 0.032 0.016

0.130 -0.563 -0.072 0.236 0.392 -0.956 -0.174 0.055 -1.538 0.680 0.998 -0.063 -0.712 -0.671 0.087 -0.715 -1.319 -0.707 -1.215 -1.364 1.127 0.837 0.736

0.001 0.002 0.007 0.022 0.014 0.058 0.014 0.007 0.028 0.013 0.038 0.076 0.028 0.028 0.034 0.028 0.014 0.028 0.012 0.016 0.007 0.008 0.028

Table continues on next page. Bold face numbers indicate statistical significance at the 5 % level.

Chapter 4

126 Table B4 continued: Men, Storstroem county. 2006 wages Estimate S.D.

2007 wages Estimate S.D.

2008 wages Estimate S.D.

Age 30 - 39 Age 40 - 49 Age 50 + Lagged Uempl. duration, 7 - 8 weeks Lagged Uempl. duration, 9 - 16 weeks Lagged Uempl. duration, 17 - 28 weeks Lagged Uempl. duration, 29 - 52 weeks Lagged Uempl. duration, 52 + weeks Baseline hazard 2 - 3 weeks Baseline hazard 4 - 5 weeks Baseline hazard 6 - 8 weeks Baseline hazard 9 - 16 weeks Baseline hazard 17 - 30 weeks Baseline hazard 31 - 52 weeks Baseline hazard 53 + weeks νn1 νn2

0.121 0.555 0.137 2.095 -0.079 0.871 -0.631 -0.380 -1.323 -1.558 -0.491 -0.526 -0.378 -0.601 -0.420 -2.958 -3.289

0.016 0.012 0.008 0.128 0.026 0.025 0.013 0.012 0.032 0.032 0.016 0.006 0.014 0.016 0.016 0.510 0.008

0.135 0.587 0.194 2.219 -0.079 0.870 -0.613 -0.394 -1.316 -1.558 -0.497 -0.523 -0.365 -0.583 -0.406 -4.763 -3.518

0.030 0.016 0.000 0.064 0.028 0.028 0.012 0.016 0.032 0.032 0.016 0.016 0.004 0.016 0.016 0.128 0.004

0.178 0.626 0.236 2.135 -0.100 0.871 -0.611 -0.392 -1.314 -1.525 -0.505 -0.522 -0.365 -0.598 -0.416 -4.186 -3.625

0.024 0.014 0.015 0.024 0.028 0.024 0.028 0.025 0.028 0.055 0.028 0.014 0.014 0.035 0.014 0.220 0.007

Wages Experience Experience squared/100 Treament Married Occupation, top 2005 Occupation, middle 2005 Occupation, base 2005 Occupation, unempl. 2005 Education, vocational 2006 Education, bachelor 2006 Education, master 2006 Western immigrant Non-western immigrant Age 25 - 29 Age 30 - 39 Age 40 - 49 Age 50 + Log Wage 2004 Log Wage 2005 Baseline wage hazard 100 - 140 dkk. Baseline wage hazard 140 - 180 dkk. Baseline wage hazard 180 - 220 dkk. Baseline wage hazard 220 - 240 dkk. Baseline wage hazard 240 - 280 dkk. Baseline wage hazard 280 - 350 dkk. Baseline wage hazard 350 + dkk. νw1 νw2

0.013 -0.056 0.090 -0.053 0.100 0.535 0.575 0.740 -0.156 -0.436 -0.494 -0.310 0.065 0.045 0.041 0.129 0.017 -0.081 -0.216 3.272 4.477 4.573 4.460 4.594 4.478 4.270 -5.401 -5.259

0.000 0.000 0.004 0.002 0.016 0.008 0.004 0.002 0.001 0.016 0.016 0.016 0.008 0.001 0.001 0.002 0.004 0.001 0.000 0.004 0.001 0.004 0.001 0.002 0.006 0.016 0.001 0.008

0.009 -0.029 0.000 -0.085 0.744 0.896 0.927 1.004 -0.066 -0.319 -0.456 -0.351 0.214 -0.109 -0.060 0.121 0.066 -0.130 -0.165 2.839 4.205 4.399 4.466 4.144 4.493 4.701 -5.578 -5.132

0.000 0.001 0.004 0.002 0.008 0.001 0.008 0.007 0.002 0.004 0.012 0.003 0.014 0.008 0.000 0.004 0.004 0.000 0.001 0.001 0.001 0.004 0.016 0.008 0.016 0.012 0.002 0.002

0.002 -0.033 -0.036 -0.015 0.580 0.878 0.913 0.935 -0.102 -0.463 -0.766 -0.233 0.287 -0.093 0.001 0.202 0.221 -0.080 -0.181 2.716 4.107 4.403 4.321 4.120 4.209 4.533 -5.648 -5.283

0.000 0.000 0.003 0.003 0.017 0.003 0.003 0.007 0.003 0.011 0.028 0.028 0.010 0.007 0.001 0.002 0.001 0.000 0.001 0.005 0.000 0.008 0.002 0.014 0.011 0.003 0.006 0.001

α1 α2 α3 α4 α5 α6 α7 α8 P r(α1 ) P r(α2 ) P r(α3 ) P r(α4 ) P r(α5 ) P r(α6 ) P r(α7 ) P r(α8 )

-11.693 -8.362 2.753 -6.725 -5.785 -5.445 -0.880 0.000 0.000 0.000 0.917 0.000 0.000 0.000 0.024 0.059

1.020 2.040 0.016 1.020 0.765 2.040 0.032

-15.138 -8.175 2.476 -7.583 -8.592 -6.253 -7.253 0.000 0.000 0.000 0.922 0.000 0.000 0.000 0.000 0.078

2.040 0.510 0.008 1.020 0.765 0.128 0.510

-16.321 -8.066 2.374 -8.136 -10.257 -5.755 -6.748 0.000 0.000 0.000 0.914 0.000 0.000 0.000 0.000 0.085

2.200 1.100 0.028 1.100 2.860 0.275 1.100

Average log likehood Individuals

-9283.37 1,446

Bold face numbers indicate statistical significance at the 5 % level.

-9084.75 1,446

-8892.02 1,446

Effects on Post-Unemployment Wages

127

Table B5: Men, Southern Jutland county. 2006 wages Estimate S.D.

2007 wages Estimate S.D.

2008 wages Estimate S.D.

Transition U → E Experience Experience squared/100 Treatment (U ≤ 30 weeks) Treatment (U > 30 weeks) Married Occupation, top 2005 Occupation, middle 2005 Occupation, base 2005 Occupation, unempl. 2005 Education, vocational 2006 Education, bachelor 2006 Education, master 2006 Entry week, 45 - 46, 2005 Entry week, 47 - 48, 2005 Entry week, 49 - 50, 2005 Entry week, 51 - 52, 2005 Entry week, 01 - 02, 2006 Entry week, 03 - 04, 2006 Entry week, 05 - 06, 2006 Entry week, 07 - 08, 2006 Western immigrant Non-western immigrant Age 25 - 29 Age 30 - 39 Age 40 - 49 Age 50 + Lagged Uempl. duration, 7 - 8 weeks Lagged Uempl. duration, 9 - 16 weeks Lagged Uempl. duration, 17 - 28 weeks Lagged Uempl. duration, 29 - 52 weeks Lagged Uempl. duration, 52 + weeks Baseline hazard 2 - 3 weeks Baseline hazard 4 - 5 weeks Baseline hazard 6 - 8 weeks Baseline hazard 9 - 16 weeks Baseline hazard 17 - 30 weeks Baseline hazard 31 - 52 weeks Baseline hazard 53 + weeks νe1 νe2

0.059 -0.184 0.124 0.418 0.194 0.445 0.645 0.478 -0.134 0.086 -0.170 -0.141 -0.274 -0.676 -0.569 -0.303 -0.297 0.080 -0.344 0.189 -0.305 -0.566 -0.468 -0.590 -0.491 -0.737 0.647 0.195 0.049 0.078 -0.178 0.824 1.003 1.083 1.126 1.362 0.660 0.683 -4.341 -3.367

0.000 0.001 0.004 0.008 0.001 0.012 0.002 0.004 0.005 0.003 0.006 0.016 0.008 0.004 0.006 0.004 0.004 0.004 0.007 0.000 0.002 0.006 0.004 0.005 0.004 0.003 0.008 0.006 0.007 0.004 0.004 0.001 0.006 0.004 0.004 0.004 0.008 0.006 0.004 0.002

0.052 -0.159 0.127 0.459 0.194 0.483 0.689 0.521 -0.126 0.107 -0.164 -0.115 -0.295 -0.697 -0.598 -0.327 -0.312 0.071 -0.357 0.171 -0.315 -0.613 -0.465 -0.577 -0.471 -0.738 0.635 0.204 0.058 0.070 -0.176 0.806 0.989 1.076 1.132 1.396 0.739 0.837 -4.492 -3.347

0.000 0.001 0.003 0.011 0.003 0.008 0.003 0.002 0.006 0.002 0.006 0.012 0.006 0.004 0.008 0.005 0.004 0.004 0.007 0.007 0.001 0.008 0.007 0.004 0.003 0.003 0.009 0.006 0.004 0.004 0.003 0.004 0.003 0.004 0.004 0.009 0.006 0.008 0.008 0.004

0.051 -0.154 0.126 0.455 0.194 0.453 0.680 0.507 -0.145 0.104 -0.160 -0.126 -0.289 -0.703 -0.597 -0.326 -0.319 0.062 -0.366 0.170 -0.327 -0.632 -0.473 -0.589 -0.488 -0.752 0.639 0.198 0.050 0.070 -0.177 0.798 0.979 1.069 1.124 1.393 0.732 0.824 -4.419 -3.297

0.000 0.000 0.001 0.004 0.001 0.004 0.000 0.002 0.000 0.002 0.002 0.004 0.002 0.000 0.002 0.001 0.002 0.002 0.002 0.002 0.000 0.002 0.002 0.001 0.002 0.002 0.002 0.002 0.004 0.001 0.001 0.002 0.004 0.001 0.002 0.002 0.001 0.004 0.004 0.001

Transition U → N Experience Experience squared/100 Treatment (U ≤ 30 weeks) Treatment (U > 30 weeks) Married Occupation, top 2005 Occupation, middle 2005 Occupation, base 2005 Occupation, unempl. 2005 Education, vocational 2006 Education, bachelor 2006 Education, master 2006 Entry week, 45 - 46, 2005 Entry week, 47 - 48, 2005 Entry week, 49 - 50, 2005 Entry week, 51 - 52, 2005 Entry week, 01 - 02, 2006 Entry week, 03 - 04, 2006 Entry week, 05 - 06, 2006 Entry week, 07 - 08, 2006 Western immigrant Non-western immigrant Age 25 - 29 Age 30 - 39

-0.060 0.115 0.282 0.034 0.234 0.912 0.358 1.451 -1.150 1.544 1.683 0.802 0.493 -0.792 1.152 -0.690 -0.932 0.499 -1.833 -0.187 1.129 -0.566 0.800 0.989

0.000 0.001 0.008 0.016 0.006 9.180 0.008 0.008 0.012 0.006 0.016 0.032 0.016 0.012 0.016 0.012 0.012 0.016 0.016 0.016 0.004 0.016 0.016 0.008

-0.045 0.076 0.238 -0.046 0.228 1.067 0.294 1.342 -1.168 1.491 1.612 0.733 0.565 -0.722 1.148 -0.635 -0.896 0.522 -1.725 -0.185 0.991 -0.617 0.632 0.845

0.000 0.001 0.010 0.019 0.010 11.220 0.004 0.008 0.016 0.008 0.016 0.064 0.022 0.016 0.032 0.016 0.011 0.028 0.016 0.016 0.002 0.022 0.016 0.016

-0.032 0.033 0.250 -0.026 0.221 1.501 0.299 1.325 -1.220 1.476 1.596 0.818 0.512 -0.759 1.061 -0.647 -0.952 0.460 -1.775 -0.268 1.043 -0.519 0.600 0.813

0.001 0.001 0.002 0.008 0.004 15.300 0.004 0.008 0.008 0.004 0.008 0.008 0.016 0.008 0.008 0.008 0.002 0.008 0.008 0.004 0.002 0.016 0.004 0.004

Table continues on next page. Bold face numbers indicate statistical significance at the 5 % level.

Chapter 4

128 Table B5 continued: Men, Southern Jutland county. 2006 wages Estimate S.D.

2007 wages Estimate S.D.

2008 wages Estimate S.D.

Age 40 - 49 Age 50 + Lagged Uempl. duration, 7 - 8 weeks Lagged Uempl. duration, 9 - 16 weeks Lagged Uempl. duration, 17 - 28 weeks Lagged Uempl. duration, 29 - 52 weeks Lagged Uempl. duration, 52 + weeks Baseline hazard 2 - 3 weeks Baseline hazard 4 - 5 weeks Baseline hazard 6 - 8 weeks Baseline hazard 9 - 16 weeks Baseline hazard 17 - 30 weeks Baseline hazard 31 - 52 weeks Baseline hazard 53 + weeks νn1 νn2

0.853 -0.302 -0.331 -1.842 -0.956 0.181 -0.066 -1.564 -2.070 -1.747 -0.675 -0.889 -0.078 2.007 -3.741 -7.951

0.008 0.008 0.032 0.016 0.008 0.012 0.012 0.016 0.032 0.008 0.012 0.010 0.016 0.012 0.007 0.016

0.709 -0.431 -0.329 -1.748 -0.915 0.154 -0.095 -1.584 -2.078 -1.766 -0.709 -0.926 -0.130 1.920 -3.479 -7.569

0.016 0.008 0.032 0.032 0.012 0.012 0.016 0.024 0.056 0.032 0.014 0.014 0.016 0.016 0.004 0.016

0.630 -0.467 -0.385 -1.732 -0.941 0.133 -0.092 -1.584 -2.085 -1.789 -0.711 -0.936 -0.163 1.865 -3.481 -7.523

0.008 0.004 0.008 0.016 0.016 0.004 0.008 0.008 0.032 0.016 0.004 0.008 0.008 0.004 0.004 0.008

Wages Experience Experience squared/100 Treatment Married Occupation, top 2005 Occupation, middle 2005 Occupation, base 2005 Occupation, unempl. 2005 Education, vocational 2006 Education, bachelor 2006 Education, master 2006 Western immigrant Non-western immigrant Age 25 - 29 Age 30 - 39 Age 40 - 49 Age 50 + Log Wage 2004 Log Wage 2005 Baseline wage hazard 100 - 140 dkk. Baseline wage hazard 140 - 180 dkk. Baseline wage hazard 180 - 220 dkk. Baseline wage hazard 220 - 240 dkk. Baseline wage hazard 240 - 280 dkk. Baseline wage hazard 280 - 350 dkk. Baseline wage hazard 350 + dkk. νw1 νw2

0.030 -0.087 0.001 -0.041 -0.016 0.232 0.210 0.312 -0.160 -0.229 -0.458 0.117 0.007 -0.183 -0.408 -0.248 -0.262 -0.047 -0.103 3.458 4.437 4.595 4.286 4.301 3.891 3.726 -5.548 -5.570

0.000 0.001 0.001 0.002 0.008 0.004 0.004 0.004 0.004 0.004 0.016 0.008 0.008 0.007 0.004 0.004 0.004 0.000 0.000 0.004 0.001 0.003 0.008 0.008 0.000 0.016 0.000 0.004

0.032 -0.134 -0.106 -0.088 -0.258 0.222 0.227 0.265 -0.160 -0.356 -1.069 -0.001 0.182 0.077 -0.120 0.049 0.203 -0.055 -0.085 2.932 4.036 4.288 4.343 4.433 3.882 4.689 -5.450 -5.173

0.000 0.000 0.002 0.004 0.016 0.001 0.001 0.008 0.003 0.008 0.014 0.006 0.009 0.004 0.004 0.008 0.002 0.001 0.000 0.001 0.004 0.001 0.016 0.003 0.016 0.012 0.004 0.008

0.054 -0.163 -0.091 -0.138 -0.172 0.351 0.264 0.431 -0.210 -0.340 -0.206 0.145 0.042 0.041 -0.158 -0.004 0.131 -0.100 -0.056 2.643 3.983 4.100 4.097 4.165 3.966 4.184 -5.557 -5.378

0.000 0.000 0.002 0.002 0.004 0.002 0.001 0.001 0.002 0.004 0.004 0.002 0.004 0.002 0.002 0.002 0.001 0.000 0.000 0.002 0.000 0.002 0.002 0.004 0.002 0.004 0.000 0.008

α1 α2 α3 α4 α5 α6 α7 α8 P r(α1 ) P r(α2 ) P r(α3 ) P r(α4 ) P r(α5 ) P r(α6 ) P r(α7 ) P r(α8 )

-9.242 -4.281 -3.748 1.347 3.750 -4.248 -0.822 0.000 0.000 0.000 0.001 0.080 0.889 0.000 0.009 0.021

0.510 1.020 0.510 0.008 0.016 4.080 0.255

-7.431 -2.614 -4.598 1.349 3.728 -4.949 -3.062 0.000 0.000 0.002 0.000 0.083 0.893 0.000 0.001 0.022

0.128 0.195 0.255 0.016 0.002 0.510 0.367

-10.410 -1.026 -3.482 1.232 3.639 -5.343 -1.082 0.000 0.000 0.008 0.001 0.079 0.881 0.000 0.008 0.023

1.020 0.004 0.128 0.002 0.008 0.510 0.255

Average log likehood Individuals

-7434.00 1,150

Bold face numbers indicate statistical significance at the 5 % level.

-7344.58 1,150

-7254.15 1,150

Effects on Post-Unemployment Wages

129

Table B6: Women, Storstroem county. 2006 wages Estimate S.D.

2007 wages Estimate S.D.

2008 wages Estimate S.D.

Transition U → E Experience Experience squared/100 Treatment (U ≤ 30 weeks) Treatment (U > 30 weeks) Married Occupation, top 2005 Occupation, middle 2005 Occupation, base 2005 Occupation, unempl. 2005 Education, vocational 2006 Education, bachelor 2006 Education, master 2006 Entry week, 45 - 46, 2005 Entry week, 47 - 48, 2005 Entry week, 49 - 50, 2005 Entry week, 51 - 52, 2005 Entry week, 01 - 02, 2006 Entry week, 03 - 04, 2006 Entry week, 05 - 06, 2006 Entry week, 07 - 08, 2006 Western immigrant Non-western immigrant Age 25 - 29 Age 30 - 39 Age 40 - 49 Age 50 + Lagged Uempl. duration, 7 - 8 weeks Lagged Uempl. duration, 9 - 16 weeks Lagged Uempl. duration, 17 - 28 weeks Lagged Uempl. duration, 29 - 52 weeks Lagged Uempl. duration, 52 + weeks Baseline hazard 2 - 3 weeks Baseline hazard 4 - 5 weeks Baseline hazard 6 - 8 weeks Baseline hazard 9 - 16 weeks Baseline hazard 17 - 30 weeks Baseline hazard 31 - 52 weeks Baseline hazard 53 + weeks νe1 νe2

-0.033 0.159 0.186 -0.016 0.081 -0.132 0.281 0.136 -0.116 0.095 0.003 0.015 0.089 -0.065 -0.026 0.146 -0.076 0.009 -0.124 -0.224 0.197 -0.210 -0.033 -0.017 -0.251 -0.431 -0.366 0.152 0.039 -0.121 -0.086 0.563 0.445 0.526 0.806 0.750 0.379 0.514 -3.786 0.179

0.000 0.001 0.003 0.008 0.003 0.008 0.002 0.004 0.004 0.002 0.004 0.010 0.007 0.005 0.008 0.006 0.004 0.007 0.004 0.008 0.002 0.008 0.006 0.003 0.004 0.004 0.018 0.008 0.008 0.004 0.003 0.008 0.007 0.005 0.004 0.004 0.004 0.006 0.001 2.040

-0.033 0.162 0.187 -0.012 0.080 -0.130 0.285 0.141 -0.107 0.094 0.003 0.019 0.090 -0.063 -0.023 0.152 -0.072 0.014 -0.118 -0.220 0.229 -0.180 -0.028 -0.009 -0.241 -0.423 -0.369 0.150 0.038 -0.120 -0.088 0.575 0.459 0.540 0.822 0.764 0.393 0.529 -3.845 0.520

0.000 0.001 0.005 0.010 0.005 0.012 0.005 0.006 0.006 0.006 0.007 0.015 0.010 0.009 0.010 0.009 0.006 0.009 0.007 0.008 0.005 0.010 0.008 0.006 0.004 0.006 0.026 0.012 0.009 0.007 0.006 0.010 0.008 0.008 0.005 0.008 0.008 0.008 0.002 6.120

-0.030 0.151 0.188 -0.016 0.079 -0.130 0.287 0.142 -0.104 0.092 0.004 0.029 0.090 -0.059 -0.020 0.160 -0.068 0.018 -0.116 -0.218 0.265 -0.138 -0.029 -0.014 -0.245 -0.426 -0.377 0.152 0.035 -0.123 -0.091 0.591 0.473 0.552 0.831 0.779 0.406 0.543 -3.904 2.227

0.000 0.000 0.001 0.004 0.001 0.008 0.000 0.002 0.004 0.002 0.002 0.008 0.004 0.004 0.004 0.004 0.002 0.004 0.002 0.004 0.001 0.004 0.002 0.002 0.002 0.002 0.008 0.002 0.004 0.004 0.002 0.004 0.004 0.004 0.001 0.001 0.004 0.004 0.001 22.440

Transition U → N Experience Experience squared/100 Treatment (U ≤ 30 weeks) Treatment (U > 30 weeks) Married Occupation, top 2005 Occupation, middle 2005 Occupation, base 2005 Occupation, unempl. 2005 Education, vocational 2006 Education, bachelor 2006 Education, master 2006 Entry week, 45 - 46, 2005 Entry week, 47 - 48, 2005 Entry week, 49 - 50, 2005 Entry week, 51 - 52, 2005 Entry week, 01 - 02, 2006 Entry week, 03 - 04, 2006 Entry week, 05 - 06, 2006 Entry week, 07 - 08, 2006 Western immigrant Non-western immigrant Age 25 - 29 Age 30 - 39

0.055 -0.327 -0.091 -0.421 -0.211 -0.018 -0.406 -0.105 -0.730 0.199 0.262 0.232 -0.003 -0.312 -0.116 0.790 -0.439 -0.402 -0.780 -0.002 0.518 0.475 -0.340 -0.660

0.000 0.002 0.008 0.012 0.004 0.032 0.006 0.010 0.010 0.007 0.012 0.032 0.016 0.016 0.012 0.016 0.009 0.012 0.008 0.016 0.005 0.016 0.010 0.007

0.063 -0.354 -0.089 -0.420 -0.200 -0.038 -0.423 -0.118 -0.740 0.198 0.267 0.226 -0.018 -0.308 -0.109 0.778 -0.441 -0.401 -0.787 -0.006 0.485 0.459 -0.368 -0.696

0.001 0.003 0.010 0.015 0.009 0.040 0.009 0.016 0.014 0.009 0.016 0.056 0.020 0.020 0.020 0.026 0.014 0.016 0.015 0.024 0.007 0.024 0.015 0.014

0.077 -0.399 -0.082 -0.413 -0.196 -0.066 -0.445 -0.133 -0.733 0.193 0.274 0.241 -0.031 -0.282 -0.090 0.785 -0.425 -0.381 -0.776 0.008 0.451 0.447 -0.392 -0.736

0.000 0.002 0.004 0.008 0.004 0.016 0.004 0.008 0.008 0.004 0.008 0.016 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.004 0.008 0.004 0.004

Table continues on next page. Bold face numbers indicate statistical significance at the 5 % level.

Chapter 4

130 Table B6 continued: Women, Storstroem county. 2006 wages Estimate S.D.

2007 wages Estimate S.D.

2008 wages Estimate S.D.

Age 40 - 49 Age 50 + Lagged Uempl. duration, 7 - 8 weeks Lagged Uempl. duration, 9 - 16 weeks Lagged Uempl. duration, 17 - 28 weeks Lagged Uempl. duration, 29 - 52 weeks Lagged Uempl. duration, 52 + weeks Baseline hazard 2 - 3 weeks Baseline hazard 4 - 5 weeks Baseline hazard 6 - 8 weeks Baseline hazard 9 - 16 weeks Baseline hazard 17 - 30 weeks Baseline hazard 31 - 52 weeks Baseline hazard 53 + weeks νn1 νn2

-0.373 -0.914 -0.329 0.563 -1.058 0.306 -0.086 -1.827 -1.537 -1.272 -0.785 -0.813 -0.180 -0.201 -0.636 -1.599

0.012 0.008 4.080 0.016 0.032 0.016 0.008 0.026 0.016 0.016 0.008 0.009 0.010 0.016 8.160 0.004

-0.429 -0.972 0.377 0.558 -1.050 0.309 -0.084 -1.839 -1.540 -1.276 -0.790 -0.818 -0.184 -0.197 0.781 -1.561

0.013 0.012 4.080 0.028 0.042 0.024 0.011 0.030 0.032 0.020 0.012 0.012 0.012 0.022 8.160 0.005

-0.492 -1.031 -0.444 0.557 -1.029 0.313 -0.085 -1.841 -1.541 -1.281 -0.791 -0.815 -0.175 -0.192 -1.141 -1.560

0.008 0.008 6.120 0.008 0.016 0.008 0.004 0.016 0.016 0.008 0.004 0.008 0.002 0.008 14.280 0.002

Wages Experience Experience squared/100 Treatment Married Occupation, top 2005 Occupation, middle 2005 Occupation, base 2005 Occupation, unempl. 2005 Education, vocational 2006 Education, bachelor 2006 Education, master 2006 Western immigrant Non-western immigrant Age 25 - 29 Age 30 - 39 Age 40 - 49 Age 50 + Log Wage 2004 Log Wage 2005 Baseline wage hazard 100 - 140 dkk. Baseline wage hazard 140 - 180 dkk. Baseline wage hazard 180 - 220 dkk. Baseline wage hazard 220 - 240 dkk. Baseline wage hazard 240 - 280 dkk. Baseline wage hazard 280 - 350 dkk. Baseline wage hazard 350 + dkk. νw1 νw2

0.004 -0.005 0.116 0.126 -0.297 0.148 0.195 0.493 -0.095 -0.258 -0.524 -0.084 -0.093 -0.145 -0.099 -0.161 -0.242 -0.066 -0.042 2.538 3.290 3.277 3.264 2.492 2.563 2.880 -4.494 -3.909

0.000 0.001 0.003 0.002 0.008 0.002 0.004 0.004 0.002 0.005 0.014 0.014 0.008 0.005 0.004 0.005 0.004 0.000 0.001 0.003 0.004 0.006 0.008 0.014 0.012 0.012 0.002 2.550

0.004 -0.041 -0.038 0.051 -0.431 0.132 0.188 0.277 -0.064 -0.338 -0.441 -0.126 0.019 -0.050 -0.221 -0.144 -0.155 -0.012 -0.044 2.736 3.366 3.386 3.765 3.124 2.784 3.802 -4.671 -4.621

0.000 0.001 0.004 0.003 0.012 0.004 0.006 0.008 0.004 0.008 0.016 0.018 0.011 0.007 0.004 0.005 0.005 0.001 0.001 0.004 0.004 0.009 0.016 0.018 0.024 0.020 0.003 10.200

0.017 -0.086 0.020 0.047 -0.201 0.229 0.142 0.247 -0.214 -0.425 -0.696 -0.301 0.051 0.099 -0.105 -0.132 0.106 -0.013 -0.033 2.778 3.596 3.597 3.629 3.702 3.507 3.643 -5.068 -4.733

0.000 0.001 0.004 0.002 0.004 0.002 0.002 0.004 0.001 0.001 0.004 0.008 0.004 0.004 0.002 0.001 0.002 0.001 0.000 0.000 0.001 0.001 0.008 0.004 0.004 0.016 0.001 2.040

α1 α2 α3 α4 α5 α6 α7 α8 P r(α1 ) P r(α2 ) P r(α3 ) P r(α4 ) P r(α5 ) P r(α6 ) P r(α7 ) P r(α8 )

-1.711 -1.757 14.576 1.370 -0.310 -3.386 -3.002 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000

3.060 3.060 1.020 2.678 1.785 4.590 4.335

-1.765 -2.189 14.654 1.467 -0.864 -2.683 -4.331 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000

3.443 6.598 1.913 7.841 2.805 4.686 6.534

-2.446 -0.969 14.856 1.074 -0.029 -2.553 -3.878 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000

4.080 2.040 0.510 3.060 2.040 4.080 5.100

Average log likehood Individuals

-6410.41 936

Bold face numbers indicate statistical significance at the 5 % level.

-6262.69 936

-6142.44 936

Effects on Post-Unemployment Wages

131

Table B7: Women, Southern Jutland county. 2006 wages Estimate S.D.

2007 wages Estimate S.D.

2008 wages Estimate S.D.

Transition U → E Experience Experience squared/100 Treatment (U ≤ 30 weeks) Treatment (U > 30 weeks) Married Occupation, top 2005 Occupation, middle 2005 Occupation, base 2005 Occupation, unempl. 2005 Education, vocational 2006 Education, bachelor 2006 Education, master 2006 Entry week, 45 - 46, 2005 Entry week, 47 - 48, 2005 Entry week, 49 - 50, 2005 Entry week, 51 - 52, 2005 Entry week, 01 - 02, 2006 Entry week, 03 - 04, 2006 Entry week, 05 - 06, 2006 Entry week, 07 - 08, 2006 Western immigrant Non-western immigrant Age 25 - 29 Age 30 - 39 Age 40 - 49 Age 50 + Lagged Uempl. duration, 7 - 8 weeks Lagged Uempl. duration, 9 - 16 weeks Lagged Uempl. duration, 17 - 28 weeks Lagged Uempl. duration, 29 - 52 weeks Lagged Uempl. duration, 52 + weeks Baseline hazard 2 - 3 weeks Baseline hazard 4 - 5 weeks Baseline hazard 6 - 8 weeks Baseline hazard 9 - 16 weeks Baseline hazard 17 - 30 weeks Baseline hazard 31 - 52 weeks Baseline hazard 53 + weeks νe1 νe2

-0.019 0.128 0.321 -0.064 -0.041 0.056 0.237 0.340 -0.093 -0.075 0.170 -0.049 -0.204 -0.205 -0.159 0.222 -0.239 -0.181 -0.213 -0.098 0.243 0.008 -0.381 -0.396 -0.521 -0.714 0.036 0.189 -0.003 0.218 -0.018 -0.084 0.112 -0.035 0.477 0.416 0.293 0.371 -3.255 -3.015

0.000 0.001 0.004 0.009 0.003 0.014 0.004 0.003 0.008 0.003 0.007 0.020 0.003 0.008 0.010 0.008 0.004 0.008 0.007 0.008 0.002 0.017 0.002 0.004 0.004 0.004 0.028 0.008 0.011 0.010 0.005 0.008 0.004 0.004 0.005 0.008 0.010 0.004 0.001 0.510

-0.009 0.093 0.312 -0.066 -0.042 0.015 0.184 0.287 -0.163 -0.083 0.160 -0.063 -0.224 -0.228 -0.186 0.198 -0.263 -0.220 -0.243 -0.143 0.164 -0.049 -0.418 -0.452 -0.582 -0.773 0.022 0.188 -0.015 0.214 -0.019 -0.161 0.034 -0.114 0.401 0.339 0.214 0.293 -3.024 -3.163

0.000 0.000 0.002 0.008 0.002 0.008 0.002 0.001 0.004 0.002 0.004 0.014 0.008 0.004 0.005 0.007 0.004 0.008 0.004 0.008 0.002 0.008 0.004 0.004 0.001 0.004 0.012 0.006 0.006 0.004 0.004 0.008 0.008 0.005 0.002 0.004 0.008 0.008 0.001 0.510

-0.006 0.085 0.313 -0.067 -0.043 0.007 0.172 0.274 -0.179 -0.085 0.157 -0.066 -0.229 -0.234 -0.194 0.190 -0.270 -0.229 -0.251 -0.154 0.142 -0.068 -0.426 -0.462 -0.594 -0.783 0.023 0.187 -0.013 0.212 -0.020 -0.183 0.012 -0.136 0.380 0.318 0.190 0.269 -2.967 -0.999

0.000 0.001 0.004 0.007 0.003 0.008 0.003 0.003 0.006 0.003 0.006 0.016 0.007 0.006 0.007 0.008 0.004 0.008 0.004 0.009 0.002 0.011 0.006 0.004 0.004 0.004 0.020 0.008 0.008 0.006 0.005 0.008 0.008 0.006 0.003 0.004 0.006 0.008 0.004 1.020

Transition U → N Experience Experience squared/100 Treatment (U ≤ 30 weeks) Treatment (U > 30 weeks) Married Occupation, top 2005 Occupation, middle 2005 Occupation, base 2005 Occupation, unempl. 2005 Education, vocational 2006 Education, bachelor 2006 Education, master 2006 Entry week, 45 - 46, 2005 Entry week, 47 - 48, 2005 Entry week, 49 - 50, 2005 Entry week, 51 - 52, 2005 Entry week, 01 - 02, 2006 Entry week, 03 - 04, 2006 Entry week, 05 - 06, 2006 Entry week, 07 - 08, 2006 Western immigrant Non-western immigrant Age 25 - 29 Age 30 - 39

0.047 -0.196 0.230 0.040 -0.080 0.376 -0.010 -0.414 -0.272 -0.022 -0.077 -0.079 -0.591 -0.364 -0.855 -0.295 -0.243 1.539 -0.295 -0.336 0.506 0.385 0.196 0.315

0.000 0.002 0.009 0.016 0.008 0.044 0.008 0.013 0.016 0.008 0.014 0.044 0.008 0.021 0.016 0.021 0.010 0.020 0.017 0.016 0.008 0.032 0.014 0.008

0.059 -0.237 0.220 0.036 -0.088 0.381 -0.038 -0.448 -0.300 -0.022 -0.071 -0.049 -0.591 -0.375 -0.869 -0.315 -0.253 1.525 -0.312 -0.341 0.441 0.364 0.152 0.254

0.001 0.002 0.004 0.008 0.004 0.016 0.004 0.006 0.005 0.004 0.006 0.012 0.008 0.008 0.011 0.016 0.002 0.012 0.006 0.012 0.004 0.010 0.004 0.005

0.064 -0.259 0.210 0.028 -0.093 0.388 -0.043 -0.457 -0.312 -0.021 -0.070 -0.050 -0.595 -0.389 -0.885 -0.336 -0.269 1.505 -0.329 -0.353 0.406 0.346 0.136 0.229

0.001 0.002 0.008 0.012 0.008 0.032 0.008 0.015 0.010 0.008 0.014 0.036 0.016 0.016 0.018 0.022 0.010 0.018 0.014 0.024 0.006 0.022 0.009 0.010

Table continues on next page. Bold face numbers indicate statistical significance at the 5 % level.

Chapter 4

132 Table B7 continued: Women, Southern Jutland county. 2006 wages Estimate S.D.

2007 wages Estimate S.D.

2008 wages Estimate S.D.

Age 40 - 49 Age 50 + Lagged Uempl. duration, 7 - 8 weeks Lagged Uempl. duration, 9 - 16 weeks Lagged Uempl. duration, 17 - 28 weeks Lagged Uempl. duration, 29 - 52 weeks Lagged Uempl. duration, 52 + weeks Baseline hazard 2 - 3 weeks Baseline hazard 4 - 5 weeks Baseline hazard 6 - 8 weeks Baseline hazard 9 - 16 weeks Baseline hazard 17 - 30 weeks Baseline hazard 31 - 52 weeks Baseline hazard 53 + weeks νn1 νn2

0.335 -0.836 -0.508 -0.500 0.378 -0.556 0.105 -1.704 -1.605 -0.833 -0.635 -0.617 -0.519 0.177 -2.884 -2.857

0.018 0.010 0.054 0.032 0.016 0.022 0.013 0.024 0.032 0.015 0.013 0.013 0.017 0.008 0.446 0.004

0.267 -0.872 -0.527 -0.520 0.386 -0.549 0.109 -1.728 -1.631 -0.849 -0.654 -0.637 -0.544 0.159 -0.670 -2.743

0.008 0.005 0.020 0.016 0.016 0.008 0.006 0.016 0.016 0.008 0.008 0.006 0.006 0.002 0.510 0.008

0.240 -0.886 -0.526 -0.518 0.388 -0.551 0.106 -1.742 -1.645 -0.865 -0.669 -0.652 -0.559 0.145 -2.516 -2.670

0.015 0.011 0.048 0.026 0.022 0.016 0.011 0.028 0.024 0.016 0.008 0.008 0.014 0.011 1.403 0.007

Wages Experience Experience squared/100 Treatment Married Occupation, top 2005 Occupation, middle 2005 Occupation, base 2005 Occupation, unempl. 2005 Education, vocational 2006 Education, bachelor 2006 Education, master 2006 Western immigrant Non-western immigrant Age 25 - 29 Age 30 - 39 Age 40 - 49 Age 50 + Log Wage 2004 Log Wage 2005 Baseline wage hazard 100 - 140 dkk. Baseline wage hazard 140 - 180 dkk. Baseline wage hazard 180 - 220 dkk. Baseline wage hazard 220 - 240 dkk. Baseline wage hazard 240 - 280 dkk. Baseline wage hazard 280 - 350 dkk. Baseline wage hazard 350 + dkk. νw1 νw2

0.015 -0.085 -0.013 0.058 -0.170 0.164 0.125 0.341 -0.060 -0.418 -0.374 0.115 -0.127 -0.214 -0.120 -0.163 -0.370 -0.004 -0.043 2.760 3.381 3.189 2.959 2.848 2.392 2.491 -4.676 -4.710

0.000 0.001 0.004 0.004 0.016 0.005 0.004 0.004 0.004 0.010 0.016 0.008 0.014 0.008 0.001 0.002 0.007 0.000 0.001 0.001 0.001 0.011 0.018 0.016 0.016 0.012 0.255 0.004

0.007 -0.081 0.000 0.102 -0.252 0.144 0.117 0.219 -0.120 -0.323 -0.535 0.159 -0.351 0.087 0.116 0.187 -0.073 -0.014 -0.050 2.832 3.471 3.494 3.326 3.217 2.508 3.510 -4.640 -4.901

0.000 0.001 0.002 0.001 0.008 0.002 0.004 0.004 0.002 0.004 0.010 0.004 0.005 0.005 0.004 0.003 0.002 0.000 0.000 0.008 0.004 0.003 0.016 0.016 0.012 0.015 0.510 0.004

0.018 -0.134 0.083 0.143 -0.506 -0.035 -0.038 -0.062 -0.052 -0.350 -0.131 0.275 -0.242 -0.047 -0.017 0.004 -0.169 0.020 0.007 3.115 3.733 3.858 3.509 3.034 3.163 3.761 -4.602 -5.517

0.000 0.001 0.003 0.003 0.016 0.003 0.002 0.006 0.003 0.005 0.018 0.010 0.011 0.005 0.004 0.006 0.005 0.000 0.001 0.001 0.008 0.009 0.013 0.016 0.014 0.016 1.020 0.001

α1 α2 α3 α4 α5 α6 α7 α8 P r(α1 ) P r(α2 ) P r(α3 ) P r(α4 ) P r(α5 ) P r(α6 ) P r(α7 ) P r(α8 )

-4.483 0.195 -0.909 11.187 3.301 -0.414 -3.111 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000

2.725 2.040 3.060 1.403 0.064 1.020 2.040

-4.239 -0.377 -0.096 12.076 1.041 -0.171 -2.222 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000

2.040 1.020 1.020 0.510 0.510 1.020 2.486

-3.069 3.463 -2.598 13.202 0.515 0.093 0.462 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000

3.315 4.399 4.208 0.462 0.829 1.785 1.020

Average log likehood Individuals

-6633.78 974

Bold face numbers indicate statistical significance at the 5 % level.

-6539.92 974

-6418.88 974

Effects on Post-Unemployment Wages

133