Technological Change, Wages and the Gender Unemployment Gap Orhan Erem Atesagaoglu SUNY - Stony Brook September 19, 2015

Abstract In the United States, the female unemployment rate had been considerably higher than the male unemployment rate since World War II. However, this gap disappeared after 1980. This article argues that the observed decrease in gender unemployment gap was due to gender-biased technological changes that led to a dramatic stagnation in male wage growth since the late-1970s. To analyze this conjecture, we build a life-cycle search and matching model with endogenous job separation and heterogeneous experience levels. We …nd that the model can account for the observed decrease in gender unemployment gap, both at the aggregate level and by age. Keywords: gender unemployment gap, gender-biased technological change, wage growth. JEL classi…cation: E24, J6

We would like to thank Alexis Anagnostopoulos, Andy Atkeson, David Autor, Eva Carceles-Poveda, Tiago Cavalcanti, Juan Carlos Conesa, Giancarlo Corsetti, Chryssi Giannitsarou, Giammario Impullitti, Jesus Fernandez-Villaverde and many seminar participants for useful comments and suggestions. All errors are my own.

Technological Change, Wages and the Gender Unemployment Gap

1.

1

Introduction In the United States, the female unemployment rate had been considerably higher than

the male unemployment rate since World War II. However, this pattern changed in the early 1980s. The gender unemployment gap, de…ned as the di¤erence between female and male unemployment rates, disappeared after 1980. While the gap was, until then, positive and around 1.5 percentage points, it suddenly dropped to roughly zero percentage points and stayed at this level up until now. Further analysis of the data shows a similar pattern for di¤erent age groups - the gender unemployment gap either narrowed, closed or reversed for workers of di¤erent ages. More speci…cally, while young workers experienced signi…cant changes in the gap, old workers observed only a modest change in the gap. Accordingly, the size of the change in gender unemployment gap declines with age. In this paper, we argue that the observed decrease in gender unemployment gap was due to the ‘gender-biased technological change’ that led to a dramatic stagnation in male wage growth since the late-1970s.1 More speci…cally, the US economy experienced important technological advances that changed the labor market prospects by gender. In particular, technological progress in information technologies, automation, service sectors and o¤shoring reduced demand for ‘physical skills’and increased demand for ‘intellectual skills’. Acemoglu and Autor (2011) argue that this process led to the stagnation of wages for workers employed in jobs with relatively high physical skill requirements, which are heavily dominated by males. Olivetti and Petrongolo (2014) and Rendall (2010) show that the new jobs that require relatively high intellectual skills were …lled mostly by women since they have a ‘comparative’ advantage in these positions. Based on these …ndings, Heathcote, Storesletten and Violante (2010) and Ngai and Petrongolo (2014), among others, argue that the nature of the recent technological change has been gender biased, favoring women, and the literature uses the 1

See Heathcote, Storesletten and Violante (2010), Black and Spitz-Oener (2010) and Ngai and Petrongolo (2014) for a discussion on the ‘gender-biased technological change’.

Technological Change, Wages and the Gender Unemployment Gap

2

term gender biased technological change to refer to this transition.2 In line with these arguments, we document the fact that while wage stagnation have been particularly intense for male workers, female workers did not experience a similar slowdown and we relate these wage dynamics to gender-biased technological change, as in Heathcote, Storesletten and Violante (2010). We argue that the observed trend changes in MPL/wage growth led to a sudden increase in job separation rates for male workers. As a consequence, male unemployment went up and the gender unemployment gap vanished. Based on this argument, the main aim of this paper is to propose an interpretation of observed unemployment dynamics in which trend changes in MPL/wage growth plays a key role. Following the modelling and calibration approach of Heathcote, Storesletten and Violante (2010), we model gender-biased technological change as an exogenous shift in the productivity growth of male workers relative to female workers, so that the model matches the actual evolution of gender di¤erences in wage growth over the period of interest. We then investigate the extend to which the observed decline in gender unemployment gap can be accounted for by the stagnation of male wages. The proposed link between changes in MPL/wage growth rates and male unemployment is as follows. We begin by showing that workers face substantial returns to labor market experience. To accumulate experience, an individual must work. In case of high MPL and wage growth, some worker-…rm pairs will continue to stay in their low surplus matches, so that the worker can accumulate experience (skills) and both parties bene…t from it in the future. When MPL and wage growth goes down, these incentives diminish since the expected future payo¤ of experience falls. This is because, lower growth rates cause future bene…ts of experience to be discounted at a higher rate - lower growth rates act as a higher discount rate for …rms and workers. In this case, the marginal …rm/worker will …nd searching for a new worker/job more attractive. This will lead to a sudden increase in the job separation rate and, in turn, an increase in the unemployment rate. In fact, that is what we observe in the 2

See, among others, Heathcote, Storesletten and Violante (2010), Black and Spitz-Oener (2010), Rendall (2010) and Ngai and Petrongolo (2014).

Technological Change, Wages and the Gender Unemployment Gap

3

data: while the job separation rate for male workers jumped to a higher level in 1980, it did not change signi…cantly for female workers. We next elaborate on this point. While gender-biased technological change took e¤ect in the mid to late 1970s, it has been a gradual process in nature as any other technological change - the gender biased demand shift in favor of female labor has been gradual. That is why male-wages experienced a ‘secular stagnation’ instead of a ‘sudden decline’.3 Nevertheless, the e¤ect of this process on gender ‘unemployment’gap dynamics was immediate. This is because a permanent trend change in MPL/wage growth e¤ects the expected ‘future payo¤’of experience and, therefore, the ‘current incentives’ for experience accumulation. Based on this causality, a decline in future productivity/earning prospects leads to a ‘sudden’increase in the job separation and unemployment rates.4 This implication of our model and the proposed mechanism is in line with one considered in Elsby and Shapiro (2012). To analyze this conjecture, we build a life-cycle search and matching model with gender heterogeneity and endogenous job separation in which (i) there are two type of workers: experienced and inexperienced, (ii) at each date, new inexperienced workers enter the labor force to replace those who exit, (iii) inexperienced workers can become experienced only if they are employed, and (iv) experienced workers are more productive and earn more with respect to inexperienced workers. We …rst calibrate our benchmark economy to match some key labor market statistics. We then simulate the model by shifting gender-speci…c productivity growth rates to match the observed wage series for each gender, and we compute the new long-run equilibrium as well as the transitional dynamics that precede it. Our numerical analysis shows that the model is consistent with the observed age patterns of unemployment, job separation and job …nding rates for both gender group. We …nd that the simulated gender 3

This implication of gender-biased technological change is similar in nature to the e¤ect of skill-biased technological change on ‘college wage premium’. More in details, while skill-biased technological change increased demand for college educated workers, this demand shift has been a gradual processs and, therefore, college wage premium experienced a gradual increase instead of a sudden jump. 4 As in Heathcote, Storesletten and Violante (2010), we model gender-biased technological progress as a trend change in gender-speci…c productivity rates, where …rms/workers have perfect foresight after the change occurs. This follows the standard modeling approach used by the literature (See Jaimovich and Siu (2014) and Elsby and Shapiro (2012) for similar modelling approaches).

Technological Change, Wages and the Gender Unemployment Gap

4

unemployment gap series track the time-series features of the data quite well: the model can account for 93% of the decrease in gender unemployment gap at the aggregate level and the transitional dynamics predicted by the model are in line with those in the data. The model can account for the observed increase in the aggregate job-separation rate for males. The model can capture fairly well the sudden changes observed in gender unemployment gap by age. This is because, in our model economy, while young male workers experience signi…cant changes in job separation rates, old male workers do not experience a similar increase. At …rst glance, one might expect that the gender unemployment gap should close also for old workers since the data shows that male workers with jobs that require relatively ‘high physical skills’are represented in all age groups. However, recall that old workers are ‘experienced’workers, which implies that a stagnation in wages will not change the experience accumulation incentives for this group and, therefore, separation rates. Accordingly, the predictions of our proposed mechanism is in line with the data (See Section 4 for details).5 A …nal remark on our calibration approach. The focus of this paper is the ‘change’ in gender di¤erences in unemployment and, therefore, providing an explanation for ‘why there are gender di¤erences in unemployment’is beyond the scope of this paper. Accordingly, we calibrate our benchmark economy to match the observed gender di¤erences in unemployment before we provide the suggested experiments. It is important to emphasize that point since the model’s prediction for the ‘percentage points change’ in gender unemployment gap is quite insensitive to whether the ex-ante gender unemployment gap is ‘positive’or ‘negative’.6 Therefore, we conclude that our calibration strategy is appropriate for the question of interest. Related Literature: This paper is closely related to the vast literature that attempts to understand the observed negative relationship between long-run productivity growth and unemployment. Theoretically, standard search and matching models have been less successful 5

The observed declines in gender unemployment gap (both at the aggregate level and by age) are ‘sudden’ changes and, therefore, di¢ cult to be explained by demographic and social changes (See Section 2.1). 6 The gender unemployment gap can be positive or negative for di¤erent sub-groups (age, marital status, education etc.). However, our focus is on two measures: the gender unemployment gap at the aggregate level and by age. Based on this, the model’s predictions for the ‘percentage points change’in gender di¤erences in unemployment is quite insensitive to whether the ex-ante gender unemployment gap is ‘positive’or ‘negative’.

Technological Change, Wages and the Gender Unemployment Gap

5

in capturing this negative correlation.7 This is because, in this class of models, trend changes in productivity growth a¤ect equally the wage and the ‡ow payo¤ from unemployment, and in the absence of this condition, the economy will converge either to zero-unemployment or zero-employment. Shimer (2010) demonstrates this result within the standard MortensenPissarides framework. Based on these …ndings, we revisit this relation by taking into account the accumulation of experience over the life cycle. We show that a slowdown in aggregate productivity growth cause future bene…ts of experience to be discounted at a higher rate, which decreases experience accumulation incentives and leads to an increase in job separation and unemployment. Moreover, the model is successful in explaining why the sensitivity of unemployment to changes in productivity growth is higher for the young than the old. There is a growing literature that studies the pattern of unemployment over the life cycle. In particular, most e¤orts have been directed to understand the life-cycle patterns of labor market ‡ow rates. To address this question, Gervais et al. (2013) build a model of occupational learning in which young workers, who are less likely to be in a match with good occupational …t, are more likely to separate and be unemployed. Menzio et.al (2013) develop a directed search model where the assignment of the right worker to the right …rm is time consuming due to search frictions, which implies that young workers are more likely to be unemployed. Gorry (2012) builds a life-cycle search model with general human capital accumulation to explore the e¤ects of minimum wages on youth unemployment. Our model di¤ers from these studies in two dimensions. First, our model incorporates endogenous job separation, growth and gender heterogeneity into a life-cycle search and matching framework. These features of our model are crucial for understanding the observed di¤erence in gender unemployment gap dynamics between young and old workers. Second, our model tries to capture not only the pattern of unemployment over the life cycle, but also the the ‘change’in the age patterns of unemployment, separation and …nding rates over the period of interest. There is a large literature that focuses on the driving forces shaping the gender di¤er7

See, among others, Blanchard (2007), Pissarides and Valanti (2007) and Miyamoto and Takahashi (2011).

Technological Change, Wages and the Gender Unemployment Gap

6

ences in employment and wage growth observed in recent decades. The most prominent explanation o¤ered by the literature is the gender-biased nature of the technological change that has occured during the same time period. Olivetti and Petrongolo (2014) and Heathcote, Storesletten and Violante (2010) show that there has been gender biased demand shifts observed in labor markets since the late 1970s. In particular, Heathcote, Storesletten and Violante (2010) documents the evolution of gender di¤erences in wage growth over the period of interest and they relate these wage dynamics to gender-biased technological change. In line with these …ndings, Acemoglu and Autor (2011) showed that the recent technological progress reduced demand for physical skills and increased demand for ‘intellectual skills’. In particular, they argue that the poor labor market performance of males was due to the fact that jobs that require relatively high physical skills were heavily dominated by males. Olivetti and Petrongolo (2014) and Rendall (2010), among others, show that the new jobs that require relatively high intellectual skills were …lled mostly by women since they have a ‘comparative’advantage in these positions. Our paper contributes to this literature by focusing exclusively on the e¤ects of gender-biased technological change and wage growth trends on ‘unemployment’, and in particular, by gender and by age. This paper is also related to the recent work by Elsby and Shapiro (2012). They …rst document that the labor force participation of low-skilled males experienced a ‘gradual’decrease from the 1970s to the 2000s, a period in which male wages stagnated. They next present a model showing that stagnant male wages can account for the observed decrease in the labor force participation rate of low skilled males. Our paper complements and di¤ers in several dimensions. First, we focus on unemployment rather than the participation margin. Second, we particularly focus on the gender di¤erences in unemployment. Third, our model incorporates and evaluates the quantitative e¤ects of several labor market frictions that are directly related to unemployment, such as search and matching. Finally, our paper aims to capture the observed ‘sudden’change in the life-cycle pro…les of unemployment and job separation. This life-cycle aspect of unemployment is the key point of our paper, whereas Elsby

Technological Change, Wages and the Gender Unemployment Gap

7

and Shapiro (2012) study changes in participation only at the aggregate level. To our knowledge, the only study that investigates the change in U.S. gender unemployment gap is Albanesi and Sahin (2013). In particular, they look at the gender di¤erences in unemployment from a ‘long-run’perspective and show that the observed secular rise in labor force attachment of women can account for the di¤erence between the gender unemployment gap in the late-1970s and the late-1990s. Our analysis di¤ers in three dimensions. First, we show that the gender unemployment gap disappeared in the early 1980s and, in line with this fact, we focus on this particular time interval and the ‘transitional dynamics’. Second, we build a link between gender unemployment gap dynamics and the observed deterioration in labor market conditions of men over the period of interest. Third, we focus on gender unemployment gap dynamics not only at the aggregate level, but also by age. The organization of the article is as follows. Section 2 documents the empirical facts motivating our analysis. Section 3 presents the model. Section 4 presents the calibration and the quantitative implications of the model by focusing on both the steady state results and the transitional dynamics. Section 5 concludes.

2.

Facts

2.1. Gender Unemployment Gap Figure 1A plots the U.S. unemployment rates by gender for the period 1948-2011.8 We observe that the gender unemployment gap was positive before the late 1950s, although tending to close during recessions. From the late 1950s to the early 1980s, the gap was more pronounced and around 1.5 percentage points. After the early 1980s, the gender unemployment gap disappeared. This pattern is more apparent if we look at the trend unemployment rates. Figure 1B plots the Hodrick-Prescott (HP) …ltered unemployment series. Evidently, while there had been a signi…cant gap between female and male unemployment rates since World 8

We use seasonally adjusted unemployment series constructed by the Bureau of Labor Statistics (BLS) using the Current Population Survey (CPS). In particular, we restrict the sample to workers aged 20 and over. See Appendix for the data used in this study.

Technological Change, Wages and the Gender Unemployment Gap

8

War II, we observe a clear break in this pattern in the early 1980s. In order to understand the timing of this break, Figure 2A takes a closer look at the gender unemployment gap. The shaded area in the …gure illustrates the …rst half of 1980. Clearly, the gap vanished in this time interval; while the gap was roughly stable until 1980, it dropped to a level of about 0 percentage points and has remained roughly constant at that level. We next focus on the gender di¤erences in unemployment by age. Figure 2B plots the changes in gender unemployment gap for di¤erent age groups over the period of interest. We observe that the gap was positive (though at di¤erent levels) for all age groups until 1980. However, during the second half of 1979 and the …rst half of 1980, the gap either narrowed, closed, or even reversed for workers of di¤erent ages. A closer look at the data shows that the gap reversed for 20-24 year olds, closed for 25-34 year olds, and narrowed for 35-54 year olds. For workers aged 55-62 years old (our oldest age group), we also observe a small decrease in the gap, but the break in the pattern is less clear. Given these observations, we …nd that the gender unemployment gap decreased (i) 3.1 percentage points for 20-24 year olds, (ii) 1.8 percentage points for 25-34 year olds, (iii) 0.8 percentage points for 35-44 year olds, (iv) 0.5 percentage points for 45-54 year olds, and (v) 0.2 percentage points for 55-62 year olds. Evidently, the size of the change in gender unemployment gap declines with age. 2.2. Wages and Marginal Productivity of Labor (MPL) Figure 3 shows the evolution of real median wage income by gender over the post-war period.9 We observe that the rate of wage growth, for both males and females, was roughly constant around 2% per year until the mid 1970s. However, we observe a sudden break in this trend in the mid 1970s: while female wages have continued to grow at the same pace, the wage growth rate for males dropped sharply to about 0% and has stagnated at this level since then. Evidently, stagnant median wages seems to be a male phenomenon. 9

We particularly focus on median wages for the following reason. While unemployment rate calculations assign the same weight to all workers, mean wage calculations assign higher weights to high-wage workers. This, together with the fact that unemployment is highest among the lowest earners, suggests that the median wage growth is the right measure for our purpose.

Technological Change, Wages and the Gender Unemployment Gap

9

In order to understand the exact timing of this break, Figure 3 also plots the evolution of gender wage gap, de…ned as the ratio of female to male median wages. We observe that, while this ratio was roughly constant until 1977, it has been increasing since then. What drives the observed di¤erence in median wage growth between male and female workers? The most prominent explanation o¤ered by the literature is the ‘gender biased technological change’hypothesis (See references and the discussion in Section 1 above). Following the modelling and calibration approach of Heathcote, Storesletten and Violante (2010), we model gender-biased technological change as an exogenous trend shift in the productivity growth of male workers relative to female workers, so that the model’s time paths for gender di¤erences in wage growth matches the trends in their empirical counterparts over the period of interest. This approach is based on ‘Marginal Productivity Theory of Wages’, which states that every worker of same skill receive a wage equal to the marginal product of that type of labor. Therefore, productivity growth for male and female workers can be inferred by looking at wage growth by gender. Accordingly, modelling the microfoundations and sources of gender-biased technological change is beyond the scope of this approach (see Heathcote, Storesletten and Violante (2010) for details). Nevertheless, in Appendix B, we provide a brief empirical analysis to shed some light on the link between gender-biased technological change and the gender di¤erences in ‘unemployment’and ‘wage growth’patterns. 2.3. Labor Flow Rates In this section, we present the observed trend changes in labor market ‡ow rates - the transition probabilities between employment (E), unemployment (U), and nonparticipation (N). The three state classi…cation system leads to six ‡ow rates across states. The six panels of Figure 4 show the ratio of male to female ‡ow rates between 1968 and 1996.10 For example, the 10

By using the monthly CPS …les and the method provided by Shimer (2012), we constructed the labor market ‡ow rates for the period 1976-2005 (See Appendix for details). While we use our estimates through out the paper, we report in this section the estimates of DeBoer and Seeborg (1989), which are almost identical to ours. This is because, while our estimates starts with the year 1976, the estimates of DeBoer and Seeborg starts from 1968 (based on unpublished CPS data for the period 1968-1976).

Technological Change, Wages and the Gender Unemployment Gap

10

f f m m …rst panel depicts the evolution of PEU =PEU ratio, where PEU and PEU denote employment-

to-unemployment ‡ow rates for male and female workers, respectively. If we look at each of the six panels, we observe di¤erent dynamics for each series. However, the time period that we need to focus on is 1979 to 1980 - the years between which the gender unemployment gap disappeared. Accordingly, the only trend change is in employment-tof m unemployment ‡ow rates. We …nd that the PEU =PEU ratio increased 30.4% between 1979

and 1980. While the actual ratio was nearly constant at around 1.05 until 1979, it suddenly increased to a level of about 1.37 in 1980 and has remained roughly constant at that level. f m Evidently, the observed increase in PEU =PEU ratio was a secular structural break, rather than m a cyclical movement. We …nd that, while PEU increased about 35% between 1979 and 1980, f there was no signi…cant change in PEU over the same time period. Motivated by this fact,

we argue that the observed increase in employment-to-unemployment ‡ow of male workers led to the decrease in gender unemployment gap. In line with this causality and the evidence discussed above, nonparticipation does not seem to be an important margin for understanding the ‘transitional dynamics’of gender unemployment gap over the period of interest.11

3.

The Model Environment. Time is discrete and indexed by t = 1; 2; ::. The economy is populated by

a continuum of ex-ante identical workers. There are two gender groups, males and females, where each group is populated by a unit measure of workers. These two genders are denoted by j 2 fm; f g, where ‘m’and ‘f ’stand for male and female, respectively. There are two types of workers within each gender group: experienced and inexperienced. These two types are denoted by i 2 fh; lg, where ‘h’and ‘l’stand for experienced (high-type) and inexperienced (low-type), respectively. In each period, workers leave the labor force with probability

2

(0; 1) and new inexperienced workers of the same gender enter the labor force to replace those who left. There are two labor market states, employment and unemployment. Each period, 11

In line with this evidence, Sahin, Song and Hobijn (2010) argues that the observed decline in gender unemployment gap in 1980 was a result of the increase in separation and unemployment rates of male workers.

11

Technological Change, Wages and the Gender Unemployment Gap

an inexperienced worker becomes experienced with probability

j

2 (0; 1), but this is possible

only if the worker is employed. An unemployed inexperienced worker does not have a chance to become experienced. The economy is populated by a continuum of ex-ante identical …rms with potentially an in…nite mass. Firms can post a vacancy of type i 2 fh; lg for gender j 2 fm; f g at a ‡ow cost cij t . When a …rm and a worker meets, the pair observes the initial productivity of the match and decides whether to form the match or not. If the match is formed, the worker-…rm pair starts the production and the wages are determined by Nash bargaining. The productivity of an existing match is subject to shocks and, thus, changes over time. If the productivity of a match declines below a reservation level, the match is endogenously destroyed. This endogenous separation decision will be described in more detail below. Production Technology. The output produced by a worker-…rm match is equal to ytij = eij z jt , where eij denotes the experience level of type i 2 fh; lg and gender j 2 fm; f g, z denotes the match-speci…c productivity level and

j t

denotes the aggregate labor productivity

in period t for gender j. The experience level eij and the match-speci…c productivity z are individual states for each match. On the contrary, aggregate productivity level

j t

represents

the macro conditions in the labor market for gender j and a¤ects all workers of the same gender at the same time. Therefore, since output is produced by one worker-one …rm matches, productivity level

j t

also represents the marginal productivity of labor (MPL) for each gender

group, which is the sole determinant of aggregate wage growth trends. The marginal labor productivity

j t

grows at a constant rate 1 + gj for each gender j. Accordingly, di¤erential

trend changes in gm and gf capture the e¤ects of gender-biased technological change by driving the wage dynamics for each gender group.12 For each gender group, the experience level can take two values eij 2 fehj ; elj g, where ehj and elj represent the returns to labor market experience for experienced and inexperienced workers, respectively. We assume that elj < ehj for each gender j, which ensures that the 12

See Heatcote, Storesletten and Violante (2010) for a similar modelling approach.

Technological Change, Wages and the Gender Unemployment Gap

12

higher the experience level, the higher the labor market return. The initial value of match-speci…c productivity z is drawn from the distribution Fj (z) = probj (z

z). For each gender group j, the output produced by an existing match is subject

to shocks and, thus, changes over time as j j t+1 = t

(i) the marginal labor productivity grows at a constant rate,

= 1 + gj ,

(ii) the experience level can change: an inexperienced worker can become experienced, _0 _

(iii) the match-speci…c productivity changes, following a markov process Gj (z =z) = probj (z 0

_0

_

z =z = z):

The markov process Gj (z 0 =z) is as follows. With probability pij , the value of z will be the same as in the previous period. With probability 1

pij , a new value of z is drawn from the

distribution Fj (z). Note that pij is type and gender speci…c. Matching Market. The number of matches formed in period t is determined by the matching function m(uij t ;

ij t ),

where uij t and

ij t

denote, respectively, the mass of unemployed

workers and posted vacancies of type-i and gender-j. The matching function m(uij t ;

ij t )

exhibits constant returns to scale. The meeting probability for an unemployed worker of type-i and gender-j is given by f (

ij t )

= m(uij t ;

ij ij t )=ut ,

where

ij t

=

ij ij t =ut

is the labor

market tightness in this market. Similarly, the meeting probability for a vacancy of type-i and gender-j is given by q(

ij t )

= m(uij t ;

ij ij t )= t .

3.1. Workers Employed workers receive a wage income of wt (z; eij ). Unemployed workers receive a ‡ow payo¤ equal to bjt (eij ) = bj (eij ) jt , a function of the experience eij and the marginal labor productivity

j t.

The assumption of bjt (eij ) being a function of

j t

is standard in the literature

and it is a necessary condition for the existence of a non-trivial balanced growth path. More speci…cally, this assumption implies that the growth rate gj a¤ect equally the wage wt (z; eij ) and the ‡ow payo¤ bj (eij ) for each type i 2 fh; lg and gender j 2 fm; f g, and in the absence of this condition, the economy will converge either to zero-unemployment or zero-employment.

13

Technological Change, Wages and the Gender Unemployment Gap

Problem of Experienced Workers. Consider the optimization problem of an experictj (ehj ; z; enced worker of gender j 2 fm; f g. Let W

j t)

denote the value of being an experienced

employed worker in period t, with a match-speci…c productivity level z. The value of being an experienced unemployed worker in period t is given by Utj (ehj ;

j t ).

Let Wtj (ehj ; z;

j t)

denote

the beginning-of-period value of an experienced worker who has the option to choose whether to work or not to work. These workers can be of two types: Type 1: An employed worker who observes a new match-speci…c productivity. (worker needs to decide either to ‘stay employed’or to ‘become unemployed’) Type 2: An unemployed worker who meets a …rm. (worker needs to decide either to ‘become employed’or to ‘stay unemployed’). Notice that the decision problem is the same for both types. This equivalence is implied by the assumption of endogenous job separation. Then, Wtj (ehj ; z; Wtj (ehj ; z; ctj (ehj ; z; Next, W ctj (ehj ; z; W

j t)

ctj (ehj ; z; = maxfW

j t ),

j t)

j j t ); Ut (ehj ;

j t)

is de…ned by

j t )g

(1)

the value of being an employed experienced worker in period t is

= wt (z; ehj ) + (1

j ) phj Wt+1 (ehj ; z;

+ (1

phj )

Z

j t+1 )

j Wt+1 (ehj ; z 0 ;

j 0 t+1 )dFj (z )

(2)

which is equal to the current wage plus the expected present value of future payo¤s. Conditional on not leaving the labor market, the worker starts the next period either with the same match-speci…c productivity (with probability phj ) or with a new value of z (with probability 1

phj ). These two cases, in both of which the worker has the option to stay in the match or

j to separate, are represented by the value Wt+1 (ehj ; :;

Similarly, Utj (ehj ; Utj (ehj ;

j t)

= bhj

j t ), j t

j t+1 ).

the value of being an unemployed experienced worker in period t is

+ (1

) (1

f( + f(

hj j t+1 ))Ut+1 (ehj ;

hj t+1 )

Z

j t+1 )

j Wt+1 (ehj ; z 0 ;

j 0 t+1 )dFj (z )

(3)

14

Technological Change, Wages and the Gender Unemployment Gap

where bhj is given by the function bj (:) evaluated at the experience level ehj . In period t + 1, conditional on not leaving the labor market, the worker either meets a …rm (with probability f(

hj t+1 ))

value

R

or does not (with probability 1 f (

j Wt+1 (ehj ; z 0 ;

j 0 t+1 )dFj (z ),

hj t+1 )).

While the former case is represented by the

j the latter case is represented by the value Ut+1 (ehj ;

j t+1 ).

Problem of Inexperienced Workers. Consider the optimization problem of an inexctj (elj ; z; perienced worker of gender j 2 fm; f g. In line with the notation above, let W

denote the value of being an inexperienced employed worker, Utj (elj ; being an inexperienced unemployed worker, and Wtj (elj ; z;

j t)

j t)

j t)

denote the value of

denote the beginning-of-period

value of an inexperienced worker who has the option to choose whether to work or not to. Then, Wtj (elj ; z; Wtj (elj ; z; ctj (elj ; z; Next, W

j t) j t)

is de…ned by the following decision problem:

ctj (elj ; z; = maxfW

j t ),

j j t ); Ut (elj ;

j t )g

(4)

the value of being an employed inexperienced worker in period t is

ctj (elj ,z; jt ) = wt (z,elj )+ (1- ) W

+ (1- j )

j

j phj Wt+1 (ehj ,z; jt+1 )+(1-phj )

j plj Wt+1 (elj ,z; jt+1 )+(1-plj )

Z

Z

j Wt+1 (ehj ,z 0 ;

j Wt+1 (elj ,z 0 ;

j 0 t+1 )dFj (z )

j 0 t+1 )dFj (z )

(5)

which takes into account the fact that the worker faces several possibilities at the start of period t + 1. First, conditional on not leaving the labor market, the worker remains inexperienced with probability (1

j ).

On the other hand, with probability

j,

the worker becomes

experienced. Whether inexperienced or experienced, workers start period t + 1 either with the same match-speci…c productivity or with a new value of z: Finally, Utj (elj ; Utj (elj ;

j t)

j t ),

= blj

the value of being an unemployed inexperienced worker in period t is j t

+ (1

) (1

f( + f(

lj j t+1 ))Ut+1 (elj ; lj t+1 )

Z

j t+1 )

j Wt+1 (elj ; z 0 ;

j 0 t+1 )dFj (z )

(6)

where blj is given by the function bj (:) evaluated at the experience level elj . The interpretation of equation (6) is similar to that given to equation (3):

15

Technological Change, Wages and the Gender Unemployment Gap

Labor Market Dynamics. Recall that (i) new workers enter the labor force as inexperienced, and (ii) inexperienced workers become experienced at a constant rate. Based on this setup, conditional on not leaving the labor market, workers experience a two-stage life-cycle. Therefore, on average, young agents are inexperienced, whereas old agents are experienced. This setup provides enough ‡exibility to capture the average life-cycle pro…le of wages observed in the data, as long as experienced workers earn more with respect to inexperienced workers wt (z; ehj ) > wt (z; elj ) for each gender group j 2 fm; f g. Moreover, in this setup, experienced and inexperienced workers can possibly have di¤erent unemployment, job separation and job …nding rates - which is the case for young and old workers in the data. 3.2. Firms Firms can post a vacancy of type i 2 fh; lg for gender j 2 fm; f g at a ‡ow cost cij jt . If the …rm succeeds in recruiting, the …rm produces ytij = eij z in period t. The assumption of cost cij

j t

j t

being a function of

and the worker earns wt (z; eij ) j t

is standard in the literature

and it is a necessary condition for the existence of a non-trivial balanced growth path. Problem of Firms Searching for Experienced Workers. Consider the optimization problem of a …rm in market i = h. Let Jbtj (ehj ; z;

j t)

denote the value of a …rm that employs

an experienced worker in period t. The value of a vacant …rm searching for an experienced worker is given by Vthj ( jt ). Let Jtj (ehj ; z;

j t)

denote the beginning-of-period value of a …rm

that has the option to choose whether to produce or not. These …rms can be of two types: Type 1: A vacant …rm meets a worker (decide either to ‘form a match’or to ‘stay vacant’). Type 2: A …rm in an existing match observes a new match-speci…c productivity. (…rm needs to decide either to ‘stay in the match’or to ‘become vacant’). Notice that the decision problem is the same for both types. Then, Jtj (ehj ; z; Jtj (ehj ; z; Next, Jbtj (ehj ; z;

j t)

= maxfJbtj (ehj ; z;

j t ),

j t)

is de…ned by

j hj j t ); Vt ( t )g

the value of a …rm matched with an experienced worker in period t is

(7)

16

Technological Change, Wages and the Gender Unemployment Gap

Jbtj (ehj ; z;

j t)

= ehj z

j t

j ) phj Jt+1 (ehj ; z;

wt (z; ehj ) + (1

+ (1

phj )

Z

j t+1 )

j Jt+1 (ehj ; z 0 ;

j 0 t+1 )dFj (z )

(8)

which is equal to the current pro…t plus the expected present value of future pro…ts. The worker-…rm pair starts period t + 1 either with the same match-speci…c productivity (with probability phj ) or with a new value of z (with probability 1 phj ). These two cases, in both of j (ehj ; :; which the …rm has the option to continue or to separate, are represented by Jt+1

j t+1 ).

The value of a vacant …rm searching for an experienced worker, Vthj ( jt ); is given by: Vthj ( jt ) =

chj

j t

+ (1

) (1

q( + q(

where chj

j t

hj hj j t+1 ))Vt+1 ( t+1 )

hj t+1 )

Z

j Jt+1 (ehj ; z 0 ;

j 0 t+1 )dFj (z )

(9)

denotes the vacancy posting cost. In period t + 1, the …rm either meets an

experienced worker (with probability q( hj t+1 )) or does not. While the former case is represented R j hj by the value Jt+1 (ehj ; z 0 ; jt+1 )dFj (z 0 ), the latter case is represented by Vt+1 ( jt+1 ). Problem of Firms Searching for Inexperienced Workers. Consider the optimiza-

tion problem of a …rm in market i = l. Let Jbtj (elj ; z;

j t)

denote the value of a …rm that employs

(matched with) an inexperienced worker in period t. The value of a vacant …rm searching for an inexperienced worker is Vtlj ( jt ). Let Jtj (elj ; z;

j t)

denote the beginning-of-period value of

a …rm that has the option to choose whether to produce or not. Then, Jtj (elj ; z; Jtj (elj ; z; Next, Jbtj (elj ; z;

j t)

= maxfJbtj (elj ; z;

j t ),

j t)

is:

j lj j t ); Vt ( t )g

(10)

the value of a …rm matched with an inexperienced worker in period t is

Jbtj (elj ; z; t ) = elj z

j t

+ (1

wt (z; elj ) ) (1

+

j

j)

j plj Jt+1 (elj ; z;

j phj Jt+1 (ehj ; z;

j t+1 )+(1

j t+1 ) + (1

phj )

plj ) Z

Z

j Jt+1 (elj ; z 0 ;

j Jt+1 (ehj ; z 0 ;

j 0 t+1 )dFj (z )

j 0 t+1 )dFj (z )

(11)

17

Technological Change, Wages and the Gender Unemployment Gap

Equation (11) implies that the match faces several possibilities at the start of period t + 1. First, notice that the type of the match can change as the worker’s type changes. If the worker remains inexperienced (with probability 1 worker becomes experienced (with probability

j ),

j ),

the match remains type-l. If the

the match becomes type h. Whether the

type of the match changes or not, the worker-…rm pair starts period t + 1 either with the same match-speci…c productivity or with a new value of z: Thus, the match can dissolve if (i) the new match speci…c productivity is too low, or (ii) the match speci…c productivity does not change but the match becomes type-h and it is not optimal to continue the match anymore. Similarly, the value of a vacant …rm searching for an inexperienced worker, Vtlj ( jt ); is Vtlj ( jt ) =

clj

j t

+ (1

) (1

q(

lj lj j t+1 ))Vt+1 ( t+1 )

lj t+1 )

+ q( where clj

j t

Z

j Jt+1 (elj ; z 0 ;

j 0 t+1 )dFj (z )

(12)

denotes the vacancy posting cost. The interpretation of equation (12) is similar

to that given to equation (9): 3.3. Wage Determination and Job Separation Wages are set by Nash bargaining, where the worker and the …rm share the surplus of the match. Let Stj (eij ; z;

j t)

denote the surplus of the match for i 2 fh; lg and j 2 fm; f g. Then,

the surplus function is Stj (eij ; z;

j t)

ctj (eij ; z; =W

j t)

+ Jbtj (eij ; z;

j t)

Utj (eij ;

j t)

Vtij ( jt )

(13)

As the outcome of Nash bargaining, the payo¤ of the worker and the …rm is, respectively, ctj (eij ; z; W

Jbtj (eij ; z;

where

and 1

j t)

j t)

Utj (eij ;

j t)

= Stj (eij ; z;

Vtij ( jt ) = (1

j t)

)Stj (eij ; z;

(14) j t)

(15)

denote the bargaining weights of workers and …rms, respectively. The

worker and …rm will agree to continue the match as long as the match surplus is positive,

18

Technological Change, Wages and the Gender Unemployment Gap

Stj (eij ; z;

j t)

> 0. Since Stj (eij ; z;

j t)

is strictly increasing in z, there exists a reservation

productivity zij for each i 2 fh; lg and j 2 fm; f g, where Stj (eij ; zij ;

j t)

= 0. Thus, the match

will dissolve if the productivity of a match falls below the reservation level, z

zij . Notice

that the worker and the …rm will separate if separation is jointly optimal. Therefore, the quit/layo¤ distinction is arbitrary, which is a standard implication of search and matching models with Nash wage bargaining. See den Haan et al. (2005) for a detailed discussion. 3.4. Vacancy Creation The free entry condition implies that the value of vacancy is zero for all types of posts. Thus, Vtij ( jt ) = 0 for all i 2 fh; lg and j 2 fm; f g. Then, equations (9) and (12) can be written as follows: chj jt clj jt

= (1 = (1

)q(

hj t+1 )

)q(

lj t+1 )

Z

Z

Jtj (ehj ; z 0 ; Jtj (elj ; z 0 ;

j 0 t+1 )dFj (z )

j 0 t+1 )dFj (z )

for j 2 fm; f g for j 2 fm; f g

(16) (17)

These two conditions, (16) and (17), determine the equilibrium market tightness. As a …nal point, (i) observe that a vacant …rm is indi¤erent between posting a vacancy of any type since the value of vacancy is zero for all types of posts, and (ii) recall that …rms do not have a type but have to post a type-speci…c vacancy. These two conditions ensure that, when an inexperienced worker becomes experienced, the match will continue - as long as it is still productive - since the …rm does not have a type. Equation (11) captures this point explicitly.

4.

Quantitative Analysis

4.1. Calibration We begin with describing the calibration of the parameters that are common to both male and female workers. We choose the model period to be one month. We set the monthly discount factor equal to

= 0:9966, which implies an annual interest rate of 4:1 percent.

Technological Change, Wages and the Gender Unemployment Gap

The probability of leaving the labor force is set to

19

= 0:002, which implies that the average

time spent in the labor force is expected to be 41:7 years (1= = 500 months). We assume that the new inexperienced workers enter the labor force at the age of 20. Therefore, with an expected working life of 41:7 years, the new entrants are expected to retire at about the age of 62. We assume that the matching function takes the standard Cobb-Douglas form, m(uij t ;

ij t )

= (uij t ) (

ij 1 t )

, where

is the elasticity of the matching function with respect

to unemployment. Following Mortensen and Nagypal (2007), we set

= 0:5, which is within

the range of estimates used in the literature. In line with this parameterization, we also set the bargaining power of workers

to 0:5, so that

=

and the Hosios condition holds.

We now describe the calibration of gender speci…c parameters. While we choose some of these parameter values based on independent evidence, we calibrate the remaining parameters jointly to match some key moments observed in the data. For the benchmark calibration, we set the growth rate gj to 0:166% for both gender j 2 fm; f g. This translates into an annual growth rate of 2%, which captures the average wage growth for both male and female workers prior to the break. For the post-1980 period, gm is set to 0% for male workers, which captures the observed stagnation in male wages. For the post-1980 period, gf is set to 0:166% for female workers, which is consistent with the fact that female wages have continued to grow at the same pace: there was no trend change in wage growth for female workers over the post-war period. The initial value of match-speci…c productivity z is drawn from the distribution Fj (:) for each gender j 2 fm; f g. We assume that the initial z is independently and identically distributed and follows a lognormal distribution ln(z) j

is the standard deviation. We set

j

N ( j;

2 j );

where

j

is the mean and

= 3 for both gender, which is just a normalization

and does not a¤ect our key unemployment measurements. This is because, in the calibration, the ‡ow payo¤ from unemployment bij is rescaled according to the choice of

j

and, therefore,

the tradeo¤ between employment and unemployment is unaltered. The standard deviation j

determines the dispersion of productivity shocks. Moreover, together with the return to

Technological Change, Wages and the Gender Unemployment Gap

experience, the parameter

j

20

determines the cross sectional dispersion of wages. Thus, for a

given level of return to experience, we calibrate

j

to match the dispersion of wages prior to

the break. Ekstein and Nagypal (2004) documents that the standard deviation of log wages was roughly constant and equal to 0:529 for male workers and 0:510 for female workers over the 1961-1979 period. In line with this evidence, we set

m

= 1:140 and

f

= 1:273 to match,

respectively, the observed cross sectional dispersion of male wages and female wages prior to the break. Of course, this procedure is based on a given level of return to experience for each gender. We next focus on the calibration of this parameter. For simplicity, we normalize elj to be equal to 1 for both gender j 2 fm; f g. Based on this normalization, the return for experience ehj and the probability of becoming experienced

j

are calibrated jointly to mimic the average life-cycle wage pro…le for each gender group. In order to follow this methodology, we …rst follow Hansen’s (1993) procedure to obtain life cycle productivity pro…les by using the CPS.13 Next, we renormalize the resulting pro…les so that productivity of a 20 year old worker is equal to 1: Finally, ehj and

j

are calibrated jointly to

match two moments: the average productivity of 45-54 year old workers (1:74 for males and 1:35 for females) and the average productivity of all workers in each gender group (1:56 for males and 1:28 for females). While the former target represents the level of productivity at its peak (determined by the return to experience ehj ), the latter moment allow us to target the overall shape of the productivity pro…le for each gender (determined by the probability of becoming experienced

j ).

In line with these, we set ehm = 1:92 and

workers and we set ehf = 1:47 and

f

m

= 0:0083 for male

= 0:0100 for female workers. Accordingly, the return to

experience is signi…cantly larger for male workers than for female workers. However, observe that the returns to labor market experience (which is 92% for males and 47% for females) does 13

We follow Hansen’s (1993) procedure to obtain life cycle productivity pro…les. To avoid the fact that cross sectional pro…les do not necessarily represent the true life-cycle wage prospects, we adopt a cohort analysis method. Although CPS does not contain enough information to do this on a panel, we can still track wages of di¤erent cohorts over time. For each cohort, we obtain the productivity pro…le by dividing the average hourly earnings for each age by the average hourly earnings over all ages (e.g. for the cohort of 1970, the productivity at age 27 is calculated by dividing the average hourly earnings of 27 year olds in 1977 by the average hourly earnings over all ages in this year). As a …nal step, in order to obtain the representative productivity pro…le that we are interested in, we average the productivity pro…les for all the cohorts of the 1970s.

Technological Change, Wages and the Gender Unemployment Gap

21

not directly translate into a one-to-one di¤erence between the ‘average’wages of experienced old and inexperienced young workers (which is 74% for males and 35% for females). This is a direct consequence of the fact that the unemployment rates (therefore the reservation wages) of inexperienced and experienced workers are di¤erent. For each gender group j 2 fm; f g, unemployment ‡ow payo¤s blj and bhj are calibrated to generate a replacement rate of 70% for inexperienced and experienced workers, respectively. As mentioned in Section 3, we assume that the unemployment ‡ow payo¤ represents the total value of unemployment insurance and leisure. Based on this de…nition, Hall and Milgrom (2008) estimate a replacement rate of 71%. This number seems to be consistent with the target values used by several studies (See Alvarez and Veracierto (2001), and Ljungqvist and Sargent (2008) among others). Thus, our target replacement rate is in line with the literature. The remaining parameters are (i) vacancy posting costs clj and chj , and (ii) probabilities plj and phj that capture the persistence of match-speci…c productivity shocks for j 2 fm; f g. For each gender group, these four parameter values are calibrated jointly to match (i) the aggregate unemployment rate, (ii) the unemployment rate of 55-62 year olds, (iii) the separation rate of 55-62 year olds, and (iv) the separation rate of 20-24 year olds. Notice that, we do not target aggregate job separation and job …nding rates. More importantly, we do not directly target the observed age patterns of unemployment and job …nding rates. Table 1 reports the full set of parameters. We now continue with the discussion of the model predicted unemployment measures for the pre-break and post-break periods. 4.2. Results In this section, we begin with presenting some of the key steady-state implications of the model. Next, we discuss the quantitative predictions of the model for the pre-break period. Finally, we explore the quantitative predictions of the model for the post-break period, by focusing on both the ‘steady state’results and the ‘transitional dynamics’.14 14

The ‘pre-break’and ‘post-break’data values for unemployment, job separation and job …nding rates refer to the actual values of these variables in 1979 Q3 and the 1980-1996 period, respectively.

Technological Change, Wages and the Gender Unemployment Gap

4.2.1.

22

Key Implications

We start with presenting the population shares of inexperienced and experienced workers among each gender group in the pre-break model economy. Figure 5A depicts the population share of workers in each state for di¤erent age groups. Note that all 20 year olds are inexperienced new entrants. As workers get older, the share of experienced workers increase within each age group for both gender. For our oldest age group (62 year olds), we …nd that the share of experienced workers is about 98% among males and 99% among females. Thus, conditional on not leaving the labor force, almost all workers become experienced. Figure 5B depicts the actual and model predicted average life-cycle wage pro…les, where the resulting pro…les are renormalized so that the productivity of a 20 year old worker is equal to 1. Evidently, the model can replicate the general behaviour of wages over the life cycle for both gender. On the contrary, while the actual wage growth stops around the age of 45 to 50 and experience a slight decrease through the end of the working life cycle for both gender, the model cannot capture these two aspects fully. More speci…cally, even though the predicted wage growth slows down considerably through the end of the life-cycle for both male and female workers, it does not stop completely. At this point, one can easily argue that the wage dynamics are a¤ected by many other factors. In this paper, we focus on the main driving force - experience - and abstract from other factors which are beyond the scope of this paper. We now discuss the equilibrium response of unemployment to the observed trend changes in wage growth rates. Recall that the empirical discussion provided above documents two facts: (i) the wage growth rate for males dropped sharply to about 0% in the late-1970s and has stagnated at this level since then, and (ii) there was no trend change in wage growth for female workers over the post-war period. In line with this evidence, our model predicts changes only in male unemployment rates in response to the observed trend changes in wage growth. Based on this …nding, Table 2A presents the model predicted changes in unemployment rates for experienced and inexperienced male workers. We …nd that the predicted increase in equilibrium unemployment rate is 3:40 percentage points for inexperienced workers and

Technological Change, Wages and the Gender Unemployment Gap

23

0:33 percentage points for experienced workers. We also …nd that the predicted increase in separation rate is 1:15 percentage points for inexperienced workers and 0:08 percentage points for experienced. Evidently, while the decline in growth rate gm has signi…cant e¤ects on the unemployment and separation rates for inexperienced male workers, this is not the case for experienced males. The intuition is as follows. In case of high MPL and wage growth, some inexperienced matches with “low surplus” continue production, so that the worker can accumulate experience and both parties bene…t from it in the future. When MPL and wage growth goes down, these incentives diminish. This is because, a lower growth rate gm causes future bene…ts of experience to be discounted at a higher rate. This leads to an increase in the separation rate and, in turn, an increase in the unemployment rate for inexperienced. However, that incentive does not exist for experienced matches since these workers are already experienced. Hence, the equilibrium response of unemployment and separation is much bigger for inexperienced workers than for experienced. Figure 6 presents the model predicted age patterns of unemployment for male workers. We …nd that the model predicted unemployment rate decreases monotonically with age. We also observe that, between the pre-break and post-break periods, the model predicted unemployment rate increases for all age groups. Our third observation is that the ‘size of the increase in unemployment rate’ declines monotonically with age, from 3:40 percentage points for 20 year olds to 0:35 percentage points for 62 year olds. This prediction of the model arises from the fact that the equilibrium response of unemployment is bigger for inexperienced workers than for experienced workers. 4.2.2.

Pre-Break Period

We begin with a detailed discussion of the economy over the pre-break period.15 First, we focus on the aggregate unemployment statistics. Table 2B presents the actual and model predicted measures. The predicted unemployment rates for males (4:22%) and for females 15

The ‘pre-break’ data values for unemployment, job separation and job …nding rates refer to the actual values of these variables in 1979 Q3.

Technological Change, Wages and the Gender Unemployment Gap

24

(5:74%) …t the data by construction. On the contrary, our calibration method does not target aggregate job separation and job …nding rates. We …nd that the model is fairly successful at replicating these two ‡ow rates. While the actual job separation rate is 1:34% for males and 1:32% for females, the model’s predictions are 1:47% and 1:42% respectively. The model does a good job at matching the job …nding rate for males, whereas it slightly underpredicts the job …nding rate for females. Based on these …ndings, Table 2B reports the actual and predicted gender gaps in unemployment, job separation and job …nding rates for the pre-break period.16 The predicted gender unemployment gap (1:52 percentage points) …ts the data by construction. The model generates a gender job separation gap of which is very close to the actual value,

0:05 percentage points,

0:02 percentage points. However, we …nd that the

actual gender job …nding gap ( 6:8 percentage points) seems to be slightly smaller than the predicted value ( 10:1 percentage points). We now focus on the age pattern of unemployment. Table 3A and Figure 7A present the actual and model predicted unemployment rates by age. Our …rst observation is that the actual unemployment rate decreases monotonically with age for both gender. The model can capture this trend. As stated in the calibration section, for the pre-break period, the predicted unemployment rates for 55-62 year olds (2:7% for males and 3:1% for females) …t the data by construction. On the other hand, the predicted age patterns of unemployment is generated endogenously by the model. Table 3A and Figure 7A show that the model is pretty successful at matching the age pro…le of female unemployment rates. Similarly, we …nd that the model can capture the unemployment rates for male workers aged 25 and over, whereas it underpredicts the unemployment rate for male workers aged 20-24 years old. While the predicted unemployment rate is 6:8% for 20-24 years old male workers, the actual rate is 8:9% for this group. Based on these …ndings, we conclude that the model (i) can capture the observed age patterns of unemployment, and (ii) can match fairly well the unemployment rate for each age and gender group. 16

Gender Gaps are calculated as the percentage points di¤erence between female and male unemployment, job separation and job …nding rates.

Technological Change, Wages and the Gender Unemployment Gap

25

Table 3B and Figure 7B present the actual and model predicted values of job separation rates by age. We observe that the actual job separation rate decreases monotonically with age for both gender. The model can capture this trend since the predicted job separation rates for 20-24 year olds (2:8% for males and 2:7% for females) and for 55-62 year olds (0:7% for both male and female workers) …t the data by construction. We …nd that the model is able to capture the job separation rate of 35-44 year olds and 45-54 year olds for both gender. For 25-34 year olds, the predicted job separation rates (1:7% for males and 1:6% for females) are slightly higher than the actual rates (1:4% for both male and female workers). In line with these …ndings, we conclude that the model performs quite well in accounting for the job separation rate for each age and gender group. Table 3C and Figure 7C present the actual and model predicted job …nding rates by age. Recall that our calibration method does not target job …nding rates, neither at the aggregate level nor by age. The model predicts that the job …nding rate decreases monotonically with age for both gender. On the other hand, while the actual job …nding rate seems to be decreasing over the life cycle for both gender, this decline does not seem to be smooth for female workers. More speci…cally, while the actual job …nding rate for female workers decreases from 29:3% for the youngest age group to 22:1% for the oldest age group, it is constant at a mid-level value of about 24:7% for all workers aged 25-54 years old. However, we …nd that the job …nding rate in the data seems to be quite noisy. To clarify this point: even though the documented age patterns of unemployment and job separation rates are robust across all years since 1976, this is not the case for the job …nding rate. We …nd that, while the job …nding rate seems to decrease by age for almost all the years since 1976, this trend is non-monotonic. Considering this fact, we do not want to put too much emphasis on the predictions of the model for job …nding rates by age. However, we argue that the model can capture the ‘overall’age pattern of job …nding rates observed in the data.

Technological Change, Wages and the Gender Unemployment Gap

4.2.3.

26

Post-Break Period : Transitional Dynamics

In this section, we discuss the quantitative predictions of the model for the post-break period by focusing on the ‘transitional dynamics’. In our simulation, the decline in MPL/wage growth is modeled as an unanticipated and permanent trend change.17 More speci…cally, we assume that the annual productivity growth gm falls from 2% to 0% unexpectedly and permanently. Second, we simulate the model by assuming that the decline in growth rate gm takes place in the …rst month of the year 1980. This coincides with the start of the observed decline in gender unemployment gap.18;19 Figure 8A depicts the actual and model predicted gender unemployment gap series. The model seems to track the time-series features of the data quite well. The transition of actual gender unemployment gap from its pre-break equilibrium level (1:52 percentage points) to its post-break long-run equilibrium level (0 percentage points) seems to be fast: the transition takes place in the …rst half of the year 1980. Evidently, the model is able to generate this rapid transition. A closer look at short-run dynamics reveals an interesting pattern: the simulated gender unemployment gap (i) …rst decreases sharply below its new long-run equilibrium level, and (ii) then starts to increase and converge to its long-run level. If we look at actual gender unemployment gap dynamics, even though the series are distorted by business cycle variations, 17

This approach follows the standard modeling approach used by the literature (See Elsby and Shapiro (2012) and Heathcote, Storesletten and Violante (2010) for a similar simulation methodology). Greenwood and Yorukoglu (1997), Heckman et al. (1998) and Guvenen and Kuruscu (2006), among many others, model skill-biased technological change as an unanticipated permanent trend change where agents have perfect foresight after the change occurs. Similarly, Jaimovich and Siu (2014) models routine-biased technological change as an unanticipated and permanent trend change in wage growth rates where agents have perfect foresight about the evolution of wages after the change. 18 If we take a closer look at the data, the stagnation of male wages starts in the mid-1970s, a couple of years before the start of the observed decline in gender unemployment gap (see Figure 3). In our simulations, we assume that the annual wage growth for males falls in the …rst month of 1980 since (i) we want to compare speci…cally the model predicted dynamics during the transition period with those observed in the data, and (ii) it is likely that there was a lag in the perception of the start of a new period with stagnant wages. 19 There is a widespread consensus in the literature that this latent technological change took e¤ect in the mid to late 1970s. In fact, in their paper titled "1974", Greenwood and Yorukoglu pose the question "Did 1974 mark the beginning of a new industrial revolution?". It is more than likely that the gender speci…c e¤ects of this technological revolution got delayed till the end of the 1970s due the mid-70s recession, which can be clearly seen in our Figure 3. Accordingly, the timing proposed in our paper is in line with the data and the literature. See Acemoglu and Autor (2011) for more empirical evidence.

Technological Change, Wages and the Gender Unemployment Gap

27

we oberve a similar pattern. Finally, when we focus on the long-run post-break equilibrium level of gender unemployment gap, we …nd that the model slightly underestimates the size of the decrease. This implication of the model can be observed in Figure 8A, and will be discussed in the next section. In order to understand the observed ‘short-run’dynamics of gender unemployment gap, we …rst need to focus on the evolution of job separation rates. Figure 8B plots both the actual and model predicted series for ‘the ratio of male to female job separation rates’over the period 1968-1996. More speci…cally, it depicts the evolution of employment-to-unemployment ‡ow f m rates of males divided by those of females, denoted by PEU =PEU . We observe that while the

actual ratio was nearly constant at around 1:05 until 1979, it suddenly increased to a level of about 1:37 in 1980 and stayed at that level since then. Further analysis of the data reveals f m increased 35% between 1979 and 1980, there was no signi…cant change in PEU that, while PEU

over the same time period. Consistent with these facts, the model seems to track time-series f m =PEU ratio. features of the data quite well and is able match the observed increase in PEU

This brings up the following question: what is the role of job separation in accounting for gender unemployment gap dynamics in our model economy? More speci…cally, we ask what would have happened if job separation rates stayed at their 1979 level? Based on this exercise, we …nd that the relative contributions of job separation and job …nding rates to the predicted decrease in gender unemployment gap is, respectively, 86% and 14%, comparing the periods 1968–1979 and 1980–1996. Therefore, we conclude that the job separation margin is the main factor behind the observed decrease in gender unemployment gap. We now can discuss the intuition behind the predicted ‘short run’gender unemployment gap dynamics. In our model economy, aggregate unemployment rates are determined by the population shares and the unemployment rates of experienced and inexperienced workers. Hence, gender unemployment gap dynamics is determined by changes in these two factors. Figure 9A presents the steady state population shares of experienced and inexperienced workers among males for the pre-break and the post-break periods. We observe that while the

Technological Change, Wages and the Gender Unemployment Gap

28

share of experienced male workers among each age group decreases, the size of these changes is small. In line with this …nding, we …nd that the share of experienced male workers among all males falls only 0:9 percentage points. Quantitatively, this shift in population shares is small and almost irrelevant for aggregate unemployment rate calculations. Thus, cohort e¤ects are small in transitional dynamics, which implies that the predicted transition is fast as in the data. Although this result may seem surprising at …rst, it is quite intuitive and can be shown analytically. See Appendix C for a detailed technical discussion. This leaves ‘the change in unemployment rates of experienced and inexperienced male workers’ as the only major factor that determines the short-run dynamics of gender unemployment gap. Recall that the stagnation of male wages has signi…cant e¤ects on the unemployment rate of inexperienced workers, whereas this does not seem to be the case for experienced. Thus, we need to focus on the change in unemployment behaviour of inexperienced male workers. For this purpose, for inexperienced male workers, Figure 9B plots the equilibrium productivity distributions for the pre-break and the post-break steady states. We observe that the equilibrium distributions have "kinks" at reservation productivity levels, where workers with a match speci…c productivity lower than the reservation level are unemployed.20 We also observe that the decline in male wage growth generates an increase in the reservation productivity level of inexperienced male workers. As a consequence, the ‘immediate reaction’of worker-…rm pairs with a match-speci…c productivity between the old and the new reservation levels is to dissolve the match. Figure 9B shows that the density of this speci…c group of workers is signi…cantly higher for the pre-break equilibrium than the post-break equilibrium. Therefore, as this group of matches dissolve all at once, male unemployment rate (gender unemployment gap) initially increases (decreases) above (below) its new long-run equilbrium level. Subsequently, as the economy converges to its new long-run 20

Recall that the distribution of ‘initial’match-speci…c productivity values is lognormal. However, ‘equilibrium’productivity distributions diverge from the distribution of initial productivity draws due to two labor market frictions: (i) job o¤er probability f ( m ), and (ii) the probability of getting a new match-speci…c productivity (1 pm ). While the former determines the ‡ows from unemployment to employment, the later determines ‡ows from employment to unemployment. As one of these frictions is more dominant, equilibrium productivity distributions have kinks and diverge from the distribution of initial productivity draws.

Technological Change, Wages and the Gender Unemployment Gap

29

equilibrium level, so do the male unemployment rate and the gender unemployment gap. This pattern can be seen more clearly in Figure 8A and is consistent with the data. 4.2.4.

Post-Break Period : Steady State Analysis

We …rst focus on the aggregate unemployment statistics.21 Table 4 presents the actual and predicted gender gaps in unemployment, job separation and job …nding rates. The predicted gender unemployment gap for the pre-break economy …ts the data by construction. For the post-break period, the model generates a gap of 0:10 percentage points. This number is close but slightly higher than the actual gap, which is zero. If we look at the change in gender unemployment gap, while the model predicts a decrease of 1:42 percentage points, the actual gap decreases by 1:52 percentage points. We …nd that the model can account for 93% of the observed change in gender unemployment gap. Notice that the decline in gender unemployment gap is accounted for solely by a change in male unemployment. This feature of the model is in line with the evidence discussed in Section 2 and is consistent with the proposed mechanism. The model generates an increase in the job separation rate of male workers, which leads to a 0:42 percentage points decrease in the predicted job separation gender gap. This number is very close to the actual decrease observed in the data (0:44 percentage points). As opposed to unemployment and job separation rates, the model generates a decline in the job …nding rate of male workers. This generates a 1:70 percentage points increase in the predicted job …nding gender gap, which seems to be lower than the actual increase (3 percentage points). The model apparently underestimates the change in UE ‡ow rates. However, recall that (i) the contribution of job …nding margin to the predicted change in gender unemployment gap is found to be small, and (ii) the data on job …nding rates seems to be quite noisy. Therefore, we do not want to put too much emphasis on the predictions of the model for job …nding rates, both at the aggregate level and by age. 21

The ‘post-break’data values for unemployment, job separation and job …nding rates refer to the average actual values of these variables in the 1980-1996 period.

Technological Change, Wages and the Gender Unemployment Gap

30

We now focus on the age-speci…c unemployment statistics. We start with looking at the model predicted changes in the age-patterns of unemployment, job separation and job …nding rates for ‘male’ workers (see Figure 10). These statistics cover only male workers because, as argued above, our model relates the observed decline in gender unemployment gap solely to changes in male unemployment. Figure 10 shows that (i) unemployment and job separation rates increase for all age groups, (ii) job …nding rates decrease for all age groups, and (iii) the size of the change in unemployment, job separation and job …nding rates declines monotonically with age. This last impliction of the model is a result of the fact that the equilibrium response of labor market ‡ow rates is bigger for inexperienced young workers than for experienced old workers. We now focus on the age-speci…c gender gaps. Table 5A presents the actual and model predicted changes in gender unemployment gap for di¤erent age groups. Our …rst observation is that, between the pre-break and post-break periods, the model predicted gender unemployment gap decreases for all age groups, which is in line with the data. Our second observation is that the size of the decrease in ‘predicted’gender unemployment gap declines monotonically with age, from 2:9 percentage points for 20-24 year olds to 0:5 percentage points for 55-62 year olds. We …nd a similar pattern in the data: the size of the decrease in ‘actual’gender unemployment gap also declines monotonically with age, from 3:1 percentage points for 20-24 year olds to 0:2 percentage points for 55-62 year olds. The predicted vs. actual decrease (increase) in gender unemployment gap (male unemployment rate) is, respectively, (i) 2:9 percentage points vs. 3:1 percentage points for 20-24 year olds, (ii) 1:7 percentage points vs. 1:8 percentage points for 25-34 year olds, (iii) 0:8 percentage points vs. 0:8 percentage points for 35-44 year olds, (iv) 0:7 percentage points vs. 0:5 percentage points for 45-54 year olds, (v) 0:5 percentage points vs. 0:2 percentage points for 55-62 year olds. Table 5B presents the actual and model predicted changes in job separation gender gap for di¤erent age groups. Between the pre-break and post-break periods, the actual gender

Technological Change, Wages and the Gender Unemployment Gap

31

separation gap decreases for all age groups and the size of the decrease in gender separtion gap declines monotonically with age. We …nd that the model is successful at replicating these facts. The model can match the observed decline in separation gender gap of 25-34 year olds and 55-62 year olds. On the other hand, the model slightly overpredicts the decrease in separation gender gap for 35-44 year olds and 45-54 year olds. While the predicted decrease is 0:3 percentage points for 35-44 year olds and 0:2 percentage points for 45-54 year olds, the actual decrease was 0:2 and 0:1 percentage points respectively. Overall, we conclude that the model can capture fairly well the changes in separation gender gap by age.

5.

Conclusion In the United States, the female unemployment rate had been considerably higher than

the male unemployment rate since World War II. However, this gap (referred to as the gender unemployment gap) disappeared in the …rst half of the year 1980. In this article, we argue that the sudden and sustained decrease in gender unemployment gap was due to genderbiased technological changes that led to a dramatic stagnation in male wage growth since the late-1970s. To analyze this conjecture, we build a life cycle search model with endogenous job separation and heterogenous experience levels. We …nd that the model can account for 93% of the observed decrease in gender unemployment gap at the aggregate level. Our numerical analysis shows that the model is consistent with the observed age patterns of unemployment, job separation and …nding rates. Finally, the model can capture fairly well the changes in gender unemployment gap by age. The model proposed in this paper provides a simple way to introduce life-cycle aspects of unemployment into search and matching setups. Therefore, the model is a useful tool for analyzing several important questions. For example, there are some recent studies focusing on the e¤ects of progressive taxation on employment (intensive margin of labor supply). It would be interesting to investigate the e¤ects of progressive taxation on unemployment (extensive margin of labor supply). We study this issue in ongoing research, Atesagaoglu

Technological Change, Wages and the Gender Unemployment Gap

32

(2014), in which we investigate the link between Reagan era tax cuts and U.S. unemployment dynamics. Similarly, the model can be used to study a number of policy issues, such as the age-speci…c e¤ects of unemployment insurance, …ring restrictions and hiring costs.

Technological Change, Wages and the Gender Unemployment Gap

33

APPENDIX A: Data Description Aggregate Unemployment Statistics: Series are constructed by the Bureau of Labor Statistics (BLS) using the Current Population Survey (CPS). In particular, we use seasonally adjusted monthly series. Unemployment Statistics by Age: Series are constructed by using the monthly CPS …les and following the methodogy provided by Shimer (2012) (For further details, see Shimer, 2012). Wage Statistics by Gender: We use annual wage income data from the U.S. Census Bureau, Historical Income Tables. In particular, we focus on real median-wage series (in 2010 CPI-U-RS adjusted dollars). Wage and Employment Share Statistics by Occupation: Wage and employment share series are based on three datasets constructed by Acemoglu and Autor (2011). For median weekly wages and employment shares by occupation, we use two datasets based on (i) Census IPUMS 5% sample for 1980, and (ii) Census American Comunity Survey for 2008. For median hourly wages by occupation, we use May/ORG CPS. Unemployment Statistics by Occupation: Series are constructed by using the Statistical Abstract of the United States for 1978-1983. Statistical Abstracts decompose unemployment rate and employment shares by ten occupation groups for each gender. Following Acemoglu and Autor (2011), these series are re-grouped under four occupation groups in order to construct the statistics reported in Table 6. Labor Market Flow Rates: Series are constructed by following the methodogy provided by Shimer (2012). Based on monthly CPS, the gross ‡ow data are estimates of the number of people moving among the three labor market states. In order to calculate the probability of moving from one state to another, the gross ‡ow is divided by the corresponding stock varible. Finaly, ‡ow rates are calculated from annual averages of month-to-month labor market transition probabilities. For details, please see Shimer (2012) and his webpage http://sites.google.com/site/robertshimer/research/‡ows. Life Cycle Productivity Pro…les: We follow Hansen’s (1993) to obtain life cycle productivity pro…les. Since cross sectional pro…les do not necessarily represent the true life-cycle prospects, we follow a cohort analysis. Although CPS does not contain enough information to do this on a panel, we can still track wages of di¤erent cohorts over time. For each cohort, we obtain the productivity pro…le by dividing the average hourly earnings for each age by the average hourly earnings over all ages (e.g. for the cohort of 1970, the productivity at the age of 27 is calculated by dividing the average hourly earnings of 27 year olds in 1977 by the average hourly earnings over all ages in the same year). As a …nal step, to obtain the productivity pro…le that we are interested in, we average the productivity pro…les for all the cohorts of the 1970s.

Technological Change, Wages and the Gender Unemployment Gap

34

APPENDIX B: Occupational Gender Composition, Wages and the Gender Unemployment Gap In this section, we provide a brief empirical analysis to shed some light on the link between gender-biased technological change and the gender di¤erences in ‘unemployment’ patterns. In particular, we investigate the interaction between occupational (skill) gender composition, wage growth and gender unemployment gap dynamics during the period of interest. To explore this link, following Acemoglu and Autor (2011), we disaggregate wage, labor force and unemployment statistics by four occupational groups: (i) routine manual, (ii) routine cognitive, (iii) non-routine manual, and (iv) non-routine cognitive occupations. An occupation is routine if its main tasks require well-de…ned set of procedures. An occupation is non-routine if its main tasks require ‡exibility, problem-solving and creativity. Finally, occupations are classi…ed as manual or cognitive based on the amount of physical or mental activity required.9 Based on this classi…cation, Table B-1 below (displayed at the end of Appendix B) shows the evolution of real median log wages by occupation group. We …nd that median wage levels for routine manual occupations stagnated between 1979 and 2007 - log wage growth averaged approximately 0 percent. On the other hand, we observe that real median wages rose relatively uniformly for all other occupation groups over the same time period: wage stagnation is observed only for routine manual occupations. This pattern is commonly referred to in the literature as “wage polarization”(See Acemoglu and Autor, 2011; Goldin and Katz, 2007). In light of this, Table B-2 reports the employment share of each occupation group by gender for the year 1979 - the year before gender unemployment gap vanished. We observe that, while the employment share of routine manual occupations was 50 percent for male workers, it was only 14 percent for females. Furthermore, we …nd that 86 percent of routine manual jobs were occupied by males in the year 1979. Evidently, male workers were disproportionately represented in routine manual jobs, which appears to be the main reason behind the observed stagnation of median wages for male workers. Next, to clarify the link between the stagnation of male wages and gender unemployment gap dynamics, Table B-3 presents the contribution of each occupation group to changes in (i) unemployment rate by gender, and (ii) gender unemployment gap. The …rst observation is that the unemployment of male workers in routine manual jobs accounts for 65% of male unemployment for the period 1977-79. On the contrary, occupational composition of female unemployment is fairly uniformly distributed - the unemployment of female workers in routine manual jobs accounts only for 24% of female unemployment for the same period. Our second observation is that, while male unemployment rate increased 2.38 percentage points between the periods 1977-79 and 1980-82, this was largely driven by job losses in routine manual occupations which account for 1.77 percentage points of the increase. However, for female 9 Based on this classi…cation, (i) routine manual occupations include production workers, operators and laborers, (ii) routine cognitive occupations include sales and clerical workers, (iii) non-routine manual occupations include service jobs such as food prep, cleaning, personal care, and (iv) non-routine cognitive occupations include professional, managerial and technical workers. See Acemoglu and Autor (2011) for details.

Technological Change, Wages and the Gender Unemployment Gap

35

workers, unemployment rate increased only 0.84 percentage points and job losses in routine manual occupations account for 0.35 percentage points of the increase. Conclusively, these facts show that the reason why gender unemployment gap vanished is the observed increase in unemployment of workers in routine manual occupations, which are heavily dominated by men. In line with this, Table B-3 reports the contribution of each occupation group to the change in gender unemployment gap. We …nd that changes in labor market status of workers in routine manual occupations account for 92% (1.42 percentage points) of the decline in gender unemployment gap. In order to clarify this point further, we perform a counterfactual experiment to investigate the role of routine manual occupations in accounting for gender unemployment gap dynamics. We ask what would have happened if the contribution of routine manual jobs to unemployment rates (for both gender) stayed at their 1979 level? What would gender unemployment gap dynamics look like? Figure B-1 below displays the actual and counterfactual series. We observe that counterfactual series imply no signi…cant change in gender unemployment gap over the period of interest. Tables and Figures for Appendix B (next page).

36

Table B-1. Levels and Changes in Median Wages by Major Occupation Groups, 1979-2007

Routine Manual Routine Cognitive Non-Routine Manual Non-Routine Cognitive

Median Log Weekly Wages

Median Log Hourly Wages

Level 1979 2007

Level 1979 2007

6.46 6.22 5.88 6.69

6.47 6.41 6.04 6.96

Change 1979-2007 0.01 0.19 0.16 0.27

2.70 2.49 2.17 2.97

2.70 2.66 2.33 3.20

Change 1979-2007 0.00 0.17 0.16 0.23

Table B-2. Employment Shares by Gender and Occupation, 1979

Table 2: Corporate Debt and Equity Markets - Period Averages (τ c-constant) Male 1964-1983 Routine Manual 50% Data Model Routine Cognitive 12% Non-Routine Manual 9% Debt / GDP 0.607 0.575 Non-Routine Cognitive 29% Tobin's q (V/k) 0.665 0.748

Female 1984-2004 14% Data Model 43% 20%0.805 0.725 23% 0.929 0.932

Note: Wage and employment share series are based on three datasets constructed by Acemoglu and Autor (2011). For median weekly wages and employment shares by occupation, we use two datasets based on (i) Census IPUMS 5% sample for 1980, and (ii) Census American Community Survey for 2008. For median hourly wages by occupation, we use May/ORG CPS. Note: Based on the classification system introduced by Acemoglu and Autor (2011), (i) routine manual occupations include production workers, operators and laborers, (ii) routine cognitive occupations include sales and clerical occupations, (iii) non-routine manual occupations include service jobs such as food prep, cleaning and personal care, and (iv) non-routine cognitive occupations include professional, manegerial and technical workers.

37 Table B-3. Contribution of Each Occupation Group to (i) Unemployment Rates, and (ii) Gender Unemployment Gap

Male l Unemployment l Level

Unemployment Rate (%) Contribution of Each Occupation Routine Manual Routine Cognitive Non-Routine Manual Non-Routine Cognitive

Female l Unemployment l Level

Change

19771979

19801982

19771979

19801982

4.74

7.12

2.38

6.18

7.02

33.07 07 0.46 0.62 0.59

44.84 84 0.61 0.90 0.77

11.77 77 0.15 0.28 0.18

11.50 50 2.28 1.60 0.80

4.74

7.12

2.38

6.18

Gender d Unemp. Gap

Change

Level

Change

19771979

19801982

0.84

1.44

-0.10

-1.54

11.85 85 2.55 1.74 0.88

00.35 35 0.27 0.14 0.08

-1.57 1 57 1.82 0.98 0.21

-2.99 2 99 1.94 0.84 0.11

-1.42 1 42 0.12 -0.14 -0.10

7.02

0.84

1.44

-0.10

-1.54

†

Total

† Contribution of each occupation to unemployment is basically the decomposition of unemployment rates by occupation based on the Statistical Abstracts of the United States. For example, for the period 1977-1979, while the average male unemployment rate was 4.74 percentage points, the contribution of unemployment of routine manual workers to that number was 3.07 percentage points. Accordingly, for the 1977-1979 period, 65% of unemployed male workers were previously employed in routine manual occupations occupations. Note: Unemployment series by occupation are constructed by using the Statistical Abstracts of the United States for 1978-1983. Statisticsl Abstracts decompose unemployment rate and employment shares by ten occupation groups for each gender. Following Acemoglu and Autor (2011), these series are re-grouped under four occupation groups in order to construct the statistics reported.

Figure B-1. Gender Unemployment Gap - Counterfactual Series 2

2

Table 2: Corporate Debt and Equity Markets - Period Averages (τ c-constant)

Tobin's q (V/k)

Gender Unemployment Gap, %

1

Debt / GDP

1.5

1964-1983

0.5

Data

Model

0.607

0.575

0.665

1984-2004

1

0.5

0.748

0

Gender Unemployment Gap, %

1.5

0

Data -0.5

-0.5

Counterfactual Series

-1

-1 1977

1978

1979

1980

1981

1982

Counterfactual series shows what would gender unemployment gap would look like if the contribution of routine manual jobs to unemployment rates (for both gender) stay at their 1979 level (see Table B3).

Data

Model

0.805

0.725

0.929

0.932

-1.42 1 42 -0.12

Technological Change, Wages and the Gender Unemployment Gap

38

APPENDIX C: Cohort E¤ects and Transitional Dynamics Recall that while the model generates a substantial increase in male unemployment rates, the predicted change in the population share of experienced male workers is minuscule. This result is important because it implies that cohort e¤ects are small in transitional dynamics and the predicted transition is fast as in the data. In this appendix, we provide a brief sketch of the proof. Let’s take a group of 20 year old inexperienced workers with measure one and the time is t = 0. Each period, an inexperienced worker becomes experienced with probability 2 (0; 1), but this is only possible if the worker is employed. Let u 2 (0; 1) denote the unemployment rate for inexperienced workers. At t = 1, the share of inexperienced workers in this cohort is equal to [1 u] + [1 | {z } | A

(1

u) {z B

(1

)] = (1 }

+ u):

The …rst term (A) is equal to the measure of inexperienced workers who were unemployed at t = 0. These workers are still inexperienced since they were unemployed in the previous period. The second term (B) denotes the measure of inexperienced workers who were employed in the previous period but did not become experienced. Finally, notice that the measure (1 + u) is less than one, which implies that the share of inexperienced workers in this cohort of 20 year olds decreased between period t = 0 and t = 1. By using forward iteration, we can calculate the share of inexperienced workers in this cohort for any future date t = T , as follows: (1

+ u)T :

In our benchmark calibration, = 0:0083 and u = 0:0773. Also, we choose the model period to be one month, which implies that a worker of age 62 spents 12 (62 20) model periods in the labor market. These parameters imply that the share of inexperienced workers among 62 year olds is equal to (1 + u)12x42 = (1 0:0083+(0:0083 0:0773))12x42 = 0:021. Thus, the share of experienced workers among 62 year olds is 0:979 for the pre-break economy. For the post-break steady state economy, the predicted unemployment rate for inexperienced workers increases to u = 0:1113. Accordingly, the share of inexperienced workers among 62 year olds is equal to (1 + u)12x42 = (1 0:0083 + (0:0083 0:1113))12x42 = 0:024 and the share of experienced workers among 62 year olds is 0:976 for the pre-break economy. These results show that even though the model predicts a signi…cant increase in the unemployment rate of inexperienced workers (from 7:73% to 11:13%), this does not generate a noticable decrease in the population share of experienced workers ( e.g. the population share of experienced workers among 62 year olds decreases from 0:979 to 0:976.

Technological Change, Wages and the Gender Unemployment Gap

39

References Acemoglu, D., Autor, D.H., 2011. Skills, Tasks and Technologies: Implications for Employment and Earnings, in O. Ashenfelter and D. Card, eds. Handbook of Labor Economics, Vol. 4. Albanesi, S., Sahin, A., 2013. The Gender Unemployment Gap, Working Paper. Alvarez, F., Veracierto, M., 2001). Severance Payments in an Economy with Frictions, Journal of Monetary Economics, Vol. 47, pp. 477-498. Autor, D.H., Levy, F., Murnane, R.J., 2003. The Skill Content of Recent Technological Change: An Empirical Investigation, Quarterly Journal of Economics, Vol. 118, No. 4, pp. 1279-1333. Autor, D.H., Dorn, D., 2012. The Growth of Low Skill Service Jobs and the Polarization of the U.S. Labor Market, American Economic Review, Forthcoming. Black, S.E., Spitz-Oener, A., 2010. Explaining Women’s Success: Technological Change and the Skill-Content of Women’s Work, Review of Economics and Statistics, Vol. 92(1), pp. 187-194. Blanchard, O.J., 2007. A Review of ‘Unemployment: Macroeconomic Performance and the Labour Market’ by Richard Layard, Stephen Nickell, and Richard Jackman, Journal of Economic Literature, Vol. 45, pp. 410-418. DeBoer, L., Seeborg, M.C., 1989. The Unemployment Rates of Men and Women: A Transitional Probability Analysis, Industrial and Labor Relations Review, Vol. 42, No. 3, pp. 404-414. Den Haan, W.J., Haefke, C., Ramey, G., 2005. Turbulence and Unemployment in a Job Matching Model, Journal of the European Economic Association, Vol. 3, No. 6, pp. 13601385. Eckstein, Z., Nagypal, E., 2004. The Evolution of US Earnings Inequality: 1961-2002, Federal Reserve Bank of Minneapolis Quarterly Review, Vol. 28, No. 2, pp. 10-29. Elsby, M.W.L., Shapiro, M.D., 2012. Why Does Trend Growth A¤ect Equilibrium Employment? A New Explanation of an Old Puzzle, American Economic Review, 102:4, pp. 1378–1413. Gervais, M., Jaimovich, N., Siu, H.E., Yedid-Levi, Y., 2013. What Should I Be When I Grow Up? Occupations and Unemployment over the Life Cycle, Working Paper. Goldin, C., Katz, L.F., 2007. Long Run Changes in the Wage Structure: Narrowing, Widening and Polarizing, Brookings Papers on Economic Activity, Vol. 2, 135-165. Goos, M., Manning, A., 2007. Lousy and Lovely Jobs: The Rising Polarization of Work in Britain, Review of Economics and Statistics, Vol. 89, February, 118-133.

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Gorry, A., 2013. Minimum Wages and Youth Unemployment, Department of Economics, European Economic Review, Vol. 64, pp. 57-75. Greenwood, J., Yorukoglu, M., 1997. "1974", Carnegie-Rochester Conference Series on Public Policy, Vol. 46, pp. 49-95. Guvenen, F., Kuruscu, B., 2006. Ben-Porath Meets Skill-Biased Technical Change: A Theoretical Analysis of Rising Inequality, Minneapolis Fed Discussion Paper 144. Hall, R.E., Milgrom, P., 2008. The Limited In‡uence of Unemployment on the Wage Bargain, American Economic Review, 98:4, pp. 1653-1674. Hansen, G.D., 1993. The Cyclical and Secular Behaviour of the Labor Input: Comparing E¢ ciency Units and Hours Worked, Journal of Applied Econometrics, Vol. 8, pp. 71-80. Heathcote, J., Storesletten, K., Violante, G.L., 2010. The Macroeconomic Implications of Rising Wage Inequality in the United States, Journal of Political Economy, Vol. 118, No. 4, pp. 681-722. Heckman, J.J., Lochner, L., Taber, C., 1998. Explaining Rising Wage Inequality: Explorations with a Dynamic General Equilibrium Model of Labor Earnings with Heterogeneous Agents, Review of Economic Dynamics, Vol. 1, No. 1, pp. 1-58. Jaimovich, N., Siu, H.E., 2014. The Trend is the Cycle: Job Polarization and Jobless Recoveries, Working Paper.. Ljungqvist, L., Sargent, T.J., 2008. Two Questions About European Unemployment, Econometrica, Vol. 76, No. 1, pp. 1-29. Menzio, G., Telyukova, I.A., Visschers, L., 2013. Directed Search over the Life-Cycle, NBER Working Paper 17746. Miyamoto, H., Takahashi, Y., 2011. Productivity Growth, On-the-Job Search and Unemployment, Journal of Monetary Economics, Vol. 58, pp. 666-680. Mortensen, D., Nagypal, E., 2007. More on Unemployment and Vacancy Fluctuations, Review of Economic Dynamics, Vol. 10, No. 3, pp. 327-347. Ngai, L.R., Petrongolo, B., 2014. Gender Gaps and the Rise of the Service Economy, Working Paper. Olivetti, C., Petrongolo, B., 2014. Gender Gaps across Countries and Skills: Supply, Demand and the Industry Structure, forthcoming Review of Economic Dynamics. Pissarides, C.A., Vallanti, G., 2007. The Impact of TFP Growth on Steady State Unemployment, International Economic Review, Vol. 48, pp. 607-640. Prat, J., 2007. The Impact of Disembodied Technological Progress on Unemployment, Review of Economic Dynamics, Vol. 10, pp. 106-125.

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Rendall, M., 2010. Brain versus Brawn: The Realization of Women’s Comparative Advantage, Working Paper. Sahin, A., Song, J., Hobijn, B., 2010. The Unemployment Gender Gap during the 2007 Recession, Current Issues - NY FED, Vol. 16, No.2, pp. 1-7. Shimer, R., 2010. Labor Markets and Business Cycles. Princeton: Princeton University Press. Shimer, R., 2012. Reassessing the Ins and Outs of Unemployment, Review of Economic Dynamics, Vol. 15, pp. 127-148.

42

Table 1. Parameter Values Male

Female 0.9966 0.002

Intertemporal Discount Rate

β

Probability of Leaving the Labor Force

γ

0.9966 0.002

Wage Growth Rate, Pre-Break Period

gh

0.00166

0.00166

Wage Growth Rate, Post-Break Period

gl

0.00000

0.00166

Worker's Bargaining Weight

Φ

0.50

0.50

Elasticity of Matching Function

α

0.50

0.50

Mean of Log Productivity Distribution

µ

3.0

3.0

Std. Dev. of Log Productivity Distribution

σ

1.140

1.273

Labor Market Return for Inexperience

el

1.00

1.00

Labor Market Return for Experience

eh

1.92

1.47

Probability of Becoming Experienced

λ

0.00833

0.01000

Unemployment Payoff - Inexperienced

bl

29.25

34.47

Unemployment Payoff - Experienced

bh

52.16

46.97

Vacancy Posting Cost - Inexperienced

cl

150.0

324.6

Vacancy Posting Cost - Experienced

ch

367.5

351.8

Probability of change in productivity - Inexperienced

1-p l

0.2273

0.2119

Probability of change in productivity - Experienced

1-p h

0.3964

0.3903

Table 2: Corporate Debt and Equity Markets - Period Averages (τ c-constant) 1964-1983

1984-2004

Data

Model

Data

Model

Debt / GDP

0.607

0.575

0.805

0.725

Tobin's q (V/k)

0.665

0.748

0.929

0.932

43

Table 2A. Response of Inexperienced vs. Experienced "Male Workers" (Model) (Steady State Analysis) Pre-Break

Post-Break

Change

Change

(Model)

(Model)

(%)

(percentage points)

Inexperienced Workers Unemployment Rate (%) Job Separation Rate (%) Job Finding Rate (%)

7.73 3.37 40.21

11.13 4.52 36.07

( 44.0 ) ( 34.1 ) ( -10.3 )

( 3.40 ) ( 1.15 ) ( -4.14 )

Experienced Workers Unemployment Rate (%) Job Separation Rate (%) Job Finding Rate (%)

2.55 0.62 23.71

2.88 0.70 23.50

( 12.9 ) ( 12.9 ) ( -0.9 )

( 0.33 ) ( 0.08 ) ( -0.21 )

Table 2B. Aggregate Unemployment Statistics: Pre-Break (Data vs. Model) (Steady State Analysis) Table 2: Corporate Debt and Equity Markets - Period Averages (τ c-constant) 1964-1983 Unemployment DataRateModel Debt / GDP

Male Workers Tobin's q (V/k) Data : Pre-Break (%) * Model : Pre-Break (%)

1984-2004 Job Finding Job Separation RateData Model Rate

0.607

0.575

0.805

0.725

0.665

0.748

0.929

0.932

4.22 4.22

1.34 1.47

Female Workers Data : Pre-Break (%) * Model : Pre-Break (%)

5.74 5.74

1.32 1.42

26.6 23.4

Gender Gap Data : Pre-Break (% points) * Model : Pre-Break (% points)

1.52 1.52

-0.02 -0.05

-6.80 -10.10

* Notes: "Pre-Break" data values refer to the actual unemployment, job separation and job finding rates in 1979 Q3.

33.4 33.5

44

Table 3A. Unemployment Rates by Age : Pre-Break (Data vs. Model) (Steady State Analysis)

20-24

25-34

35-44

45-54

55-62

Male Workers Data : Pre-Break (%) * Model : Pre-Break (%)

8.9 6.8

4.3 4.7

3.0 3.4

2.7 2.8

2.7 2.7

Female Workers Data : Pre-Break (%) * Model : Pre-Break (%)

10.0 10.4

6.4 6.5

4.6 4.2

3.8 3.4

3.1 3.1

Table 3B. Job Separation Rates by Age : Pre-Break (Data vs. Model) (Steady State Analysis)

20-24

25-34

35-44

45-54

55-62

Male Workers Data : Pre-Break (%) * Model : Pre-Break (%)

2.8 2.8

1.4 1.7

1.0 1.0

0.8 0.8

0.7 0.7

Female Workers Data : Pre-Break (%) * Model : Pre-Break (%)

2.7 2.7

1.4 1.6

1.0 1.0

0.8 0.8

0.7 0.7

Table 3C. Job Finding Rates by Age: Pre-Break (Data vs. Model) (Steady State Analysis)

20-24

25-34

35-44

45-54

55-62

Male Workers Data : Pre-Break (%) * Model : Pre-Break (%)

35.5 39.0

34.5 35.0

32.9 29.9

29.3 26.6

24.0 25.1

Female Workers Data : Pre-Break (%) * Model : Pre-Break (%)

29.3 23.7

24.8 23.5

24.7 23.2

24.7 23.0

22.1 22.9

* Notes: "Pre-Break" data values refer to the actual unemployment, job separation and job finding rates in 1979 Q3.

Table 2: Corporate Debt and Equity Markets - Period Averages (τ c-constant) 1964-1983

1984-2004

Data

Model

Data

Model

Debt / GDP

0.607

0.575

0.805

0.725

Tobin's q (V/k)

0.665

0.748

0.929

0.932

45

Table 4. Aggregate Unemployment Statistics: Pre-Break vs. Post Break 1 , 2 (Steady State Analysis) Unemployment Rate

Job Separation Rate

Job Finding Rate

Male Workers Model : Pre-Break (%) Model : Post-Break (%)

4.22 5.64

1.47 1.89

33.5 31.8

Female Workers Model : Pre-Break (%) Model : Post-Break (%)

5.74 5.74

1.42 1.42

23.4 23.4

Gender Gaps: "Model" Model : Pre-Break (% points) * Model : Post-Break (% points) * Change (% points)

1.52 0.10 (-1.42)

-0.05 -0.47 (-0.42)

-10.10 -8.40 (1.70)

Gender Gaps: "Data" 1 , 2 Data : Pre-Break (% points) * Data : Post-Break (% points) * Change (% points)

1.52 0.00 (-1.52)

-0.02 -0.46 (-0.44)

-6.80 -3.80 (3.00)

1

"Pre-Break" data values refer to the actual gender gaps in unemployment, job separation and job finding rates in 1979 Q3.

2

"Post-Break" data values refer to the actual gender gaps in unemployment, job separation and job finding rate averages for the 1980-1996 period.

* "Gender Gaps" are calculated as the percentage points difference between female and male unemployment, job separation and job finding rates.

Table 2: Corporate Debt and Equity Markets - Period Averages (τ c-constant) 1964-1983

1984-2004

Data

Model

Data

Model

Debt / GDP

0.607

0.575

0.805

0.725

Tobin's q (V/k)

0.665

0.748

0.929

0.932

46

Table 5A. Unemployment Rates by Age : Pre-Break vs. Post Break 1 (Steady State Analysis)

20-24

25-34

35-44

45-54

55-62

Male Workers Model : Pre-Break (%) Model : Post-Break (%)

6.8 9.7

4.7 6.4

3.4 4.2

2.8 3.5

2.7 3.2

Female Workers Model : Pre-Break (%) Model : Post-Break (%)

10.4 10.4

6.5 6.5

4.2 4.2

3.4 3.4

3.1 3.1

(-1.7) (-1.8)

(-0.8) (-0.8)

(-0.7) (-0.5)

(-0.5) (-0.2)

1

Change in "Gender Unemployment Gap" Model : Change (% points) (-2.9) Data : Change (% points) (-3.1) 1

"Gender Unemployment Gap" is defined as the difference between female and male unemployment rates for each age goup.

Table 5B. Job Separation Rates by Age : Pre-Break vs. Post Break 1 (Steady State Analysis) Table 2: Corporate Debt and Equity Markets - Period Averages (τ c-constant) 1964-1983

20-24

25-34

Data

Model

0.607

0.575

Male Workers Debt / GDP Model : Pre-Break (%)q (V/k) Tobin's Model : Post-Break (%)

2.80.665 3.7

Female Workers Model : Pre-Break (%) Model : Post-Break (%)

2.7 2.7

1.7 0.748

1984-2004

35-44

45-54

Data

Model

0.805

0.725

2.2

1.0 0.929 1.3

1.6 1.6

(-0.5) (-0.5)

0.9320.8

55-62

1.0

0.7 0.8

1.0 1.0

0.8 0.8

0.7 0.7

(-0.3) (-0.2)

(-0.2) (-0.1)

(-0.1) (-0.1)

1

Change in "Gender Job Separation Gap" Model : Change (% points) (-0.9) Data : Change (% points) (-1.1) 1

"Gender Job Separation Gap" is defined as the difference between female and male job separation rates for each age group.

47

12

10

10

8

8

6

6

4

4

Male

2

Unemployment Rate, %

Unemployment Rate, %

(A) Unemployment Rates by Gender (20+) 12

2

Female

1950

1960

1970

1980

1990

2000

2010

(B) Unemployment Rates by Gender - HP filtered (20+) 12

12

Table 2: Corporate Debt and Equity Markets - Period Averages (τ c-constant) 10

10

8

1984-2004 8

Unemployment Rate, %

Unemployment Rate, %

1964-1983 Data

Model

Data

Debt / GDP 6

0.607

0.575

0.805 6 0.725

Tobin's q (V/k)

0.665

0.748

0.929

4

0.932

4

2

2

Male Female 1950

1960

1970

1980

1990

2000

Model

2010

Figure 1. Unemployment Rates By Gender: (A) Actual Series ; (B) HP Filtered Notes: Series are constructed by the Bureau of Labor Statistics (BLS) using the Current Population Survey (CPS). In Particular, we use seasonally adjusted mothly series.

48 (A) Gender Unemployment Gap 3

3

   

2.5

2.5

2

1.5

1.5

1

1

0.5

0.5

0

0

-0.5

-0.5

Data Trend

-1

Gender Unemploymemt Gap, %

Gender Unemploymemt Gap, %

2

-1

-1.5

-1.5 1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

(B) Gender Unemployment Gap by Age 20-24

25-34

35-44

percentage points

Table 2: Corporate Debt 2and3 Equity Markets - Period Averages (τ c-constant) 2 3 2.5 2.5 1

1

0

0

-1

-1

-2

-2

1964-1983

2

Debt -3 / GDP 1981

1982

Model

1

0

0.607

0.575

0

1978

0.665 0.748 -1 1979 1980 1981 1982

1.5

1

1.5

1

1

0.5

0

0

0.5 -1

   1980

1.5 Model

0.805

0.725

   1978

0.5

0.929 0.932 1980 1981 1982

1979

1981

1982

-1

   1978

1979

1980

1981

(Percentage Points)

Age

Change

20-24

-3.1

25-34

-1.8

35-44

-0.8

45-54

-0.5

55-62

-0.2

20-62

-1.52

1982

Figure 2. Gender Unemployment Gap: (A) Aggregate ; (B) By Age Notes: Gender unemployment gap is defined as the difference between female and male unemployment rates. Series are constructed by using the BLS calculations based on CPS. We use seasonally adjusted monthly series. 55-62

  

1 0 -1 1978

1

Change in Gender Unemployment Gap 1

1979

0.5

Data

55-62 2

1978

1984-20042

1

   -1

45-54 2

percentage points

1.5

Data

  

-4

2

1

-3

-4 Tobin's q1979(V/k) 1978 1980

2

1 0 -1 1979

1980

1981

1982

49

3

3 GENDER WAGE GAP

( 2010 Dollars - normalized by 1957 levels )

2.5

2

2

1977

1.5

1.5

1

Male

1

Female

1950

1960

1970

1980

1990

2000

2010

Figure 3. Median Wage Income by Gender ( 2010 Dollars - normalized by 1957 levels ) 3

2

1

1950

1960

1970

1980

1990

2000

2010

Notes: Real median wage series are from the U.S. Census Bureau, Historical Income Tables (in 2010 CPI-U-RS adjusted series).

Median Wage Income (normalized)

Median Wage Income (normalized)

2.5

50

E-U

U-E

1.5

1.5

1.4

1.4

1.3

1.3

1.2

1.2

1.1

1.4

1.4

1.3

1.3

1.2

1.2

1.1

1.1

1.1

1

1

1968

1972

1976

1980

1984

1988

1992

1996

1968

1972

1976

E-N

1980

1984

1988

1992

1996

N-E

0.7

0.7

2 0.6

2

0.6

0.5

0.5

0.4

0.4

1968

1972

1976

1980

1984

1988

1992

1.8

1.8

1.6

1.6

1.4

1.4

1.2

1.2

1996

1968 1972 1976 1980 1984 1988 1992 1996

N-U

U-N 0.8

0.8

0.7

0.7

2

0.6

0.6

0.5

0.5

0.4

0.4

1968

1972

1976

1980

1984

1988

1992

1996

2

1.8

1.8

1.6

1.6

1.4

1.4

1.2

1.2 1968

1972

1976

1980

1984

1988

1992

1996

Figure 4. Labor Market Flows : The Ratio of Male-to-Female Flow Rates (E: Employment, U: Unemployment, N: Nonparticipation) Notes: Based on CPS, flow rates are calculated from annual averages of month-to-month labor market transition probabilities. Based on these series, the ratio of male-to-female flow rates are calculated. For example, the first panel depicts the evolution of E-to-U flow rates of males divided by those of females.

51

(A.1) Share of Experienced Male Workers Among Males (B.1) Share of Experienced Workers (Male Workers)

(A.2) Share of Experienced Female Workers Among Females

(Pre-Break Model Economy)

(Pre-Break Model Economy)

11

1 1

0.8 0.8

0.6 0.6

Experienced Share of of Experienced Share ofShare Experienced

1

0.8 0.8

0.8

0.6 0.6

0.6

1

0.8

Share of Inexperienced

Share of Inexperienced Share of Inexperienced

0.4 0.4

0.2 0.2

00

Share of Inexperienced 0.4 0.4

0.4

0.4

0.2 0.2

0.2

0.2

0 0

20 20

25 25

30 30

35 35

40 40 Age Age

45 45

50 50

55 55

0

0

60 60

20

25

30

35

40

45

50

55

Age

(B) Average Life-Cycle Wage Profiles * Table 2: Corporate Debt and Equity Markets - Period Averages (τ c-constant)

Figure 5. (A) Average Life-Cycle Wage Profiles (Pre-Break Economy) 1964-1983

1.8

1984-2004

1.8

(B) Share of Experienced (Pre-Break Data Workers Model Data Economy) Model 1.6

Debt / GDP

0.607

0.575

0.805

0.725

Tobin's q (V/k)

0.665

0.748

0.929

0.932

1.6

(A) Average Life-Cycle Wage Profile

Data 1.4

1.8

1.4

Model

1.6

1.8 1.6

1.4

1.2

1.2

1.4

Data (Male) 1.2

1.2

Data (Female) Model (Male)

1

1 20

25

30

35

40

45

1

1

Model (Female) 50

55

60

Age

20

25

30

35

0.6

Share of Experienced

40

45

50

55

60

Age

* Data : CPS - fitted quadratic polynomials

Figure 5. (A) Share of Experienced vs. Inexperienced Workers (Pre-Break Economy) (B) Average Life-Cycle Wage Profiles (Pre-Break Economy)

1.8

Data (Men)

1.8

1.6

Data (Female)

1.6

60

52

12

12

Unemployment Rates for Male Workers : "Pre-Break" Unemployment Rates for Male Workers : "Post-Break"

10

Unemployment Rate, %

11 10

9

9

8

8

7

7

6

6

5

5

4

4

3

3

2

2 20

25

30

35

40

45

50

55

Unemployment Rate, %

11

60

Age

Unemployment Rates by Age : Male Workers (Model) 12 11 10 98 675 43 2

12 11 910 8 675 43 2 20

25

30

35

40

45 Age

50

55

60

Unemployment Rate, %

Unemployment Rate, %

Figure 6. Unemployment Rates by Age for Male Workers (Model Implied)

53

(A) Unemployment Rates by Age (Pre-Break) FEMALE

MALE 12

12

10

10

8

8

8

8

6

6

6

6

4

4

4

4

2

2

2

2

Data

Unemployment Rate, %

10

12

Data

Model

20-24

25-34

35-44

45-54

10

Model

20-24

55-62

25-34

35-44

45-54

Unemployment Rate, %

12

55-62

(B) Job Separation Rates by Age (Pre-Break) MALE

FEMALE

3

3

3

3

2.5

Data

Model

2

2.5 2

1.5

1.5

1

1

0.5

0.5

20-24

25-34

35-44

45-54

2.5

Model

2

2

1.5

1.5

1

1

0.5

55-62

2.5

Separation Rate, %

Separation Rate, %

Data

0.5

20-24

25-34

35-44

45-54

55-62

(C) Job Finding Rates by Age (Pre-Break) FEMALE

MALE

Data

40

45

31

40

29

31

Data

Finding Rate, %

29

Model

Model 35

35

27

27

30

30

25

25

25

25

23

23

20

20

21

21

20-24

25-34

35-44

45-54

55-62

20-24

25-34

35-44

45-54

55-62

Figure 7. Unemployment, Job Separation and Job Finding Rates (Pre-Break Economy) (Steady State Analysis) Notes: "Pre-Break" data values refer to the actual unemployment, job separation and job finding rates for workers of different age groups in 1979 Q3.

Finding Rate, %

45

54

(A) Gender Unemployment Gap 3

3

2.5

2

2.5

2

1

2

1.5

0

Data

Gender Unemploymemt Gap, %

Gender Unemploymemt Gap, %

Gender Unemployment Gap

1.5

Model

1

1978

1979

1980

1981

1

1982

0.5

0.5

0

0

-0.5

-0.5

Data Model

-1

-1

-1.5

-1.5 1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

(B) The Ratio of Male-to-Female Job Separation Rates 1.5

1.5

Table 2: Corporate Debt and Equity Markets - Period Averages (τ c-constant) 1.4

1.4

1964-1983 1.3

Debt / GDP 1.2

Tobin's q (V/k)

1984-2004

Data

Model

Data

0.607

0.575

0.805

0.665

0.748

0.929

1.1

1.3

Model 0.725

1.2

0.932

1.1

Data Model

1

1

0.9

0.9 1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

Figure 8. (A) Gender Unemployment Gap (B) The Ratio of Male-to-Female Job Separation Rates * 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998

*Notes : The ratio of male-to-female job separation rates depicts the evolution of employment to unemployment flow rates of males divided by those of females.

55 (A) Share of Inexperienced Workers (Pre-Break vs. Post Break Steady States) (Male Workers) 1

1

Pre-Break : Experienced Post-Break : Experienced

0.8

0.8

Population Shares

0.6

Pre-Break Inexperienced Workers Experienced Workers

32.4% 67.6%

0.6 Post-Break 33.3% 66.7%

0.4

0.4

0.2

0.2

Pre-Break : Inexperienced Post-Break : Inexperienced

0

0 20

25

30

35

40

45

50

55

60

Age

Figure 9. (A) Steady State Equilibrium Probability Density Functions (pdf) of Match Specific (B) Steady State Equilibrium Probability Density Functions (pdf) of Match Specific Productivity Levels

(Inexperienced Male Workers) Productivity Levels (Inexperienced Male Workers) 0.003Share of Inexperienced Workers (Pre-Break vs. Post Break) (Male 0.003 (B) Workers)

Pre-Break Equilibrium PDF Table 2: Corporate Debt and Equity Markets - Period Averages (τ c-constant)

20

25

30

35

40

0.0025 1984-2004 12 11 10 897 65 43 2

45

50

55

60

Age

Data

Model

Data

0.002

Unemployment Rate, %

1964-1983

0.0025

Model

0.002

0.607

0.575

0.805

0.0015 Tobin's q (V/k)

0.665

0.748

0.9290.0015 0.932

0.001

0.001

0.0005

0.0005

0

0.725 probability

Debt / GDP probability

Unemployment Rate, %

Post-Break Equilibrium PDF

Unemployment Rates by Age : Male Workers (Model) 12 11 10 897 564 32

0 0

1

2

3

4

5

6

ln(z)

Figure 9. (A) Share of Inexperienced Workers (Pre-Break vs. Post Break) (Male Workers) (B) Steady State Equilibrium Probability Density Functions (pdf) of Match Specific Productivity Levels (Inexperienced Male Workers)

FIGURE 12: UNEMPLOYMENT RATE BY AGE (MODEL)

56

(A) Unemployment Rates by Age for Male Workers 12 Model: Pre-Break

Unemployment Rate, %

10

10

Model: Post-Break 8

8

6

6

4

4

2

2 20-24

25-34

35-44

45-54

Unemployment Rate, %

12

55-62

(B) Job Separation Rates by Age for Male Workers 4

4 Model: Pre-Break

Separation Rate, %

Model: Post-Break 3

3.5 3

2.5

2.5

2

2

1.5

1.5

1

Separation Rate, %

3.5

1

0.5

0.5 20-24

25-34

35-44

45-54

55-62

(C) Job Finding Rates by Age for Male Workers

Model: Pre-Break

40

40

35

35

30

30

25

25

20-24

25-34

35-44

45-54

Finding Rate, %

Finding Rate, %

Model: Post-Break

55-62

Figure 10. Unemployment, Job Separation and Job Finding Rates for "Male Workers" ( "Pre-Break" vs. "Post Break" Steady State Analysis )