An Empirical Model of Life-Cycle Earnings and Mobility Dynamics Florian Ho mann Vancouver School of Economics University of British Columbia

Version: April 2017 PRELIMINARY AND INCOMPLETE VERSION

Abstract Estimates of Dynamic Discrete Choice (DDC) Models of life-cycle career dynamics with human capital accumulation, such as those in Keane and Wolpin's seminal study, suggest that up to 90 percent of earnings inequality is driven by heterogeneity in unobserved pre-labor market skills. This is in sharp contrast with ndings from statistical earnings processes which associate only about half of these inequalities to pre-labor market skills. Explaining the discrepancy between these ndings is important for gaining a deeper understanding of the sources of life-cycle inequality since DDC models feature multi-dimensional skills, endogenize the part of earnings risk that is associated with worker mobility, and are attractive for counterfactual analysis. In this study I argue that this discrepancy can be fully accounted for by speci cation error in DDC-models without persistent earnings risk. In particular, common speci cations of DDC-models only allow for a permanent and a fully transitory component in the earnings equation, and a large role of pre-labor market skills becomes hard-wired into the model. Guided by an extensive descriptive analysis of earnings- and mobility dynamics of workers, I enrich the Keane-Wolpin framework to reach a model that is explicitly built for studying the sources of labor market inequalities. The primary additions are a frictional search process for better matches between employers and rms that ties worker mobility to earnings dynamics, and an earnings process with persistence. I develop a computationally feasible estimation procedure that calibrates a number of parameters, pre-estimates skill prices using a \ at-spot" method and returns to tenure using an IV-strategy, and structurally estimates the remaining parameters. Expected value functions are shown to be continuously di erentiable, which helps using modern Sparse-Grid approximation methods that are uniformly convergent and have near-optimal rates of convergence. The model is estimated on administrative worker-level data from Germany that follow workers from labor market entry until up to 35 years into their career. Although I use di erent data like Keane-Wolpin, I reach at an almost identical estimated role of pre-labor market skills for life-cycle earnings inequality when estimating their speci cation. In particular, 91 percent of the variation of life-cycle earnings is explained by type heterogeneity. However, once I introduce persistent shocks to skills, match heterogeneity and search, my conclusions change dramatically. The estimated role of pre-labor market skills decreases from 91 to only 41 percent. Furthermore, while the more restrictive speci cation cannot match the covariance structure of earnings, my preferred model is successful in doing so. Since I explicitly model and parameterize the income-tax- and unemployment insurance systems, my framework is well suited for studying how and whether results from counterfactual experiments depend on model misspeci cation.

This study uses the weakly anonymous IAB Employment Sample. Data access was provided via on-site use at the Research Data Centre (FDZ) of the German Federal Employment Agency (BA) at the Institute for Employment Research (IAB) and remote data access. I thank Philip Oreopoulos, Shouyong Shi and Victor Aguirregabiria for their help. I also thank Gueorgui Kambourov, Thomas Lemieux, Jean-Marc Robin, Aloysius Siow and participants of various seminars and conferences. Benedikt Hartmann, Daniela Hochfellner, Peter Jacobebbinghaus and other sta members at the FDZ-IAB provided invaluable help for setting up the data. The usual disclaimer applies.

1

1

Introduction

Few questions have inspired as much research across academic disciplines as the question of what the sources of lifecycle inquality in individual labor market outcomes are.1 It remains an open and controversial issue whether such inequalities are predominantly driven by di¤erences acquired prior to labor market entry or by shocks accumulated subsequently. Economists have two main approaches for answering this question. One approach, innovated by early studies of the covariance structure of earnings, relies explicitly on panel data to estimate earnings processes that decompose earnings variation within and between workers into permanent, persistent and transitory components.2 Some recent work has integrated such processes into structural models of job search or human capital accumulation.3 The second approach, formulated in some generality by Acemoglu and Autor (2011), formulates Roy-type models of the cross-sectional occupational wage- and employment structure and explores whether it can rationalize its complex long-run trends. There is very little work that combines the most promising features of these two approaches for developing quantitative models of the joint dynamics of career choices and earnings for the study of life-cycle inequality in labor market outcomes. This is an important omission, for at least two reasons. First, modeling career choices, that is, the allocation of workers across broad occupational groups that are de…ned by their skill requirements, may help uncover the multidimensionality of the skill structure. This in turn may explain why individuals who are permanently stuck in jobs that experience little to no earnings growth coexist with workers who move quickly through the ranks. In particular, if di¤erent occupational groups require a di¤erent set of skills, then dispersion in aggregate skill price growth across careers may translate into persistent inequality among workers who entered the labor market with similar earnings but in di¤erent careers. Moreover, gains to occupational- and job mobility may be substantial only for a subset of workers with a particular skill endowment. This source of earnings inequality will be absent from models with single-dimensional abilities. Second, the dynamics of career choices and their comovement with earnings are informative about the structure of unobserved skills and the sources of risk that individuals are subjected to. Empirically, these dynamics turn out to be rich. For example, in the data I will be using in this study – a German administrative panel data set on labor market outcomes that tracks individuals for up to 35 years –there is a signi…cant net reallocation of workers across careers over the life-cycle. Following Acemoglu and Autor (2011) in grouping 3-digit occupations into four aggregate occupation groups that have distinct skill requirements and referring to them as "careers", Figure 1 plots age-pro…les of career-speci…c employment shares for male workers between the ages 25 and 50, cleaned from time-e¤ects that control for secular changes in the occupational employment structure. This reveals a strikingly strong reallocation of workers over the life-cycle into Managerial, Professional and Technical occupations, with 1 Works that document the interdisciplinary nature of this topic are for example Heckman, Stixrud and Urzua (2006) and the book by Asbury and Plomin (2013). 2 Seminal studies are Lillard and Weiss (1979), Hause (1980) and MaCurdy (1982). More recent examples are Guvenen (2009), Hryshko (2012) and Ho¤mann (2016). Mo¢ tt and Gottschalk (2002), Baker and Solon (2003) and Blundell, Pistaferri and Preston (2009) are examples of studies that estimate the evolution of di¤erent variance components over time. 3 Kaplan (212) and Heathcote, Storesletten and Violante (2014) formulate and estimate quantitative general equilibrium models with heterogeneous agents and partial insurance in which individuals are subjected to shocks of di¤erent persistences. Huggett, Ventura and Yaron (2011) calibrate a Ben-Porath model of human capital accumulation with an earnings process to quantify the sources of life-cycle inequality. Cahuc, Postel-Vinay and Robin (2006) and Bagger, Fontain, Postel-Vinay and Robin (2014) structurall estimate equilibrium search models and use it to study the importance of frictions in generating earnings inequality. Low, Meghir and Pistaferri (2010) integrate an earnings process into a single-agent model of …rm mobility and consumption choices.

2

an employment share that doubles from initially ten percent to twenty percent of the employed and that draws workers from all other occupation groups except low-skill service occupations. This net reallocation comes with complex earnings dynamics. For example, earnings growth between the ages of 25 and 50 is signi…cantly related to the career choice at age 50, as documented in table 1. In particular, …fty years old managers, professionals or technicians experience on average between 20 and 30 percentage points higher life-cycle earnings growth than operatives, production workers or low-skill service workers of the same age. In addition, there is a signi…cant wage growth premium from upgrading into managerial occupations and, somewhat surprising, a signi…cant penalty for horizonal or downward mobility, and these results hold no matter if one controls for cohort e¤ects or not. Importantly, these averages hide signi…cant heterogeneity in wage growth on the individual level and point towards a substantial amount of risk, as I will show in an extensive descriptive analysis. Modeling the joint dynamics of individual earnings and mobility choices is therefore a promising approach for deepening our understanding of the sources of life-cycle inequality. In this paper I formulate and estimate a structural model of life-cycle earnings and career dynamics that is explicitly built for carrying out this task. The model structure enriches a dynamic Roy-model of career mobility with endogenous human capital accumulation as considered in Keane and Wolpin’s (1997) seminal study of career dynamics of young men. The model in KW97, as I refer to Keane-Wolpin (1997) for the rest of this paper, is the appropriate empirical framework to build on since it is one of the very few studies that bridges the gap between the literature on earnings dynamics and the literature on the occupational earnings- and employment structure. Its major …nding is striking: Over 90 percent of inequality in life-cycle earnings between workers in the NLSY can be attributed to unobserved pre-labor market skills. This result has motivated many studies in the literature on the determinants of skill heterogeneity among adolescents.4 At the same time, it remains controversial since it is seemingly in contradiction with estimates of statistical earnings processes and from structural estimates of equilibrium search models, both of which tend to associate between 40 and 60 percent of life-cycle inequality with ex-ante heterogeneity.5 Furthermore, there is mounting evidence from quasi-experimental studies that plausibly exogenous career disruptions, such as …rm closures or aggregate labor market conditions close to labor market entry, have substantial and persistent e¤ects on individual labor market dynamics.6 The key questions addressed in this paper is why di¤erent approaches to modeling individual labor market dynamics produce such dramatically di¤erent conclusions, whether there is scope for reconciliation and whether it matters for counterfactual analysis. Do models with one-dimensional skills that abstract from the endogeneity of career choices, whether purely statistical or nested within a structural model of human capital accumulation or search, miss a crucial dimension of ex-ante heterogeneity? Or, conversely, does the KW97 framework tend to overstate the role or pre-labor market skills because of model misspeci…cation? As I demonstrate empirically in this 4 Examples of studies in this literature that use this result explicitly as motivation are Todd and Wolpin (2007), Raquel (2008), Raquel and Keane (2010), Erosa, Koreshkova and Restuccia (2010), Fiorini (2010), and Caucutt and Lochner (2012). 5 This point is made forcefully in Storesletten, Telmer and Yaron (2004). Many of the studies cited in footnotes 2 and 3 reach similar conclusions. 6 The persistent e¤ects of job loss on earnings due to mass layo¤s or …rm closures have been documented for various countries, for example in Jacobson, LaLonde and Sullivan (1993) and Davis and von Wachter (2011) for the United States, and in von Wachter and Bender (2006) for Germany. There is also a sizeable literature studying the e¤ect of entering the labor market during a recession. Again, the e¤ect on earnings is persistent and negative and has been shown for various countries. See for example Kahn (2010) for the US and Oreopoulos, von Wachter and Heisz (2012) for Canada and von Wachter and Bender (2008) for Germany.

3

study, the latter interpretation is likely to be more appropriate. Computational constraints and data limitations have forced KW97 and the majority of subsequent work estimating structural life-cycle models of post-graduation career dynamics to abstract from many important determinants of earnings and mobility dynamics, such as persistent shocks to skills, match heterogeneity and search for better job opportunities. Potentially, this leads to an upward bias in the estimated role of pre-labor market skills for career development because di¤erences in post-graduation outcomes that are due to factors omitted from their analysis may be, at least to some extent, interpreted as outcomes from di¤erences in pre-labor market skills. More speci…cally, the earnings structure in KW97 allows for two variance components, a permanent multidimensional "pre-market skill endowment" and transitory shocks with zero persistence. While this delivers computational tractability, a large role of pre-market skills becomes hard-wired into the model since transitory shocks are largely averaged out over the life-cycle and since career choices are mainly determined by the initial skill endowment.7 Empirically, this structure generates dynamics in the second moments of earnings that is at odds with the robust empirical …nding that earnings early and late in the career are relatively weakly correlated once one conditions on observable measures of skills. For example, the correlation of residual earnings at age 25 with residual earnings one year later in my data is :842, but it falls below :3 at age 50. Furthermore, the decline is stricly monotonic and smooth, as shown in Figure 2.8 Lag-pro…les of this shape are inconsistent with an earnings structure that only involves permanent and transitory components. At the same time, they are the prime empirical variation for identifying the parameters of the earnings process and provide moments of …rst-order importance to be matched by any model that is used for quantifying the sources of life-cycle earnings inequality. Motivated by an extensive descriptive analysis of earnings- and career dynamics I thus add two major components to KW97. First, workers search for better matches across …rms and careers, thereby introducing an earnings process that links dynamics in residual earnings to job- and career mobility. As a consequence, two workers who enter the labor market with identical sets of observable and unobservable skills and initially work in the same occupation may experience very di¤erent career outcomes because only one of them is ”lucky”and …nds a particularly good careeror …rm match before human capital considerations permanently tie individuals to a particular career. Consequently, the mobile worker experiences a discrete and permanent jump of wages at the time of a job change that, when not controlled for in the structural model, will be interpreted as di¤erences in comparative advantages established prior to labor market entry. Topel and Ward’s (1992) …nding that one third of wage growth in US administrative data is explained by job mobility suggests this bias may be substantial. Second, to match the covariance structure of earnings, which displays complex dynamics even among workers who have settled into stable careers, I add a process with persistence to the unobserved component. These two additions require some important modi…cations to the overall model structure so that each model component is logically coherent with each other. Most importantly, job mobility is modeled as a frictional search process for better matches in which workers draw outside-o¤ers only periodically. Switching employer or career thereby adds an earnings component that persistently alters the relative attractiveness of a career to a worker. It therefore can be interpreted as a shock to a worker’s comparative 7 If skills and shocks were unidimensional, transitory shocks would not contribute to inequaliy in life-cycle earnings, as long as the life-cycle is su¢ ciently long. This is not true in KW97 since multidimensional transitory shocks a¤ect career choices and thus the stock of human capital. Hence, transitory shocks have a non-negligible role on life-cycle earnings. 8 Similar properties of lag-pro…les have been documented for data from the US, Canada and the UK. See for example Haider (2001) and Guvenen (2009) for the former and Baker and Solon (2003) for the latter.

4

advantage that is partially determined ex-ante. It is therefore natural to abandon the assumption of discrete unobserved heterogeneity that is popular in the Dynamic Discrete Choice literature and to work with continuous unobserved skill components instead. Structural estimation of a dynamic discrete choice model ultimately faces two challenges. First, the estimation criterion, whether it is a likelihood or a moment-based criterion, does not have an analytical representation. Furthermore, simulating the model requires solving a high-dimensional dynamic program problem repeatedly. The computational burden is therefore formidable. Second, the estimation necessarily requires worker-level panel data that follow individuals over a substantial part of their labor market career and that record earnings and choices. I address the …rst issue as follows. On the one hand, I explore the possibility of calibrating and pre-estimating a number of structural parameters to decrease the parameter space of the structural estimation. Most importantly, under the assumptions of the structural model, occupation-speci…c skill prices can be estimated using a "‡at-spot method" innovated by Heckman, Lochner and Taber (1998), and the returns to occupational tenure can be estimated using the Instrumental Variable strategy in Altonji and Shakotko (1987) and Altonji and Williams (2005). On the other hand, estimating the remaining structural parameters by fully solving the model is unavoidable. Recent advances in econometrics that propose methods which avoid solving the dynamic program during estimation, commonly referred to as CCP-estimation innovated by Hotz and Miller (1994), are not applicable because the frictional search process breaks the invertibility of a map between value functions and conditional choice probabilities. Instead I rely on modern computational methods that approximate high-dimensional value functions using sparse-grid interpolation. These methods have recently been proven to have "near optimal" rates of convergence as long as the function to be approximated is at least …rst-order di¤erentiable.9 This condition is satis…ed in my computational approach to solving the dynamic program, as long as one approximates expected value functions. To address the second issue I rely on high-quality administrative data from Germany which come from social security records and follow workers from labor market entry until up to 35 years into their career, no matter whether they are employed or unemployed. Furthermore, in contrast to North-American administrative data they record 3-digit occupations using a time-consistent coding. Hence, they are ideally suited for the purpose of this study.

I begin my empirical analysis with estimating a version of KW97 that is nested within my full structural model. Although I use di¤erent data, I reach at an almost identical estimated role of pre-labor market skills for life-cycle earnings inequality. In particular, 91 percent of the variation of life-cycle earnings is explained by type heterogeneity, compared to 90 percent as found in Keane and Wolpin for individuals in the NLSY. However, once I introduce permanent shocks to skills, match heterogeneity and search, my conclusions change dramatically. The estimated role of pre-labor market skills decreases from 91 to only 41 percent. Furthermore, using counterfactual exercises I …nd that excluding match heterogeneity from the full model decreases the standard deviation of life-cycle earnings by 27 percent. Thus, a large fraction of life-cycle income inequality usually interpreted as the outcome of type heterogeneity is in fact rooted in match heterogeneity among workers of the same skill type. Employees who are initially ”endowed” with the same abilities and enter the labor market with identical observable and unobservable credentials experience very di¤erent career trajectories because they have di¤erent outcomes to job search and are 9 See

for example Bungartz and Griebel (2004).

5

hit by di¤erent permanent shocks. When not controlling for these systematic earnings changes that take place over a career, they will be included in the estimates of skills that are initially carried into the labor market. Importantly, my model …ts the correlation structure between earnings early and later in a life-cycle, as depicted in …gure 2, almost perfectly, while the more restrictive KW97 does not. It is in this sense that my model is explicitly built for quantifying the source of life-cycle inequality. Notice however that I parameterize the detailes of the income tax system and the unemployment bene…ts system. Hence, my quantitative framework is useful for counterfactual policy analysis as well.

2

Data and Sample Construction

In this section I give an overview of the data base used in this study, describe in some detail the sample restrictions I impose, and de…ne "careers" in terms of broad occupational groups. I will use two di¤erent samples in the empirical analysis which I will refer to respectively as "estimation sample" and "older-worker sample", each serving a di¤erent purpose. The estimation sample will be the main sample of interest and follows individuals from the time of labor market entry. This is the sample used for the descriptive analysis of life-cycle earnings- and career dynamics and for the structural estimation. On the other hand, the older-worker sample is used to calibrate a number of parameters without solving the model explicitly, following the "‡at spot" identi…cation strategy in Heckman, Lochner and Taber (1998). The primary idea of using this sample for pre-estimation is that older workers have sorted into their best career- and …rm matches, make choices with little considerations for human-capital investments, and are secured from layo¤s relative to younger workers, with the consequence that earnings variation re‡ects exogenous forces and can be used to identify some structural parameters without estimation of the full model. Consistent with this idea I will determine age-cuto¤s for this sample by explicitly relying on empirical transition rates between jobs, employment, unemployment and non-employment.

2.1 2.1.1

Data and Samples The German Administrative Social Security Data (SIAB)

I use the con…dential version of a 2%-extract from German administrative social security records for the years 1975 to 2010, called SIAB and administered by the Institute for Employment Research (IAB). These data are representative of the population of workers who are subject to compulsory social insurance contributions or who collect unemployment bene…ts, amounting to approximately 80% of the German workforce. Once an individual is drawn, it is followed for the rest of the sample period. Labor-force participants not covered by these data are the self-employed and civil servants. These exclusion criteria are potentially problematic since selection into government jobs or self-employment is endogenous. However, since I will construct a sample that follows workers from a young age I will lose only those who enter a public-sector job or self-employment directly after high school. Workers making this transition later in their life will be observed for some time before exiting the sample. I will thus model endogenous sample attrition explicitly in my structural framework.

6

A number of advantageous features of these data compared to publicly available panel data or administrative panel data from other countries are worth discussing in some detail. First, the data are spell-based and record each spell with exact start- and end dates. Earnings and other job-speci…c characteristics of any employment spell are submitted by …rms, under the threat of severe legal sanctions for misreporting. Reported earnings are gross earnings after the deduction of the employer’s social security contributions. The German Employment Agency combines these data with its own information on unemployment bene…ts collected by individuals. Spells end if there is a change in employment status, a change in employer or occupation, or a change in whether the worker is working full- or part-time. Any spell that is active at the end of a calendar year needs to be reported by a …rm. Similarly, unemployment spells are submitted by local unemployment agencies. A consequence of this design is that measurement error and non-response are not a major concern, in contrast to publicly available panel data sets, such as the PSID or the NLSY in the United States or the GSOEP in Germany. Furthermore, because the data cover the years 1975 to 2010 I observe up to 35 years of a worker’s career, an unusually long time-series of workers that is unplagued by non-response or, for a large share of workers, sample attrition. Second, because of the spell-based recording I can calculate transition rates of various types on the daily level. While I do not exploit this information explicitly in my structural analysis for computational reasons, it can nevertheless be put to good use. The samples used in my empirical analysis will be aggregated to the annual level, following common practice in the literature on life-cycle earnings and career dynamics. At which point I measure the end of a model period in the data is arbitrary, however. It is here where daily transition rates are helpful because I can use them for testing if there is a time of the year when workers are particularly mobile. As it turns out, this is indeed the case. A surprisingly high share of job spells, over 58 percent, end on December 31st, and an equal share of jobs are formed on January 1st. Hence, using the calendar year as the unit of time will minimize aggregation bias in earnings and mobility dynamics.10 More details on the aggregation will be given below. Third, the data contain a time-consistent occupational variable on the 3-digit variable, …rm identi…ers, and one stock- and one ‡ow-variable relating to educational attainment. I will extensively rely on this information in my empirical analysis, which, apart from the …rm identi…ers, is not available in North-American administrative panel data on workers. There are also a number of drawbacks of using these data, most importantly the top coding of earnings at the social insurance contribution limit, a structural break in the earnings records in 1984, and the lack of a variable that records the hours worked. Most of these issues can be addressed directly by applying sample restrictions that are common in the literature. First, I focus on male workers and use a part-time work indicator contained in the data to drop part-time work spells, thereby ruling out earnings dynamics to be driven by unobservable hours changes along the intensive margin.

11

Second, the estimation sample will contain only workers who are observed from

a young age on, as described in detail below, and who are therefore quite young, if present at all, in 1984. As discussed in detail in Ho¤mann (2016), this has the implication that earnings records are not noticeably a¤ected by the 1984 structural break. The third issue of top coding is more di¢ cult to resolve. In a …rst step I drop highly 1 0 A similar argument is used in Card, Kline and Heining (2016), who estimate earnings regressions with worker,- …rm-, and matchspeci…c …xed e¤ects on the IAB-data, to justify aggregation to the calendar year. 1 1 As discussed in Card, Kline and Heining (2016), this has a miniscule e¤ect on the properties of earnings dynamics since the share of male part-time workers is quite small in Germany.

7

educated workers, de…ned as those who have a technical college or a university degree. This group represents a relatively small share of the population, as shown in the next subsection. At the same time, it is the only group for which the fraction of top-coded earnings is su¢ ciently high, exceeding 50 percent, to prohibit a meaningful analysis of earnings dynamics. For the remaining observations I will build a correction for top-coding directly into the structural estimation.

2.1.2

Focus on Workers with Apprenticeship Degree

Before …nalizing the description of sample construction, which relies heavily on the educational information, it is helpful to brie‡y summarize the main features of the German education system. Germany operates a secondary schooling system in which students are segregated into three di¤erent streams after grade 4, based on an IQ-test and teacher recommendations. All three streams are institutions of general education and di¤er by di¢ culty and speed at which the course material is taught. Only students who …nish successfully the academic stream, depending on the state after grades 12 or 13, are given access to universities or technical colleges. The share of this student group is surprisingly small, at least when viewed from an international perspective. For example, it was 23 percent among all individuals with a post-secondary degree in the nationally representative Mikrozensus of 2004.12 Compared to the estimation sample, this is likely to be an upper bound since my focus on tracking a large part of workers’ life-cycles has the e¤ect that older cohorts, who were less educated, are over-represented.13 Another particularity of the German educational system is the apprenticeship program, which is the largest of its kind in the world. Apprenticeships are occupation-speci…c programs that are designed to provide occupational skills and, depending on the occupation, take two to three-and-a-half years to completion. They are o¤ered in over 500 occupations, ranging from carpenter, mason, cook or industrial-, electrical- or car-mechanic to nurse, lab technician or …nancial accountant. During an apprenticeship, workers are trained on the job for approx. 60 percent of the time and are required to visit a government-sponsored school of general education that teaches skills such as mathematics, languages, social sciences, and accounting for the rest. The on-the-job component is usually provided by private-sector …rms that hold a training certi…cation and need to pay a training wage that is bargained between industry-speci…c employer associations and unions. The apprenticeship program can be accessed by any student with a secondary degree, no matter the stream. In practice, the overwhelming majority of the German workforce chooses to do so. For example, sixty-…ve percent of all individuals included in the SIAB data who are at least sixteen years old hold a vocational degree. This number will be even higher in my …nal sample because of the focus on males who are present in the data for some part of their working life-cycle. One may be worried that this number is not nationally representative because public servants or the self-employed may be less likely to complete an apprenticeship. However, in the 1995 Mikrozensus the number is very similar, with a share of 62.5 percent.14 In the empirical analysis that follows I will focus on workers who hold, at some point of their observed career, 1 2 The

year 2004 is the …nal year in my estimation sample. The data for 2005 to 2010 will be used for evaluating the external …t of my model. The Mikrozensus can be viewed as the German analogue of the US March CPS. 1 3 The corresponding share in 1995 was substantially lower, with a value of 18.4 percent. These shares were created from the variables EF121 and EF259, whose empirical distribution is available online at www.gesis.org/missy/metadata/MZ/1995/ 1 4 The 1995 sample is the last wave of the Mikrozensus for which this number can be computed from publicly accessible information (variable EF122). In subsequent years, the information conditions explicitly on workers who have any post-secondary degree (variable EF290). With full access to the Mikrozensus data one could identify workers without any formal post-secondary degree. However, the data are expensive and not accessible from outside of Germany for legal reasons.

8

a formal apprenticeship degree. However, for a test of robustness and for obtaining an upper bound estimate for the role of pre-labor market skills on life-cycle inequality I also estimate the model an a sample that includes all education groups, given that a worker is observed from the time of labor market entry on.

That being said, a

restriction of the sample on a single education group, or estimation of a structural model group by group, is common practice in the literature on life-cycle earnings dynamics and related areas of research, such as empirical equilibrium search or estimation of Ben-Porath models of human capital accumulation on-the-job. A popular justi…cation is that income inequality across education groups has been dwarfed by income inequality within groups in recent decades, so that the analysis of residual inequality has taken center stage. Another reasoning is that structural parameters themselves are likely to vary too much across education groups for estimating one model that applies to all groups. This applies to Germany as well. For example, Ho¤mann (2016) shows that the covariance structure of earnings is strikingly di¤erent for those without any formal post-secondary degree compared to either the highest educated or those with an apprenticeship degree. As it turns out, the same is true for mobility dynamics, where the least educated tend to remain in low-skill occupation groups over the entire life-cycle, making identi…cation of a multi-skill model di¢ cult. In contrast, Dynamic Discrete Choice modeling of labor market outcomes has traditionally put endogenizing educational choices at the forefront. Indeed, some of the most in‡uential studies, such as Keane and Wolpin (1997), Belzil and Hansen (2002) or Keane, Todd and Wolpin (2006) are motivated by questions that are directly related to educational choices. The focus of my study is quite di¤erent however, and the restriction to workers who hold an apprenticeship degree is directly justi…ed by this focus. More speci…cally, I build a model that is rich enough for studying the quantitative importance of permanent unobserved heterogeneity and external shocks on career progression and life-cycle labor market inequality. One challenge that has been recognized for some time is that career dynamics close to labor market entry may be driven by information revelation about individual abilities, a mechanism that is hard to model with multidimensional skills, search and a ‡exible earnings process. It is also hard to identify separately from exogenous persistent shocks to skills because Bayesian learning about permanent unobserved skill heterogeneity generates a unit-roots process of earnings in the reduced form. The primary advantage of estimating the model on a sample of workers with a vocational degree is that an important reason for …rms to train their workers may be learning about their skills. This is consistent with the results from a survey of German …rms conducted by the German Federal Institute for Vocational Education and Training (BiBB) in 2008/09 about the reasons for …rms to hire and train apprentices.15 Respondents were asked to rank a list of eleven potential reasons according to whether they deemed them "very important/important", "not important at all" or "neither important nor unimportant". The second- and third most important reasons were the ability to hire the best workers and avoiding hiring poor workers, both after completion of the apprenticeship program, with 70 and 60 percent of respondents ranking them as very important respectively.16 In contrast, only 55 percent deemed using apprentices as productive workers important. It is also consistent with …ndings from the SIAB data in Caines, Ho¤mann and Kambourov (2016) who document a downgrading in the occupational skill space directly after completion of an apprenticeship for a sizeable share of workers. Taken together, these results 1 5 BiBB

stands for "Bundesinstitut fuer Berufsausbildung". most important reason is to train workers to have the skills necessary to be successful in the …rm, which can be interpreted as "human capital accumulation", with 84 percent of respondents ranking it as very important. 1 6 The

9

seem to imply that …rms view the apprenticeship training program as an investment, where an important perceived bene…t is learning about workers’ skills. Workers who are perceived as unable to perform well in an occupation downgrade persistently into low-skill occupations after completion of the program. In the empirical analysis I therefore maintain the assumption that the skill endowment after apprenticeship is common knowledge and that the earnings process is not driven by information revelation. It is the context of the apprenticeship program, with its signi…cant on-the-job-training component, that makes this assumption particularly plausible.

2.1.3

The Estimation Sample

The estimation sample is the sample of primary interest for the empirical analysis of life-cycle earnings and career dynamics. It follows individuals from labor market entry until the last year in the sample. I choose 2004 instead of 2010 as the …nal year and use the discarded years 2005 to 2010 for evaluating the external …t of the model.17 I de…ne labor market entry as the point of a career at which an individual has completed an apprenticeship and starts a job or is actively searching for one. This point is not entirely straightforward to identify in the data, for various reasons. These issues are discussed in the appendix on sample construction, together with a detailed description of how they are addressed. The …nal estimation sample contains cohorts who are likely to enter the labor market after 1974 and who have at least …fteen years of labor market participation before 2010. The latter restriction is imposed because I will need to extrapolate skill price dynamics for cohorts who are not entering retirement before 2011 in the …nite horizon Dynamic Programming Problem, and I want this extrapolation period to be as short as possible. The cohorts left in the sample after these restrictions are born between 1955 and 1973. I also drop the …rst observation for any individual since there are indications that they contain some individuals who are in the terminal year of their apprenticeship, an issue that is caused by time aggregation of the data, or that they are immediately interrupted by a year of compulsory military service. Further details are provided in the appendix.

2.1.4

The Older-Worker Sample

The sample of older workers is exclusively used for preestimation of some structural parameters, most importantly skill prices, roughly following the "‡at spot" method innovated by Heckman, Lochner and Taber (1998) and applied by Huggett, Ventura and Yaron (2011) and Bowlus and Robinson (2012). The identifying assumption allowing this preestimation step is that workers settle down into stable careers at some point in their life-cycle, at which point human capital considerations and job search do not play an important role for career choices anymore. As discussed below, my structural model of career choices and earnings dynamics generates age e¤ects in worker transition rates between careers, employers and employment states. Conversely, if there is a period of a life-cycle in which one cannot detect such age e¤ects, then workers must …nd it optimal to remain on their present job, and solving the full structural model will have little bite on the data. These arguments suggest that an e¤ective way of locating a "‡at spot" is estimating models of worker transition rates with …xed e¤ects for age and then locating a range of age groups for which the age e¤ects are not statistically 1 7 The

year 2004 is chosen because of the many large-scale labor market reforms that were implemented that year.

10

signi…cant from each other. I implement this approach by estimating linear probability models with age …xed e¤ects, using three di¤erent outcomes, namely dummies for whether an individual switches employer, transits into from employment into unemployment, or switches from unemployment to employment. These models are estimated on the sample of male workers who hold a vocational degree. Since the age structure in the data is likely to be correlated with time I also include time …xed e¤ects. For all three outcomes I …nd substantial age e¤ects. Transition rates are highest close to labor market entry, fall afterwards at a declining rate and are nearly constant between the ages of 50 and 54 before rising thereafter. In particular, conditional on time e¤ects the coe¢ cients on age are not statistically distinguishable for workers who are between 50 and 54 years of age. The subsequent increase is likely driven by career considerations close to retirement and a change in sample composition because of endogenous sample attrition. Indeed, the rates of attrition increase dramatically after the age of 55. For these reasons I the older-worker sample is composed from workers with a vocational degree who are between 50 and 54 years old.

2.1.5

Time Aggregation, Earnings and Sample Sizes

There are a number of further sample restrictions that I apply to both samples and that are quite standard in studies relying on the SIAB data.18 First, I only keep male workers whose entire career took place in Western Germany to abstract from the e¤ects of the German Reuni…cation on Eastern German workers. Second, for parallel job spells I only keep the spell with the highest earnings. Third, I drop so called "mini-jobs", which are marginal employment spells that are included in the data only since 1999 and which are exempt from social security contributions since the labor market reforms in 2003-2005. The …nal step involves aggregation to the annual level. For reasons explained above I de…ne the relevant job spell for a year as the one that is active on December 31st. Earnings reported in the raw data are daily wages or unemployment bene…ts, that is, total earnings paid by a …rm or the unemployment agency for a particular spell devided by the duration of the spell in calendar days (including weekends). I thus aggregate these wages to the annual level by multiplying them by 365 (or 366 for leap years) and de‡ate them by the CPI. In total there are 44,618 workers starting a career in the estimation sample and 752,996 worker-year observations. Of these workers, 38,998 are still present after 10 years and 18,477 after 20 years. The oldest cohort is observed for 29 years, up to age 49. The older-worker sample is relatively large because of the less severe sample restrictions. It contains 648,221 worker-year observations for …ve age groups only. The number of workers decreases from 137,797 at age 50 to 121,268 at age 54.

2.2

De…nition of Occupational Classes

With a focus on quantifying the sources of life-cycle earnings inequality and their interactions with career dynamics in a setting with multidimensional skills, any occupational classi…cation into more aggregated groups should re‡ect heterogeneous skill requirements in a meaningful way. KW97 split occupations into white- and blue-collar occupations, but this is likely too course given recent evidence on the task content of occupations suggesting that skill requirements vary substantially within blue- and white collar occupations. I thus adopt the classi…cation into 1 8 See

for example Card, Kline and Heining (2013), who also o¤er an extensive discussion of these sample restrictions.

11

four aggregate groups suggested by Acemoglu and Autor (2011), which is explicitly derived from the task content of three digit occupations in US data. Any information relating to the occupational classi…cation can be found in Appendix C. The four groups, which I refer to as careers, are: (i) managerial, professional and technical occupations; (ii) sales, clerical and administrative support occupations; (iii) production, craft, repair and operative occupations; and (iv) low-skill service occupations. As Acemoglu and Autor write (p. 1078): "Broadly speaking, managerial, professional, and technical occupations are specialized in abstract, non-routine cognitive tasks; clerical, administrative and sales occupations are specialized in routine cognitive tasks; production and operative occupations are specialized in routine manual tasks; and service occupations are specialized in non-routine manual tasks." This categorization captures well the dimensions of occupational skill requirements along which skill prices and employment shares have evolved dramatically di¤erent over the last few decades, namely the relatively poor economic performance of occupations that attract workers with comparative advantages in solving routine cognitive or routine manual skills. To investigate the skill content of each of the careers I list the share of each education group for the four careers in panel A of appendix table C.1 and the share of each career group for the six education groups in panel B of the same table. These shares are computed from the entire sample rather than the older-worker or the estimation subsamples. Workers with an apprenticeship are the largest group in any of the four occupation groups, a re‡ection of the overall population share of this education group. However, they are relatively underpresented in occupations at the top and the bottom of the career latter, with 58 percent of all Managers and of all Low-Skill Service workers having an apprenticeship degree. The corresponding shares for the two remaining careers are over 70 percent. On the other hand, workers with a university- or technical college degree are overrepresented in managerial occupations. At the same time, they are essentially non-present in production- and related occupations and in low-skill service occupations. The opposite is true for those without any formal degree, who are grossly overrepresented in lowskill service occupations. Similar conclusion arise when computing the employment shares of each career, split by education group. In particular, the highest educated tend to sort into managerial, professional and technical occupations, while the lowest educated choose to work predominantly in production and operative occupations or low-skill service occupations. It is in this sense that the …rst career group stands at the top of the career latter and the last career group presents the bottom of the career latter. Another measure of the skill content are earnings levels. In appendix table C.2 I show parameter estimates from regressions of real earnings on career …xed e¤ects. I explore robustness by showing results from regressions that include all possible combinations of age- and time …xed e¤ects. I view these tables as part of a purely descriptive analysis and I thus use real earnings levels rather than logs. I also use the entire SIAB 1975-2010 sample so that the estimates re‡ect both earnings di¤erentials within education groups and education-composition e¤ects across careers. On average, workers in managerial, professional and technical occupations, which is the comparison group in the table, earn 34; 000 EUR. Workers in clerical and sales occupations and in production and operative occupations earn between 7; 800 and 8; 500 EUR less. The most dramatic earnings di¤erence is for low-skill service workers, who earn over 17; 000 EUR less and thus just half of what top-level occupations make. Taken together, the conclusions about the skill content and the hierarchical standing of the occupations is robust. Managers, Professionals and Technicians are at the top of the career level, attract the highest educated workers

12

and earn by far the most. Clerical and Sales Occupations and Production and Operative occupations tend to be in the middle of the occupational hierarchy, attract predominantly workers with an apprenticeship degree and pay on average about three-quarters of top-level earnings. Workers in low-skill service occupations are the least educated and have, by far and large, the lowest earnings.

3

Descriptive Analysis of Life-Cycle Earnings and Career Dynamics

In this section I carry out a descriptive analysis of career- and earnings mobility over the life-cycle. This has three main purposes. First, it presents a number of stylized facts, some of which con…rm existing empirical evidence and some of which are new. Second, it serves to show which empirical features a structural model needs to match to be a useful empirical framework for studying the sources of life-cycle income inequality. Third, it provides some direct evidence that speaks against a KW97 type model with only a permanent and a perfectly transitory component of individual earnings dynamics. I start with some facts about worker mobility between careers, …rms and various employment states in stocks and ‡ows. Afterwards I move on to earnings dynamics and their relationship to worker mobility. All statistics presented in this section are constructed from the estimation sample, and they will be target statistics in the structural estimation. The life-cycle variable is potential experience rather than age, de…ned as the years since labor market entry. For life-cycle pro…les that are cleaned from time e¤ects I regress the explanatory variable of interest on …xed e¤ects for potential experience and time and show the coe¢ cient estimates on the former.

3.1 3.1.1

Career Choices over the Life-Cycle: Stocks and Flows Net Labor Reallocation over the Life-Cycle

I start with showing in …gure 3 the life-cycle pro…les of employment shares for each of the four careers once without and with an adjustment for time e¤ects. The latter corresponds to …gure 1, but applied to the estimation sample and with age replaced by potential experience. The results show a dramatic and rather steady reallocation of labor across careers. The employment share of production and operative occupations drops by 25 percentage points, from three quarters to just half of the employed. Low-skill service sector occupations also decrease in relative size, but due to its small importance in the German labor market for the cohorts included in the estimation sample this decline is quantitatively unimportant. The lion’s share of labor net reallocation is to the group of managerial, professional and technical occupations. Its employment share increases from only …ve percent among labor market entrants to over 20 percent among workers with 25 years of labor market experience. Interestingly, the rate of net reallocation is not constant, with a slow increase over the …rst …ve years of labor market participation, a peak reallocation rate for workers who have between …ve and ten years of potential experience, and a slowdown towards a steady but positive rate among older workers. Clerical and sales occupations also become larger in size among more experienced workers, but the reallocation is slower and remarkable steady. These results are robust to the inclusion of time …xed e¤ects, which control for secular trends such as skill-biased technological change or the increasing importance of occupations that are intensive in non-routine tasks. The most noticeable di¤erence between the results without

13

and with an adjustment for time e¤ects is that the relative size of clerical- and sales occupations is larger in the latter case, at the expense of both production and operative occupations and low-skill service occupations. This is most probably a re‡ection of technological change that has favored higher-skill occupations. Figure 1 conditions on employment. This hides dynamics in the unemployment rate, which are non-trivial. Unemployment rates are almost eight percent over the …rst …ve years of a life-cycle and then drop quite rapidly to a steady-state level of about 5.5 percent. I do not show the pro…les in the …gure to avoid clutter.

3.1.2

Net Flows: Career- and Firm-Mobility are distinct Phenomena

The natural next step is to analyze the ‡ows underlying these large shifts of the labor force over the life-cycle. Figure 4 plots annual transition rates between careers and …rms in the left panel and between employment and unemployment and vice versa in the right panel. These are conditional probabilities computed from individual-level data. As an example, for career transitions they are calculated from individual dummy variables that are nonmissing for workers who are employed in two subsequent periods and that are equal to one if a career transition takes place in between. They are adjusted for time e¤ects by estimating linear probability models using …xed e¤ects for experience- and calendar time, and the …gures show the coe¢ cients on the former. Generally, workers are quite mobile. In the …rst year of a career, approximately one in …ve workers change their employer, and this rate declines steadily afterwards. The rate seems to stabilize after about 22 years of potential labor market experience at a rate of 7 percent. Career changes on the other hand happen much less frequently. However, their life-cycle dynamics are dramatically di¤erent. After some initial decline from a level of 4 percent to below 3.5 percent right after labor market entry, re‡ecting the occupational downgrading that happens frequently after completion of an apprenticeship degree as documented in Caines, Ho¤mann and Kambourov (2016), the rates actually increase as workers accumulate labor market experience. Only after 8 years of potential labor market experience do they start to decline monotonically until career moves become rare events later in the life-cycle. This hump-shaped pattern mirrors the accelerating speed of worker net reallocation into managerial and related occupations between …ve and 10 years of labor market experience as illustrated in …gure 3 and discussed above. These …ndings demonstrate that career changes and …rm-to-…rm transitions are two distinct phenomena. Career changes do not take place very often, and they tend to occur after workers have spent some time in the labor market, consistent with the model of career progression in Gibbons and Waldman (1999, 2006). They also come with a change in employer more often than not, with a share of 64 percent of all career transitions. In contrast, …rm transitions happen quite frequently initially and drop steadily thereafter, as predicted by job search models with a job latter, and this process can generate substantial earnings risk, as argued for example in Low, Meghir and Pistaferri (2010). As it turns out, in the German data they tend to take place within career, with only 16 percent of all …rm-to-…rm transitions coinciding with a career switch. Interestingly, these transition rates are fairly similar between and common in all careers. They are smallest in managerial occupations, with a value of almost 8 percent, and highest in low-skill service occupations, with value of 12 percent. Hence, …rm mobility is a potential source of earnings variation that is taken advantage of by workers in all types of careers. The right panel of …gure 4 shows transition rates between employment and unemployment (EU) and vice versa (UE). These rates are quite important in disentangling various sources of earnings inequality because earnings

14

components that are lost upon a EU-transition have di¤erent predictions on the relationship between unemployment duration and re-entry wages than permanent unobserved heterogeneity. Both rates drop substantially over the lifecycle, the former from initially 5 percent to less than two percent and the latter from over 60 percent to under 20 percent. The decline in EU rates is rapid, with a stable rate of about 2 percent reached after about 15 years of potential labor market experience. In contrast, UE rates never quite stabilize, with a life-cycle pro…le that is almost linear. It is perhaps surprising that only 20 percent of older unemployed workers make a transition back into employment within a year. However, for this group the rate of dropping out of the sample, is quite high, possibly due to discouragement or a switch into self-employment.

3.1.3

Gross-Flows and their Implications for Modeling Career Dynamics

Next I study the entire one-period transition matrix between careers, unemployment and attrition. Results are shown in the three panels of table 2. Rows and columns correspond to states at experience t and (t + 1) respectively. Numbers in rows add up to one since they are conditional transition probabilities. Since attrition is an absorbing state, there are less rows than columns, with an understanding that the missing row has a diagonal element equal to one. To keep the number of statistics manageable I show these matrices for the entire sample, those with at most 5 years and those with at most 10 years of labor market experience. Life-cycle patterns can then be inferred from comparison of the matrix for the youngest workers, the older workers and the entire sample. Naturally, it is hard to establish any sharp results from this type of non-parametric analysis. Yet, there are a number of …ndings that have important implications for modeling. Perhaps most importantly, there are large gross ‡ows underlying the net reallocation documented in …gure 3 in terms of stocks and in …gure 4 in terms of overall transition rates. In particular, there is no single-directional ‡ows towards the occupational group experiencing the largest net gains in terms of employment, namely managerial, professional and technical occupations. In fact, this career is, apart from low-skill services, the least stable occupation, with an annual survival rate of :918. Though the di¤erence to the next stable career, the clerical and sales occupations, is just 1:5 percentage points it needs to be kept in mind that small di¤erences in annual rates can translate into large di¤erences in, say, decennial rates. Furthermore, the rate at which workers ‡ow from this career to the occupation group with the largest net decline, namely production workers, is higher than the rate at which workers ‡ow into the opposite direction. The fact the aggregate net ‡ows from production to management are positive nevertheless is simply a re‡ection of the sheer size of the former. Comparing results from the three panels clarify that this …nding is qualitatively similar at each stage of a life-cycle. At the same time, managerial occupations are quite distinct in the sense that they draw and lose workers from and to each other career and employment state. In contrast, clerical occupations do not attract workers from either low-skill services or from production occupations, and low-skill service occupations do not attract workers from any occupations. Whether workers ‡ow into and out of the same groups of occupations, for example from clerical occupations into managerial occupations and back, is important for understanding the persistence and transferability of skills. In the most extreme situation where skills are purely transitory, workers would randomly bounce through occupational space. This is evidently false. On the other hand, if skills are persistent and multidimensional, then workers will

15

tend to be attracted to the same types of careers. One way of exploring this issue is calculating transition matrices for two periods, three periods etc. A more parsimonious approach of getting at the same issue is computing a life-cycle transition matrix. For a purely descriptive analysis this seems to be too crude. However, it is a powerful piece of information disciplining the parameters in the structural estimation. A model that can match one-periodand life-cycle transition matrices is likely to match medium-term transitions as well, and this can be checked as a test of external …t. Transition rates between the most frequent careers early and late in a career are shown in table 3. Qualitatively, the patterns of this matrix re‡ect the one-period transition matrices quite well. In particular, workers from all occupations move into managerial occupations, and the same is true in the opposite direction. In contrast, very few workers who start in non-service occupations move into low-skill service occupations, and the transition rates between production occupations and clerical and sales occupations are lower than transitions rates between either of these occupations and managerial occupations. Given this apparent and tight relationship between short- and long-run transition matrices it is more likely that a typical worker only samples from a subset of careers over a life-cycle than that he moves freely through occupational space. These …ndings are hard, if not impossible, to reconcile with a model of unidimensional skills. Clerical and Sales occupations on the one hand and production- and low-skill service occupations seem to operate in distinct labor markets, as manifested by very low transition rates between them. On the other hand, each occupation provides some chance of upgrading into managerial, professional and technical occupations, suggesting that a "managerial skill" in combination with any other skill can produce managers. The …ndings are also hard to be explained by a model in which career dynamics are, to a large extent, determined by unobserved pre-labor market skills in conjunction with purely transitory shocks, as in KW97. It is true that transitory worker-level shocks to occupational skills can generate gross-‡ows in excess of net ‡ows. However, in the presence of career-speci…c human capital accumulation such ‡ows tend to happen early in the life-cycle, and because of the excess returns observed in managerial occupations they are unlikely to take place once workers have reached the top of the occupational ladder. In contrast, the transition matrices presented in this section seem to suggest that gross-‡ows in excess of net ‡ows are present at each stage of a life-cycle, and the top of the occupational ladder does not provide the largest job security. Rather, career transitions themselves may be a signi…cant source of earnings risk, though quantifying this requires structural estimation.

3.2

Life-Cycle Earnings Dynamics and their Relation to Worker Mobility

A central advantage of a structural model of earnings- and mobility dynamics is that it explicitly models the joint evolution of earnings and mobility choices of workers over the life-cycle, thereby tying together within-worker variation in earnings and in career-, …rm- and employment choices. In this subsection I document a number of descriptive statistics that capture some of the most salient features of these joint dynamics. I start with documenting life-cycle pro…les of unconditional log-earnings in averages and standard deviations in …gure 5, which is useful for putting the descriptive results in the context of the earnings dynamics literature with single-dimensional skills and for comparing key features of the life-cycle earnings distribution in the estimation sample with existing evidence from other countries. Earnings in this and all other subsequent …gures and tables are skill-price adjusted, with

16

skill-prices estimate from a "‡at-spot" strategy innovated by Heckman, Lochner and Taber (1998) and Bowlus and Robinson (2012) and described in more detail in the next section. Over a span of 25 years, an average worker experiences an increase in real earnings of almost 50 percent, from approx. exp(9:75) ' 17; 150 EU R to exp(10:15) ' 25; 590 EU R. Though the rate of earnings growth decreases as workers age, the experience-earnings pro…le is strictly monotonic and concave. Somewhat surprisingly, even after 25 years into labor market participation workers still have substantial real annual earnings gains net of skill-price increases. In contrast, the standard deviation of log-earnings does not evolve monotonically. It declines from a value of :24 at labor market entry to a value of :22 four years later, remains relatively ‡at for the next three years and then increases steadily and close to linearly thereafter. After ten years of labor market experience, earnings inequality as measured by the standard devation of log-earnings is larger than at labor market entry, and for workers with 25 years of potential experience it has reached a value of :28. Qualitatively, the shape of this pro…le is surprisingly similar to the corresponding …gure computed from US data, such as Guvenen (2009). An initial decline is commonly thought to be consistent with worker sorting into better …rm-or career matches either via job search or because of shocks to worker skills before human-capital considerations slow down worker mobility. It is thus natural to view experience-inequality pro…les as important source of identi…cation for parameters governing the earnings process.

3.2.1

The Covariance Structure of Residual Earnings is Inconsistent with KW97

The covariance structure of residual earnings is heart and center of the literature on quantifying the sources of life-cycle inequality using statistical models of earnings processes. This is because covariances between current and future earnings re‡ect the strength of the relationship between a worker’s current and future standing in the earnings distribution. If for example earnings can be decomposed into purely transitory shocks, say "it , and a permanent component capturing ex-ante heterogeneity, say

i,

then the covariance matrix of residual earnings

has diagonal elements equal to var ("it ) + var ( i ) and o¤-diagonal elements equal to var ( i ), which is also the covariance structure of the error term in a textbook random e¤ects panel data model. KW97 adopt exactly this assumption to a setting in which

i

and "it are vectors with as many elements as there are careers, and integrate this

earnings process into a Dynamic Discrete Choice model with human capital accumulation. In this setting, purely transitory shocks can have persistent e¤ects on earnings through career choices and thereby through accumulation of career-speci…c human capital. However, conditional on occupational tenure and the other observed state variables of the model, the covariance structure of residual earnings will still have the properties of a random e¤ects model. This is strongly at odds with the data, as implied by Figure 6. This …gure presents lead pro…les, that is the covariance between current earnings and earnings l years apart, for four di¤erent experience groups, namely labor market entrants and those with …ve, ten or …fteen years of experience. Skill-price adjusted earnings have been residualized by regressing them, separately for each career, on a second-order polynomial in actual labor market experience and occupational tenure. Conditional on educational attainment, these two variables are the human capital accumulation variables in KW97. The lead-pro…les are monotonically declining, seemingly at a geometric rate. As a consequence, the long-run value is substantially smaller than …rst-order covariance terms. This …nding is direct evidence against the results in KW97 that around 90% of life-cycle inequality is determined by factors

17

already present at labor market entry since lag-pro…les would have a very di¤erent shape in this case.19

3.2.2

Occupation-Speci…c Earnings Intercepts and Slopes: A Potential Mechanism for Worker Reallocation

The results from career-speci…c regressions of skill-price adjusted earnings on actual labor market experience and career tenure, used to compute earnings residuals from which …gure 6 was constructed, are interesting in their own right. Results are displayed in table 4. It is immediately apparent that returns to experience and to tenure vary substantially across broad occupational groups, consistent with …ndings in Firpo, Fortin and Lemieux (2011) who …nd substantial variation in intercepts and returns to skills across forty occupations in US data.20 Returns to experience are estimated between 1.4 percent for production and operating occupations and almost 6 percent for managerial, professional and technical occupations, while returns to tenure range between 1 percent for the latter occupational group and 2.7 percent for the former occupation group and low-skill service occupations. Hence, there seems to be a tradeo¤ between returns to experience and returns to tenure, and the former tend to be higher than the latter. Furthermore, there is a weak tradeo¤ between returns to experience and intercepts, since the occupation with the highest intercept is also the occupation with the lowest slope and since the occupation with the highest slope has a relatively low intercept. This is in fact very similar to what is assumed in the Gibbons-Waldman (1999, 2006) model of career progression and what is found in KW97. Indeed, the primary mechanism of career dynamics in these models, where workers start in low-ranked occupational and switch into managerial- and other high-ranked occupations over the life-cycle, is the tradeo¤ between intercepts and slopes of experience pro…les of log-earnings.

3.2.3

Worker Mobility, the Distribution of Earnings Changes and Risk vs. Heterogeneity

To what extent are these earnings dynamics related to worker mobility and career choices? The rest of this section addresses this question using descriptive empirical analysis. I start with computing life-cycle pro…les of averages and standard deviations of log-earnings, exactly like in Figure 5 but split by both current career and initial career choices, where the initial career is de…ned as the career which is most frequently observed for a worker over the …rst …ve years after labor market entry. Results for the averages are shown in the two panels of …gure 7, and the corresponding results for standard deviations are plotted in …gure 8. Notice that intercepts di¤er between the two panels in both …gures since workers are mobile so that the "initial career" is not necessarily identical to the career choice in the very …rst year after labor market entry. Two results are particularly noteworthy. First, life-cycle pro…les of …rst- and second moments of the earnings distribution di¤er substantially across careers. Production workers and operatives have relatively high initial earnings, but low subsequent earnings growth. The opposite is the case for Managers, Professionals and Technicians on the one hand and clerical- and sales occupations on the other hand. These two broad groups of occupations 1 9 It should be noted that the lag-pro…les are very much in line with …ndings from panel data on earnings in the US, Canada and Great Britain, among others. The conclusions drawn from …gure 6 have thus strong external validity. 2 0 Firpo, Fortin and Lemieux (2011) estimate repeated cross-sectional models of wage changes over time. Their measure of skills is the occupational wage in a base period. Although this is a very di¤erent model from the one estimated in table 4, the …ndings have a similar interpretation: In regression models of wage growth over time or over the life-cycle both intercepts and the returns to skills vary signi…cantly between occupations.

18

also have surprisingly similar pro…les in …rst moments, though they di¤er somewhat in the second moments. This …nding itself shows clearly that it is hard to rank occupations by skills and points directly to the importance of allowing for multidimensional skills. The least attractive occupation group is low-skill services, which has both low initial earnings and low earnings growth. Arguably the more striking result is the di¤erence in life-cycle pro…les of …rst- and second moments between the right and the left panels of the two …gures. Starting with …gure 7 one can see that earnings growth is substantially larger when splitting the sample by current instead of initial career choice, and this applies to each of the four occupation groups. Di¤erences in growth start to be noticeable after around …fteen years of labor market experience. For example, earnings of managerial occupations are 82 percent higher among those with 25 years of labor market experience than among labor market entrants, but they increase by only 76 percent among workers who choose either of these two occupations directly after entering the labor market. Similar discrepencies of earnings growth between contemporaneous and initial career choices are present for each of the other three occupation groups. This contains important information about the dynamics of worker sorting across careers. On the one hand, average earnings by career choice are a¤ected by the changing composition of worker skills and matches within career. On the other hand, average earnings by initial career are a¤ected by inequality of career dynamics among workers who make initially the same choices. The fact that the two di¤er substantially implies that career mobility is an important source of earnings dynamics. Moreover, the …ndings suggest that some workers switch careers with low or even negative earnings growth but that such switches are generally favorable in terms of the skill composition within each career. For otherwise it is hard to explain why earnings growth is substantially higher within contemporaneous career. This lines up quite well with the corresponding …ndings in …gure 8, where the standard deviation of log-earnings is observed to grow faster when computed for workers with identical initial rather than current career choices. These …ndings are consistent with a mechanism whereby initially observationally identical workers experience di¤erent labor market trajectories, thereby generating earnings inequality, while workers tend to be matched increasingly better within career. More direct evidence on this mechanism is presented in table 5, where I compute sample average, standard devation and the 10th, 50th and 90th percentile of the distribution of annual earnings growth. The …rst three columns show these statistics for all employment spells, …rst for all workers and then for workers with at most …ve or ten years of potential labor market experience. On average, workers experience 2:8 percent real earnings growth over the …rst 25 years of their working life-cycle, and this rate is substantially higher for the youngest workers, with a value of 6:6 percent. The variation across workers is substantial however. At each point of the life-cycle, there is a substantial share of workers who experience negative earnings growth. The tenth percentile is below

6 percent

and remarkably stable in the full sample, the sample of the youngest workers and the sample of workers with at most ten years of labor market experience. Furthermore, the median is always lower than the average, so that the distribution is quite skewed. Workers at the upper tail make substantial gains, and these gains depend strongly on the age of the sample. In particular, the 90th percentile is 13 percent in the full sample, but is almost 23 percent among those with at most …ve years of labor market experience. The next three columns show corresponding results for earnings growth at career transitions. Two main differences to the full sample of earnings changes emerge. First, as expected earnings growth tends to be somewhat

19

higher, especially early in the life-cycle when workers who change careers see their earnings grow on average by 8:7 percent, compared to 6:6 percent among all workers in the same age group. Second, there is a striking dispersion in earnings growth, with a value between

21 and

22 percent at the bottom of the distribution for any experience

group, and a value of up to 43:2 percent at the top of the distribution for young workers. As in the full sample, the lower tail of the distribution is relatively stable over the life-cycle, while the upper tail is not. These …ndings alone document that career changes have a substantial impact on the entire earnings distribution.

3.2.4

Earnings Changes and Career- vs. Employer Mobility

In the section on worker mobility it was shown that the life-cycle pattern of career mobility is quite distinct compared to …rm mobility. One may therefore wonder whether the same is true for the impact of employer transitions compared to career transitions on earnings. This is particularly important in light of the fact that there is a substantial literature on …rm mobility and earnings dynamics, which generally tends to view search for better worker-employer matches as an important source of earnings risk. The last three columns of table 5 take a …rst shot at this question. They suggest that employer- and career mobility have similar relationships to earnings growth. In fact, on average the former generates more earnings growth, but with less dispersion; both lower- and upper-tail risk is larger when it comes to career changes. Interestingly, just as EE transition rates are similar across careers, so are earnings changes that correspond with EE transitions, as shown in table 5. Combined these …ndings suggest that worker mobility across employers is an important source of residual earnings inequality within each career, potentially generating substantial earnings dispersion among individuals who entered the labor market with similar credentials. Given these results one may conjecture that …rm- and career mobility have a similar impact on earnings dynamics. However, career changes are likely to come with more drastic changes in skill requirements and career progression and may thus be attractive to a di¤erent set of individuals than a change of employer. A simple approach to investigating this issue is to relate earnings growth to earnings levels before various types of transitions. I therefore plot percentiles of the residual earnings distribution before career- and …rm transitions in Figure 9. As above, the residuals come from regressions of skill-price adjusted log-earnings on a polynomial in actual labor market experience and career tenure, with coe¢ cients allowed to vary freely across the four occupation groups. For comparison I also show the plots for residual earnings before transitions into unemployment or sample attrition. While the lines for career- and …rm transitions look fairly similar, there are important di¤erences that can be noticed on closer inspection. Just as the distribution of earnings changes has less dispersion for EE-transitions than career transtions, so is the distribution of earnings levels narrower before EE-transitions as well. Career switchers are more likely to be very low or very high earners than …rm switchers, and the di¤erence at the top of the distribution is quite substantial.

3.2.5

Modeling Sample Attrition is Important

An interesting comparison group turns out to be those who drop out of the sample. This can be for various reasons, such as weak labor market attachment or a transition into public- or self-employment. As can be expected, earnings

20

at the lower tail of the distribution among those who drop out of the sample are extremely low, much lower than those for workers who change careers and …rms and even workers who become unemployed subsequently. What is more striking however is how similar high-earning career switchers and high earning workers who drop out of the sample look alike. Starting from the 80th percentile, the plots are nearly identical. One interpretation of this is that for high skill individuals a career upgrade and a move into self-employment are similarly attractive. This is an important …nding because it implies that attrition from the sample needs to be modelled explicitly, for otherwise one would not capture the changing skill composition of the workers who remain in the sample, a serious problem if one wants to quantify the sources of life-cycle income inequality.

3.2.6

Earnings Changes and the Potential Importance of Forward-Looking Behavior

Finally, I also produce the entire matrix of earnings changes for each possible career change in table 7, once for one-period earnings growth in panel A and once for life-cycle earnings growth in panel B. This table is the analogue of tables 2 and 3, but applied to earnings growth rather than worker mobility. These tables produce a number of important …ndings. First, in most cases o¤-diagonal elements are larger than diagonal elements, suggesting that career changes are optimal, even if they come with a downgrade. Second, upgrades from production- and service occupations come with negative one-period earnings growth, but with a substantial growth premium over the lifecycle. For example, workers who change from a production occupation into a managerial occupation experience, on average, an earnings loss of 2:7 percent from one period to the next. At the same time, workers who are employed in production occupations early in the life-cycle and become managers later on have a long-run earnings growth of almost 30 percent, compared with 22 percent for those who stay in the production occupation. One natural interpretation of this result is that individuals are willing to take earnings cuts in the short-run in expectation of larger labor market opportunities in the future. This is strong evidence against models in which workers act myopically. Forward-looking behavior is one approach to rationalizing these facts.

3.3

The Model

In this section I formulate an empirical model of the joint dynamics of career choices and earnings over the life-cycle, building on the structural econometric framework in KW97. The KW97 model is a dynamic discrete choice (DDC) model with predetermined multidimensional skill heterogeneity, purely transitory skill shocks and transferable and career-speci…c human capital accumulation. It is well-suited for rationalizing some of the key facts established in my descriptive analysis of the SIAB 1975-2010 data. In particular, transitory shocks to occupation-speci…c skills on the worker level can generate complex patterns of worker transitions across occupations, and career-speci…c human capital accumulation can generate overall declining transition rates later in the life-cycle. Permanent skill heterogeneity can explain the substantial correlation between current earnings and earnings many years later, and the multidimensionality of skills can explain why the earnings distributions for di¤erent careers that seem to require di¤erent skills are overlapping.

21

With unobserved heterogeneity only consisting of a permanent ex-ante component and purely transitory shocks, the model is unlikely to match some of the stylized facts established in the descriptive section. Speci…cally, to become suitable for quantifying the sources of life-cycle inequality, the model needs to explain why lead-pro…les of residual earnings are negatively sloped and converge to their long-run value at a fairly low rate. It also needs to generate a systematic relationship between worker transitions between careers and …rms on the one hand and earnings dynamics on the other hand. I thus incorporate two additional features into the KW97 model. First, workers search for better matches across …rms and careers, thereby introducing an earnings process that links dynamics in residual earnings to job- and career mobility. Second, to match the covariance structure of earnings, which displays complex dynamics even among workers who have settled into stable careers, I add an AR(1)-process to the unobserved component. These two additions require some important modi…cations to the overall model structure so that each model component is logically coherent with each other. In particular, search for better matches goes hand in hand with a search process in which workers draw outside-o¤ers only periodically. Hence, I model worker behavior as a frictional search process. Match heterogeneity coupled with job search persistently alters the relative attractiveness of a career to a worker and can be interpreted as a shock to a worker’s comparative advantage determined ex-ante by multidimensional skill heterogeneity. It is therefore natural to abandon the assumption of discrete unobserved heterogeneity that is popular in the Dynamic Discrete Choice models and to work with continuous unobserved skill components instead. The rest of this section is organized as follows. I …rst describe the model structure in a non-parametric setup. This helps relating it to the extensive literature on the econometrics of DDC-models, which commonly relies on a very speci…c set of assumptions that are not imposed in my model. Next, I introduce and justify the parameterization chosen for the various model components. Afterwards I establish a number of smoothness properties of the expected value functions in the state variables and the parameters. These properties feature heavily in the design of the computational algorithm to estimate the model structurally.

3.4

Theoretical Setup and Notation

The theoretical model is a …nite horizon controlled Markov process with discrete choices and randomly evolving consideration sets. Age is indexed by a and takes integer values in f0; 1; :::; Ag. In each period of a life-cycle of length (A + 1) an individual needs to choose an element

from a discrete list of options !, called the consideration

set, that is a contained in the set of all choice alternatives

. The distinction between ! and

is important because

of the random nature of consideration sets. It is helpful to de…ne the following sets: C

= fmanagerial; clerical; production; servicesg

EE

= fswitch employer; do not switch employerg

e

= f

n

= funemployment; attritiong :

c

EE g

(1)

22

These are the sets respectively of all career options ( involving employment (

e

C

), of making an EE-transition or not ( n

), and of non-employment choices (

and has ten elements. Consideration sets are subsets !

EE

), of all choices

). The set of all choice alternatives is

=

e

[

n

, and the model will specify transition probabilities

between these subsets from one period to the next. Singleton elements of

will be denoted by

and referred to as

choice alternatives. Workers maximize expected life-cycle utility that is a discounted sum of the utilities ua at age a, with discount factor

2 (0; 1).21 Let Wanet (

a)

be a measure of a net monetary payo¤ and let

a

(

a)

be a preference shock,

both of which are functions of choices. Also de…ne SaW as the payo¤-relevant states, Sa as the full state, and VA+1 as the continuation value after the terminal period of the working part of a life-cycle. Choices are made at the beginning of each period, and all state variables are observed by the decision maker, but not necessarily by the econometrician. Expected life-cycle utility takes the form U =E

XA

a

a=0

ua Wanet

W a ; Sa

;

a

While the argument for the utility function reduces to (Sa ;

(

a) ;

a ),

a ; Sa

+ VA+1 (

A ; SA )

:

(2)

the notation used here emphasizes two main

components of the empirical model speci…ed below. First, preferences depend explicitly on the monetary payo¤, which is observable for the chosen alternative. Second, there are choice-speci…c preference shocks that generate heterogeneous choices conditional on SaW . Notice that the combination of these two features are the essence of the Roy-model, of which my model is a dynamic extention. Over an above these two variables, (

a ; SA )

can have a

direct in‡uence on utility, for example because of …xed costs to mobility. Importantly, the speci…cation of preferences nests two cases that are predominant in the empirical search literature and in labor market applications of DDC models. One is the life-cycle income maximizer, which is the case of a risk-neutral worker with ua Wanet ;

a;

a ; SA

= Wanet

W a ; Sa

+u ea ( a ;

a ; SA ) :

The other is the risk averse worker who values consumption and who does not have access to the capital market. In this case, utility is a function of consumption, and in each period the worker consumes the entire income earned concurrently. In either case, savings are not a choice and assets are not a state-variable, an assumption that is commonly justi…ed by either computational intractability or the lack of appropriate data. Net monetary payo¤s Wanet are related to some underlying gross monetary payo¤ Wagross via a function G: Wanet

W a ; Sa

= G Wagross

W a ; Sa

:

(3)

In the empirical version, monetary payo¤s will be earnings, gross and net of earnings taxes, and the function G will be the mapping from gross- to net earnings as determined by the income tax system. The state-variables depend on the particular parametric assumptions imposed on the monetary payo¤ function and the ‡ow utility. In its most general form it evolves according to the stochastic law-of-motion Sa+1 = F (Sa ;

a; a)

(4)

2 1 All variables in the choice problem will be indexed by age a to highlight the life-cycle aspect of the model. Alternatively, one could include age in the vector of state variables and supress the subscript.

23

where

a

is a vector of transitory shocks whose length remains unspeci…ed at this point. This law-of-motion has great

generality for controlled Markov-processes. In particular, since the probability distribution of states next period conditional on the current state in a Markov process is the probability distribution of a transitory disturbance, this speci…cation admits serial correlation in stochastic state variables.22 Serial correlation in observed and unobserved states will be a crucial feature of the empirical speci…cation. The model is closed by specifying the distributions of transitory disturbances

a

and initial states (S0 ; ! 0 ), which

will be H ; HS and H! respectively. The dynamic decision problem can then be written as

max U = E A a ga=0

f

subject to Wanet

W a ; Sa a

(

G Wagross

=

a)

Sa+1

XA

a

ua Wanet

a=0

W a ; Sa

with

a

W a ; Sa

;

a

(

a) ;

a ; Sa

+ VA+1 (

A ; SA )

(5)

2 !a

H =

(6)

F (Sa ; ! a ;

S0

HS and ! 0

a; a) ,

with

H

a

H! (initial conditions).

This decision problem will be solved via Dynamic Programming. Value and policy functions at age a will be written as Va (Sa ) and

a

(Sa ), respectively. It is notationally convenient to also de…ne a policy function

that captures the career dimension of choices, therefore taking values in

3.5

C a

(Sa )

C 23

.

Econometric Speci…cation and Parameterization

obs Data Let workers be indexed by i and let Wa;i ,

a;i

and Xa;i be their observed annual gross labor earnings,

choices and states at age a.24 The number of workers entering the sample is N , and the age a worker exits is Ai . There are three important cases of observed life-cycles. In the …rst case, an entire life-cycle is recorded in the data, so that ti + Ai

2004 and Ai = A. In the second case, one observes an individual from labor market entry until

the …nal sample year, but Ai < A. For such individuals, the dynamic program must be partially solved out of sample and thus requires extrapolation. The third case involves sample attrition, with ti + Ai < 2004, Ai < A and Ai +1;i

= fattritiong. In this case, attrition is interpreted as a choice, so that

Ai +1;i

is treated as observable and

(WAi +1;i ; XAi +1;i ) as missing.

Preferences I adopt the common assumption in the DDC-literature that workers are risk-neutral and face switching costs. In particular, ua Wanet ;

a;

a ; SA

= Wanet

(

N

a 2 2 For

a)

W a ; Sa a

;

2 a

+

a

(

a)

; for each

+I( a

2

a

6=

a 1)

K

a; a

1

(7)

:

example, if the state was one dimensional and followed an AR (1)-process with parameter , say xa+1 = xa + "a , then Sa = xa and a = "a . 2 3 Formally, one can set C (S ) = ? if n and C (S ) = c if e , where c; d index elements in C and a a (Sa ) 2 a a (Sa ) = fc; dg a a EE respectively. 2 4 In the following, "observable" and "unobservable" is formulated from the point of view of the econometrician. As noted above, all states at the beginning of a period are observed by workers.

24

where I ( and K

a

a; a

6= 1

a 1)

is an indicator variable equal to one if choices in the current and the previous periods di¤er,

is a switching cost function de…ned on the discrete domain

by the three factors net earnings, non-monetary preference components

. Utility at age a is thus determined a,

and a switching cost. Since earnings are

observed in the data but preference shocks and transition costs are not, I choose a rich structure for the former and a parsimonious parameterization for the latter two components. Starting with the non-monetary utility component, I choose the following speci…cation: (

a)

a

(u)

N

u;

(exit)

N

exit ;

a

a

=

(

a)

for

a

C

2

(8)

2 u 2 exit

where u denotes unemployment. That is, for employment choices,

: a

is a constant that captures systematic dif-

ferences in non-monetary job quality across career choices and that is shared by all workers. It is assumed to be non-stochastic because the earnings process introduced below features several sources of shocks that generate individual-level di¤erences in the attachment to certain careers. In contrast, the model allows for transitory shocks to the utility of non-employment alternatives because earnings are calibrated deterministically to unemployment bene…ts on the one hand and are unobserved for workers who exit the sample on the other hand. As a consequence, transitory shocks to

a

(

a)

for the non-employment alternatives,

will be the only source of non-degenerate conditional choice probabilities a

2

n

. Identi…cation requires normalization of one of the

0

s, and I set

(m) = 0. Switching costs are usually introduced into DDC-models to generate state-dependence in transition rates. Without switching costs DDC models tend to generate too much individual mobility, whether between careers like in KW97, between cities like in Kennan and Walker (2011), or between being an exporting …rm or not. In my model, it will be search frictions that take over this role. Since it is di¢ cult to separately identify two types of frictions that depress worker mobility rates I will restrictthe switching cost function to the speci…cation K

a; a

1

=

K if

a

= "managerial" and 0 otherwise.

a

6=

a 1

:

(9)

The idea of this assumption is as follows. On the one hand, the non-monetary e¤ect of switching careers horizontally should be captured by the unobserved preference shocks

a.

On the other hand, a substantial share of upgrades

into managerial, professional and technical careers involve moves into the foreman-occupation. Such moves require acquisition of an extra educational degree, which is usually taught in specialized educational institutions at night or on weekends. Hence, it is plausible to make the assumption that upgrading into such occupations involve a direct utility cost, which will be captured by the parameter K. To keep the state-space manageable I assume that workers who return to such careers, possibly after a temporary downgrade or a spell of unemployment, must repay this cost, which can thus be interpreted as a "reclassi…cation or recerti…cation cost".

Labor Earnings and Taxes The earnings process is formulated in terms of gross labor earnings. For career alternatives

2

C

the model speci…es a list of potential gross earnings for a worker i of age a who works for …rm

j in calendar year t. This includes elements

with the property that f g

EE

is not in the current consideration

25

set ! a;i . Gross earnings are a product of career-speci…c skill prices Pt and a career- and worker-speci…c skill index Ha;ij . Dropping the superscript "gross" for notational simplicity yields: log Wa;ijt = log (Pt ) + log Ha;ij ; for all

C

2

:

(10)

Skill-prices will be treated deterministically, equivalent to assuming that individuals have perfect foresight over aggregates.25 On the other hand, skill-indices evolve stochastically and involve individual risk and heterogeneity components. Let tena;i be the years an individual has spent without interruption in career c at age a, and let expera;i be the years actively spent working since labor market entry.26 I assume the following structure for career-speci…c skill indices: ;spec log Ha;i = log Ha;ij + log Ha;i;gen ; for all

C

2

;

(11)

+ "a;i }

(12)

with ;spec = log Ha;ij

and log Ha;i;gen =

|

1

|3

tena;i + 2 {z

tena;i

obserable

expera;i + 4 {z

obserable

2

}

+

| 2

i

+

a;ij

{z

unobservable

(expera;i ) + }

za;i |{z}

.

(13)

unobservable

Equation (11) postulates that skills can be decomposed into a speci…c and a transferable component. This dichotomy turns out to be quite powerful and ties together all model components in a logically coherent way. Start with equation (12), which involves observable and unobservable state variables. The observable part is a standard tenure-earnings pro…le, with tenure serving as a measure of career-speci…c skill accumulation. Slopes are allowed to vary across careers, as indicated by the superscript on the parameters (

1;

2 ).

The unobserved part involves three error

i

is career-speci…c ex-ante heterogeneity and

components, ordered by declining persistence. The …rst component

is constant over the life-cycle. This is the multidimensional pre-labor market skill part that explains so much of life-cycle earnings variation in KW97. The second component

a;ij

is match-speci…c and evolves endogenously

over time. It is one of the central features that distinguishes my model from KW97. How exactly a match is de…ned requires a description of the search process, given below. The …nal component "a;it is a purely transitory worker-career shock and is the sole source of gross-‡ows in excess of net-‡ows in KW97. An important implication of this equation is that any of its components govern the life-cycle dynamics of a worker’s comparative advantage. In particular, tenure accumulation, match heterogeneity and transitory shocks can all be interpreted as updates of the predetermined multidimensional skill endowment. Next, consider equation (13) which describes the transferable or general skill component of log-earnings. The observable part of this component is an experience-earnings pro…le, where experience is measured in actual rather than potential years spent working. The returns to general experience are allowed to vary across careers, consistent with the reduced-form evidence presented in the descriptive section and with US evidence in Gibbons, Katz, Lemieux and Parent (2005) and Firpo, Fortin and Lemieux (2011). This assumption is the prime source of net reallocation of 2 5 More realistically, one could assume that skill prices evolve stochastically. This would require estimating the parameters of this process and would expand further the already large state space. For the main resuls of this paper the assumption of perfect foresight over aggregate skill prices is unlikely to have a major impact. 2 6 Time indices can be dropped since it does not add any information about individual i0 s experience and tenure once one conditions on age.

26

workers over the life-cycle into occupations with high returns and is directly adopted from KW97 and the theoretical model of career progression in Gibbons and Waldman (1999, 2006). The …nal component is unobserved and adds a skill process that is common to all careers to the model. Again, this process can be thought of as an update of a skill component. However, in contrast to the match speci…c and the purely transitory components, this process changes the absolute advantage of a worker, thereby altering the relative attractiveness of employment versus unemployment but not the relative attractiveness of careers. The earnings equations (11) to (13) are an extension of KW97 that allows for true dynamics in the residual part of earnings. The decomposition of the unobserved term into a permanent, persistent and transitory component together with match heterogeneity is quite standard in the literature on the returns to tenure and the sources of earnings inequality, such as Altonji and Shakotko (1987, 2005) or Card, Kline and Heining (2013). The prime distinction of the speci…cation above is the multidimensionality of skills and with it the interpretation of the di¤erent sources of earnings risk. Importantly, match heterogeneity adds an explicit link between worker mobility on the one hand and earnings dynamics on the other hand, and it persistently modi…es the attachment of a worker to a particular career. A mapping from gross to net earnings is not available in the data. This requires speci…cation of the tax schedule, which corresponds to a speci…cation of the G-function in equation (3). Since choices are discrete and do not involve calculation of marginal returns, the decision-relevant taxes are average tax rates on earnings. De…ning

t

(W ) as

the average tax schedule in calendar year t as a function of earnings W yields the following relationship between potential gross earnings and potential net earnings as a function of career choices net; Wa;ijt = 1

The Search Process

t

Wa;ijt

Wa;ijt .

2

C

: (14)

Before describing the dynamics of the error components in equations (12) and (13) it is

necessary to characterize the frictional search process. This process is the link between the match-speci…c component (12) and career opportunities. I adapt a search technology that has been popular in recent work on single-agent models of the dynamics of earnings, hours of work and consumption, such as Low, Meghir and Pistaferri (2010) or Erosa, Fuster and Kambourov (2016). This speci…cation takes the earnings process as a model primitive rather than an equilibrium outcome from bargaining between worker and …rms. It has the advantage of making rich dynamics in the earnings process theoretically and computationally tractable, at the cost of restricting the types of counterfactual experiments that can be conducted. In the context of my model the search process is made complicated by the fact that job mobility can take place between …rms and between careers, an issue that has been recognized at least since Neal (1999). I simplify this process by following Neal (1999) in imposing that any career change necessarily requires a switch of employer. As a consequence, the match component of earnings is a combination of employer- and career match. To keep a meaningful distinction between the earnings dynamics related to career and employer transitions I allow the distribution of match e¤ects to depend on whether the o¤er comes with a career switch or not. First consider the group of labor market entrants. Labor market ‡ows from the previous period are ill-de…ned for this group, and any frictional parameters need to be identi…ed from employment stock variables. As a consequence,

27

one cannot estimate the rate at which labor market entrants draw job o¤ers. Yet, given that a substantial share of entrants have the option of starting formal employment with their former training employer, it is reasonable to assume that their job search process is inherently di¤erent from the process for more senior workers. I thus assume that a share p0 of labor market entrants has simultaneous o¤ers from each career, while a share (1 have any job o¤ers. Unemployment arises because of two mechanisms. First, a share (1

p0 ) does not

p0 ) does not have a

pending o¤er from the training …rm and needs to search for a new job through unemployment. Second, a share p0 does have the opportunity to choose in which career to work, but unemployment is chosen voluntarily. This introduces a relationship between initial unemployment and the skill endowment of a worker. Next, consider workers who have been in the labor force for some time. Unemployed workers …nd job o¤ers with probability

u

and are free to choose which career to re-enter. For employed workers the search process explicitly

depends on the current career choice. An existing job is destroyed with exogenous probability . Among those who experience job loss, a fraction

has the opportunity to start a new job in a career of choice in the same period,

and the rest is forced to enter unemployment. Workers who are not displaced receive outside o¤ers with probability . A share

of these workers receive simultaneous o¤ers from each career, while a share (1

) receives an o¤er

from the same career. The event of drawing o¤ers from di¤erent careers simultaneously features heavily in the model. A more ‡exible speci…cation would be to allow arrival rates to depend freely on the current career and the career from which the o¤er arrives. The speci…cation considered here has the advantage of being tightly parameterized while combining the frictionless choice process in KW97 with a frictional search process in which some workers can switch jobs only within career and others have multiple career options at the same time. In particular, the KW97 choice structure is available to a share

u

of the unemployed and a share [

+ (1

)

] of the employed. The

event that an employed worker is laid o¤ and draws o¤ers from each career simultaneously in the same period is introduced to rationalize why some workers switch jobs and careers even though they experience a substantial decline in earnings.27 Notice that the restrictions on the search process imply that, for any a > 0, the transition law for the consideration sets does not depend on any state variables other than the current consideration set. Hence, the transition law in (4) can be decoupled into

where the superscript ! a+1 given (! a ;

! Sa+1

=

F

! a+1

=

F ! (! a ;

!

Sa ;

! stands for exlusion of ! and where

a; a w a; a ) w a

w

(15)

is a random variable that has the distribution of

28

a ).

Earnings Process and Human Capital Accumulation

Having speci…ed the search process it is now possible

to describe the dynamics of observable and unobservable state variables in the cross-sectional earnings equations 2 7 This speci…cation is commonly used in the empirical search literature for the same reason REFERENCES. Notice that not every job transition that comes with a wage decrease needs to be rationalized in this way. As shown in the descriptive section, negative wage growth at a career transition can come with substantial wage future wage growth and may thus re‡ect an optimal choice. 2 8 For example, if ! = and a = funemplg, then ! a+1 = with probability and ! a+1 = 3 with probability (1 ). a

28

(11) to (13). Career tenure and actual labor market experience are initialized at zero and evolve endogenously according to the laws of motion tena+1;i expera+1;i exper0;i

= I

C a

(Sa ) =

= I ( (Sa ) 2 =

tena;i + 1 + 1 e

) (expera;i + 1) + (1

0 and ten0;i = 0 for each

2

C

C a

I

(Sa ) =

I ( (Sa ) 2

0; for each e

2

C

:

(16)

)) expera;i

:

The …rst equation is vector-valued and states that tenure in career

increases in increments if

is chosen and falls

back to zero if not. The second equation states that actual labor market experience increases by increments of one if a worker chooses employment and remains at the current level if not. These equations incorporate two implicit assumptions. One is that tenure is fully career speci…c while experience is fully transferable, and the other is that tenure depreciates fully upon exit from a career while experience does not depreciate when leaving employment. The combination of speci…city and full depreciation has been popular in structural models of occupation-speci…c human capital accumulation, such as Kambourov and Manovskii (2009), and is attractive from a computational point of view since it eliminates past tenure in all occupations but the currently chosen one as a state variable. Given the coarse de…nition of occupational groups in my framework, this assumption is also reasonable if workers who return to a career after a spell of absence are likely to perform di¤erent tasks in that career. On the other hand, the assumption that the general human capital component does not depreciate during unemployment is harder to defend. Optimally one would like to estimate the rate of depreciation, as in Adda and Dustmann (2017). However, in my model it is di¢ cult to separate the behavioral and the earnings e¤ects of human capital depreciation from other model components, in particular multidimensional skill heterogeneity and match heterogeneity. Speci…cally, loss of general human capital during unemployment increases unemployment duration and depresses re-entry earnings, but the same is true if low-skill individuals are more likely to choose unemployment and if the match component is lost upon a transition from employment to unemployment. The no-depreciation assumption can thus be interpreted as an identifying restriction. That being said, the human capital stock does depreciate during a spell of unemployment because of the loss of speci…c human capital accumulation, and the e¤ective depreciation rate will depend on the relative importance of speci…c and general human capital in producing overall earnings potential. Initializing both human capital components at zero is an identifying restriction as well because any heterogeneity in initial conditions will be absorbed by the multidimensional ex-ante heterogeneity component

i.

This component

is vector valued, with as many elements as there are careers. It is assumed to have distribution i

where

N( ;

is an unrestricted covariance matrix. The vector

);

(17)

are the intercepts of the earnings equations (11). Notice

that human capital accumulation during apprenticeship will be part of this heterogeneity component. Normalizing initial experience and tenure at zero thus works in favor of …nding a larger role of ex-ante heterogeneity on life-cycle labor market outcomes. The search process and earnings potential interact as follows. Workers, whether employed or unemployed, receive job o¤ers from employers periodically, and the only component that is speci…c to such an o¤er is the match e¤ect a;ij .

If the o¤er allows a worker to stay in his current career , then the match e¤ect is a random draw from the

29

distribution H stay . Otherwise the match e¤ect is distributed according to H move . Earnings gains from job mobility are thus allowed to depend on whether the transition takes place within or across careers. If a worker receives o¤ers from multiple careers simultaneously, their match-speci…c components are independent of each other. For example, unemployed workers receive job o¤ers from all four careers at rate they are four independent draws from H move . Once accepted,

u,

a;ij

and conditional on all other variables in SaW

remains constant for the duration of a match.

As a consequence, match e¤ects act like transitory shocks to potential earnings that morph into a highly persistent component once a job o¤er is accepted, thereby tying together choice- and earnings dynamics. The distributions H stay and H move are taken exogenously. Equilibrium search models that endogenize these objects are a valuable guide for the parameterization of H stay and H move . They commonly produce equilibrium wage o¤er distributions that deviate substantially from Normality. This is also con…rmed by the …nding in the descriptive section that the distribution of earnings changes at job mobility has heavy tails. Since the link between worker mobility and earnings dynamics is important for disentangling ex-ante from ex-post heterogeneity, I thus use a ‡exible speci…cation. Speci…cally, I assume that H stay and H move are of the Singh-Maddala type with parameter vectors

stay

and

move

. The Singh-Maddala distribution has three parameters that determine location, scale and

shape and is known to approximate well a wide range of distributions that are relevant for studying earnings inequality. I use the notation SM

stay

a;ij

SM and assume that initial conditions are non-degenerate: 0;ij

SM

if move

move

= C a 1 (Sa otherwise

for each

1)

e

2

:

(18)

(19)

The latter condition can explain why initial earnings are highly, but imperfectly correlated with subsequent earnings. It will also have implications for the relationship between initial earnings and worker mobility across employers and careers. The two remaining components of unobserved heterogeneity are transitory shocks to comparative advantage and persistent shocks to absolute advantage. The transitory component "a;i is a four-element vector of serially uncorrelated shocks, one for each of the four potential earnings equations. In contrast to KW97 I assume that transitory shocks are uncorrelated across careers as well, so that their joint distribution factors into the product of marginals, with "a;i

N 0;

2 ";

for each

2

e

:

(20)

This assumption can be justi…ed by the presence of the persistent component za;i which is not career-speci…c and thus a¤ects a worker’s absolute but not comparative advantage. It’s process is an AR (1) process with persistence and intial condition

2

;0 :

za;i

=

N 0;

a;i

var (z0;i )

za

=

2

1;i

+

a;i

(21)

2

;0 .

Importantly, this component introduces a correlation between residual earnings of the same individual between careers even with independent transitory shocks.

30

Unemployment and Sample Attrition Unemployment and sample attrition are two outside options that are available to any worker at any age. Utility of the unemployment choice is the sum of a monetary component and a utility component, just like for the employment choices. Unemployment bene…ts received are observable for the universe of the unemployed in the SIAB 1975-2010 data, and potential bene…ts for employed workers next period can be imputed using the institutional rules. The calibration of the unemployment bene…t system will be described in the empirical section. Modeling attrition is more di¢ cult since workers exit the sample permanently when this choice is made. Yet, the endogeneity of attrition is apparent from the descriptive analysis. In particular, those with the lowest and the highest earnings are relatively more likely to exit the sample than workers in the middle of the earnings distribution. Hence, if there is a strong permanent component in wage dynamics, then sample attrition will cause a downward bias in the estimated importance of pre-labor market conditions. It is therefore important to endogenize sample attrition. I borrow from the literature on worker ‡ows between employment, unemployment and non-employment over the business cycle that allows the value of non-market work to depend on a measure of earnings potential. Let Vaexit (Sa ) be the value of choosing non-employment or self-employment at age a. Let W gross 1;i be the gross earnings potential of an individual as de…ned by W gross 1;a;i =

Wagross ;i for

= min fk : a k (Sa k ) 2 max f i g otherwise.

1g

and

6= ?

:

(22)

This is either the last earnings received on the job or, if the individual has been unemployed since labor market entry, the largest component in the multidimensional skill endowment vector Vaexit (Sa ) = F V a; W gross 1;a;i +

exit

i.

I assume that (23)

where exit

N 0;

2 exit

(24)

and where F V is a ‡exible parametric function of age and earnings potential at age a. The dependence on age is introduced because the value of a particular earnings potential changes over the life-cycle. In essence, equation (23) is a reduced-form approximation to the value of exiting that is required since neither choice- nor earnings dynamics are observed once an individual …nds exiting worthwhile. The parameterization is discussed in the empirical section.

Terminal Condition

Solving the dynamic decision problem of forward-looking agents requires a terminal condi-

tion for the value functions. I assume that workers settle into the stable part of a career at age (A + 1), which lasts until the o¢ cial retirement age of R1 . Afterwards they enter retirement which ends deterministically at age R2 with a continuation value of zero. Retirees receive bene…ts that are

percent of the last gross earnings. To approximate

the progression of the German social insurance system I assume that bene…ts are taxed. The primary characteristic of the stable part is that workers do not make active career choices anymore, unless they are unemployed. Hence, a worker who chooses employment in career

2

C

at age A remains employed in that career until age R1 , and the

workers’skill endowment remains constant at HA;i . As a consequence, earnings grow at the rate of aggregate skill prices, P (t). Workers who are unemployed at age A continue to receive o¤ers from all careers simultaneously at a rate

A.

O¤ers from career

pay the potential earnings at age A, WA , times the growth of aggregate skill prices.

31

The assumption that individual life-cycle labor market dynamics evolve exogenously after age A is similar in spirit to the "‡at spot approach" to estimating skill prices or returns to human capital accumulation in Heckman et al and Huggett et al respectively and is imposed for several reasons. First, most cohorts who enter the sample directly after completion of an apprenticeship degree are not observed after age 50, so that any speci…cation of labor market dynamics past this age involves out-of-sample predictions. Second, for older cohorts that are in the sample at a later stage of their life-cycle there are two major stylized facts. On the one hand, between the age of 50 and 54 their earnings and labor market transition rates do not display any age e¤ects. This is the criterion by which I have chosen the "older worker sample" in the data section. It is therefore natural to set A = 50 in the following. Since the dynamic choice process of the model generates endogenously declining worker transition rates and increasing earnings, this suggests that it does not have any bite during this stage of the life-cycle. Workers seem to have settled into their preferred career, and the remaining dynamics are driven by exogenous shocks. On the other hand, labor market dynamics start to pick up again as workers approach retirement, and these dynamics involve raising variances in earnings, increasing transitions into unemployment and non-employment, and an increasing importance of part-time work. As my model is not built to explain these dynamics, I abstract from them alltogether. Implicit is the assumption that these dynamics are also driven by exogenous shocks, such as declining health, that are unpredictable at age A and which risk-neutral workers do not try to ensure against through selecting into particular careers. It is unlikely that these assumptions have any quantitatively important impact on the model predictions of labor market dynamics early in the life-cycle. Even though earnings evolve exogenously after age A, workers still need to make predictions about the evolution of aggregate variables to calculate continuation values. Since this requires out-of-sample predictions, I impose a number of additional restrictions. For employed workers, individual tax rates on labor income are assumed to remain constant at their age-A values during the period of stable employment. This is an approximation to actual adjustments in the tax schedule by the …scal authority in reaction to aggregate earnings growth. Furthermore, all cohorts expect to face identical growth in aggregate skill prices and average tax schedules at the time they enter the stable part of a career. At …rst, this seems to be a strong restriction. Notice however that the oldest cohort in the main sample turns 50 in 2005 and that most cohorts in the sample enter the stable part of a career after 2010, which is the …nal sample year 2010. Furthermore, there were no major changes in the tax- and unemployment bene…ts system after 2005, and, as shown below, the rate of growth in skill prices was rather stable. As such, the assumption is a re‡ection of data limitations on the one hand and empirical facts on the other hand. Matters are somewhat more complicated for those who are unemployed at age A since they may or may not accept an employment o¤er that arrives during the stable part of a career. Initially workers are eligible for a replacement rate that is a function of calendar time, age, and unemployment duration. For the same reasons as for the average tax schedule, this rate is calibrated to the value the oldest cohort faces when becoming A years old. This removes time as a state variable from the replacement rate function, which I write as rA (dur). From age (A + 1) the replacement rate drops to the social insurance level, which is 35 percent, and remains there during retirement.29 Neither unemployment- nor retirement bene…ts are taxed. Since I neither observe nor model the detailed dynamics after age A, it is necessary to impose some additional restrictions on how the arrival- and acceptance process of job 2 9 The

value of 35 percent is taken from von Wachter.

32

o¤ers works. Most importantly I assume that any job o¤ers that are deemed acceptable at some point between the ages of (A + 1) and R1 are accepted as soon as they arrive and that they are kept until retirement.30 In the appendix I show that these assumptions have the following implications. First, the value of a job in career can be written as a function of gross earnings W and past choices is linear and continuously di¤erentiable in W

A 1.

This function, written VeA (W ;

and has an analytical expression. Second, the value of remaining

unemployed for the rest of the life can be written as a function of past earnings W and the preference shock

u

A 1 ),

. This function, written VAu;u (W

u

1 ; dur;

1,

), is linear in W

unemployment duration dur 1

and

u

and is continuously

di¤erentiable in all its arguments. Similarly, the value of being unemployed at age A and accepting an o¤er from career

as soon as it arrives is a function of the same state variables and of the potential earnings in career

age A. This function is written as VAu W

4

1 ; dur; fW

g

2

VAu; C

;

(W u A

1 ; dur; W

;

u A ).

= max VAu;u (W

at

The value of unemployment is thus 1 ; dur;

u

) ; fVAu; (W

1 ; dur; W

;

u A )g 2

C

Designing a Computationally Feasible Solution Algorithm

Estimating Dynamic Discrete Choice models is computationally challenging because of the need to solve a dynamic program repeatedly and because of the di¤ulty of constructing the estimation criterion. Let the vector of structural parameters be

, the data be

and the estimation criterion be z. Then the structural estimation consists of

…nding b = arg optim fE [z ( ; )]g ;

(25)

where the optim operator is either the maximizer or the minimizer, depending on whether one uses a likelihoodor moment-based estimation procedure. In any case, one will encounter three distinct computational challenges. The …rst is the computation of the structural model, which involves solving a high-dimensional dynamic program. The second is a high-dimensional integration for constructing the estimation criterion. The third is the numerical optimization for …nding the estimate b .

A sizeable literature in empirical industrial organization and econometrics, based on the seminal work by Hotz

and Miller (1994), has studied identi…cation and inference for a class of estimation methods that avoids solving the dynamic program alltogether. The idea is that under certain restrictions on the model structure, there is an invertible map between value functions and choice probabilities. Hence, if one assumes that observed choices are dynamically optimal, then one can recover value functions after non-parametric estimation of conditional choice probabilities (CCP). In the context of my model, this approach is infeasible for two reasons. First, the state-space of my model is large and contains several unobservables. As a consequence, estimates of CCP will be imprecise and may even su¤er from a support problem. Second, and more severe, my model features frictions. Hence, there will be several value functions, one for each possible realization of the job arrival process. For example, the observed choice of unemployment can be rationalized as an unconstrained optimum over the entire space of possible alternatives 3 0 Without uncertainty and aggregate growth in skill prices it cannot be optimal to reject an o¤er that is accepted later on. The assumption imposed here thus means that workers do not strategically delay acceptance of an o¤er to wait until skill prices have risen enough. This is plausible given that the total growth of skill prices during the stable part of a career is quite small.

33

, or as a constrained optimum over the consideration set

n

consisting of only the two choices "unemployment"

and "attrition". Since there are now several value functions that need to be characterized to calculate continuation values, one for each possible realization of the consideration set, there cannot be an invertible map to choice probabilities. Fortunately, with the appropriate choice of a computational algorithm it is not even necessary to avoid solving the Dynamic Program. I thus follow a similar stragety of direct attack of the problem like in KW97, though the details of my computational algorithm are quite di¤erent. These are discussed in detail in the computational appendix. The essence is an algorithm that is in the spirit of Approximate Dynamic Programming, as described in detail in Powell (2009). In a …rst step one reduces the state space of the function to be approximated by focusing on expected continuation values de…ned on post-decision state variables. This approach has already been used implicitly in the discussion of the terminal condition above, where terminal value functions are de…ned on earnings rather than all the components of the earnings function. Similar formulations can be chosen for all other expected value functions as well. The point is that once one has made a choice, the value does not depend directly on the composition of earnings anymore. However, a number of variance components of earnings need to be kept in the state space, such as pre-labor market skills. In a second step one then can reduces the state-space further by explicitly exploiting the model structure. For example, conditional on making a certain career choice, all other occupation-speci…c human capital endowments become irrelevant because they depreciate fully. After these two steps, there are 10 post-decision state variable for the expected value function, compared to 24 state variables in the conventional value function de…ned on ex-ante state variables. Yet, the choices delivered in both cases are identical, as shown in Powell. Furthermore, the expected value function is continuously di¤erentiable in state variables and parameters, while the conventional value function is not. As a consequence, I can use a sparse-grid Chebyshev interpolation method, which has a "near-optimal" convergence rate, as shown for example in Bungartz and Griebel.

This leaves the remaining two computational issues - the high-dimensional integration necessary for computing the estimation criterion and its numerical optimization. I address the former simply by using Indirect Inference. As is well known in the econometrics literature, Indirect Inference has better statistical properties than Simulated Maximum Likelihood (SML) then the number of simulation draws is limited.31 In my application, it has the additional bene…t that the estimation can be performed outside of the research data center of the IAB since aggregate moments can be taken out while individual-level data, required for SML, cannot. To address the remaining computational problem I proceed as follows. First, I reduce the size of the parameter space in (25) by exploring the possibility of calibration and pre-estimation of parameters. For example, the unemployment bene…ts and income tax systems are given deterministically and can thus be calibrated, and skill prices can be pre-estimated using a ‡at-spot methods. This will be described in detail in the section on estimation. Second, I rely on the di¤erentiability of the estimation criterion, which is an implication of the results in Norets (2010) as long as one chooses an appropriate simulation method.32 Hence, I can use modern solvers for high-dimensional 3 1 See

for example the book on simulation-assisted econometric methods by Gourieroux and Monfort (1993). shown in the next subsection, expected value functions are continuously di¤erentiable, and so are payo¤s. Furthermore, all targeted moments are integrals over either choice probabilities, which are di¤erentiable functions of payo¤s and continuation values. Theoretically, the estimation criterion is thus di¤erentiable. In practice, this result can be broken by using poorly behaved simulation procedures, such as the crude frequency simulator for choice probabilities. In the actual estimation, one thus needs to use a well-behaved 3 2 As

34

optimization problems that rely only on …rst-order di¤erentiability conditions.33

5

Estimation

5.1

General Approach

I divide the structural parameters of the model into three groups and estimate them in separate stages. The …rst stage is a calibration of the discount rate, the earnings tax schedule and the unemployment insurance system, the …rst of which is well-known to be poorly identi…ed in DDC-models and the last two of which are set by the government. In a second stage I explore the possibility of estimating a number of structural parameters without fully solving the model. The goal is to develop an estimation strategy that is consistent with the assumptions of the structural model, yet does not require simulation of the model economy. This strategy works for two sets of parameters, the skill prices and the returns to tenure. The third stage structurally estimates the remaining parameters by Indirect Inference.

5.2

First Stage: Calibration

Discount Factor and Taxes on Labor Earnings The annual discount rate is assumed to be 5%, a value commonly used in the structural labor literature.34 The calibration of the tax schedule is more involved. For each year since 1975 I use the online tool provided by the German Ministry of Finance to calculate average income taxes at selected income values. Starting from the lower threshold I sample income levels in intervals of increasing length and compute the average tax rates. I choose a progressively wider income grid since the average tax rate function is highly non-linear in income near the lower threshold while approaching a linear function at higher income levels. The grid was adjusted accordingly in each year. As it turns out, tax rates are a nearly linear function of log-income in each sample year. As a consequence, I parameterize the tax schedule by estimating a bivariate linear regression of tax rates on log-income separately for each year. The R2 for this speci…cation is above :99 in all years. The tax rates used in the estimation are then the maximum of the predicted value and zero, the latter of which applies to earnings below the threshold. The raw data used for calibration are shown in appendix table D.1. The estimates from the linear regression models together with the R2 are listed in appendix table D.2. Notice that the approximation of the value function relies on the continuity of time as a state variable. As a consequence, the tax schedule needs to be evaluated o¤ the grid of integer-valued calendar years. To this end I interpolate the average tax rates as a function of time using a spline. This guarantees that the ‡ow payo¤ functions are di¤erentiable in both, state variables and parameters and is important for accuracy of the polynomial sparse-grid approximation. simulation procedure. Details are provided in the appendix. 3 3 I have experimented with KNITRO and SNOPT, both called from the TOMLAB environment. 3 4 See for example Lise and Robin (2016).

35

Unemployment Insurance The German unemployment system provides unemployment insurance to individuals that are based on previous earnings, age, and whether the individual satis…es an "experience requirement", meaning that he has paid su¢ ciently many years into the system. An apprenticeship explicitly counts towards the experience requirement. Since I focus on individuals who hold an apprenticeship degree, and since long-term unemployment is rare in my sample, I assume that every worker satis…es the experience requirement since otherwise the number of state variables would increase even further. The entitlement is the calculated as follows. As workers enter unemployment, they receive "unemployment insurance" which is a fraction of previous earnings, called the replacement rate. This rate is above 60% in all years, but only up to a certain level of unemployment duration. Afterwards the replacement rate falls to a lower value, called "unemployment assistance", and remains there inde…nitely. The duration of unemployment insurance depends on age and changes over time. Parameters of this system are taken from Hunt (1995) and Schmieder, von Wachter and Bender (2011) and are shown in appendix table E.1. Again, I interpolate these parameters between calendar years using a spline to maintain the assumption of di¤eretiability of the payo¤ function.

5.3

Second Stage: Reduced-Form Regressions and IV-estimation

Skill Prices To pre-estimate skill prices I use the ‡at-spot method innovated by Heckman, Lochner and Taber (1998). Applied to my context, the important observation is that the model generates age-e¤ects in earnings and worker transition rates via human capital accumulation and search. Conversely, if one cannot reject the hypothesis of "no age e¤ects", then the behavioral content of the structural model, which is essentially a selection e¤ect, is weak. Since workers will eventually accumulate su¢ ciently much speci…c human capital and will reach their best match, this is most likely the case for older workers. As shown in section 2, the hypothesis of constant transition rates between careers, …rms, and between employment and unemployment cannot be rejected for workers between the age of 50 and 54. Conditional on time …xed e¤ects, earnings are not growing over this part of the life-cycle either. Now consider a regression of log-earnings on time …xed e¤ects, esimated separately for each career

2

e

and

restricted to this age group: log Wa;ijt = 't + ! a;ijt ;

(26)

where I use the same notation for gross-earnings like in the description of the structural model and where ! a;ijt is an error term. Even though workers have settled into stable careers, estimates of the …xed e¤ects 't will not converge in probability to skill prices Pt . This is because the composition of workers within each career may change over time so that cov 't ; ! a;ijt 6= 0. If for example relative growth of skill prices in managerial occupations draws in more workers over time, then the estimated skill prices for this occupation will be biased downwards. There is a straighforward solution to this issue: Estimate the regression in …rst di¤erences rather in levels, conditioning on workers who remain on the same job in two consecutive years. In this case, any earnings growth on the job will be interpreted as growth in skill prices. Under the assumption that the returns to human capital accumulation net of depreciation are zero for this group of workers, which is supported by the lack of any age e¤ects in the older-worker sample, then this "‡at spot" method is valid. Simply spoken, while compositional e¤ects

36

are important in levels, they are irrelevant in growth, since there is no systematic growth other than time e¤ects anyways.

Returns to Tenure: Altonji-Shakotko IV The structural model features returns to both, transferable and speci…c human capital. This relates it to early studies of the speci…city of human capital, such as Altonji and Shakotko (1987) or Topel (1991). The primary di¤erence is that these studies focus on …rm-speci…c human capital while my model features career-speci…c human capital. However, once one conditions on career, then my earnings equation is in fact identical to the speci…cation in Altonji and Shakotko (1987). As a consequence, I can adopt their IV-approach separately for each career. Speci…cally, I use the deviation between current tenure and average tenure within match as an instrumental variable, where tenure is de…ned over the match between worker and …rm-career. Under the assumption of constant match heterogeneity, this strategy is valid as long as the behavioral e¤ect of the AR(1)-process of absolute advantage is not too strong. Altonji and Shakotko (1987) and Altonji and Williams (2005) argue this to be the case. A well-known issue is that the simultaneous estimation of returns to tenure using Altonji and Shakotko (1987) and skill-prices is a source of inconsistency. I avoid this issue by estimating skill-prices in a …rst step using the ‡at-spot method and by implementing the IV-strategy on earnings data that are cleaned from these time e¤ects.

5.4

Third Stage: Structural Estimation

The remaining parameters are estimated by Indirect Inference. The estimation algorithm is essentially a nested …xed point algorithm, where the inner loop approximates the expected value function using sparse grid Chebyshev interpolation by backward induction, and where the outer loop searches for the parameter minimizing the Indirect Inference estimation criterion. Choices of targets are clear for most parameters. For example, the distribution of match e¤ects will have …rst-order e¤ects on the distribution of earnings changes when workers change employers or careers; the returns to experience have …rst-order e¤ects on the shape of career-speci…c experience-earnings pro…les; and frictional parameters have …rst-order e¤ects on worker transition rates. In an exploratory analysis, it was clear that the only identi…cation challenge is the distribution of multidimensional skill-heterogeneity. The parameters describing this distribution cannot be identi…ed from the covariance structure of earnings within careers only, since one also needs to recover the o¤-diagonal components of the distribution of pre-labor market skills. Instead, one also needs to take into account the dynamics of choices. I thus match all statistics shown in the descriptive section. In addition, I also match the covariance structure conditional on initial choices. Coupled with the detailed worker transition matrices and the earnings distributions before various types of mobility, as shown in …gure 9, this approach turned out to deliver precise estimates.

6 6.1

Results (Preliminary) Parameter Estimates

Skill price estimates from the ‡at-spot method are shown in Figure 10. These con…rm previous …ndings, such as those in Dustmann, Schoenberg and Ludsteck (2009). Most importantly, low-skill service occupations and workers

37

in production- and operative occupations have dramatically lost ground in terms of skill-price growth relative to the other two occupational groups. In particular, they have not experienced any aggregate earnings growth since the early 1990s and may have even seen their earnings decline. In contrast, workers in managerial, technical and professional occupations, but also in clerical- and sales jobs have gained continuously over the same time period. As a consequence, one expects that workers with comparative advantages in the poorly performing occupationa groups have experienced persistent relative earnings losses. The remaining estimates of structural parameters, including those obtained from the Altonji-Shakotko IVstrategy, are shown in appendix table A. Two main results worth highlighting. First, the structural returns to tenure tend to be larger than those from simple OLS-regression, shown in table 4. As a consequence, the returns to experience decrease relative to the OLS-analogues. At the same time, managerial occupations remain to be those with the highest returns to labor market experience, as assumed in Gibbons and Waldman (1999, 2006). Second, frictions are large. Only about a quarter of employed workers receive outside o¤ers each month. The majority of these o¤ers, about 87 percent, come from within career. Hence, allocation across careers is a highly frictional process. This is consistent with …ndings in KW97 and Kennan and Walker (2011), who estimate DDC-models without search frictions, that the monetary costs to worker mobility is high. Simply stated, given the population distribution of earnings, one would expect workers to be much more mobile. Given that they are not suggests that there are factors that depress worker mobility. These factors are captured by search frictions in my model, where workers search for better matches, and by costs to mobility in KW97 and Kennan and Walker (2011).

6.2

Sources of Life-Cycle Income Inequality

In this section I present the results from numerous counterfactual exercises that investigate the numerical impact of di¤erent model components on life-cycle earnings inequality and earnings mobility. I use discounted life-cycle earnings, in the following refered to as ”wealth”, as the primary outcome of interest since they are commonly thought to better capture di¤erences in welfare than period-by-period earnings. All counterfactual experiments are conducted by simulating complete life-cyle career trajectories for as many individuals as in the estimation sample, using the actual parameter estimates, but with one set of parameters adjusted to re‡ect the counterfactual exercise in question. Table 8 shows results of shutting down various channels of wealth inequality. Inequality is measured by the standard deviation of log-wealth. Each row in the table refers to a di¤erent counterfactual experiment, and each column refers to a di¤erent model speci…cation. I consider the Roy-model with type heterogeneity as estimated in KW97 and the full model with search frictions. As shown in row one of column one, eliminating type heterogeneity from the Keane-Wolpin speci…cation would reduce the variance of the wealth distribution by almost 74 percent. Another measure of the importance of type heterogeneity for life-cycle inequality is the fraction of wealth inequality that is explained by type …xed e¤ects. This is the measure used in Keane and Wolpin, but it cannot be used for model components that vary over time, such as match heterogeneity and transitory or permanent shocks. Results from such variance decompositions are listed in the lower panel of the table. In the Roy-model, 91 percent of life-cycle variation is explained by type heterogeneity, an estimate that is strikingly close to the Keane and Wolpin’s estimate of 90 percent obtained from the NLSY. Hence, according to this result, over 90 percent of wealth inequality

38

is determined even before individuals enter the labor market. Column two lists the results from counterfactual experiments when using the full model with frictions. The conclusions are dramatically di¤erent: When eliminating type heterogeneity, wealth inequality decreases by 34 percent only, almost a half of the number from the Keane–Wolpin model. Similarly, only 41 percent of the earnings variation is driven by type heterogeneity. Furthermore, excluding transitory shocks from the full model does not have an impact on inequality at all, while the corresponding impact in the Keane-Wolpin model is a reduction of inequality by 14 percent. Ruling out match heterogeneity, an element of unobserved heterogeneity that is absent from the Keane-Wolpin speci…cation, would reduce inequality by 27 percent. Hence, the quantitative implications of type and match heterogeneity are estimated to be very similar.

7

Conclusion

To be added.

39

References [1] Abowd, J. M. and D. Card (1989): “On the Covariance Structure of Earnings and Hours Changes.” Econometrica, vol. 57(2), pp. 411-445. [2] Abowd J., F. Kramarz and D. Margolis (1999): “High-Wage Workers and High-Wage Firms.” Econometrica, 67(2), pp. 251-333. [3] Acemoglu, D. and D. Autor (2011): “Skills, Tasks and Technologies: Implications for Employment and Earnings.” Handbook of Labor Economics, Chapter 12, Vol. 4b. [4] Adda, J., C. Dustmann, C. Meghir and J.-M. Robin (2009): “Career Progression and Formal versus On-the-Job Training.” Mimeo, University College London. [5] Adda, J., M. Costa Dias, C. Meghir and B. Sianesi (2009): “Labor Market Programmes and Labor Market Outcomes.” Mimeo, University College London. [6] Aguirregabiria, V. and P. Mira (2002): “Swapping the nested …xed point algorithm: A class of estimators for discrete markov decision models.” Econometrica, vol. 70(4), pp. 1519–1543. [7] Aguirregabiria, V. and P. Mira (2007): “Sequential Estimation of Dynamic Discrete Games.” Econometrica, vol. 75(1), pp. 1-53. [8] Aguirregabiria, V. and P. Mira (2009): “Dynamic Discrete Choice Structural Models: A Survey.” Journal of Econometrics, forthcoming. [9] Asbury, K. and R. Plomin (2013): “G is for Genes: The Impacts of Genetics on Education and Achievement.” Wiley-Blackwell. [10] Altonji, J., A. Smith Jr. and I. Vidangos (2013): ”Modeling Earnings Dynamics”, Econometrica, vol. 81(4), pp. 1395-1454. [11] Bagger, J., F. Fontaine, F. Postel-Vinay and J.-M. Robin (2014): “Tenure, Experience, Human Capital, and Wages: A Tractable Equilibrium Search Model of Wage Dynamics.” American Economic Review, 104(6), pp. 1551-1596. [12] Baker, M. (1997): ”Growth Rate Heterogeneity and the Covariance Structure of Life Cycle Earnings”, Journal of Labor Economics, 15, pp. 338-375. [13] Baker, M., and G. Solon (2003): ”Earnings Dynamics and Inequality Among Canadian Men, 1976-1992: Evidence from Longitudinal Income Tax Records”, Journal of Labor Economics, 21, pp. 289-321. [14] Baker, M. and A. Melino (2000): ”Duration Dependence and Nonparametric Heterogeneity: A Monte Carlo Study”, Journal of Econometrics, vol. 96(2), pp. 357–393. [15] Belzil, C. and J. Hansen (2002): "Unobserved Ability and the Return to Schooling." Econometrica, vol. 70(5), pp. 2075-2091.

40

[16] Bernal, R. (2008): "The E¤ect of Maternal Employment and Child Care on Children’s Cognitive Development." International Economic Review, vol. 49 (4), pp. 1173-1209. [17] Bernal, R., and M. P. Keane (2010): "Quasi-structural estimation of a model of childcare choices and child cognitive ability production." Journal of Econometrics, vol. 156 (1), pp. 164-189. [18] Blundell, R., L. Pistaferri and I. Preston (2009): ”Consumption Inequality and Partial Insurance”, American Economic Review, 98(5), pp. 1887-1921. [19] Bowlus, A. J. and C. Robinson (2012): ”Human Capital Prices, Productivity, and Growth,” American Economic Review, 102(7), pp. 3483-3515. [20] Cahuc, P., F. Postel-Vinay, and J.-M. Robin (2006): “Wage Bargaining with On-the-Job Search: Theory and Evidence.” Econometrica, vol. 74(2), pp. 323-364. [21] Caucutt, E. M., and L. Lochner (2012): "Early and late human capital investments, borrowing constraints, and the family." NBER working paper, w18493. [22] Caines, C., F. Ho¤mann and G. Kambourov (2016): “Training Programs, Skills, and Human Capital Accumulation: A Life-Cycle Approach.” mimeo, University of British Columbia. [23] Cameron, A. C. and P. K. Trivedi (2005): “Microeconometrics.” Cambridge University Press. [24] Caucutt, Elizabeth and Lance Lochner (2008): “Early and Late Human Capital Investments, Borrowing Constraints, and the Family.” Mimeo. University of Western Ontario. [25] Cunha, F., J. J. Heckman (2007): “The Technology of Skill Formation.” American Economic Review, vol. 97(2), pp. 31-47. [26] Cunha, F., J. J. Heckman (2007): “The Evolution of Inequality, Heterogeneity and Uncertainty in Labor Earnings in the U.S. economy.” NBERworking papers, w13526. [27] Cunha, F., J. J. Heckman (2008): “Formulating, Identifying and Estimating the Technology of Cognitive and Noncognitive Skill Formulation.” Journal of Human Resources, vol. 43(4). [28] Davis, S. and T. von Wachter (2011): "Recessions and the Costs of Job Loss." Brookings Papers on Economic Activity, Fall 2011. [29] Devereux, P. (2002): “Occupational Upgrading and the Business Cycle.” Labour, vol. 16(3), pp. 423-452. [30] Drews, N. (2007): ”Variablen der schwach anonymisierten Version der IAB-Beschaeftigten-Stichprobe 19752004”, FDZ Datenreport 03/2007, Nuernberg. [31] Eckstein, Z. and K. Wolpin (1990): “Estimating a Market Equilibrium Search Model from Panel Data on Individuals.” Econometrica, vol. 58(4), pages 783-808. [32] Erosa, A., T. Koreshkova, and D. Restuccia (2010): "How important is human capital? a quantitative theory assessment of world income inequality." Review of Economic Studies, vol. 77 (4), pp. 1421-1449.

41

[33] Fiorini, M. (2010): "The e¤ect of home computer use on children’s cognitive and non-cognitive skills." Economics of Education Review, vol. 29 (1), pp. 55-72. [34] Firpo, S., N. Fortin and T. Lemieux (2011): “Occupational Tasks and Changes in the Wage Structure.”mimeo, University of British Columbia. [35] Fitzenberger, B., A. Osikumino and R. Voelter (2007): ”Imputation Rules to improve the EducationVariable in the IAB Employment Subsample”, Schmollers Jahrbuch (Journal of the Applied Social Sciences), forthcoming. [36] Gibbons, R. and M. Waldman (1999): “A Theory of Wage and Promotion Dynamics inside Firms.”Quarterly Journal of Economics, vol. 114(4), pp. 1321-1358. [37] Gibbons, R. and M. Waldman (2006): “Enriching a Theory of Wage and Promotion Dynamics inside Firms.” Journal of Labor Economics, vol. 24(1), pp. 59-108. [38] Gottschalk, P., and R. A. Mo¢ tt (1994): ”The Growth of Earnings Instability in the U.S. Labor Market”, Brookings Paper on Economic Activity, 25(2), pp. 217-272. [39] Gourieroux, C. and A. Monfort (1996): “Simulation-Based Econometric Methods.” CORE Lectures, Oxford University Press. [40] Gourinchas, P.-O., and J. A. Parker (2002): ”Consumption over the Life-Cycle”, Econometrica, 70(1), pp. 47-89. [41] Guvenen, F. (2009): ”An Empirical Investigation of Labor Income Processes”, Review of Economic Dynamics, 12(1), pp. 58-79. [42] Guvenen, F. and A. A. Smith Jr. (2009): “Inferring Labor Income Risk from Economic Choices: An Indirect Inference Approach.” mimeo, University of Minnesota. [43] Haider, S. (2001): ”Earnings Instability and Earnings Inequality of Males in the United States: 1967-1991”, Journal of Labor Economics, 19(4), pp. 799-836. [44] Hall, R. E., and F. S. Mishkin (1982): ”The Sensitivity of Consumption to Transitory Income: Estimation from Panel Data on Households”, Econometrica, 50(2), pp. 461-481. [45] Hause, J. (1980): “The Fine Structure of Earnings and the On-the-Job Training Hypothesis.” Econometrica, vol. 48(4), pp. 1013 –1029. [46] Heathcote, J., K. Storesletten, and G. L. Violante (2014): ”Consumption and Labor Supply with Partial Insurance: An Analytical Framework”, American Economic Review, 104(7), pp. 2075-2126. [47] Heckman, J. J. and B. Singer (1984): “A Method of Minimizing the Impact of Distributional Assumptions in Econometric Models of Durations Data.” Econometrica, vol. 52(2), pp. 271-320.

42

[48] Heckman, J. J., L. Lochner and C. Taber (1998): “Explaining Rising Wage Inequality: Explorations with a Dynamic General Equilibrium Model of Labor Earnings with Heterogeneous Agents.” Review of Economic Dynamics, vol. 1(1), pp. 1-58. [49] Heckman, J. J., J. Stixrud and S. Urzua (2006): “The E¤ects of Cognitive and Noncognitive Abilities on Labor Market Outcomes and Social Behavior.” Journal of Labor Economics, vol. 24(3), pp. 411-482. [50] Ho¤mann, F. (2016): ”HIP, RIP and the Robustness of Empirical Earnings Processes.” mimeo, University of British Columbia. [51] Hornstein, A., P. Krusell and G. Violante (2006): “Frictional Wage Dispersion in Search Models: A Quantitative Assessment.” CEPR Discussion Paper 5937. [52] Hotz, V. J. and R. A. Miller (1993): “Conditional choice probabilities and the estimation of dynamic models.” The Review of Economic Studies, 60(3), pp. 497–529. [53] Hryshko, D. (2012): ”Labor Income Pro…les are not Heterogeneous: Evidence from Income Growth Rates.” Quantitative Economics, 3, pp. 177-209. [54] Huggett, M., G. Ventura, and A. Yaron (2011): ”Sources of Lifetime Inequality.”American Economic Review, 101(7), pp. 2923-54. [55] Imai, S., N. Jain, and A. Ching (2006): “Bayesian estimation of dynamic discrete choice models.” mimeo, Rotman School of Business at the University of Toronto. [56] Jacobson, L., R. LaLonde and D. Sullivan (1993). "Earnings Losses of Displaced Workers." American Economic Review, 83(4): pp. 685-709. [57] Jolivet, G., F. Postel-Vinay, and J.-M. Robin (2006): “The Empirical Content of the Job Search Model: Labor Mobility and Wage Distributions in Europe and the U.S.”European Economic Review, vol. 50(4), pp. 877-907. [58] Jovanovic, B. (1979): ”Job Matching and the Theory of Turnover.” Journal of Political Economy, 87(5), pp. 972-90. [59] Judd, K. L. (1998): “Numerical Methods in Economics.” The MIT Press, Cambridge, Massachusetts. [60] Kahn, L. (2010): "The Long-Term Labor Market Consequences of Graduating from College in a Bad Economy." Labour Economics, 17(2), pp. 303-316. [61] Kambourov, G. and I. Manovskii (2009): “Occupational Mobility and Wage Inequality.” Review of Economic Studies, vol. 76(2), pp. 731-759. [62] Kaplan, G. (2012): ”Inequality and the Life Cycle”, Quantitative Economics, 3, pp. 471-525. [63] Keane, M. P., and K. I. Wolpin (1997): ”The Career Decisions of Young Men”, Journal of Political Economy, 105(3), pp. 473-522.

43

[64] Keane, M. P., P. E. Todd and K. I. Wolpin (2006): ”Assessing the Impact of a school subsidy program in Mexico: Using a social experiment to validate a dynamic behavioral model of child schooling and fertility”, American Economic Review, 96(5), pp. 1384-1417. [65] Krueger, D., and F. Perri (2006): ”Does Income Inequality Lead to Consumption Inequality? Evidence and Theory”, Review of Economic Studies, 73(1), pp. 163-193. [66] Lillard, L. and Y. Weiss (1979): “Components of Variation in Panel Earnings Data: American Scientists, 1960-70.” Econometrica, vol. 47(2), pp. 437 –54. [67] Lise, J. (2007): “On-the-Job Search and Precautionary Savings: Theory and Empirics of Earnings and Wealth Inequality.” Mimeo, University College London. [68] Low, H., C. Meghir and L. Pistaferri (2010): "Wage Risk and Employment Risk over the Life-Cycle." American Economic Review, 100(4), pp. 1432-67. [69] MaCurdy, T. E. (1982): “The Use of Time Series Processes to Model the Error Structure of Earnings in a Longitudinal Data Analysis.” Journal of Econometrics, vol. 18, pp. 83-114. [70] Miller, R. (1984): ”Job matching and Occupational Choice.” Journal of Political Economy, 92(6), pp. 10861120. [71] Mincer, J. (1974): Schooling, Experience and Earnings, Columbia University Press, New York. [72] Mo¢ tt, R. A., and P. Gottschalk (2002): ”Trends in the Transitory Variance of Earnings in the United States”, Economic Journal, 112, pp. C68-C73. [73] Neal, D. (1999): ”The Complexity of Job Mobility among Young Men.” Journal of Labor Economics, 17(2), pp. 237-61. [74] Norets, Andriy (2009): “Inference in Dynamic Discrete Choice Models with Serially Correlated Unobserved State Variables.” Econometrica, vol. 77(5), pp. 1665-1682. [75] Oreopoulos, P., T. von Wachter and A. Heisz (2012): ”The Short- and Long-Term Career E¤ects of Graduating in a Recession”, AEJ-Applied Economics, vol. 4(1), pp. 1-29. [76] Pavan, R. (2011): “Career Choice and Wage Growth.” Journal of Labor Economics, 29(3), pp. 549-587. [77] Postel-Vinay, F. and J.-M. Robin (2002): “Equilibrium Wage Dispersion with Worker and Employer Heterogeneity.” Econometrica, vol. 70(6), pp. 2295-2350. [78] Postel-Vinay, F. and H. Turon (2009): “On-the-job Search, Productivity Shocks, and the Individual Earnings Process.” International Economic Review, forthcoming. [79] Rust, J. (1987): “Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher.” Econometrica, Vol. 55(5), pp. 999-1033.

44

[80] Storesletten, K, C. Telmer, and A. Yaron (2004): ”Cyclical Dynamics in Ideosyncratic Labor Market Risk”, Journal of Political Economy, 112, pp. 695-717. [81] Sullivan, P. (2009): “A Dynamic Analysis of Educational Attainment, Occupational Choices, and Job Search.” International Economic Review, forthcoming. [82] Todd, P. E., and K. Wolpin. (2007): "The production of cognitive achievement in children: Home, school, and racial test score gaps." Journal of Human capital, vol. 1(1), pp. 91-136. [83] Topel, R. H., and M. P. Ward (1992): “Job Mobility and the Careers of Young Men.” Quarterly Journal of Economics, 107(2), pp. 439 - 479. [84] Train, K. (2003): “Discrete Choice Methods with Simulation.” Cambridge University Press. [85] von Wachter, T. and S. Bender (2006): "In the Right Place at the Wrong Time: The Role of Firms and Luck in Young Workers." American Economic Review, 96(5), pp. 1679-1705. [86] von Wachter, T. and S. Bender (2008): "Do Initial Conditions Persist between Firms? An Analysis of FirmEntry Cohort E¤ects and Job Losers using Matched Employer-Employee Data." in S. Bender, J. Lane, K. Shaw, F. Andersson, and T. von Wachter (eds), "The Analysis of Firms and Employees: Quantitative and Qualitative Approaches", University Chicago Press. [87] Wenzelmann, F., G. Schoenfeld, H. Pfeifer and R. Dionisius (2009): “Betriebliche Berufsausbildung: Eine lohnende Investition fuer Betriebe.” BiBB-Report, Heft 8, Forschungs- und Arbeitsergebnisse aus dem Bundesinstitut fuer Berufsausbildung, ZKZ 77289.

45

Appendix A A.1

Some More Details about Sample Construction Estimation Sample

A pimary goal of sample construction is identifying workers who are observed from labor market entry. This is not straightforward, however. One reason is that workers who are observed in 1975 may have entered the labor market years earlier. This is problematic since any earnings di¤erences among these workers will be a combination of initial conditions and earnings innovations that have accumulated up to that point. Another reason is the potential presence of workers who start their career as civil servants or in self-employment and transfer into formal employment later in their life-cycle, or workers who exit the labor market temporarily after …nishing an apprenticeship degree to complete military service. To address these issues I start with exploiting the fact that earnings received during apprenticeship are subject to social security contributions and that the SIAB data provide a ‡ow variable recording whether an individual is currently in an apprenticeship training program. Labor market entry is then de…ned as the …rst spell in the data for which an individual switches from being in training to being formally employed or unemployed. At this point a second educational variable that measures the stock of educational attainment in six categories switches from "no formal degree" to "holds vocational degree".35 To rule out that individuals participated in the labor market for a substantial amount of time before entering an apprenticeship program I restrict the sample to those who are observed in an apprenticeship at a su¢ ciently young age, at most twenty years for those who went through the non-academic tracks and at most twenty-two years for those who did. I also drop workers who are observed in training for more than four years, workers with less than four observations in the data, and any workers who either have no formal degree at any point in their career or whose highest educational attainment is a universityor technical college degree.36 After application of these restrictions one …nds a substantial share of workers who have very low earnings in their initial spell, drop the sample temporarily afterwards and return after one to two years with much higher earnings. This is likely a combination of two events. First, because of the aggregation to the annual level it is possible that some initial spells that are recorded as employment are in fact the terminal year of an apprenticeship program. This is plausible since wages received during apprenticeship are low. Second, most of the individuals in my sample are part of cohorts that needed to complete approximately one year of mandatory military service after the age of 18. Military service can be delayed until after completion of an apprenticeship degree. Since military service is mandatory and not a choice I thus simply drop the …rst observation for each individual from the sample and de…ne the second spell as the …rst year of active labor market participation. As a consequence, I will use years since labor market entry instead of age as the variable de…ning a life-cycle.

A.2

Occupational Grouping

As stated in the main test, the occupational grouping used in this paper generates a natural occupational hierarchy, with the …rst occupation at the very top, attracting workers from the two middle groups of occupations, and lowskill service occupations at the bottom that does not seem to o¤er any direct possibilities for advancement. To see this, I list in appendix table C.3, separately for each of the four careers, all 3-digit occupations in the SIAB 1975-2010 data. This table was constructed as follows. The map from three digit occupations to more aggregated 3 5 I …rst use a re…ned version of the algorithm described in Fitzenberger et al. (2007) to generate a consistent time series of the categorial variable recording educational attainment. 3 6 The second restriction is justi…ed as follows. As noted above, I will endogenize sample attrition in the structural model because it may re‡ect a switch into government employment, self-employment, higher education, or withdrawel from the labor force, all of which is likely to depend on skills and labor market opportunities. This requires observing individuals for some time, and I impose this to mean at least four observations per individual.

46

occupation groups in the US Census data used by Acemoglu and Autor (2011) is available on David Autor’s website. I crosswalk the three digit occupations in the US data to the German SIAB 1975-2010 data as much as possible. Interesting examples are "wholesale and retail trade buyers" or "Landlords, agents and auctioneers", both of which are assigned to management occupations in Acemoglu and Autor and which have a direct analogue in the German data. For the remaining occupations in the German data that have no direct analogue in the US data the occupational descriptor is su¢ ciently informative for assignment to one of the career groups. The only occupation in which I deviate from Acemoglu and Autor is "Foremen", which require a special degree in Germany and are seen as a low-level management occupation. I thus allocate Foremen to the …rst career. Perusing the rest of the table, most assignments seem intuitive and plausible. The fact that the …rst career includes any occupations that involve management puts it naturally on top of the occupational hierarchy. It is worthwhile to note however that this hierarchical structure runs a bit deeper than that. For example, many of the technical or engineering occupations in this group seem to be upgrades from occupations in the group of production, craft, repair and operative occupations. Examples are Chemistry and Physics Technicians, which have a lower-rank analogue in Chemical Laboratory Workers, or Mechanical and Motor Enginners, with a lower-rank analogue in Motor Vehicle Repairers. Similarly, various occupations in the Sales and Clerical Occupation category have a higher rank analogue, such as Data Processing Specialists that upgrade to Statisticians or Accountants who upgrade to Chartered Accountants and Tax Advisers.

B

Value Functions: Terminal Condition

In this section I characterize the value functions of workers who are A years old. These functions serve as initial conditions for the backward recursion in the Dynamic Programming Algorithm. Under certain assumptions on individual labor market dynamics during the stable part of a career they can be characterized analytically. Among others, this requires imposing assumptions on the evolution of skill prices, tax rates and unemployment bene…ts, partly out of sample. Since the value of exiting the sample at age A is approximated by the parametric function VAexit (SA ) as described in the main text, with parameters being estimated from the data, only the terminal conditions for the value of unemployment and of choosing employment in career 2 C need to be speci…ed. Employment Consider a worker who enters the stable part of a career at age A in period (t + 1). In the following, treat calendar time as a continuous variable that is sampled in discrete intervals. A worker who chooses employment in career 2 C remains employed for the rest of the working part of a life-cycle, ending at age R1 , and is retired from age (R1 + 1) to R2 . The continuation value after age R2 is zero. Earnings are assumed to grow at the same rate as skill prices between age (A + 1) and R1 . Retirement bene…ts are 50 percent of the last gross earnings. Average tax rates on labor income are assumed to remain constant for an individual during the period of stable employment. This approximates adjustments in the tax schedule to aggregate in‡ation. In the following it is convenient to de…ne the following discount factor, computed from the point of view of a worker who is A + k years old and was A years old in period t: ! ! (R1 A) (k 1) (R2 R1 ) X(R1 A) P (t + l) P (t + R1 A) 1 (l k) vA+k (t) = + (27) l=k P (t) 2 P (t) 1 and Bk =

1

(R1 A) (k 1)

1

!

:

(28)

The function vA+k (t) is the discount factor of earnings received from age (A + k) on, taking into account growth in aggregate skill prices and the 50% decline after retirement. It can be simpli…ed considerably when taking into account that empirically any worker in the sample enters the stable part of a career past the year ????. Hence, any assumption about the skill prices involves out-of-sample statements. One can therefore impose the assumption that

47

expected aggregate growth rates of skill prices during the stable part of a career are identical across cohorts. Let fg g 2 C be the collection of these annual growth rates for the four careers and use the approximation P (t + l) P (t)

1+g

l:

(29)

Then vA+k (t) becomes a constant in t, given by vA+k

= Bk + g

1

(R1 A) (k 1)

+

2

!

h

Bk+1

(1 + g

(R1 A) k

(R1

A))

((R1

A)

k)

i

(R2 R1 )

1 1

!

:

(30)

The attractive property of this object is that it can be computed once before structural estimation. Let VA (SA ; A 1 ) be the value of choosing 2 C at age A given the vector of continuous state variables SA W and the previous choice A 1 . Let WA = WAgross ; SA be gross earnings received at age A from choosing given gross W W WA ; SA ; t be the corresponding average tax rate. For the payo¤-relevant states SA , and let A (t) = same reasons as for aggregate skill prices, it is plausible to impose the assumption that all cohorts expect to face identical average tax schedules at the time they enter the stable part of a career. In the empirical implementation I use the schedule for ????, which is the year the oldest cohort enters the stable part of a career. Hence, one can drop t as an argument, with the understanding that A is still a function of gross earnings because of non-linear taxation. Then VA (SA ; A 1 ) is given by VA (SA ;

A 1)

=

WA

(1

A)

vA + WA (1

B0 + K if A ) vA +

A

= fmanagerialg and B0 otherwise.

A

6=

A 1

(31)

This expression can be explained as follows. Net earnings in career , given by WA (1 A ), grow at the rate of skill prices until retirement. The present value of these earnings accrued over the stable part of a career can be shown to be net earnings multiplied by the …rst two terms in equation (30). The present value of retirement bene…ts is net earnings times the third term in (30). The non-monetary utility component is received only over the working part of the remaining life-cycle, with present value B0 . Switching costs need to be paid only if an individual moves into managerial occupations. One can use equation (31) to de…ne a set of value functions that depend on state variables which are directly relevant for utility from the point of view of a decision maker who is A years old and has decided to choose . In the language of Approximate Dynamic Programming, this is the value function de…ned on post-decision state variables. It is given by VeA (W;

A 1)

=

W

(1

(W )) vA + W (1

This function is linear in net earnings W an assumption I impose in the following.

(1

B0 + K if (W )) vA +

A

= fmanagerialg and B0 otherwise.

(W )). It is also di¤erentiable as long as

A

6=

A 1

(32)

(W ) is di¤erentiable,

Unemployment A worker who is unemployment at age A may or may not accept an employment o¤er arriving during the stable part of a career. Since I neither observe nor model the detailed dynamics after age A, it is necessary to impose some additional restrictions on how the arrival- and acceptance process works. I assume that unemployed workers receive o¤ers from all careers simultaneously at a rate A . O¤ers from career pay the potential earnings at age A, WA , times the growth of aggregate skill prices. Any job o¤ers that are deemed acceptable at some point of the stable part of a career are accepted as soon as they arrive, and they are kept until retirement. The initial replacement rate is a function of calendar time, age, and unemployment duration and is written rA (dur). This rate is calibrated to the value the oldest cohort faces when becoming A years old. I thus drop the time subscript. From

48

age (A + 1) the replacement rate drops to the social insurance level, which is 35 percent, and remains there during retirement. Neither unemployment- nor retirement bene…ts are taxed. Consider a worker who is entitled to unemployment bene…ts rA (dur) W 1 at age A and who has a draw of the non-monetary utility component of uA . Let W : 2 C be the collection of potential earnings in each career at W age A, given payo¤-relevant states SA . De…ne VAu;u (W 1 ; dur) as the value of being unemployed at age A and the remaining part of the life-cycle. The discounted stream of earnings for this outcome has a simple analytic solution, given by VAu;u (W 1 ; dur; uA ) = W 1 [rA (dur) + B u;u ] + uA B0 (33) with B

u;u

(R2 A)

1

= 0:35

1

!

:

(34)

Alternatively the worker may accept an o¤er from career as soon as it arrives. De…ned on post-decision state variables, an o¤er from career that is accepted at age (A + k) has value VeA+k (W ;

A 1)

W

=

(1

(W )) vA+k + Bk + K if WA (1 (W )) vA+k +

A

= fmanagerialg and Bk otherwise.

A

6=

A 1

: (35)

P (t+k) the only modi…cation relative Since potential earnings in career at age (A + k) are assumed to be WA P (k) to (32) is the discounting. The value of remaining unemployed until receiving and accepting an o¤er from can thus be written as

VAu; (W

1 ; dur; W

;

u A)

u; ] 1 [rA (dur) + B XR 1 A k k + (1 A)

= W

1 A

k=1

with B

u;

= :35

"

[

(1

A )]

1

[ 1

(1 [

(R1 A) 1 A )]

(1

A )]

+[

VeA+k (W ;

(R1 A)

(1

A )]

1

A 1) :

(R2 R1 )+1

1

(36)

!#

:

(37)

The value of being unemployed at age A is thus VAu = max VAu;u ; fVAu; g

2

In the following it is more convenient to work with VAu;u and fVAu; g

C

2

: C

(38) directly.

49

FIGURE 1 - AGGREGATE EMPLOYMENT SHARES OF FOUR CAREERS OVER THE LIFECYCLE

NOTES: This figure shows employment shares of the four Acemoglu-Autor (2011) occupation groups ("careers") for employed male workers in the SIAB 1975-2010 sample who are between 25 and 50 years old. Employment shares are the coefficients on age fixed effects in repeated crosssectional linear probability models of career choice on age- and time fixed effects, estimated separately for each of the four careers. Workers with a university- or technical college degree are excluded from the sample to keep comparability with the earnings sample.

FIGURE 2 - CORRELATION OF RESIDUAL EARNINGS AT AGE 25 WITH FUTURE RESIDUAL EARNINGS

NOTES: This figure shows the correlation of residual earnings at age 25 with residual earnings at each age between 25 and 50 years. This type of relationship is often called "lead-profile". The sample comes from the SIAB 1975-2010 data and is restricted to male workers who are between 25 and 50 years old and do not have a university- or technical college degree. Residual earnings are computed by regressing log-earnings on fixed effects for age, education and calendar time.

50

FIGURE 3 - EMPLOYMENT SHARES OF FOUR CAREERS OVER THE LIFE-CYCLE IN THE ESTIMATION SAMPLE

NOTES: This figure shows employment shares of the four Acemoglu-Autor (2011) occupation groups ("careers") for employed workers in the estimation sample. Time-adjusted employment shares are the coefficients on experience fixed effects in repeated cross-sectional linear probability models of career choice on experience- and time fixed effects, estimated separately for each of the four careers.

FIGURE 4 - TIME-ADJUSTED TRANSITION RATES OVER THE LIFE-CYCLE IN THE ESTIMATION SAMPLE

NOTES: This figure shows various annual transition rates, adjusted for time effects, of workers in the estimation sample. The left figure shows transition rates across careers and across firms, conditional on employment. The right figure shows transition probabilities between employment and unemployment and vice versa. Time-adjusted transition rates are the coefficients on experience fixed effects in regressions of transition dummies on experience- and time fixed effects. For example, the career transition dummy is equal to one if a worker is employed in two subsequent periods during which he changes the career, and it is equal to zero for any other employed worker.

51

FIGURE 5 - LIFE-CYCLE PROFILES OF SKILL-PRICE ADJUSTED LOG-EARNINGS IN AVERAGES AND STANDARD DEVIATIONS

NOTES: This figure plots averages and standard deviations of log-earnings against potential labor market experience, calculated from the SIAB 1975-2010 estimation sample. Log-earnings are skill-price adjusted, using the skill prices estimates obtained from a "flat-spot" estimation strategy (Heckman, Lochner, Taber 1998).

FIGURE 6 - COVARIANCE STRUCTURE OF RESIDUAL LOG-EARNINGS: LEAD PROFILES FOR FOUR EXPERIENCE GROUPS

NOTES: This figure shows the correlation of residual earnings of four groups of workers with their future residual earnings, computed from the SIAB 1975-2010 estimation sample. This type of relationship is often called "lead-profile". The four groups of workers are labor market entrants and those with 5, 10 and 15 years of potential labor market experience. Residual earnings are computed as follows: In a first step earnings are adjusted by skill prices that were estimated using a "flat-spot" empirical strategy (Heckman, Lochner, Taber, 1998). In a second step I regress, for each career separately, the adjusted earnings on a second-degree polynomial in actual labor market experience and career tenure.

52

FIGURE 7 - LIFE-CYCLE PROFILES OF AVERAGE SKILL-PRICE ADJUSTED LOG-EARNINGS, BY CURRENT AND INITIAL CAREER CHOICE

NOTES: This figure plots average skill-price adjusted log-earnings against potential labor market experience, calculated from the SIAB 1975-2010 estimation sample. Skill prices are estimated using a "flat-spot" estimation strategy (Heckman, Lochner, Taber 1998). The left-hand panel splits the sample by current career choice, while the right-hand panel splits the sample by the career chosen most frequently in the first five years of a career. The intercepts of each life-cycle profile are different in the two panels because some individuals switch career over the first five years of labor market participation.

FIGURE 8 - LIFE-CYCLE PROFILES OF THE STANDARD DEVIATION OF SKILL-PRICE ADJUSTED LOG-EARNINGS, BY CURRENT AND INITIAL CAREER CHOICE

NOTES: This figure plots the standard deviation of skill-price adjusted log-earnings against potential labor market experience, calculated from the SIAB 1975-2010 estimation sample. Skill prices are estimated using a "flat-spot" estimation strategy (Heckman, Lochner, Taber 1998). The left-hand panel splits the sample by current career choice, while the right-hand panel splits the sample by the career chosen most frequently in the first five years of a career. The intercepts of each life-cycle profile are different in the two panels because some individuals switch career over the first five years of labor market participation.

53

FIGURE 9 - TWENTY PERCENTILES OF THE RESIDUAL LOG-EARNINGS DISTRIBUTION BEFORE VARIOUS WORKER TRANSITIONS

NOTES: This figure plots twenty percentiles of the log-earnings distribution, calculated from the estimation sample. Log-earnings are first skill-price adjusted, using the skill prices estimates obtained from a "flat-spot" estimation strategy (Heckman, Lochner, Taber 1998). They are then residualized by regressing them on a second-order polynomial in actual labor market experience and career tenure. Coefficients are allowed to vary freely across careers.

FIGURE 10 - LOG SKILL PRICES

NOTES: This figure plots the estimates of log-skill prices, estimated from the old-worker sample. Skill prices estimates are obtained from a "flat-spot" estimation strategy (Heckman, Lochner, Taber 1998). They are equal to the annual earnings growth of workers between the ages 50 and 54, holding constant the employer and career in two subsequent years.

54

TABLE 1 - LIFE-CYCLE EARNINGS GROWTH VS. CAREER CHOICES AT AGES 45 TO 50 Average Earnings Growth: Managerial, Professional, Technical

0.442 (0.004)

***

0.436 (0.004)

***

0.441 (0.004)

***

Earnings Growth Relative to Managerial, Professional and Technical Occupations : Clerical, Sales

-0.002 (0.005)

Production, Operators

-0.227 (0.004)

***

-0.220 (0.004)

***

-0.215 (0.004)

***

Low-Skill Service

-0.293 (0.006)

***

-0.284 (0.006)

***

-0.266 (0.006)

***

Horizontal or Downgrade

-0.064 (0.003)

***

-0.062 (0.003)

***

-0.051 (0.003)

***

Upgrade

0.033 (0.006)

***

0.040 (0.006)

***

0.036 (0.005)

***

Cohort Fixed Effects

No

Yes

Yes

Weighted

No

No

Yes

0.003 (0.005)

0.005 (0.005)

Effect of Career Changes on Earnings Growth

Number of Observations

85,958

NOTES: This table shows results from life-cycle earnings growth regressions estimated on the SIAB 1975-2010 data. Each column corresponds to a different regression. Workers with a university- or technical college degree are excluded because of a high rate of top-coded earnings. Earnings growth is computed by calculating, for the same worker, average earnings before the age of 30 and average earnings between the ages of 45 and 50 and then taking the difference in their logs. The coefficients in the table come from a regression of earnings growth on career fixed effects. A career is defined as the occupational group most frequently observed for the worker between the ages 45 and 50. Weights used in one specification is the number of observations per worker. Occupational groups are those suggested in Acemoglu and Autor (2011). Standard errors are in parantheses. Significance level: *** 1%; ** 5%; * 10%.

55

TABLE 2 - ONE-PERIOD WORKER TRANSITION MATRIX BETWEEN CAREERS, UNEMPLOYMENT AND EXIT PANEL A: ALL OBSERVATIONS EMPLOYMENT STATE AT EXPERIENCE t+1

Managerial Clerical, Sales EMPLOYMENT STATE AT Production EXPERIENCE t Service Unemployment

Managerial

Clerical

Production

Service

Unempl

Non-Empl

0.918

0.024

0.023

0.003

0.017

0.016

0.021

0.933

0.017

0.002

0.015

0.012

0.013

0.006

0.940

0.003

0.031

0.007

0.013

0.009

0.044

0.871

0.048

0.015

0.054

0.043

0.335

0.031

0.487

0.050

Unempl

Non-Empl

PANEL B: AT MOST 5 YEARS OF ACTUAL LABOR MARKET EXPERIENCE

Managerial Clerical, Sales EMPLOYMENT STATE AT Production EXPERIENCE t Service Unemployment

EMPLOYMENT STATE AT EXPERIENCE t+1 Production Service

Managerial

Clerical

0.873

0.045

0.039

0.005

0.029

0.009

0.024

0.916

0.029

0.002

0.020

0.009

0.010

0.008

0.932

0.003

0.043

0.004

0.013

0.011

0.067

0.834

0.068

0.007

0.053

0.042

0.427

0.035

0.426

0.017

Unempl

Non-Empl

PANEL C: AT MOST 10 YEARS OF ACTUAL LABOR MARKET EXPERIENCE

Managerial Clerical, Sales EMPLOYMENT STATE AT Production EXPERIENCE t Service Unemployment

EMPLOYMENT STATE AT EXPERIENCE t+1 Production Service

Managerial

Clerical

0.897

0.031

0.031

0.004

0.021

0.016

0.023

0.925

0.022

0.002

0.017

0.011

0.013

0.007

0.935

0.003

0.036

0.006

0.014

0.010

0.054

0.854

0.055

0.013

0.059

0.044

0.378

0.033

0.451

0.035

NOTES: This table shows the one-period Markov transition matrix between career choices and employment states in two subsequent periods, computed from the worker-level estimation sample in the SIAB 1975-2010. For example, the first element in the matrix is the probability that a worker employed in a managerial occupation after t years of potential labor market experience is still employed in a managerial occupation one period later. Rows add up to one. Since non-employment in the sample corresponds to sample attrition, it is an absorbing state and is thus not included as a state at experience t. The first panel shows transition rates for the entire estimation sample, while panels B and C show corresponding rates for workers with at most 5 years and 10 years of potential labor market experience, respectively. Each rate conditions on a worker being present in the sample in two consecutive periods.

56

TABLE 3 - LIFE-CYCLE CAREER TRANSITION RATES CAREER AFTER 15 TO 25 YEARS OF EXPERIENCE

CAREER AT EXPERIENCE OF AT MOST 5 YEARS

Managerial

Clerical

Production

Service

Managerial

0.6563

0.2165

0.1094

0.0178

Clerical, Sales

0.1299

0.7599

0.1004

0.0098

Production

0.1673

0.0644

0.7418

0.0265

Service

0.1354

0.1107

0.2378

0.5161

NOTES: This table shows the life-cycle transition matrix between career choices, computed from the worker-level estimation sample in the SIAB 19752010. The initial state is the most frequent career choice of an individual for the first five years after labor market entry. The terminal state is the most frequently observed career choice after 15 to 25 years of potential labor market experience. For example, the first element in the matrix is the probability that a worker most frequently observed in a managerial occupation over the first five years of the life-cycle is still observed in the same career ten to twenty years afterwards. Rows add up to one. Rates are calculated conditional on employment.

57

TABLE 4 - ESTIMATES OF REDUCED-FORM LOG-EARNINGS REGRESSIONS IN THE REPEATED CROSS-SECTION, SKILL-PRICE ADJUSTED

Managerial, Professional, Technical

Full Sample

Production, Operators

Clerical, Sales

Service

Actual Experience

0.026 (2.58E-04)

***

0.059 (6.11E-04)

***

0.049 (6.15E-04)

***

0.014 (3.82E-04)

***

0.026 (1.20E-03)

***

Actual Experience squared

-0.0005 (1.12E-05)

***

-0.0014 (2.32E-05)

***

-0.0013 (2.67E-05)

***

-0.0003 (1.78E-05)

***

-0.0005 (5.05E-05)

***

Career Tenure

0.022 (2.42E-04)

***

0.010 (5.07E-04)

***

0.020 (5.71E-04)

***

0.027 (3.62E-04)

***

0.027 (1.29E-03)

***

Career Tenure squared

-0.0008 (1.15E-05)

***

-0.0004 (2.52E-05)

***

-0.0004 (2.70E-05)

***

-0.0008 (1.78E-05)

***

-0.0011 (6.88E-05)

***

Intercept

9.69 (8.43E-04)

***

9.56 (3.37E-03)

***

9.55 (2.18E-03)

***

9.74 (9.39E-04)

***

9.51 (4.23E-03)

***

Number of Observations R-squared

704,055 0.25

92,231 0.30

108,750 0.39

472,343 0.22

30,731 0.18

NOTES: This table shows results from regressions of skill-price adjusted log-earnings on polynomials in actual labor market experience and career tenure, estimated on the worker-level estimation sample in the SIAB 1975-2010. Skill-prices are estimated using a "flat-spot" empirical strategy (Heckman, Lochner, Taber, 1998). Actual experience is the number of years a worker has spent working since labor market entry. Career Tenure is the number of years spent in a particular career. Given the administrative nature of the SIAB 1975-2010, these variables can be computed with high accuracy. The regressions in this table should be interpreted as repeated cross-sectional models. Standard errors are heteroscedasticity-robust. Significance: *** 1%; ** 5%; * 10%.

58

TABLE 5 - DISTRIBUTION OF ANNUAL SKILL-PRICE ADJUSTED LOG-EARNINGS CHANGES ALL EMPLOYMENT SPELLS

CAREER CHANGES

All Workers

At Most 5 Years of Exper

At Most 10 Years of Exper

Avg

0.028

0.066

Std

0.132

p10

EMPLOYER CHANGES

All Workers

At Most 5 Years of Exper

At Most 10 Years of Exper

All Workers

At Most 5 Years of Exper

At Most 10 Years of Exper

0.043

0.030

0.087

0.054

0.043

0.094

0.065

0.181

0.150

0.261

0.307

0.274

0.243

0.282

0.259

-0.065

-0.061

-0.063

-0.223

-0.211

-0.213

-0.201

-0.186

-0.194

p50

0.015

0.036

0.025

0.020

0.061

0.039

0.029

0.065

0.046

p90

0.130

0.227

0.163

0.300

0.432

0.345

0.293

0.403

0.340

616,780

150,868

324,577

18,346

5,201

11,266

71,047

24,275

44,596

N

NOTES: This table shows selected sample moments and percentiles for the distribution of annual changes of skill-price adjusted log-earnings in the estimation sample. Skill-prices are estimated using a "flat-spot" empirical strategy (Heckman, Lochner, Taber 1998). The results are shown for all employment spells, for earnings changes that correspond with a career switch, and earnings changes that correspond with a change of employer. The results are split further into those for all workers, workers who have at most 5 years or at most 10 years of potential labor market experience.

TABLE 6 - ONE-PERIOD AVG. SKILL-PRICE ADJUSTED EARNINGS CHANGES WITHIN CAREER, AT EMPLOYER TRANSITIONS

All Workers

GROUP OF WORKERS At Most 5 Years of Exper

At Most 10 Years of Exper

Managerial

0.0426

0.1234

0.0826

Clerical, Sales

0.0610

0.1140

0.0911

Production

0.0410

0.0903

0.0606

Service

0.0566

0.1013

0.0728

NOTES: This table shows avg. annual changes of skill-price adjusted log-earnings in the estimation sample for pairs of employment spells that correspond with a change of employer, but not a career switch. The sample is split by career choice. Skill-prices are estimated using a "flat-spot" empirical strategy (Heckman, Lochner, Taber 1998).

59

60

TABLE 7 - ONE-PERIOD- AND LIFE-CYCLE SKILL-PRICE ADJUSTED EARNINGS GROWTH, BY CURRENT AND FUTURE CAREER PANEL A: ONE-PERIOD EARNINGS GROWTH

Managerial

EMPLOYMENT STATE AT EXPERIENCE t

EMPLOYMENT STATE AT EXPERIENCE t+1 Clerical Production Service

Unempl

Managerial

0.027

0.102

0.130

0.090

-0.551

Clerical, Sales

0.049

0.039

0.144

0.109

-0.563

Production

-0.027

-0.038

0.029

-0.047

-0.626

Service

-0.020

-0.004

0.125

0.029

-0.564

Unemployment

0.647

0.595

0.686

0.606

-0.051

PANEL B: LIFE-CYCLE EARNINGS GROWTH

Managerial Managerial CAREER AT Clerical, Sales EXPERIENCE OF AT MOST 5 Production YEARS Service

CAREER AFTER 15 TO 25 YEARS OF EXPERIENCE Clerical Production

Service

0.402

0.514

0.331

0.308

0.496

0.472

0.361

0.066

0.297

0.239

0.222

0.056

0.276

0.299

0.282

0.234

NOTES: The first panel of this table shows annual skill-price adjusted one-period earnings growth, by current and future career choices in two subsequent years. The second panel repeats this exercise, but by the most frequent career choice early and late in the life-cycle. Statistics are computed from the worker-level estimation sample in the SIAB 1975-2010. Skill-prices are estimated using a "flat-spot" empirical strategy (Heckman, Lochner, Taber 1998).

61

TABLE 8: THE ROLE OF DIFFERENT VARIANCE COMPONENTS ON LIFE-CYCLE INEQUALITY

PANEL A: PERCENTAGE CHANGE OF THE STANDARD DEVIATION OF WEALTH IN COUNTERFACTUAL EXPERIMENTS: Model Specification

Multi-Period Roy Model (KW97)

Full Model With Frictions

Type Heterogeneity (Continuous)

-73.8

-34.2

Transitory Shocks

-14.0

-0.3

Permanent Shocks

-

-7.1

Match Effects

-

-27.3

Frictions

-

5.2

91.2

40.9

PANEL B: ACROSS TYPE VARIATION IN WEALTH:

NOTES: This table displays results from counterfactual experiments. Each column refers to a different specification of the Dynamic Discrete Choice Model. Each of the cells in Panel A show the percentage changes of wealth inequality, measured by its standard deviation of the log of discounted life-cycle earnings, from a different counterfactual experiment. Counterfactuals are constructed as follows: The model is simulated for as many individuals as in the sample using the original parameter estimates, with one set of parameter estimates per row adjusted. For example, the row "Transitory Shocks" lists the effect on wealth inequality when simulating a particular model specification using the original parameter estimates, but with the variance of transitory shocks set to zero. Panel B displays results from a simple across-type variance decomposition.

62

APPENDIX TABLE A - ESTIMATES OF STRUCTURAL PARAMETERS PANEL A: Career-Specific Parameters Managerial, Professional, Technical

Clerical, Sales

Production, Operators

Service

0.031

0.050

0.034

0.032

-0.0006

-0.0011

-0.0009

-0.0009

0.054

0.043

0.017

0.015

-0.0012

-0.0010

-0.0003

-0.0004

Variance of Transitory Shocks

0.007

0.005

0.003

0.003

Variance of Permanent Component

0.025

0.021

0.015

0.019

Altonji-Shakotko IV: Career Tenure Career Tenure squared

Structural Estimation Actual Experience Actual Experience squared

PANEL B: Other Parameters Variance of Match Effects within Career

0.027

Variance of Match Effects across Careers

0.024

Variance of AR(1)-shock

Probability of Getting Job Offer: unemployed

0.780

0.002

employed within career

0.250 0.860

Variance of Initial Condition of AR(1)

0.087

across career

0.140

Persistence of AR(1)-shock

0.910

Job Breakup Probability

0.023

NOTES: This table shows the estimates of structural parameters for the full model. Other than the returns to tenure, which are IV-estimates from the Altonji-Shakotko (1987) strategy, all estimates come from estimation of the structural model via Indirect Inference. Expected value functions are approximated by sparse grid Chebyshev interpolation, using the approach described in Bungartz and Griebel (2004).

63

APPENDIX TABLE C.1 - OCCUPATIONAL CLASSIFICATION: CAREERS AND EDUCATION PANEL A: Education Group Shares, conditional on Career (Rows add up to one)

HS Dropout

HS, Apprenticeship

Academic HS

Academic HS, Apprenticeship

Technical College

University

Managerial, Professional, Technical

0.021

0.577

0.009

0.067

0.128

0.198

Clerical, Sales

0.066

0.771

0.012

0.069

0.032

0.050

Production, Operators

0.248

0.728

0.003

0.013

0.005

0.003

Low-Skill Service

0.380

0.581

0.007

0.019

0.006

0.006

HS Dropout

HS, Apprenticeship

Academic HS

Academic HS, Apprenticeship

Technical College

University

Managerial, Professional, Technical

0.031

0.192

0.280

0.362

0.715

0.733

Clerical, Sales

0.128

0.329

0.456

0.478

0.228

0.238

Production, Operators

0.616

0.402

0.176

0.119

0.043

0.020

Low-Skill Service

0.225

0.076

0.088

0.040

0.013

0.009

PANEL B: Career Shares, conditional on Education (Columns add up to one)

NOTES: This table shows the joint empirical distribution of career choices and educational attainment. Careers are defined by the broad occupational groups in Acemoglu and Autor (2011). Educational attainment is a stock variable contained in the SIAB data, with all six possible values listed in this table. The sample from which these statistics are computed contains all individuals between the ages of 30 and 64 who work in Western Germany and who are not employed in an agricultural occupation.

64

APPENDIX TABLE C.2 - EARNINGS DIFFERENCES BETWEEN CAREERS, RELATIVE TO MANAGERIAL, PROFESSIONAL AND TECHNICAL OCCUPATIONS (1)

(2)

(3)

(4)

Clerical, Sales

-8,477 (9.43)

***

-8,491 (9.42)

***

-8,430 (9.27)

***

-8,445 (9.26)

***

Production, Operators

-8,261 (8.95)

***

-8,282 (8.94)

***

-7,814 (8.84)

***

-7,841 (8.83)

***

Low-Skill Service

-17,203 (13.30)

***

-17,311 (13.30)

***

-17,008 (13.07)

***

-17,116 (13.08)

***

Fixed Effects: Age Time Number of Observations Sample Avg. of Earnings for Comparison Group:

No No

Yes No

No Yes

Yes Yes

9,654,090 34,003

NOTES: This table shows results from regressions of real earnings on career dummies. The unit of observation is worker-time. Careers are defined by the broad occupational groups in Acemoglu and Autor (2011). The omitted group is composed of managerial, professional and technical occupations. The sample from which these statistics are computed contains all individuals between the ages of 30 and 64 who work in Western Germany and who are not employed in an agricultural occupation.

65

APPENDIX TABLE C.3 - OCCUPATIONAL CLASSIFICATION: CAREERS VS. 3-DIGIT OCCUPATIONS 3-Digit-Occupation, SIAB 1975-2010

Career (Acemoglu-Autor, 2011) 3-Digit Code Managerial, Professional, Technical

31 32 52 61 601 602 603 604 605 606 607 611 612 621 622 623 624 625 626 627 628 629 631 632 635 681 684 703 704 705 721 722 726 751 752 753 761

Description Managers in agriculture and animal breeding Agricultural engineers, agriculture advisors Garden architects, garden managers Forestry managers, foresters, hunters Mechanical, motor engineers Electrical engineers Architects, civil engineers Survey engineers Mining, metallurgy, foundry engineers Other manufacturing engineers Other engineers Chemists, chemical engineers Physicists, physics engineers, mathematicians Mechanical engineering technicians Electrical engineering technicians Building technicians Measurement technicians Mining, metallurgy, foundry technicians Chemistry, physics technicians Remaining manufacturing technicians Other technicians Foremen, master mechanics Biological specialists Physical and mathematical specialists Technical draughtspersons Wholesale and retail trade buyers, buyers Druggists/chemists (pharmacy) Publicity occupations Brokers, property managers Landlords, agents, auctioneers Navigating ships officers Technical ships officers, ships engineers Air transport occupations Entrepreneurs, managing directors, divisional managers Management consultants, organisors Chartered accountants, tax advisers Members of Parliament, Ministers, elected officials

Detailed Recode Managers Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Technicians Technicians Technicians Technicians Technicians Technicians Technicians Technicians Managers Technicians Technicians Technicians Managers Technicians Professionals Managers Managers Professionals Professionals Professionals Managers Managers Managers Managers

66

762 763 811 812 813 814 821 822 823 831 832 833 834 835 836 837 838 841 842 843 844 851 852 853 861 862 863 864 871 872 873 874 875 876 877 881 882 883 891 893 911 922

Senior government officials Association leaders, officials Arbitrators Judicial administrators Legal representatives, advisors Judicial enforcers Journalists Interpreters, translators Librarians, archivists, museum specialists Musicians Artists' agents Visual, commercial artists Scenery, sign painters Artistic and assisting occupations (stage, video and audio) Interior, exhibition designers, window dressers Photographers Performers, professional sportsmen, auxiliary artistic occupations Physicians Dentists Veterinary surgeons Pharmacists Non-medical practitioners Masseurs, physiotherapists and related occupations Nurses, midwives Social workers, care workers Home wardens, social work teachers Work, vocational advisers Nursery teachers, child nurses University teachers, lecturers at higher technical schools and academies Gymnasium teachers Primary, secondary (basic), special school teachers Technical, vocational, factory instructors Music teachers, n.e.c. Sports teachers Other teachers Economic and social scientists, statisticians Humanities specialists, n.e.c. Scientists n.e.c. Ministers of religion Religious care helpers Restaurant, inn, bar keepers, hotel proprietors, catering trade dealers Consumer advisors

Managers Managers Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Professionals Managers Professionals

67

Clerical, Sales

682 683 685 687 688 691 692 693 694 701 702 706 731 732 733 734 771 772 773 774 781 782 783 784 856

Salespersons Publishing house dealers, booksellers Pharmacy aids Commercial agents, travellers Mobile traders Bank specialists Building society specialists Health insurance specialists (not social security) Life, property insurance specialists Forwarding business dealers Tourism specialists Cash collectors, cashiers, ticket sellers, inspectors Post masters Postal deliverers Radio operators Telephonists Cost accountants, valuers Accountants Cashiers Data processing specialists Office specialists Stenographers, shorthand-typists, typists Data typists Office auxiliary workers Medical receptionists

Sales Sales Office and admin Sales Sales Sales Sales Sales Sales Sales Sales Office and admin Office and admin Office and admin Office and admin Office and admin Office and admin Office and admin Sales Office and admin Office and admin Office and admin Office and admin Office and admin Office and admin

Production, Operators

53 71 72 81 82 83 91 101 102 111 112 121 131 132 133 134 135

Florists Miners Mechanical, electrical, face workers, shot firers Stone crushers Earth, gravel, sand quarriers Oil, natural gas quarriers Mineral preparers, mineral burners Stone preparers Jewel preparers Stoneware, earthenware makers Shaped brick, concrete block makers Ceramics workers Frit makers Hollow glassware makers Flat glass makers Glass blowers (lamps) Glass processors, glass finishers

Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Operators, fabricators and laborers

68 141 142 143 144 151 161 162 163 164 171 172 173 174 175 176 177 181 182 191 192 193 201 202 203 211 212 213 221 222 223 224 225 226 231 232 233 234 235 241 242 243 251 252 261 262

Chemical plant operatives Chemical laboratory workers Rubber makers, processors Vulcanisers Plastics processors Paper, cellulose makers Packaging makers Book binding occupations Other paper products makers Type setters, compositors Printed goods makers Printers (letterpress) Printers (flat, gravure) Special printers, screeners Copiers Printer's assistants Wood preparers Wood moulders and related occupations Iron, metal producers, melters Rollers Metal drawers Moulders, coremakers Mould casters Semi-finished product fettlers and other mould casting occupations Sheet metal pressers, drawers, stampers Wire moulders, processors Other metal moulders (non-cutting deformation) Turners Drillers Planers Borers Metal grinders Other metal-cutting occupations Metal polishers Engravers, chasers Metal finishers Galvanisers, metal colourers Enamellers, zinc platers and other metal surface finishers Welders, oxy-acetylene cutters Solderers Riveters Steel smiths Container builders, coppersmiths and related occupations Sheet metal workers Plumbers

Production, craft and repair Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Production, craft and repair Production, craft and repair Operators, fabricators and laborers Production, craft and repair

69 263 270 271 272 273 274 275 281 282 283 284 285 286 291 301 302 303 304 305 306 311 312 313 314 315 321 322 323 331 332 341 342 343 344 346 351 352 353 355 356 357 361 362 371 372

Pipe, tubing fitters Locksmiths, not specified Building fitters Sheet metal, plastics fitters Engine fitters Plant fitters, maintenance fitters Steel structure fitters, metal shipbuilders Motor vehicle repairers Agricultural machinery repairers Aircraft mechanics Precision mechanics Other mechanics Watch-, clockmakers Toolmakers Precision fitters n.e.c. Precious metal smiths Dental technicians Opthalmic opticians Musical instrument makers Doll makers, model makers, taxidermists Electrical fitters, mechanics Telecommunications mechanics, craftsmen Electric motor, transformer fitters Electrical appliance fitters Radio, sound equipment mechanics Electrical appliance, electrical parts assemblers Other assemblers Metal workers (no further specification) Spinners, fibre preparers Spoolers, twisters, ropemakers Weaving preparers Weavers Tufted goods makers Machined goods makers Textile processing operatives (braiders) Cutters Clothing sewers Laundry cutters, sewers Hat, cap makers Sewers, n.e.c. Other textile processing operatives Textile dyers Textile finishers Leather makers, catgut string makers Shoemakers

Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Production, craft and repair Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Production, craft and repair Production, craft and repair

70 373 374 375 376 378 401 402 403 412 421 422 423 424 431 432 433 441 442 451 452 453 461 462 463 464 465 466 470 471 472 481 482 483 484 485 486 491 492 501 502 503 504 511 512 513

Footwear makers Coarse leather goods finishers, truss makers Fine leather goods makers Leather clothing makers and other leather processing operatives Skin processing operatives Butchers Meat, sausage goods makers Fish processing operatives Ready-to-serve meals, fruit, vegetable preservers, preparers Wine coopers Brewers, maltsters Other beverage makers, tasters Tobacco goods makers Milk, fat processing operatives Flour, food processors Sugar, sweets, ice-cream makers Bricklayers Concrete workers Carpenters Roofers Scaffolders Paviors Road makers Tracklayers Explosives men (except shotfirers) Land improvement, hydraulic engineering workers Other civil engineering workers Building labourer, general Earth movers Other building labourers, building assistants, n.e.c. Stucco workers, plasterers, rough casters Insulators, proofers Tile setters Furnace setter, air heating installers Glaziers Screed, terrazzo layers Room equippers Upholsterers, mattress makers Carpenters Model, form carpenters Cartwrights, wheelwrights, coopers Other wood and sports equipment makers Painters, lacquerers (construction) Goods painters, lacquerers Wood surface finishers, veneerers

Production, craft and repair Operators, fabricators and laborers Production, craft and repair Operators, fabricators and laborers Operators, fabricators and laborers Production, craft and repair Production, craft and repair Operators, fabricators and laborers Operators, fabricators and laborers Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Operators, fabricators and laborers Operators, fabricators and laborers Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Production, craft and repair Operators, fabricators and laborers

71

Low-Skill Service

514 521 522 531 541 542 543 544 545 546 547 548 549 633 634 686 711 712 713 714 715 716 723 724 725 741 742 743 744 857 935 936 937

Ceramics, glass painters Goods examiners, sorters, n.e.c. Packagers, goods receivers, despatchers Assistants (no further specification) Generator machinists Winding engine drivers, aerial ropeway machinists Other machinists Crane drivers Earthmoving plant drivers Construction machine attendants Machine attendants, machinists' helpers Stokers Machine setters (no further specification) Chemical laboratory assistants Photo laboratory assistants Service-station attendants Railway engine drivers Railway controllers, conductors Other traffic controllers, conductors Motor vehicle drivers Coachmen Street attendants Deck seamen Inland boatmen Other water transport occupations Warehouse managers, warehousemen Transportation equipment drivers Stowers, furniture packers Stores, transport workers Medical laboratory assistants Street cleaners, refuse disposers Vehicle cleaners, servicers Machinery, container cleaners and related occupations

Production, craft and repair Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers Operators, fabricators and laborers

51 391 392 411 791 792 793 794 801 802

Gardeners, garden workers Bakery goods makers Confectioners (pastry) Cooks Factory guards, detectives Watchmen, custodians Doormen, caretakers Domestic and non-domestic servants Soldiers, border guards, police officers Firefighters

Food prep, buildings and grounds, cleaning Food prep, buildings and grounds, cleaning Food prep, buildings and grounds, cleaning Food prep, buildings and grounds, cleaning Protective service Protective service Protective service Protective service Protective service Protective service

72

Agriculture

803 804 805 854 855 901 912 913 921 923 931 932 933 934

Safety testers Chimney sweeps Health-protecting occupations Nursing assistants Dietary assistants, pharmaceutical assistants Hairdressers Waiters, stewards Others attending on guests Housekeeping managers Other housekeeping attendants Laundry workers, pressers Textile cleaners, dyers and dry cleaners Household cleaners Glass, buildings cleaners

Protective service Protective service Protective service Personal care and personal services Personal care and personal services Personal care and personal services Personal care and personal services Personal care and personal services Personal care and personal services Personal care and personal services Personal care and personal services Personal care and personal services Personal care and personal services Personal care and personal services

11 12 21 41 42 43 44 62

Farmers Winegrowers Animal breeders Land workers Milkers Family-member land workers, n.e.c. Animal keepers and related occupations Forest workers, forest cultivators

Agriculture Agriculture Agriculture Agriculture Agriculture Agriculture Agriculture Agriculture

NOTES: This table shows the 3-digit occupations that enter each career. The classification is carried out by constructing a cross-walk from the Acemoglu-Autor (2011) classification, which is based on the 1990 3digit occupational codes in the Census and is available on David Autor's website.

73

APPENDIX TABLE D.1 - AVERAGE TAX RATES BY SELECTED INCOME GROUPS, 1975 - 2010 PANEL A: 1975 - 1993 Tax Year

Nominal Income in EUR

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1534 1790 2045 2301 2556 2812 3068 3323 3579 3835 4602 5113 6391 7669 8948 10226 15339 20452 25565 35790 40903 51129 66468 81807 102258 153388

0 2.7 5.05 8.36 12.95 15.2 20.5 26.4 30.8 34.1 40.4 43.1 46 49.5 -

0 2.7 5.05 8.36 12.95 15.2 20.5 26.4 30.8 34.1 40.4 43.1 46 49.5 -

0 2.7 5.05 8.36 12.95 15.2 20.5 26.4 30.8 34.1 40.4 43.1 46 49.5 -

0 3.4 5.4 7 12 14.5 16 20.1 26.1 30.6 34 40.3 43.1 46 49.5 -

0 1.2 3.4 5.3 10.9 13.6 15.3 18.4 23.7 28.5 32.1 39.2 42.1 45.25 47.3 49 -

0 1.2 3.4 5.3 10.9 13.6 15.3 18.4 23.7 28.5 32.1 39.2 42.1 45.25 47.3 49 -

0 0.8 2.9 6.1 9.2 12.5 14.4 17.3 21.5 25.9 29.8 37.6 40.9 44.3 46.5 48.4 50.1

0 0.8 2.9 6.1 9.2 12.5 14.4 17.3 21.5 25.9 29.8 37.6 40.9 44.3 46.5 48.4 50.1

0 0.8 2.9 6.1 9.2 12.5 14.4 17.3 21.5 25.9 29.8 37.6 40.9 44.3 46.5 48.4 50.1

0 0.8 2.9 6.1 9.2 12.5 14.4 17.3 21.5 25.9 29.8 37.6 40.9 44.3 46.5 48.4 50.1

0 0.8 2.9 6.1 9.2 12.5 14.4 17.3 21.5 25.9 29.8 37.6 40.9 44.3 46.5 48.4 50.1

0 1.45 3.31 4.9 8.2 11.8 13.8 15.1 16.9 20.1 25 28.7 36.4 39.6 43.1 45.5 47.6 50.4

0 1.45 3.31 4.9 8.2 11.8 13.8 15.1 16.9 20.1 25 28.7 36.4 39.6 43.1 45.5 47.6 50.4

0 0.5 2.4 4.1 7.6 11.3 13.4 14.8 15.8 16.7 20 23.3 26.3 31.3 33.4 36.7 40.6 43.5 46 49.3

0 0.5 2.4 4.1 7.6 11.3 13.4 14.8 15.8 16.7 20 23.3 26.3 31.3 33.4 36.7 40.6 43.5 46 49.3

0 0.7 2.1 3.3 4.3 6.8 8.1 10.4 12.1 13.4 14.6 17.7 20 22 25.5 27.2 30.4 35 38.4 41.3 45.2

0 0.7 2.2 3.4 4.5 7 8.4 10.8 12.6 13.9 15.1 18.3 20.7 22.8 26.5 28.2 31.5 36.3 39.8 42.9 46.9

0 0.7 2.2 3.4 4.5 7 8.4 10.8 12.6 13.9 15.1 18.3 20.7 22.8 26.5 28.2 31.5 36.3 39.8 42.9 46.9

0 0.7 2.1 3.3 4.3 6.8 8.1 10.4 12.1 13.4 14.6 17.7 20 22 25.5 27.2 30.4 35 38.4 41.3 45.2

74

PANEL B: 1994 - 2012 Tax Year

Nominal Income in EUR

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2812 3068 3323 3579 3835 4602 5113 6136 6391 6647 6902 7158 7414 7669 7925 8181 8436 8692 8948 9715 10226 15339 20452 25565 30678 35790 40903 46016 51129 66468 81807 102258 153388

0 0.7 2.1 3.3 4.3 6.8 8.1 10.4 12.1 13.4 14.6 17.7 20 22 25.5 27.2 30.4 35 38.4 41.3 45.2

0 0.7 2.1 3.3 4.3 6.8 8.1 10.4 12.7 14.4 15.6 19 21.5 23.6 27.4 29.2 32.7 37.7 41.3 44.4 48.6

0 0.34 1.3 2.2 3.1 3.9 4.6 7.7 10.9 17.3 21 23.6 25.6 27.4 29.2 32.7 37.7 41.3 44.4 48.6

0 0.34 1.3 2.2 3.1 3.9 4.6 7.7 10.9 17.3 21 23.6 25.6 27.4 29.2 32.7 37.7 41.3 44.4 48.6

0 0.8 1.7 2.6 3.4 4.1 7.3 9.9 16.8 20.5 23 25.1 26.9 28.7 32 37 40.5 43.6 47.7

0 0.3 1.1 1.9 2.7 4.1 6 8.7 16 20 22.8 25 26.8 28.6 32 36.9 40.5 43.6 47.7

0 0.4 1.1 1.9 2.6 3.2 5 7.6 14.8 18.9 21.9 24.3 26.5 28.4 30.3 32 36.7 39.9 42.7 46.4

0 0.2 0.9 1.5 2.1 3.2 3.8 6.2 13.1 17.1 20.1 22.6 24.8 26.8 28.7 30.5 35.2 38.2 40.8 44.2

0 0.1 0.8 1.5 2.1 3.2 3.8 6.1 13 17.1 20.1 22.6 24.8 26.8 28.7 30.5 35.1 38.2 40.7 44.2

0 0.1 0.8 1.5 2.1 3.2 3.8 6.1 13 17.1 20.1 22.6 24.8 26.8 28.7 30.5 35.1 38.2 40.7 44.2

0 0.2 0.7 1.6 2.1 3.4 4.2 11.1 15.3 18.4 21 23.2 25.2 27.1 28.8 33.1 35.8 38.2 41.3

0 0.1 0.6 1.5 2 3.2 4 10.9 15 18 20.4 22.5 24.3 26 27.6 31.5 33.9 36 38.7

0 0.1 0.6 1.5 2 3.2 4 10.9 15 18 20.4 22.5 24.3 26 27.6 31.5 33.9 36 38.7

0 0.1 0.6 1.5 2 3.2 4 10.9 15 18 20.4 22.5 24.3 26 27.6 31.5 33.9 36 38.7

0 0.1 0.6 1.5 2 3.2 4 10.9 15 18 20.4 22.5 24.3 26 27.6 31.5 33.9 36 38.7

0 0.28 0.72 1.1 1.6 2.7 3.5 10.3 14.6 17.6 20 22.1 24 25.7 27.3 31.2 33.7 35.8 38.6

0 0.4 0.8 1.3 2.4 3.2 9.9 14.3 17.3 19.8 21.9 23.8 25.5 27.1 31.1 33.5 35.7 38.6

0 0.4 0.8 1.3 2.4 3.2 9.9 14.3 17.3 19.8 21.9 23.8 25.5 27.1 31.1 33.5 35.7 38.6

0 0.4 0.8 1.3 2.4 3.2 9.9 14.3 17.3 19.8 21.9 23.8 25.5 27.1 31.1 33.5 35.7 38.6

NOTES: This table shows selected average income tax rates for the years 1975 to 2012, including the Eastern German Transfer Tax ("Solidaritaetszuschlag"), for individuals who are married or in a legal partnership. The tax rates were calculated from an online tool provided by the German Ministry of Finance, available on the website https://www.bmf-steuerrechner.de/ekst/ekst.jsp . Zero entries are for the lower threshold. Since the table shows average tax rates there is no upper threshold. For each year separately I sampled income levels in Deutsche Mark (DM), starting in intervals of 500 DM from the lower threshold and then proceeding by increasing the width of the intervals. I chose a progressively wider income grid since the average tax rate function income is highly nonlinear in income near the lower threshold while approaching a linear function at higher income levels. The grid was adjusted accordingly in each year.

75

APPENDIX TABLE D.2 - PARAMETERS OF CALIBRATED TAX SCHEDULE

1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

Lower Threshold

Intercept

Slope

R-Squared

1534 1534 1534 1790 1790 1790 2045 2045 2045 2045 2045 2301 2301 2301 2301 2812 2812 2812 2812 2812 2812 6136 6136 6391 6647 6902 7158 7158 7158 7669 7669 7669 7669 7669 7925 8181 8181 8181

-83.99 -83.99 -83.99 -87.86 -91.69 -91.69 -92.51 -92.51 -92.51 -92.51 -92.51 -93.61 -93.61 -90.48 -90.48 -85.06 -88.26 -88.26 -85.06 -85.06 -92.70 -131.01 -131.01 -129.53 -134.86 -135.79 -133.62 -133.72 -133.72 -131.07 -123.85 -123.85 -123.85 -123.85 -125.04 -125.62 -125.62 -125.62

11.62 11.62 11.62 11.97 12.23 12.23 12.15 12.15 12.15 12.15 12.15 12.17 12.17 11.70 11.70 10.77 11.17 11.17 10.77 10.77 11.69 15.17 15.17 14.97 15.44 15.47 15.11 15.12 15.12 14.68 13.90 13.90 13.90 13.90 13.98 14.02 14.02 14.02

0.995 0.995 0.995 0.995 0.994 0.994 0.990 0.990 0.990 0.990 0.990 0.992 0.992 0.993 0.993 0.990 0.990 0.990 0.990 0.990 0.991 0.995 0.995 0.996 0.996 0.997 0.997 0.997 0.997 0.996 0.993 0.993 0.993 0.993 0.994 0.994 0.994 0.994

NOTES: This table shows the parameters for the calibrated schedule of average tax rates as a function of income. The lower threshold is taken from appendix table D.1. The intercept and slope parameters come from a regression of tax rates on the logarithm of income, with data coming from appendix table D.1 as well. The R-squares from these regressions are shown in the last column of the table. Calibrated tax rates in the estimation will be the maximum of zero and the predicted value from the regression estimates.

76 APPENDIX TABLE E.1 - PARAMETERS OF GERMAN UNEMPLOYMENT INSURANCE SYSTEM, BY YEAR AND AGE GROUP Unemployment Assistance (ALH until 2004; ALG II from 2005)

Unemployment Insurance (ALG until 2004; ALG I from 2005) Years with Constant UI Benefit Parameters 1975 - 1983

Experience Requirement

Duration of Entitlement

1 year

1 year

3 years

3 years

under 42

2 years

1 year

63%

35%

42-48

3 years

1.5 years

63%

35%

49-53

4 years

2 years

63%

35%

at least 54 years

5 years

2.5 years

63%

35%

under 45

2 years

1 year

63%

35%

45-51

3 years

1.5 years

63%

35%

at least 52 years

4 years

2 years

63%

35%

Age Group

1984 - 1986

1999-2004

2005

2006 - 2007

since 2008

50% of potential earnings

none

Apprentices/Labor Market Entrants

35% 50% of potential earnings

none

Apprentices/Labor Market Entrants

40% 50% of potential earnings

63%

none

Apprentices/Labor Market Entrants

Replacement Rate 75% of potential earnings

68%

none

Apprentices/Labor Market Entrants any Age Group

1987-1998

none

Apprentices/Labor Market Entrants any Age Group

Replacement Rate

50% of potential earnings

under 45

2 years

1 year

60%

35%

at least 45

3 years

1.5 years

60%

35%

none

Apprentices/Labor Market Entrants

50% of potential earnings

under 55

2 years

1 year

60%

35%

at least 55

3 years

1.5 years

60%

35%

none

Apprentices/Labor Market Entrants

50% of potential earnings

under 50

2 years

1 year

60%

35%

50 - 58

3 years

1.5 years

60%

35%

at least 58

4 years

2 years

60%

35%

NOTES: This table shows the parameters of the UI monetary payoff equation, calibrated to the German unemployment system for different time periods and age groups. Depending on accumulated labor market experience, age and duration, the unemployed can claim unemployment insurance (ALG) for a limited amount of time. Afterwards the benefits drop to the level of unemployment assistance (ALH). Parameter values are taken from Hunt (1995) and Schmieder, von Wachter and Bender (2011) and involve some aggregation of information contained in these studies. For example, there were several changes in the period 1984 to 1986 that affected workers above the age of 42, and I allocate all these changes to the post-1987 period. This is valid in my study since the oldest workers in my sample in the 1984-1986 period are younger than 42 and are thus unaffected by the changes. Benefits may also vary by marital status, number of children, wealth, and spousal income, which I abstract from in the calibration. The calibrated parameters are for recipients without children. The calibrated replacement rate for ALH is two-third of the actual replacement rate. This is because the rate is means-tested, and Schmieder, von Wachter and Bender (2011) report an actual replacement rate of approx. 35% in their sample.