Why Didn’t the College Premium Rise
Everywhere? Employment Protection andOn-the-Job Investment in Skills*
Matthias Doepke

Ruben Gaetani

Northwestern University

University of Toronto

July 2022
Abstract
Why has the college wage premium risen rapidly in the United States since the1980s, but not in European economies such as Germany? We argue that differencesin employment protection can account for much of the gap. We develop a model inwhich firms and workers make relationship-specific investments in skill accumulation.
The incentive to invest is stronger when employment protection creates an expectationof long-lasting matches. We argue that changes in the economic environment have
reduced relationship-specific investment for less-educated workers in the UnitedStates, but not for better-protected workers in Germany.

* We thank Marco Bassetto, Samuel Bentolila, Alex Bick, Christian Hellwig, Gueorgui Kambourov,
Claudio Michelacci, Moritz Kuhn, Elena Pastorino, Todd Schoellman, Robert Ulbricht, Jon Vogel, David
Wiczer, and participants at many seminar and conference presentations for comments that helped to greatly
improve the paper. We gratefully acknowledge financial support from the National Science Foundation(grant SES-1260961). Doepke: Department of Economics, Northwestern University, 2211 Campus Drive,
Evanston, IL 60208 (e-mail: doepke@northwestern.edu). Gaetani: University of Toronto, 105 St. George
Street, Toronto, ON M5S 3E6, Canada (e-mail: ruben.gaetani@utoronto.ca).

1Introduction

In the United States, the wage gap between workers with and without a college education
has risen by more than 30 percentage points since the 1980s (Heathcote, Perri, and Violante2010). During this period, Canada and the United Kingdom also saw substantial growthin the college wage premium (Krueger et al. 2010). In contrast, the premium for collegeeducated workers has barely changed in a number of continental European economies(Fuchs-Schündeln, Krueger, and Sommer 2010; Jappelli and Pistaferri 2010). In this study,
we focus on the particular case of Germany, the largest European economy. In Germany,
the college wage premium actually fell between 1980 and 2006, and though it did go on
to rise slightly, in 2013 the premium was about the same as in 1980.
What explains these diverging trends between otherwise similar countries? Canonicalexplanations for rising skill premia such as skill-biased technological change (SBTC) do
not offer an immediate answer, because modern high-income economies are likely tohave comparable exposure to technological shocks. Instead, we focus on the potential
role of a factor that does differ sharply between the United States and Europe, namely
employment protection. In the United States, most workers are employed at will, meaning
they can be dismissed at any time if the employer so chooses. Conversely, labor markets
are highly regulated in most European economies, which enact employment protection
measures such as firing costs. In Germany, regular employees can only be dismissed fora limited set of reasons. Moreover, German law requires firms who lay off workers tofollow a Sozialauswahl (i.e., social criteria) when deciding which workers to dismiss,with special protection given to older workers and those with high tenure. In practice,
this means that German workers enjoy considerable protection from layoffs after a few
years with a given employer, unless the firm shuts down an entire establishment.
We argue that employment protection matters for the college premium because it affects
both firms’ and workers’ incentives to invest in the relationship. To this end, we develop
a quantitative model of the labor market in which on-the-job skill accumulation is a major
source of income disparity between workers. Investment in skills is two-sided: firms
can decide to create either high-quality jobs that allow for accumulation of skills, or lesscostly, low-quality jobs in which workers’ productivity remains stagnant. Workers with ahigh-quality job decide how much effort to put into accumulating skills.
The expected length of the employment relationship is an essential consideration in suchdecisions. Firms and workers will be more inclined to invest in their relationship when1

they expect more durable matches as a result of employment protection. If, as we argue,
the skills of college-educated workers are less firm-specific than those of less-educatedworkers, their skill accumulation decisions will depend less on the expected duration of agiven employment spell. Employment protection will thus have a differential impact on
the skill accumulation of college-educated and less-educated workers, which is important
for the college wage premium.
Our model predicts that the college wage premium will evolve differentially over time
between countries with and without employment protection if there is a rise in thefrequency of shocks that temporarily depress the productivity of existing firm-worker
matches. If such productivity shocks are rare, firms have little reason to dismiss workers
and expected job duration is high even without employment protection. Under such conditions, the college premium will be similar in economies with and without employment
protection. However, when shocks become more frequent, the duration of employment
spells will fall in economies with less employment protection. Firms will have fewer
incentives to create high-quality jobs for less-educated workers (whose skills are more
job-specific), and these workers will have fewer opportunities to accumulate skills andreduced incentives to acquire them. As a result, the college wage premium will rise. In
contrast, the impact of the change will be muted in economies with more employment
protection, resulting in little change in the college premium.
We use data from the Panel Study of Income Dynamics (PSID) in the United States and theGerman Socio-Economic Panel (SOEP) to verify that observed changes in the job-tenure
distribution align with our explanation for shifts in the college premium. We focus onchanges in the number of workers who spend most of their working lives with a single
firm. Specifically, we measure the fraction of male full-time workers aged 45–54 who haveworked for their current employer for at least 20 years.1 We find that in the early 1980s,
the fraction of high-tenure workers in the United States was similar for both more- andless-educated workers: around 42 percent for both groups. The fraction of high-tenure
workers subsequently declined to about 35 percent in 2010. In Germany, in the 1980s
the share of high-tenure workers was similar to that of the United States. Subsequently,
high tenure declined for college-educated workers but actually increased slightly forless-educated workers. This is exactly what our model predicts should happen in an
economy with employment protection in response to a higher frequency of shocks. The
1

We consider male workers because the evolution of average job tenure for female workers during
the same period is primarily driven by rising labor force participation of married women rather thanseparation shocks or employment protection.

2

different trends between education groups arise because more educated workers (whoseskills are more transferable) are able to take their skills to a new employer when a shockhits, whereas less-educated workers rely on employment protection to continue with
their current employer.
We use our model to assess the quantitative importance of on-the-job investment forchanges in the college wage premium. In our first exercise, we calibrate the model tomatch a number of data moments from the United States in 1980 that include the college
wage premium, returns to experience, returns to tenure, and the job-tenure distribution
by education. We allow a number of model parameters to vary over time to also match a
set of data moments in the year 2010. In addition to the on-the-job investment channel(triggered by a changed frequency of match-specific productivity shocks), the changes
we allow for in the model include shifts in overall skill bias and in returns to experience,
which represent forces such as SBTC or variations in the relative supply of more- andless-educated workers. We use this model to understand the drivers of changes in the
US wage structure between 1980 and 2010. A decomposition exercise shows that theon-the-job investment channel can account for a large fraction of the rise in the college
premium in the United States: up to 41 percent in our preferred calibration. Most of thischange is due to a decline in the creation of high-quality jobs for less-educated workers.
We also compare the trends in the college wage premium among various cohorts in ourmodel compared to the data during the transition path. The model output coincides withthe observation that the college premium rose primarily among younger workers from1980 to 1990, whereas the pattern had reversed by 2010, with a larger college premium
among older workers compared to 1980 in that year (Card and Lemieux 2001). Theseobservations on the transition path were not targeted, yet our model matches them well.
The final step of our analysis examines the role of employment protection by considering
the case of Germany. In our model exercise, we take the position that Germany issubject to the same technological forces as the United States, but has a different regimeof employment protection. We introduce employment protection in the form of a firing
cost that increases with job tenure. The level of the firing cost is set to match observationsof the share of high-tenure workers in Germany. Then, we ask how this more protectedeconomy reacts to the same shocks that we introduced in our quantitative exercise for theUnited States. It turns out that the increase in the college wage premium is almost halved
compared to the economy without firing restrictions. We conclude that the combinationof differences in employment protection and the on-the-job investment channel can go a3

long way in explaining the different trends in the college wage premium between the
United States and Germany.
Our analysis has implications for the welfare consequences of imposing employment
protection. The quantitative model includes a number of frictions that may lead toinefficient job-creation and skill-investment decisions, including frictional labor markets
and a lack of firms’ and workers’ ability to commit to long-term contracts that arecontingent on skill investment. Given these frictions, we find that moderate firing
restrictions can indeed improve welfare, primarily because they induce firms to create
relatively more high-quality jobs that allow for the accumulation of skills. While ourmodel also captures negative repercussions of labor protection, such as lower job creationand higher unemployment (e.g., Bentolila and Bertola 1990; Cahuc, Malherbet, andPrat 2019), it abstracts from additional negative effects of firing restrictions, such as lessadoption of productive but risky technologies (Saint-Paul 2002; Bartelsman, Gautier, and
De Wind 2016). Thus, our analysis does not provide an unqualified argument in favorof more protection. Nevertheless, we believe that the channel identified in our model isimportant for evaluating the full consequences of employment regulations such as those
now in place in Germany and many other advanced economies.
The following section relates our work to the existing literature on the college wage
premium and the effects of labor regulation. In Section 3, we describe the main empiricalpatterns that motivate this study, including new findings on shifts in the number ofworkers with high job tenure in the United States and Germany. Our quantitative model
is described in Section 4, and in Section 5 we explain how we calibrate the model to thedata. In Section 6 we describe our results, and Section 7 concludes.

2

Relationship to Literature

The best-known explanations for the upward trend in the college wage premium in the
United States include factors such as SBTC and trade liberalization (Katz and Murphy
1992; Katz and Autor 1999; Krusell et al. 2000; Autor, Levy, and Murnane 2003; Goldin andKatz 2008; Guvenen and Kuruscu 2009; Jaimovich et al. 2019). The authors who propose
these explanations take the view that workers with higher education have benefited
disproportionately from the technological and institutional shifts that have occurredsince the 1980s. Our quantitative analysis allows for factors that increase the productivityof highly educated workers, and we do find that these factors play a significant role.

4

Nevertheless, the on-the-job investment channel that we propose focuses primarily on
the skills of less-educated workers, and implies that in the United States such workers
currently have fewer opportunities for accumulating skills than in the past. This channel
is consistent with new evidence on the recent deterioration of the labor market opportunities of less-educated workers, a trend that directly contributes to increased inequality
between education groups (Autor 2019). Deteriorating outcomes for less-educated workers are evident in stagnating income levels even as aggregate productivity keeps growing(Guvenen et al. 2017), in worsening measures of job quality and security (Segal and
Sullivan 1997; Hollister 2011; Binder and Bound 2019), and in other indicators of economic well-being (Coile and Duggan 2019). Our analysis proposes a specific mechanismthat can explain the increasing scarcity of “good jobs” for less-educated workers. Our
mechanism is also consistent with the literature on the increasing polarization of thelabor market (Autor and Dorn 2013), which documents the disappearance of jobs in the
middle of the wage distribution (that, in our framework, correspond to high-quality
jobs for less-educated workers) and the increasing prevalence of low-quality jobs at thebottom of the wage distribution.
Alternative explanations for the deterioration of labor market outcomes for less-educatedworkers include automation and robotization (Hémous and Olsen 2018, Acemoglu andRestrepo 2020) and exposure to trade (Autor, Dorn, and Hanson 2013). More closely
related to our analysis, Acemoglu (1999) develops a model in which changes in macroeconomic conditions generate a shift in the type of jobs offered by firms. In his setting, as
the supply of skilled workers increases, firms transition from a pooling equilibrium withsimilar jobs offered to all workers to a separating equilibrium in which jobs are specificto each skill type, which benefits educated workers but harms the less educated.
The studies mentioned thus far do not offer an explanation for why trends in wage
inequality have progressed differently in the United States and European countries suchas Germany. Among the earlier contributions on this specific issue, Acemoglu (2003)
does focus on the potential role of more regulated labor markets in Europe. Specifically,
based on Acemoglu and Pischke (1999b), he develops a model in which a high minimum
wage may lead firms to adopt productivity-enhancing technologies for less-educatedworkers. While related, this mechanism is less likely to be relevant for Germany, whereminimum wages were introduced only a few years ago.
Beaudry and Green (2003) argue that the diverging trajectories of the college premium in
the United States and Germany can in part be explained by differences in the accumu5

lation of physical relative to human capital. Their theory is consistent with the declineof wages for less-educated workers in the United States and with the observation thatunemployment has increased for all education groups in Germany. Our model showsthat those empirical patterns are also consistent with a mechanism of accumulation ofskills on-the-job combined with employment protection, while additionally accounting
for changes in the tenure distribution.
Guvenen, Kuruscu, and Ozkan (2013) develop a mechanism complementary to ours,
arguing that increasingly progressive taxation lowered European workers’ incentives toinvest in their skills, thus compressing the skill distribution relative to the United States
and lowering observed skill premia. While also focused on the accumulation of skills on
the job, the main changes in their setting occur at the top of the skill distribution, whereas
our model deals mainly with less-educated workers. This focus is shared with Alon (2017),
who argues that features such as apprenticeship programs in Germany provide lesseducated workers with differentiated skills, whereas investment in vocational training
for less-educated workers in the United States has decreased over time, leading to a
deterioration of skills in this group. This mechanism is also complementary to ours, as
it concentrates on the initial acquisition of skills by more- and less-educated workers,
whereas our model is concerned with investments in on-the-job skills acquisition. One
advantage of the employment-protection mechanism developed in our study is its distinct
implications for the tenure distribution and returns to tenure in different educationgroups, which can be empirically tested.
Our work also contributes to a literature on the macroeconomic consequences of differences in labor regulation between the United States and European economies. In
particular, we build on Ljungqvist and Sargent (1998), who similarly develop a mechanism by which differences in labor regulation interact with changes in the economic
environment. However, they consider a different set of policies and outcomes, namely
the impact of unemployment insurance on unemployment levels. Other contributions
that focus on unemployment include Blanchard and Summers (1986), Bertola and Ichino(1995), Nickell (1997), Den Haan, Haefke, and Ramey (2005), Hornstein, Krusell, andViolante (2007), and Kitao, Ljungqvist, and Sargent (2017). Our paper adds a new angle
to this literature by arguing that the level of employment protection has repercussions
for education premia in the labor market.
While the focus of this paper is on the college premium, our framework accounts for thefact that vacancy creation is affected by firing costs, which is important to understand6

the effect of employment protection on unemployment and welfare (Hopenhayn andRogerson 1993; Ljungqvist and Sargent 2008). This margin is potentially relevant for the
study of inequality since, as suggested by Heckman (2002), income disparities might beunderstated in Germany because of differences in employment rates across educationgroups. However, consistent with the findings in Krueger and Pischke (1997) andFreeman and Schettkat (2000), our quantitative model suggests that unemployment rates
increased to a similar extent for college-educated and less-educated workers as a resultof employment protection.
Our work is also related to the literature on on-the-job investment in skills and thedistinction of general versus firm-specific skills. There are a variety of reasons why
investment in skills on the job may fail to be efficient; see Acemoglu and Pischke (1999a)for a discussion. We build, in particular, on the analysis by Wasmer (2006) of investment
in general versus firm-specific skills in a frictional labor market. Wasmer argues thatsearch frictions make investing in general skills less attractive, because such skills pay
off relatively more in future matches with other firms, which are harder to find if there
are search frictions. Similarly, employment protection makes job-specific skills more
attractive. The link between employment protection and investment in specific skills
is also central to our mechanism. However, Wasmer’s analysis does not extend to theimplications for the college wage premium and cross-country inequality trends.
A separate literature, starting from Jovanovic (1979), explains returns to tenure andexperience by postulating a learning process on match quality (Moscarini 2005; Gorry
2016) or on workers’ comparative advantage (Papageorgiou 2014). While our model
assumes no variation in match quality, the process of skill accumulation can be interpreted
as reflecting, in reduced form, a learning component by workers and firms. Similarly,
in the literature on job ladders (see Moscarini and Postel-Vinay 2019 and Jarosch 2021
for recent contributions) an additional source of wage growth consists of changes in the
distribution of surplus between worker and firm that results from bargaining with outsideoffers. While we abstract from changes in the distribution of surplus between worker
and firm, quantitative findings in this literature (e.g. Jarosch 2021) suggest that changing
negotiation rents are important primarily at the low end of the tenure distribution,
whereas human capital loss after separation (the element which we emphasize) is crucial
for generating long-term effects of job loss on earnings. Given that we are primarily
interested in education premia at the high end of the tenure distribution, these findings
support our focus on human capital dynamics.
7

Our analysis does not hinge on a particular reason for why the transferability of skills
differs across workers. One possibility is that the higher transferability of skills of
more-educated workers reflects higher technological adaptability, as originally proposed
by Nelson and Phelps (1966). Another relevant possibility is that skills are primarily
occupation specific, as argued by Kambourov and Manovskii (2009b). Occupationspecific skills translate into differences in skill transferability by education if less-educatedworkers have a higher likelihood of occupational displacement following separation.
One mechanism that would give rise to such a relationship is that educated workers
are prevalent in occupations that are applicable to many sectors (including managerial
occupations) whereas less-educated workers are concentrated in occupations that are in
demand in only a single industry. The higher transferability of skills of college-educatedworkers may also allow them to leverage job-to-job transitions to increase their lifetime
wage growth, as shown by Engbom (2022). While our framework abstracts from job-tojob transitions, our estimates of the loss of skills upon separation may be interpreted asalso reflecting, in a reduced-form way, the ability to obtain a higher salary by transitioning
across jobs, a margin that is likely to be more relevant for college-educated workers.
Finally, our empirical findings on shifts in the job-tenure distribution are relevant toa recent literature on reduced dynamism in the US labor market. At first sight, thisliterature may appear to contradict our finding of declining rates of high tenure. For
example, Hyatt and Spletzer (2016) document that average job tenure has risen in the
United States since 1980, as has the fraction of workers with at least five years of tenure.
These observations can be reconciled by noting that part of the shift towards higher tenureis due to population aging. Furthermore, there has been a shift towards reduced churn atthe beginning of employment spells, decreasing the fraction of workers with very low job
tenure (Pries and Rogerson 2020). This form of declining turnover does not contradict theidea of rising turbulence as originally formulated by Ljungqvist and Sargent (1998), whoemphasize increasing instability in the labor market due to firms’ exposure to changes inthe technological and competitive environment, a channel that does not relate directly
to the decline in churn at the lower end of the tenure distribution. The facts that we
document here become apparent only when focusing on the share of older workers
with very high tenure (15 years or above), which is a part of the tenure distributionthat earlier papers usually did not look at specifically. One exception is Molloy, Smith,and Wozniak (2020), who document changes in the entire tenure distribution for theUnited States and find, as we do, that the share of older workers with high tenure has
declined. In our quantitative model, we include a churn shock that destroys a proportion8

of recently created matches to generate an overall tenure distribution that closely matches
the data. Our calibrated model is therefore consistent with both the evidence on declining
long-term tenure that we document here and with results on declining labor market
dynamism that is driven by less churn at the low end of the tenure distribution.

3 The College Premium, Long-Term Tenure, and Returns to Tenure in
the United States and Germany
In this section, we document the empirical facts that motivate our study and which
our quantitative model aims to account for. We focus on the evolution of key labormarket variables in the United States and Germany since the early 1980s. To this end,
we employ the 1981–2013 waves of the Panel Study of Income Dynamics (PSID) for theUnited States, and the 1984–2013 waves of the German Socio-Economic Panel (SOEP)
for Germany (Goebel et al. 2019).2 These data sets provide individual-level information
on job tenure, wages, and education, allowing us to perform a comparative analysis of
the US and German experiences. We focus on men aged 25 to 64 with at least a highschool education.3 In the German data, we focus on the original sample of the SOEP
(which only includes families in West Germany), so that results are not influenced by
the different work histories of East German men that were sampled after reunification.
We also construct a system of weights that keeps the age distribution by education fixedwith respect to the first year of the sample (1981 for the PSID and 1984 for the SOEP). All
the statistics in this section are constructed using this system of weights. Appendix A
contains details on sample selection and the construction of the main variables for the
analysis.
3.1 Education Premia and the Share of College Graduates in the United States andEuropeAs has been widely documented (Heathcote, Storesletten, and Violante 2010), the US
economy has experienced a sharp rise in the college wage premium since the 1980s.
The solid lines in the top panel of Figure 1 display the college wage premium trend in
the United States from 1981 to 2013, obtained by regressing log real wages on a college
2

The PSID was collected every year until 1997, and every other year from 1997 onwards. 1984 was thefirst wave of the SOEP.
3
We limit our attention to men because changes in women’s job tenure over this period were dominatedby the large shifts in female labor force participation that occurred during this period.

9College Premium

0.55
0.5
0.45
0.4
0.35
0.3
0.25
1985

1990

1995

2000

2005

2010

2005

2010

Share of College Graduates

0.45
0.4
0.35
0.3
0.25
0.2
0.15
1985

1990

1995
United States

2000
Germany

Figure 1: Top panel: The college wage premium (log difference of average wages) in the
United States and Germany among workers aged 25–64, 1981 to 2013. Bottom panel:
Share of college graduates among workers aged 25–64, 1981-2013. Each data point isconstructed using data from the five years around the focal year. Thick lines represent
the series smoothed using a Hodrick-Prescott filter with a smoothing parameter equal to100.
education dummy (thin line) and computing the trend component using a HodrickPrescott filter (thick line). The estimated trend displays a sharp increase starting in theearly 1980s, leading to a peak at almost twice the original value in the mid-2000s andstabilizing thereafter (Valletta 2016).
This increase in the returns to education coincided with a contemporaneous rise in therelative supply of college-educated workers. The solid lines of the bottom panel of Figure
1 show the changing share of college graduates among US male workers starting in 1981,
revealing a steady upward trend from 36 percent in 1981 to 45 percent in 2013.
Beginning with studies by Katz and Murphy (1992), Krusell et al. (2000), and Acemoglu(2002a), a sizeable literature has rationalized the contemporaneous increase in the market
price and the relative supply of skilled workers in the United States by suggesting thattechnological advancements in recent decades have disproportionately favored collegeeducated workers. Yet this explanation for the issue at hand is limited in that different1045%ȱChangeȱinȱSkillȱPremium

USA
35
25

CAN

15

SWE

UK

5
Ȭ5 0

5

10

15 GER

20 ITA

Ȭ15
Ȭ25
Ȭ35

OECDȱIndexȱofȱEmploymentȱProtection

SPA

Figure 2: Labor protection in the early 1990s and the change in the education premiumfrom 1980 to 2006. Data from Krueger et al. (2010) and Nickell (1997).
high-income countries use similar technologies and have also experienced a similar risein the supply of college-educated workers, but patterns in the college wage premiumvary widely.
Germany is a case in point. The relative labor supply of college-educated workers inGermany closely tracks US trends, but Germany did not see a comparable increase in
the college wage premium. The dashed lines in the top panel of Figure 1 shows that thecollege wage premium was similar in the United States and Germany in the early 1980s,
but subsequently rose in the United States while remaining flat in Germany.
These divergent trends suggest that country-specific factors have a substantial impact on
the college wage premium. Our study is motivated by the observation that changes in
the college premium across countries are empirically correlated with measures of labor
protection. Figure 2 plots the percentage change in the college premium between 1980
and 2006 in the sample of OECD countries surveyed in Krueger et al. (2010) against theOECD labor protection index. The graph shows a strong negative correlation between
growth in the college wage premium and the labor protection index. Among the countries
plotted, the United States has the least-regulated labor markets and the fastest rise in
the college wage premium. At the other end of the scale, Germany, Italy, and Spain—allcountries with high levels of employment protection—actually experienced a decline in
the college wage premium over the same period.
While this is a simple correlation and not necessarily a causal relationship, it motivates11

our analysis of a channel through which employment protection can impact changes in
the college premium. Specifically, we argue that employment protection can increase
the incentives for workers and firms to make relationship-specific investments that pay
off if workers stay with the same firm for a long time. For workers, these investments
take the form of the costly acquisition of firm-specific skills. For firms, they take the formof the creation of jobs that utilize such firm-specific skills and allow workers to acquirethem. In our model, if worker-firm matches are subject to frequent productivity shocks,
employment protection can lead to an expectation of a longer duration of matches, which
in turn increases the incentive to invest in the relationship. The employment-protection
mechanism links changes in skill premia in the labor market to shifts in employment
duration for different groups of workers. Next, we show that this connection is supported
by evidence from the United States and Germany.
3.2

The Fall in Long-Term Tenure

The link between employment regulation and the evolution of wage premia that we propose in this paper relies on the notion that workers in economies with more employment
protection experience less job turnover and hence are more likely to achieve long-term
tenure with a given employer. The PSID and the SOEP data sets can be used to verify
whether this is actually the case.
We focus on the share of workers aged 45 to 54 who have been with their current
employer for at least 20 years, a group we term “long-term tenure” workers. Such workers
have spent most of their working lives with their current employers, and are therefore
especially likely to benefit from relationship-specific investments. Figure 3 displays thechanging share of long-term tenure workers in the United States and Germany from the
1980s to the 2010s, charted separately for college graduates and less-educated workers. In
the United States, this share displays a clear downward trend for both education groups,
declining from about 42 percent in 1981 to about 35 percent in 2013.4
The pattern for less-educated workers in Germany is strikingly different. While theirlong-term tenure share is only slightly above the US level in 1984, there is no clear
downward trend in the following decades. The long-term tenure share first increases
substantially and then falls, returning to 1984 levels by 2013.
The US-Germany difference is less pronounced among college-educated individuals(Figure 3, bottom panel), whose share of long-term tenure workers declines in both
4

The substantial share of high-tenure workers in earlier US data is also noted by Hall (1982).

12

High-School Graduates

0.6
0.55
0.5
0.45
0.4
0.35
0.3
1985

1990

1995

2000

2005

2010

2005

2010

College Graduates

0.5

0.45

0.4

0.35

0.3
1985

1990

1995
United States

2000
Germany

Figure 3: Share of workers aged 45–54 with tenure of over 20 years at their current
employer in the United States and Germany, 1981-2013. Top panel: High-school graduates.
Bottom panel: College graduates. Each data point is constructed using data from thefive years around the focal year. Thick lines represent the series smoothed using a
Hodrick-Prescott filter with a smoothing parameter equal to 100.
countries. Our quantitative model accounts for this pattern because college-educatedworkers have skills that are more transferable from one employer to another. Thisimplies that these workers are more likely to end up with a new employer in response tomatch-specific shocks, even in economies with stringent labor market policies.
The trends in Figure 3 remain if we exclude public-sector workers. Specifically, excluding
public-sector employment somewhat reduces the share of workers with high tenure inboth countries, consistent with higher job security for public-sector workers, but does
not change the general trends over time.
3.3

Returns to High Tenure for High School and College Graduates

The employment-protection mechanism relies on the presumption that the skills of college
graduates are more transferable between employers, meaning that their skill investment
is less affected by shocks that destroy long-lasting firm-worker matches. In our model,
differential transferability of skills results in less-educated workers having higher returns
13

to job tenure (i.e., the time worked at their current employer), whereas more-educatedworkers have low returns to tenure but high returns to experience (the overall time
worked in the labor market across all employers). These patterns are supported by recent
findings in the empirical labor literature on returns to experience and job tenure.
Measuring returns to job tenure is complicated by possible selection bias: more skilledworkers may be more likely to be retained by the employer and achieve high tenure, meaning that observed returns could partially reflect workers’ ability. Altonji and Shakotko(1987) argued that selection accounts for much of the empirical correlation of job tenure
and wages. However, this conclusion has been revised by Altonji and Williams (2005),
among others, who do find substantial returns to tenure. Buchinsky et al. (2010) address the relationship between education and returns to tenure in the United States,
demonstrating that less-educated workers (especially workers with less than a highschool education) have higher returns to tenure and lower returns to experience than docollege-educated workers, which is the pattern in our model. Studies that use events suchas mass layoffs to estimate the firm-specificity of human capital reach similar findings.
For example, Kletzer (1989) shows that blue-collar workers suffer large losses of accumulated returns to job tenure after displacement, whereas managerial, professional, andtechnical workers are much less affected5 . To the extent that less-educated workers are
more likely to be blue-collar workers, these findings align with our analysis. Dustmann
and Meghir (2005) use German firm closure data for identification to examine returns
to tenure and experience. They document that the least-educated workers have low
returns to experience but substantial returns to firm-specific tenure, also in line with theemployment-protection mechanism.
One question that remains unsettled is why less-educated workers have higher returns
to job tenure. It may be that the tasks performed by less-educated workers are indeed
more firm-specific and less transferable across employers. Another possibility is thatthe accumulation of skills is primarily occupation-specific (Kambourov and Manovskii
2009b), and that less-educated workers are more likely to be displaced from their current
occupation after a job loss. This distinction may have important policy implications. Thatsaid, for our objective of explaining changes in the college wage premium, what matters
5

In an overview of the job displacement literature, Kletzer (1998) characterizes the evidence as follows:“The far larger dropoff in the contribution of predisplacement tenure to postdisplacement earnings forblue-collar workers reveals the importance of factors such as specific human capital and job match effects
for these workers. In contrast, individual ability and transferable skills are a more important part of the
returns to tenure for the skilled white-collar group.”

14

Log of hourly wage (ages 45–54)
US (PSID)
1981–1995
Tenure >= 20, High school

1996–2013

0.272***

0.257***(0.043)(0.030)Tenure >= 20, College

0.180***

0.187***(0.064)(0.045)Experience (polynomial)

yes

yes

yes

yes

Year FE

yes

yes

yes

yes

Observations

1,895

1,197

2,606

1,836

R2

0.126

0.048

0.073

0.044

Notes: Standard errors clustered at individual level in parentheses. The sample
consists of male workers aged 45 to 54 who report between 500 and 5,000 hours
worked in a year. Each column consists of a separate regression of log wages
on a year fixed effect, a third-degree polynomial of potential experience, and an
indicator variable for 20 years of tenure or more on the current job. *** p < 0.01,** p < 0.05, * p < 0.1.

Table 1: Returns to high tenure for college- and less-educated workers in the UnitedStatesis that returns to job tenure differ by education.
For the purposes of our quantitative analysis, we need to ensure that our model incorporates a quantitatively plausible gap in the returns to high job tenure for college- andless-educated workers. We therefore compute empirical returns to high job tenure basedon PSID data for the United States and SOEP data for Germany. To ensure consistency
with our earlier analysis of high-tenure workers, we focus on the returns to working
with a given employer for at least 20 years. Table 1 reports the estimated coefficients ofindividual-level regressions of log-hourly wages on a set of year fixed effects, a thirddegree polynomial of potential experience,6 and a dummy variable that is one if theworker has been with the same employer for at least 20 years. We run these regressions
on the sample of male PSID respondents aged 45 to 54 who report at least 500 hours ofyearly employment. We compute the returns to high tenure separately for workers with6

We define potential experience as current age minus (years of education + 6).

15

Log of hourly wage (ages 45–54)
Germany (SOEP)
1984-1995
Tenure >= 20, High school

1996-2013

0.098***

0.158***(0.024)(0.029)Tenure >= 20, College-0.042-0.087*(0.057)(0.044)

Experience (polynomial)

yes

yes

yes

yes

Year FE

yes

yes

yes

yes

Observations

4,008

1,066

3,816

1,247

R2

0.044

0.079

0.257

0.296

Notes: Standard errors in parentheses. Standard errors are clustered at individual level. The sample consists of male workers aged 45 to 54 who report aminimum of 20 hours worked per week in the last year. Each column consists ofa separate regression of log wages on a year fixed effect, a third-degree polynomial of potential experience, and an indicator variable for 20 years of tenure or
more on the current job. *** p < 0.01, ** p < 0.05, * p < 0.1.

Table 2: Returns to high tenure for college- and less-educated workers in Germany
a high school and college education,7 and also split the sample into an early (1981–1995)
and late period (1996–2013) to assess whether returns to high tenure change over time.
In line with the literature, the estimated coefficients show that returns to high tenure
are much smaller for college-educated workers. The change between the early and lateperiod is small: workers with high tenure have a substantial pay advantage in both
periods, though there are considerably fewer such workers by the late period (Figure 3).
Table 2 reports the results of an analogous set of regressions performed on the German
SOEP sample. The average measured returns to high tenure are smaller than in the US
data, but the gap between more- and less-educated workers is similar. Patterns are alsosimilar between the earlier and the later periods.
To further validate the patterns reported in Tables 1 and 2, we run separate pooled
regressions on the PSID and SOEP samples that include all workers aged 45 to 54 andregress the log-hourly wage on a set of year fixed effects, college attainment, and long7

Individuals with some college education who have not completed a four-year tertiary degree arecounted as high-school graduates.

16

term tenure dummy variables, as well as the interaction between the latter two. The
results are reported in Appendix Table B.1. The coefficients of the interaction terms
are negative, consistent in magnitude, and statistically significant in both samples. The
size of the estimates implies that the premium enjoyed by high-tenure workers with ahigh-school education is 10.7 percentage points higher than that for college-educatedworkers in the United States, and 16.6 percentage points higher in Germany.
The results in Tables 1 and 2 do not control for selection effects arising from endogenous
separation decisions, and therefore should not be interpreted as estimates of the causal
effect of high tenure on wages. Rather, we view these regressions as data moments that aquantitative model of on-the-job skill accumulation should be able to match. Like thedata, our model allows for endogenous separations, and hence tenure premia are subject
to analogous selection effects. In our quantitative analysis below, we discipline the model
to generate the observed empirical link between high tenure and wages, which includes
both selection and skill-accumulation effects. Crucially, however, the quantitative exercise
is less concerned with the level of returns to high tenure (where selection is likely tomatter more) than the gap in empirical returns between more- and less-educated workers.
To further address potential concerns about the role of selection effects, we can exploit thepanel dimension of the PSID and the SOEP data to verify, using the method proposed by(Altonji and Shakotko 1987), that the gap in the returns to tenure is not primarily driven
by differential selection into high-tenure between more- and less-educated workers.
In particular, (Altonji and Shakotko 1987) propose to instrument for job tenure using
deviations from the average tenure within each employment spell, since such deviations
are, by construction, orthogonal to match quality. Appendix Table B.2 shows that theestimates for the returns to tenure using this method are qualitatively in line with theresults that do not control for selection. In particular, in the specification with individual
fixed effects, the gap between less- and more-educated workers in the returns to 10 yearsof tenure is 11.9 percentage points in the United States and 10.0 percentage points inGermany.

4

A Labor Search Model with Skill Upgrading

In this section, we develop a quantitative model of job creation and on-the-job accumulation of human capital that can account for the facts described in Section 3. The key
elements of the model are a life-cycle structure and relationship-specific investments
by both firms and workers. Firms decide to create jobs that either do or do not allow
17

for the accumulation of skills. If they have a job that allows for skills accumulation,
workers decide how much effort to invest in acquiring skills. The incentives to undertakethese two-sided investments depend on the expected length of the firm-worker relationship which, in turn, is determined by the economic environment and by the extent of
employment protection.
4.1

Demographics and the Labor Market

Every year, a new cohort of workers enters the labor market. Workers’ education e
is heterogenous, with e = H denoting college education and e = L a lower level of
education. A cohort enters the labor market at age 25 and retires at age 65. Workers
are risk neutral and discount future periods with a yearly discount factor β < 1. A
worker’s instantaneous utility is given by consumption minus the cost of effort z exerted
to acquire skills on the job. After retirement, workers’ continuation utility is independentof their skill accumulation. The continuation utility therefore does not affect decisions
and is normalized to zero. In addition to education e, each worker is characterized bya productivity level h on a skill ladder, h ∈ {h1 , . . . , hI }. When workers enter the labormarket at age 25, their initial productivity is drawn from a distribution F (h).
There is a large mass of potential firms that open vacancies and create jobs. Their decision
to post vacancies happens in two steps. In the first step, each potential firm can decide topost a vacancy for workers of education e at cost q e or not to post any vacancy. Denoting
by v e and ue the mass of vacancies and unemployed workers of education e, the mass ofmatches me created in each period is given by the matching functionme = (v e )µ (ue )1−µ ,where µ ∈ (0, 1). Hence, an unemployed worker of education e is matched with a firmeewith probability λe = m
every period, and firms generate ζ e = mve matches for each unitueof vacancies posted. A firm that does not post a vacancy earns zero profits, so that inequilibrium the expected profit from posting a unit of vacancies for workers of educatione must be equal to the cost of posting the vacancies, q e .
In a second step, a matched firm has to decide whether to make an investment suchthat the created job allows the worker to accumulate skills (type-A job), or to forgo
this investment such that no skills can be accumulated (type-N job). The type of a job
is denoted by p ∈ {A, N }. We interpret this investment as a technology choice. For18

example, a restaurant can be set up to rely primarily on heating up ingredients that comealready prepared, or alternatively in a way where all food is made from scratch by ateam including a chef, sous-chefs, and others all the way down to entry-level employees,
who in the process of working in such an environment acquire skills that allow them toadvance. Similarly, houses can be alternatively built by assembling pre-made components
or from the ground up using a variety of craft skills. In either case, the more elaborate
production process allows for more accumulation of skill among the workers.
Jobs that allow for such skill accumulation can ultimately result in a higher-quality product which makes them more profitable, but such jobs are also more costly to create. Thereis heterogeneity across firms with respect to the cost of creating an accumulation-type job,which makes the supply of these jobs responsive to relative profitability. Specifically, after
creating the vacancies, the firm draws the investment cost k from a uniform distribution
with limits [ce0 E [JNe ] , ce1 E [JNe ]], where ce1 > ce0 > 0 and E [JNe ] is the expected profitabilityof type-N jobs.8 This investment represents the cost of creating an accumulation-type
job. Scaling the distribution by the factor E [JNe ] guarantees that proportional shifts tothe profitability of all jobs (say, through an increase in overall productivity) do not affectthe fractions of type-A and type-N jobs created.9 Given this cost, the firm will createa type-A job if and only if the cost k is lower than the difference between the expected
returns from the two types of jobs:k ≤ E [JAe ] − E [JNe ] .
Hence, the share νAe of type-A jobs for workers of education e will be equal to:νAe = min




max

E [JAe ] − E [JNe ]c̃e1− c̃e0 , 0
E [JNe ]




,1 ,

(1)

ce

1
e
0
where c̃e0 = ce −ce and c̃1 = ce −ce . Equation 1 illustrates that the share of jobs for e workers
10
10that allow for accumulation of skills is an increasing function of the relative expected
profitability of the two types of jobs, E [JAe ] /E [JNe ].
8

We use a uniform distribution because our quantitative results depend primarily on the fraction of
type-A jobs and on how strongly this number varies with relative profitability, which pins down the twoparameters of the uniform distribution. Other distributions would give similar results provided that they
match the level and slope of the supply of type-A jobs in our calibrated model.
9This scaling could arise from the investment requiring an input of unskilled labor; unskilled wages arelinked to profits through wage bargaining.

19

4.2

Production and Turbulence Shocks

Once worker and firm are matched, they start producing. Under normal conditions, amatch between a firm and a worker of education e, skill level h, and potential experiencex (where x = 1 at age 25 and x = 40 at age 64) produces output y e (x, h) = ae (x)h. For agiven match, this initial output level changes over time for two reasons: a change in theexperience profile ae (x) or a change in skill h, provided that the job type allows for theaccumulation of skills. The term ae (x) captures all sources of life-cycle wage growth thatare not due to investment in skill by the worker.10
The output level can also be affected by turbulence shocks, which are temporary but
persistent decreases in match-specific productivity. New matches in the first period of
the firm-worker relationship are not affected by these shocks. Before production takes
place in later periods, the match is affected by turbulence with probability γ. If the shockhits, the match productivity is reduced to a fraction ϵ < 1 of regular productivity, where ϵ
is drawn from a distribution G(ϵ). A match can be subject to multiple turbulence shocks,
i.e., subsequent reductions in productivity by a fraction ϵ. A turbulence shock lasts until
separation or until productivity returns to the regular level. The probability of the shock
being reversed is also given by ϵ (i.e., the size of the shock), implying that more severe
shocks (lower ϵ) are more persistent.
In addition to turbulence shocks, the match can also be hit by an irreversible negative
shock that permanently reduces match productivity to zero, leading to immediate separation. The probability of this separation shock depends on the worker’s tenure at theircurrent job and is denoted by θ(t), where t ≥ 1 is tenure. The separation shock allows us
to match observed trends in the prevalence of short-duration jobs separately from that in
the share of workers with long-term tenure.11
4.3

Skill Accumulation and Skill Loss

Workers with jobs that allow for human capital accumulation choose how much effort
to exert in accumulating skills. A worker with education e ∈ {H, L}, experience x, and
10Note that even though productivity does not explicitly depend on the relative aggregate supply of
more- and less-educated workers, this is without loss of generality because the supply of skills is exogenous
in the model. In the quantitative analysis below, we include an overall skill-bias parameter that captures
both the effects of relative supply of skills and of skill-biased technological change.
11
A rich literature has documented a decline in the rate of job turnover that is largely explained by
the decline in jobs with a very short duration. See, among others, Hyatt and Spletzer (2016), Pries andRogerson (2020), and Molloy, Smith, and Wozniak (2020).

20

current productivity level hi can exert effort z at cost ae (x)hi z 2 . If the effort is successful,a worker with skill level hi upgrades their skills to hi+1 , which happens with probability:p(z) = ψ

z
,
z+1

(2)

where ψ > 0 is a parameter. We assume that, for given worker characteristics, the effort
exerted during regular times does not change when a turbulence shock hits.12 Upon
separation from a job, workers potentially suffer a downgrading of their skills, so thata worker of education e ∈ {H, L} and skill level hi transitions to skill level hj withprobability Qe (i, j). Here Qe (i, j) = 0 if j > i, meaning that separation can never result inhigher skills. The Qe (i, j) are defined as follows:
Qe (i, j) = σ e Qe (i, j + 1)iX

for j < i,

Qe (i, j) = 1.

(3)
(4)

j=1

The parameter σ e ≥ 0 captures the job specificity of the accumulated skills. A lower
value of σ e implies a distribution of Qe (i, j) that first-order stochastically dominates the
distribution for a higher value of σ e . For example, a value of σ e = 1 induces a uniform
distribution over skill levels smaller than or equal to the current one, whereas a value of
σ e = 0 implies that current skills are fully retained. Our calibration below implies thatσ L > σ H , that is, less-educated workers experience greater skill loss upon separation
than do college-educated workers. Put differently, the skills of less-educated workers are
more job-specific, and hence less-educated workers’ investment in skills depends moreon expected job tenure.13
4.4

Wage Setting, Separations, and Employment Protection

In continuing matches, wage bargaining between worker and firm takes place every
period. Wages are set via Nash bargaining, such that the worker retains a share α of the
12This can be justified by assuming that effort is decided before turbulence is observed. This assumption
is introduced for computational convenience; allowing for effort to be set endogenously during turbulent
times would not qualitatively alter the results.
13
Differences in the transferability of skills may also imply a different ability to leverage job-to-job
transitions to increase wage growth over the life time, as proposed by Engbom (2022). Since our framework
abstracts from job-to-job transitions, the parameters σ e may be interpreted as also reflecting, in a reducedform way, the ability to obtain a higher salary by moving to a different job, which may vary across educationgroups.

21

resulting surplus. We denote the resulting wage by wpe (x, h, t), where e ∈ {L, H} andp ∈ {A, N }. Worker and firm bargain only over the current wage; the effort that theworker puts into accumulating skills cannot be contracted, so the individually-optimal
effort is taken as given in the negotiation. Since wages can be renegotiated every period,
the expected continuation value of the match is also taken as given when the current
wage is set.
If the surplus of the match turns negative, separation occurs and the firm must pay afiring cost that depends on the worker’s level of tenure and is proportional to the level of
output of the match in normal times:Φep (x, h, t) = f (t)ae (x)h.
The coefficient f (t) captures the strength of employment protection for workers with t
years of tenure. The revenue generated by the firing cost goes to the government andhelps finance unemployment benefits. The firing cost is zero in the model economy
calibrated to the United States,14 but a positive firing cost applies when we match themodel to German data.
The wage setting process in the model is a source of potential inefficiency. Nash bargaining does not provide the efficient level of incentives for investing in skills, because
the worker bears the effort cost of investing but captures only a fraction of the surplus
generated. We do not model the frictions that give rise to this inefficiency, but rather
impose a specific wage-setting process. The on-the-job training literature has establishedthat first-best contracts are difficult to achieve and that a variety of frictions can lead toinefficient investment. In our setting, an efficient contract would require a long-term commitment to a contingent contract by worker and firm and contractibility of the worker’s
effort. Hence, inefficiencies will arise if the worker’s effort is unobservable or unverifiable, or if worker and firm cannot commit not to renegotiate a contract in the future.
These frictions are likely to be relevant in our context: for example, workers are generally
unable to commit not to quit a job, and can therefore use the threat of quitting to force a
renegotiation.
14

Since the OECD index of employment protection was first compiled in 1985, the value for the UnitedStates has been consistently the lowest among OECD countries.

22

4.5

The Decision Problems of Workers and Firms

We now have all of the pieces in place to describe the decision problems faced by workers
and firms in the model economy.15 First, consider a worker with education e ∈ {H, L},
experience x, skill h, and tenure t, who is currently employed in a type-A job (accumulation of skills is possible). The only decision that this worker makes is how much effort z
to put into acquiring more skills. If the worker-firm match is not currently experiencing
a turbulence shock, the decision problem for this worker is described by the following
Bellman equation:nheVAe (x, h, t) = max wA(x, h, t) − ae (x)hz 2 + β (1 − θ(t))(1 − γ)Eh′ (VAe (x + 1, h′ , t + 1))
z


io
e
′
e
′
′
′
+ (1 − θ(t))γEh ,ϵ ṼA (x + 1, h , t + 1, ϵ) + θ(t)Eh (U (x + 1, h )) .
Here, U e (x + 1, h′ ) is the value function in case of unemployment tomorrow and ṼAe (x +1, h′ , t + 1, ϵ) is the value of being in an employment relationship tomorrow with turbulence shock ϵ, which can be equal to the utility of unemployment if ϵ is sufficiently low
to induce separation. If the relationship continues, the expectation over h′ is governedby effort z through the upgrade probability p(z) defined in Equation (2). If the worker
becomes unemployed, expectations over h′ depend on the skill-loss probabilities definedby Equations (3) and (4). The expectation over the size of the turbulence shock ϵ isgoverned by the distribution function G(ϵ).
Workers with a job that does not allow for skill accumulation have no decisions to make.
Their utilities are described by the Bellman equation:e
VNe (x, h, t) = wN
(x, h, t) + β

h(1 − θ(t))(1 − γ)VNe (x + 1, h, t + 1)i
+ (1 − θ(t))γEϵ ṼNe (x + 1, h, t + 1, ϵ) + θ(t)Eh′ U e (x + 1, h′ ) .

If the worker-firm match is currently experiencing a turbulence shock and separation
does not occur (that is, the match surplus is still positive), the value function for a worker
with a type-A job is:e
ṼAe (x, h, t, ϵ) = wA(x, h, t) − ae (x)hz ∗ (x, h, t)215

To simplify the exposition, we present the value functions of workers and firms under the assumptionthat separations only occur during turbulence shocks or churn shocks. While in principle the match surplus
could turn negative in normal times, this does not happen in the calibrated model.

23

h


+ β (1 − θ(t))(1 − γ)(1 − ϵ)Eh′ ṼNe (x + 1, h′ , t + 1, ϵ)′e+ (1 − θ(t))(1 − γ)ϵEh′ VN (x + 1, h , t + 1)i
+ (1 − θ(t))γEh′ ,ϵ′ ṼNe (x + 1, h′ , t + 1, ϵ′ ) + θ(t)Eh′ U e (x + 1, h′ ) .
The value function reflects the possibility of productivity returning to the regular level(with probability (1 − θ(t))(1 − γ)ϵ) and the possibility of being hit by an additional
turbulence shock (with probability (1 − θ(t))γ). The value function under turbulence for
type-N jobs is analogous but does not include the cost of effort and the possibility of askill upgrade.
The utility of unemployed workers is described by the Bellman equation:hihi
U e (x, h) = (1−λe ) ae (x)hb+βU e (x+1, h) +λe νAe VAe (x+1, h, 1)+(1−νAe )VNe (x+1, h, 1) .
Here, νAe is the equilibrium share of type-A vacancies that allow for the accumulationof skills. Note that unemployed workers find a new job right away with probability
λe . Given that our model is formulated at an annual frequency, requiring at least one
period of unemployment after a layoff would imply a counterfactually long duration ofunemployment. Unemployment compensation is given by a fraction b < 1 of regularmatch productivity ae (x)h.
We now turn to firms. The expected profit of a firm currently employing a worker witheducation e, experience x, skill h, and tenure t in a job of type p ∈ {A, N } is given by:
Jpe (x, h, t) = ae (x)h − wpe (x, h, t) + β(1 − θ(t))
h



i
(1 − γ)Eh′ Jpe (x + 1, h′ , t + 1) + γEh′ ,ϵ J˜pe (x + 1, h′ , t + 1, ϵ) .
This Bellman equation imposes that the expected profit after an exogenous separation iszero. In type-N vacancies, there is no possibility of skill upgrade, so the distribution of
future skill levels, h′ , has a unique mass point at h. By equating the vacancy posting costto the expected firm’s profits it is straightforward to derive a free entry condition thatpins down the mass of vacancies, v e .
Next, consider the value of a matched firm in a type-p vacancy currently experiencing aturbulence shock ϵ. If separation does not occur (that is, if the match surplus is positive),
the value of the firm is:24J˜pe (x, h, t, ϵ) = ae (x)hϵ − wpe (x, h, t) + β(1 − θ(t))
h(1 − γ)(1 − ϵ)Eh′ J˜pe (x + 1, h′ , t + 1, ϵ) +i
(1 − γ)ϵEh′ Jpe (x + 1, h′ , t + 1) + γEh′ ,ϵ′ J˜pe (x + 1, h′ , t + 1, ϵ′ ) .
Also in this case, in type-N vacancies the distribution of future skill levels, h′ , has aunique mass point at h.
If endogenous separation occurs (that is, if the match surplus is negative), the firm must
pay the firing cost, so that its value is equal toJ˜pe (x, h, t, ϵ) = −Φep (x, h, t).
After a worker retires, the value of the firm and the utility of the worker are both zeroirrespective of the skill level. As a result, the optimal choice of effort in the period
preceding retirement is equal to zero. We also assume that the government finances
unemployment benefits and spends revenues from the firing cost via lump-sum taxes
and transfers that are identical for all workers. Given that utility is linear in consumption,these taxes and transfers do not affect any decisions. They therefore do not appear in
the value functions, which should then be interpreted as utility net of the consumption
derived from lump-sum transfers and taxes.

5

Model Calibration: Matching US Data for 1980 and 2010

In this section, we calibrate the model to match salient features of the US labor market in
the 1980s and the 2010s. This calibrated model allows us to quantify the extent to which
the rise of economic turbulence can account for changes in education wage premia. We
then explore how labor protection legislation can help explain the different trends in the
US and German economies following rising turbulence starting in the 1980s.
Our calibration procedure is comprised of two steps. In the first step, we directly assign
values to a subset of parameters that are common in the literature. In the second step, wecalibrate the remaining parameters such that the steady states of the model match a set oftarget moments for the US economy in 1980 and 2010. In this calibration, the parametersthat characterize our turbulence mechanism as well as parameters that underlie otherexplanations for changes in the college wage premium (such as SBTC) are allowed tovary over time.
25

Parameter

Interpretation

Value

Source/Target

βDiscount rate

0.95

Yearly interest rate 5.25%

λe

Job finding rate

0.8

Av. duration unempl. 3 months

αBargaining weight

0.5

Gertler and Trigari (2009)µElast. of matches to vacancies

0.5

Gertler and Trigari (2009)b

Non-market productivity

0.2

Half receive replacement rate 40%ϵ̄Prod. loss in turbulence

0.6

Minimum 40% loss

Table 3: Directly assigned model parameters
Step 1: Assigned parameters We set the model period to be one year. The discountfactor is β = 0.95, which implies a yearly interest rate of 5.3 percent. The worker’s
bargaining weight, α, and the elasticity of matches to the number of vacancies, µ, are set
to 0.5, consistent with Gertler and Trigari (2009). We set the job finding rate to λe = 0.8,
implying an average job search duration of three months. Given this value of the job
finding rate, we can back out the implied cost of posting vacancies, q e . The coefficient of
the flow value of unemployment is set to b = 0.2, which reproduces an average ratio of
non-market to market production of 20 percent, consistent with an average replacement
ratio of 40 percent for half of the currently unemployed labor force. The distributionof turbulence shocks G(ϵ) is given by a uniform distribution on the interval [0, ϵ̄]. We
set the value of ϵ̄ to 0.6, implying a minimum productivity loss of 40 percent of regular
productivity during turbulent times. This choice can be interpreted as a normalization,
since the model can rationalize the empirical share of workers with long-term tenure withmultiple combinations of frequencies of turbulence shocks, γ, and minimum productivity
losses, ϵ̄. In Appendix E.1 we explore robustness to alternative values of ϵ̄ and show that
our main results do not depend on the particular choice of this parameter. In the case ofa repeated turbulence shock, the new ϵ is once again uniformly distributed but on theinterval [0, ϵ̂], where ϵ̂ is the current turbulence shock. Table 3 summarizes the assigned
parameters.

Step 2: Matching the 1980 and 2010 US steady states Next, we jointly calibrate theremaining parameters to match a set of target moments that characterize the US economy
in the early 1980s and in the years around 2010. The key moments of interest are theoverall college wage premium, lifetime wage growth, and the returns to long-term tenure
26

for college-educated and less-educated workers, as well as the share of workers withlong-term tenure.
We impose two normalizations to help calibrate the model parameters. A first normalization concerns the share of jobs that allow investment in skills. Since returns to experiencecan be explained by different combinations of fractions of type-A jobs and exogenous
returns to experience, we impose that in 1980 all the vacancies for L and H workers areeof type A, i.e. νA,80= 1 (meaning that the parameter ce1 defining the upper bound forthe cost of creating a type-A job is sufficiently low). What matters for our quantitative
findings is the change in the share of type-A jobs over time rather than the initial level ofsuch jobs.
A second normalization concerns workers’ exogenous lifetime productivity-experience
profile, ae (x). In this analysis, we impose that the exogenous productivity term for collegeeducated workers, aH (x), is constant in experience, meaning that the lifetime wage
growth of college graduates is entirely accounted for by the endogenous accumulation ofskills on the job. The constant productivity level for college-educated workers in the 1980s
calibration is denoted by AH
80 . Given the parameters that control the accumulation andloss of skills, we can then calibrate the productivity process for less-educated workers,aL (x), to match the profile of the college premium across different age groups. We imposethat the exogenous productivity term grows with experience at a constant rate, denotedLby g80:
L x−1
aL80 (x) = AL80 (1 + g80) ,where we choose units so that AL80 = 1.
To calibrate the time-invariant parameters and the time-varying parameters in the initialsteady state, we match a set of target moments derived from the PSID for the years
1981–1986.16 Similarly, to calibrate the time-varying parameters in the late steady state,
we match a set of target moments derived from the PSID for the years 2009–2013. Though
the parameters do interact, there is a specific target moment for most parameters thatplays an outsized role in setting the parameter value.
We start by discussing the parameters and target moments relevant for the initial steadystate. The distribution of skills for workers entering the labor market, F (h), is assumed to
be a Pareto with shape parameter η. The value for η is set to match the standard deviationof log hourly wages for high-school graduates at age 25, which was 0.364 in 1981–1986.
16

We use multiple years for the calibration to reduce measurement error.

27

Parameter

Interpretation

Value

Related Targets

Panel A: Time-invariant parametersσL

L skill specificity

0.309

L tenure premiumσH

H skill specificity

0.053

H tenure premiumψProb. skill upgrade

0.498

Experience and college premiaη

Pareto initial skills

4.574

L std. dev. log wage at age 25

Panel B: Time-varying parameters (1980)
Lg80

L productivity growth

0.0004

Experience and college premia

AH
80

Skill bias

1.286

College wage premium

γ80

Prob. turbulence shock

0.020

Long-term tenureθ80 (1)

Prob. separation shock

0.208

Short-term tenure

Panel C: Time-varying parameters (2010)∆g10

Change product. growth

0.007

Experience and college premia

L
νA,10

Share of type-A jobs

0.513

Experience and college premia

H
νA,10

Share of type-A jobs

0.950

Experience and college premia

AH
10

Skill bias

1.495

Experience and college premia

γ10Prob. turbulence shock

0.053

Long-term tenureθ10 (1)

Prob. separation shock

0.175

Short-term tenure

Table 4: Calibrated parameter values for the 1980 and 2010 steady states
The parameters that control the loss of skills upon separation, σ L and σ H , are set tomatch the wage premium enjoyed by long-tenure workers. Specifically, we target thewage premium of workers aged 45–54 with job tenures of between 20 and 30 years overworkers in the same age range with tenures of between 0 and 10 years. The calibrated
values imply a substantial loss of skills for workers of type L (σ L is calibrated to be 0.309),
while the loss of skills for workers of type H is considerably smaller (σ H is calibrated tobe 0.053). These calibrated values imply that less-educated workers acquire skills thatare more job-specific compared to college graduates. Appendix Figure B.1 displays the
distribution functions over skill levels hi after job loss. A less-educated worker withcurrent skill h = h10 (i.e., the 10th step of the ladder) loses an average of 6.1 percent of
their skills upon separation, compared to only 0.8 percent for a college-educated worker.

28

The parameters controlling the accumulation of skills on the job, ψ, and the exogenousL
productivity growth with age for L-workers, g80, are calibrated to target college wage
premia for the age groups 25–34, 35–44, and 45–54, and the experience premia of Hworkers aged 35–44 and 45–54 compared to workers aged 25–34. This procedure targets
the difference in the steepness of the age-earning profile between college-educated andless-educated workers and, hence, the increase in the college premium over the life cycle.
The parameters controlling the frequency of turbulence shocks and exogenous separations
are determined by the share of workers with short-term and long-term tenure with theircurrent employer. Specifically, the probability of a turbulence shock in the early period,
γ80 , is set to match the share of workers of ages 45–54 with current job tenure between
20 and 30 years, which is 41.4 percent. As for exogenous separations, we impose aprocess that declines to zero at a constant rate over the first 10 years of a job relationship.
This process is parameterized by the exogenous separation probability in the first year
θ80 (1). We pick the value of θ80 (1) to match the share of short-tenure jobs (less than
two years of tenure) among workers aged 35–44, which is 15.4 percent in the early
period. Introducing this additional source of separations will allow us to account for thesimultaneous decline in jobs with long-term tenure and the stable fraction of jobs withshort tenure. The calibrated process for exogenous separations as a function of tenure in
the 1980 calibration is depicted by the solid line of Appendix Figure B.2.17
The calibrated time-invariant parameters and time-varying parameters for the 1980 US
steady state are listed in Panels A and B of Table 4, respectively, and Panel A of Table 5compares the fit for the target moments between model and data. In both the modeland the data, we define the wage premium between any two groups of workers as the
log-difference between the average wage of workers in those groups. The calibrated
model successfully replicates the education and experience premia, tenure premia, andthe tenure distribution observed in the data.
To pin down the time-varying parameters that drive the wage structure in the late steadystate, we target a set of moments from the years 2009–2013. Our primary objective is todetermine the sources of the increase in the college wage premium from the 1980s to the17

Our choice to target the share of workers with long-term tenure in the age group 45–54 is motivatedby the fact that shares in the older age group (55–64) are likely to be affected by endogenous retirement
choices, from which we abstract in our setting. Similarly, our choice to target the share of workers withshort-term tenure in the age group 35–44 is motivated by the fact that short-term tenure is more common
in this age group compared to older groups, and, contrary to the younger age group (25–35), short-term
tenure is better measured and less likely to reflect selection into the labor force or individual preferences
for short-term employment.

29

Moment

Data

Model

L tenure premium

0.238

0.228

H tenure premium

0.126

0.129

Long tenure share

0.414

0.415

Short tenure share

0.154

0.156

L standard deviation log wage at 25

0.364

0.369

College premium 25–34

0.244

0.233

College premium 35–44

0.282

0.302

College premium 45–54

0.367

0.356

H experience premium 35–44

0.229

0.210

H experience premium 45–54

0.383

0.395

Change long tenure share-0.081-0.081

Change short tenure share

0.009

0.009

H experience premium, 35–44

0.307

0.273

H experience premium, 45–54

0.506

0.523

College premium 25–34

0.408

0.409

College premium 35–44

0.541

0.537

College premium 45–54

0.645

0.647

Panel A: Model fit (1980)

Panel B: Model fit (2010)

Table 5: Model fit for 1980 and 2010 steady states
2010s. The calibration procedure allows for multiple sources of changing wage premia,
including changes in turbulence and changes in the overall skill bias of technology. The
calibration procedure helps to identify these different channels by matching observedchanges in returns to experience, returns to college, and the tenure distribution.
In the calibration, we treat the share of type-A jobs for workers of education e ∈ H, L,e
νA,10, as parameters. We later back out the values of the structural parameters ce0 and ce1 ,eewhich generate the calibrated shares νA,80
and νA,10
following Equation (1), and use theseparameters to generate counterfactuals and decompositions.

30

We allow for two sources of change in the wage structure that are unrelated to theturbulence mechanism. First, we allow for an overall change in returns to experience,e
g10, which applies equally to college-educated and less-educated workers. This shift isdenoted by ∆g10 , and serves to capture changes in the age-wage profile that are not due
to investment in skills on the job. Second, we allow for a shift in the overall skill bias AH
10 ,i.e., the overall productivity of college-educated versus less-educated workers, which
captures factors such as skill-biased technical change. Including these elements allows us
to match the change in the college wage premium exactly and then decompose it into
contributions from different channels.
The skill bias parameter, AH
10 , the change in returns to experience, ∆g10 , and the job
ecomposition parameters, νA,10 , are calibrated by matching the college wage premia for
age groups 25–34, 35–44, and 45–54, as well as the experience premia of H-workers aged
35–44 and 45–54 (again compared to workers aged 25–34). The calibration implies anincrease in overall returns to experience (∆g10 > 0), a substantial decline in the share of
type-A jobs for less-educated workers, and a minor decline in the share of type-A jobs
for college-educated workers. These findings reflect an increase in the steepness of theage-earnings profile for college-educated workers and a rise in the college wage premium
among older workers.
To estimate the frequency of the turbulence shocks in the late period, γ10 , we target thechange in the share of workers aged 45–54 with current tenures of between 20 and 30
years from the 1980s to the 2010s. This share declines by 8.07 percentage points, implying
a 2.40 percentage point increase of the estimated value for γ.18 Similarly, to pin down thefrequency of exogenous separations for short-duration jobs, θ10 (t), we target the change
in the share of workers aged 35–44 with current tenure below two years from the 1980s to
the 2010s. The calibrated value of θ(1) declines by 3.43 percentage points, consistent withobservations in the literature (e.g., Hyatt and Spletzer 2016, Molloy, Smith, and Wozniak
2020) documenting a recent decline in the prevalence of short-duration jobs. Appendix
Figure B.2 illustrates how the estimated process for exogenous separations has changed
between the 1980 and 2010 steady states.
Parameter values for the 2010 steady state are summarized in Panel C of Table 4, and Panel18

A potential concern for this choice of target is that the share of workers with long-term tenure might
have been negatively affected by the Great Recession. However, we do not observe that the share ofhigh-tenure workers was significantly lower in the years of our calibration (2009–2013) compared to theyears right before the Great Recession. In fact, the share of workers with long-term tenure in the two wavesof the PSID before the Great Recession (2005–2007) is 0.314, slightly lower than the corresponding share in
the years of our calibration (0.333).

31

B of Table 5 displays the fit for targeted moments. The model successfully reproduces theobserved changes in the tenure distribution, returns to experience, and the college wage
premium at different ages.
In Appendix Figure B.3 we show that, despite the parsimony in our choice of calibration
targets, our modelling of separations via a combination of exogenous splits and endogenous decisions closely reproduces the empirical tenure distribution for all the age groups
and levels of tenure in both steady states.
Further details on the calibration procedure are provided in Appendix C.

6

Findings from the Quantitative Model

We now examine the extent to which the model can account for variation in the college
wage premium over time and across countries. First, we examine the sources of theincrease in the college wage premium in the United States, and then ask whether strict
employment protection can account for the relatively stable college wage premium inGermany.
6.1

The Rise in the College Wage Premium in the United States

The model calibration for the United States fully accounts for the increase in the college wage premium between 1980 and 2010. In this section, we examine the relative
importance of the turbulence mechanism in accounting for this change.
Figure 4 provides a snapshot of the mechanism through which labor market turbulence
affects the college wage premium in the model. The figure displays the probability that aworker with one year of tenure and at the bottom of the skill ladder (t = 1, h = h1 ) will
move up to the next step of the ladder, based on age and education.19 The probability of
upgrading skills declines for older workers, which reflects the shorter investment horizon
for workers who are closer to retirement.
In the 1980 steady state, the probability of accumulating skills is only slightly higher forcollege-educated workers (solid line) than for less-educated workers (dashed line). In
contrast, less-educated workers are much less likely to upgrade their skills in the 2010
steady state. This is due to the higher level of turbulence shocks: workers and firms areboth aware that matches are less likely to be long-lived, which reduces the incentive to
19

The trends are qualitatively similar for workers with higher tenure and skill levels.

32

0.12

Probability of Skill upgrade

0.1

0.08

0.06

0.04

0.02

0
5

10

15

20

25

30

35

40

Experience

Non-College, 1980

College, 1980

Non-College, 2010

College, 2010

Figure 4: Probability of skill upgrading by years of experience for L (dotted lines) andH (solid lines) workers with tenure t = 1 and skill h = h1 , US calibration for 1980 (plain
lines) and 2010 (marked lines).
make match-specific investments. For college-educated workers, investment in skills
does not decrease. Because these workers primarily accumulate transferable skills, theirinvestment depends less on the level of turbulence and, therefore, on the longevity ofmatches. In fact, the likelihood that they upgrade their skills increases slightly due to thesteeper productivity profile implied by ∆g10 , which induces higher incentives to exert
effort in skill accumulation.
The decline in skill upgrading for less-educated workers from 1980 to 2010 reflects lower
investment from both sides: firms create fewer vacancies that allow for the accumulationof skills, while workers in jobs that do allow for skill accumulation invest less in onthe-job skill acquisition. In the calibrated model, the firm investment channel is more
important: the lower availability of accumulation-type jobs accounts for over 90 percentof the wider gap in skill upgrading among workers with no experience (x = 1) andminimum skills (h = h1 ).
While the increase in the frequency of turbulence shocks lowers the availability ofaccumulation-type jobs for all workers, the decline in type-A jobs is much smaller forcollege-educated than for less-educated workers. There are two reasons behind thisfinding. First, the decline in the profitability of type-A jobs relative to type-N jobs issmaller for college-educated compared to less-educated workers since, given their higher
33

1
0.9

Cumulative probability at age 64

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1

1.5

2

2.5

3

3.5

4

Skill level

Non-College, 1980

Non-College, 2010

Non-College, 2010, Fixed job comp.

College, 1980

College, 2010

Figure 5: Distribution of the skills of less-educated (dashed lines) and college-educated(solid lines) workers at age 64, US calibration for 1980 (plain lines) and 2010 (marked
lines). The line with diamond markers denote the case in which only turbulence shocks
and individual effort are changed to the 2010 values, while the composition of vacancies
is kept at the 1980 value.
transferability of skills, H-workers’ incentives to invest in skills are less affected byhigher turbulence. Second, the supply of type-A jobs for college-educated workers is lesssensitive to relative profitability compared to less-educated workers. In our calibration,
the term c̃H
1 , that controls the sensitivity of the supply of type-A jobs to the relative
profitability of the two types of vacancies (Equation 1), is estimated to be 0.61, while theestimate for the corresponding term for less-educated workers, c̃L1 , is 3.51.
The decline in the investment in relationship-specific capital among less-educated workers results in a decline in their average human capital, and hence in a rise in the measured
college wage premium. The solid lines of Figure 5 show that the end-of-career (age 64)
skill distribution of college graduates stays roughly the same between the two steadystates. For these workers, the skill loss due to higher turbulence is moderate and fullycompensated by an increase in on-the-job investment in skills. By contrast, the distribution of skills for less-educated workers (dashed lines) shifts downward. A large partof this shift is due to the endogenous adjustment of job creation towards more type-N
jobs that do not allow accumulation of skills. However, even when the job compositionis held constant at the 1980 values (diamond markers), the increase in turbulence and34Setting

College Premium

1980

0.32

2010: turbulence and skill-biased technical change

0.59

2010: only turbulence (changing job composition)

0.43

2010: only turbulence (fixed job composition)

0.34

Table 6: The college wage premium in the model (log difference of average wages), 1980
and 2010 calibrations, full model versus models with only the turbulence mechanism
the resulting surge in separations result in a substantial decline in accumulated humancapital.
Table 6 breaks down how these changes affect the college wage premium in the model
economy. The first two rows show the college premia in the 1980 and 2010 calibrations,which closely match the data since college wage premia by age were included as target
moments. The overall college premium increases by 27 percentage points, nearly doubling between the two steady states. This is partially due to the mechanism of on-the-job
investment in skills and partially to the rise in the overall skill bias parameter. In order
to separate those channels, the third row of Table 6 shows the college premium thatthe model generates in 2010 if we only feed in the larger turbulence shocks. For thiscounterfactual, we focus entirely on the turbulence channel by leaving wages and otherparameters (including overall skill bias) unchanged at the 1980 level, but changing thefrequency of turbulence shocks and imposing the policy functions that affect investment
in skills by firms and workers to reflect their values in the 2010 calibration. We see that
this mechanism alone leads to a 11 percentage point rise in the college wage premium,
which amounts to 41 percent of the overall increase. Hence, in the quantitative model,
the mechanism of skill accumulation accounts for a substantial fraction of the rise in thecollege premium. The remainder of this increase is primarily due to the rise in the skill
bias parameter AH , which captures channels already documented by the literature, suchas skill-biased technical change.
Higher turbulence shocks increase the college premium in part because firms create
fewer jobs for less-educated workers that allow for the accumulation of skills, and inpart because less-educated workers who do have such jobs have fewer incentives toaccumulate skills and are fired more frequently. The last row of Table 6 shows the change
in the college premium if we also fix the composition of job types at the 1980 level,
35and hence isolate the effect of worker investment in skills. The increase in the college
premium is still positive but much smaller in magnitude (two percentage points, ascompared to 11 percentage points due to turbulence). Hence, the shift towards jobs that
do not allow for accumulation of skills accounts for most of the effect of turbulence on
the college premium.
6.2

The College Wage Premium Across Cohorts During the Transition

So far, we have focused on a comparison of the college wage premium across the 1980 and2010 steady states of our model. Given its life-cycle structure, the model also generates
rich transitional dynamics. While we do not take a stand on the exact timing of the change
in economic turbulence, a robust implication of the theory is that there are pronounced
cohort effects during the transition. When economic turbulence rises, the workers who are
initially most affected are young workers who have just entered the labor market. These
workers have not yet accumulated any relationship-specific skills, and the composition ofjobs available to them (in terms of the possibility of accumulating skills) will immediatelyreflect the change in turbulence. In contrast, older workers continue to benefit from skills
they have already accumulated, as well as from the fact that many of them have jobs
created in the past that allow for the accumulation of skills.
To illustrate the transitional dynamics of the model, we start the economy in the steadystate corresponding to the 1980 calibration. Then, in 1981, the degree of turbulence γ andthe job composition for vacancies (νAe ) changes unexpectedly and permanently to theirvalues in the 2010 calibration. We then compute the transition path of the economy assubsequent cohorts enter the labor market.20
Figure 6 shows how the college wage premium evolves differentially for younger andolder workers during the transition. The graphs display the college premium relative to1980 separately for younger (25 to 39) and older (40 to 54) workers. Since we impose a
one-time change in the economic environment, all transitional dynamics are due to theendogenous progression of state variables. The figure shows that the college premium
among younger workers rises substantially by 1990, whereas there is little change for theolder workers. This reflects that a substantial fraction of older workers in 1990 are still in
20
In computing the transitional dynamics, we keep the parameters constant at their 1980 calibrated
values, while all endogenous decisions (including investment on the worker’s side) are determined inequilibrium. This allows us to isolate the effect of increased turbulence on the college premium acrosscohorts during the transition without the need to take a stance on the timing of the changes in the otherfactors (e.g., the skill-biased technology component).

36

1980

1990

2

2

1.5

1.5

1

1

0.5

0.5

0

0
25-39

40-54

25-39

2000

40-54

2010

2

2

1.5

1.5

1

1

0.5

0.5

0

0
25-39

40-54

25-39

40-54

Figure 6: The college premium (log difference of average wages) by age over time after a
one-time increase in turbulence, relative to 1980 (model)
jobs that were created before the shock took place in 1981. The next panels show that by
2000, the impact on younger and older workers is about even, and by 2010 older workers
are more affected than younger ones. The larger effect on older workers in 2010 reflects
the importance that the model places on the life-cycle accumulation of skills, meaningthat the long-run impact on wages is larger for older workers at the end of their life cycles
than for younger workers.
Figure 7 presents the same statistics in the data. The changes in the college premium
are quantitatively larger because the dynamic model simulation only focuses on the
turbulence channel. Qualitatively, however, the pattern in the data is exactly the sameas in the model: in the first decade after 1980, the college premium rises primarily forthe young, in the second decade the impact evens out, and in the long run it is the older
workers who are more affected.21 This empirical pattern is suggestive of a mechanismthat affects successive cohorts when they first enter the labor market. Our model ofon-the-job investment in skills provides such a mechanism. It is encouraging that the key
prediction of cohort effects in the rise of the college wage premium is supported by the21

The fact that the rise in the skill premium initially affected younger workers was first pointed out byCard and Lemieux (2001).

37

1980

1990

2

2

1.5

1.5

1

1

0.5

0.5

0

0
25-39

40-54

25-39

2000

40-54

2010

2

2

1.5

1.5

1

1

0.5

0.5

0

0
25-39

40-54

25-39

40-54

Figure 7: The college premium (log difference of average wages) by age over time, relative
to 1980 (US data)
data.
6.3

Labor Protection and the College Wage Premium in Germany

We now examine the extent to which labor protection legislation can help explain themuch lower rise in the college premium in Germany compared to the United States from1980 to 2010. We view the US and German economies as sharing the same overall technological environment, and hence both economies are subject to skill-biased technologicalchange and increased turbulence. However, we propose that the impact of these changes
was mitigated in Germany by stronger employment protection.
To isolate the role of employment protection, we compute the college wage premiumin the “Germany” variant of the 1980 and 2010 steady states. These are identical to the
US calibration except for the firing cost that firms have to pay when laying off workers(which is zero in the US calibration). Given that there was little change in employment
protection for regular workers in Germany over this period, we impose the same firing
cost in 1980 and in 2010.22
22

We note that the “Hartz” labor market reforms of the Schroeder government in the early 2000s reduced38College Premium
Setting

No Firing Cost

Firing Cost

“United States”“Germany”

1980

0.32

0.32

2010: turbulence and skill-biased tech. change

0.59

0.47

2010: only turbulence

0.43

0.33

Table 7: The rise in the college wage premium (log difference of average wages) with andwithout employment protection
Recall from Section 4.4 that the firing cost takes the form:Φep (x, h, t) = f (t)ae (x)h.
To capture the fact that workers with higher tenure enjoy more employment protection,
we stipulate that the term f (t) increases linearly with tenure over the first ten years of aworker-firm match, and is constant afterwards. Hence, the firing cost is solely defined by
the initial value of f (1). Actual German employment protection laws do not take the formof an explicit firing cost, but rather consist of detailed rules on conditions under whicha layoff is permissible, which include protections for older and higher-tenure workers.
We pin down the extent of the firing cost for the “Germany” calibration by focusing on
the effects of employment protection. Specifically, we target the share of workers aged
45–54 with current tenure of 20 to 30 years in Germany in the early steady state.23 This
procedure results in f DE (1) = 0.40, implying that the firing cost is equal to 40 percentof the regular output in the first year of a worker-firm relationship. The left panel ofAppendix Figure B.4 shows how f DE (1) is identified by the share of long-tenure workers,
while the right panel depicts the magnitude of the estimated firing cost as a function oftenure.
Table 7 shows how labor protection affects the change in the college wage premium overprotection for temporary contracts (while leaving protections for high-tenure, regular-contract workers
intact), and this led to considerable changes in the labor market for less experienced workers. Arguably,
the rise in the college premium in Germany since the mid-2000s may be related to these reforms. Given
our focus on experienced, high-tenure workers, we believe that positing continuing high employment
protection is the right starting point for our analysis, but accounting for the effects of the Hartz reforms in
our framework would be an interesting extension.
23
We compute the share of high-tenure workers using the years 1984–1986 in the SOEP.

39

time in the model economy.24 The left column reproduces the findings from Table 6 forthe model without employment protection (“United States”). The right column showsthe effect of labor protection on the college wage premium in the “Germany” calibration
with labor protection for 1980 and 2010. The effect of labor protection on the 1980 steadystate is almost nil. This reflects the fact that low labor market turbulence reduces theimportance of the firing cost. In the 2010 steady state (second row), the college wage
premium in the “Germany” model increases by 15 percentage points, far less than the 27
percentage point increase observed in the “United States” model. Employment protection
therefore reduces the increase in the college premium by close to 45 percent and canaccount for much of the divergent trends in the college wage premium between the
United States and Germany displayed in Figure 1. The last row of the table shows theimpact of employment protection in the model with turbulence shocks but without
additional skill-biased technological change. Here we see that employment protection
prevents almost the entire 11 percentage point rise in the college wage premium that
occurs without protection. Hence, while employment protection does not offset generalskill-biased technological change, it does insulate the economy from the bulk of theeffects of increasing turbulence.
Table 8 illustrates the economics behind these findings. The top row displays the relative
profitability of type-A over type-N vacancies for less-educated workers in the US calibration across the two steady states. The increase in turbulence induces a decline in therelative profitability of type-A vacancies, prompting a shift towards type-N vacancies
and depressing the accumulation of skills for less-educated workers, which leads toan increase in the college wage premium. By contrast, in the “Germany” model with
employment protection (second row), the relative profitability of type-A vacancies forless-educated workers actually increases after the rise in turbulence. Employment protection induces firms to retain workers even when relatively large turbulence shocks
hit, regardless of the type of job. When the frequency of turbulence shocks increases,
the profitability of type-N jobs sees a greater reduction because the lower value of a
type-N match makes retaining a worker in times of turbulence relatively more costly. As
a result, the fraction of type-A vacancies does not decline as turbulence increases and, inequilibrium, the probability of a skills upgrade increases slightly (Figure 8, left panel).
The same qualitative effect is observed for college-educated workers (third and fourth24

In computing the “Germany” variant of the model, we keep the sensitivity of the supply of type-A
jobs to relative profitability, c̃e1 , at the calibrated baseline, and adjust the constant of Equation (1), c̃e0 , to beecompatible with νA= 1 in the 1980 steady state.

40

1980

2010

Less-educated workers“United States”

1.668

1.529

“Germany”

1.767

1.844

College-educated workers“United States”

1.713

1.631

“Germany”

1.819

1.858

Table 8: Relative profitability of type-A compared to type-N vacancies across the twosteady states in the “United States” economy (no firing cost) and in the “Germany”
economy (with firing cost)rows of Table 8). However, in this case, the impact of turbulence on relative profitability issmaller (both in absolute and relative terms), since the higher transferability of their skills
implies that their incentives to invest in them are not dampened by the surge in turbulence.
Moreover, the lower sensitivity of type-A vacancies to relative profitability implies thatcollege-educated workers’ opportunities to accumulate skills are not significantly affectedby turbulence regardless of labor protection. The right panel of Figure 8 shows theprobability of skills upgrade for college-educated workers, illustrating that the effect of
the firing cost on their skill accumulation is negligible.
A testable implication of our framework is that the relationship between experience andthe college premium should evolve differently as a result of turbulence in economies
with and without employment protection. To the extent that turbulence decreases the
incentives to invest in job-specific skills, higher turbulence should result in a steeper
experience-college premium profile. Panel A of Table 9 illustrates this point by displaying
the college premium by age group in the “United States” economy (without employment
protection) in the 1980 and 2010 steady states. Since the college premium by age groupis directly targeted in the calibration, the full model reproduces the data closely in both
steady states. Moreover, the counterfactual that isolates the effect of turbulence on thecollege premium (displayed in the rightmost column) fully accounts for the observed
steepening of the experience-college premium profile. Both in the full model and thecounterfactual, the college premium for the 45-54 age group is roughly 14 percentage
points higher than for the 25-34 age group. By contrast, as illustrated in Panel B of Table
9, the impact of turbulence on the experience-college premium profile is muted in the
41

1980
Data

2010

Model

Data

Model
Full

Turb.

Panel A: “United States”
Age 25-34

0.244

0.234

0.408

0.409

0.236

Age 35-44

0.282

0.302

0.541

0.537

0.370

Age 45-54

0.367

0.356

0.645

0.647

0.489

Panel B: “Germany”
Age 25-34

0.157

0.226

0.291

0.370

0.232

Age 35-44

0.308

0.297

0.281

0.439

0.305

Age 45-54

0.412

0.347

0.365

0.491

0.367

Table 9: College premium by age group in the “United States” (Panel A) and the “Germany” (Panel B) economies in 1980 and 2010.
“Germany” economy with employment protection. In the SOEP data, the relationshipbetween age and the college premium does not become steeper in the 2010 steady statecompared to the 1980 one. In fact, the college premium increases for the 25-34 age group,and slightly decreases for the 35-44 and 45-54 age groups. Although these moments are
not directly targeted in our calibration, the model with employment protection delivers
an experience-college premium profile that is not significantly steeper in the 2010 steadystate compared to the 1980 steady state, both in the full model (second to last column) andin the counterfactual that isolates the effect of increased turbulence (rightmost column).25
A potential concern is that employment protection in periods of frequent turbulence
shocks could induce a disproportionate negative effect on the job finding rate of lesseducated compared to college-educated workers, potentially worsening inequality acrosseducation groups. Since our model includes a margin of endogenous vacancy creation,
we can confront this concern directly. While we find that employment protection has
a negative impact on vacancy creation, which is negatively affected by turbulence, wefind that the decrease in the job finding rate is not larger for less-educated compared to25

In Appendix E.2 we report results of an alternative calibration in which we directly target theexperience-college premium profile in the German data and the remove the firing cost to simulate theUnited States economy, and we find the same qualitative patterns.

42Non-College

0.12

0.1

Probability of Skill upgrade

0.1

Probability of Skill upgradeCollege

0.12

0.08

0.06

0.04

0.08

0.06

0.04

0.02

0.02

0

0
0

5

10

15

20

25

30

35

0

40

5

10

15

20

25

30

35

40

Experience

Experience

U.S., 1980

U.S., 2010

Germany, 2010

Figure 8: Probability of skill upgrading by years of experience for L workers (left panel)and H workers (right panel) with tenure t = 1 and skill h = h1 , “United States” calibrationfor 1980 (plain line) and 2010 (dotted line) and “Germany” calibration for 2010 (markedline).
college-educated workers. The job finding rate (which is set to 0.8 in the “United States”
economy) is found to be 0.776 for both education groups in the 1980 “Germany” steadystate, and 0.745 and 0.739 for less-educated and college-educated workers, respectively,in the 2010 “Germany” steady state.
6.4

The Impact of Labor Protection on Welfare

Table 10 describes how imposing employment protection affects output and average
welfare (in consumption units) in the economy. Compared to the 1980 benchmark, turbulence shocks on their own lower output and welfare because they lead to more frequent
separations and hence a greater destruction of job-specific capital (third row). Employment protection lowers these losses both in terms of output and welfare (fourth row).
This result arises because a portion of the separations that occur in response to turbulence
shocks in our model are inefficient. Excessive separations generate an expectation of ashort work relationship and hence dampen workers’ and firms’ incentives to invest in
job-specific skills. Employment protection can prevent some of these separations, limit
the destruction of skills, and produce incentives for greater accumulation of job-specificskills. However, the welfare effects of employment protection are not unambiguous,
since firing costs can increase the unemployment rate by reducing firms’ incentives tocreate jobs.
43Setting

OutputWelfare1

11980 model, empl. protection

0.996

0.994

2010 model with turbulence

0.891

0.877

2010 model with turbulence, empl. protection

0.919

0.909

2010 model with turb., empl. protection (only job creation)

0.852

0.857

2010 model with turb., empl. protection (only investment)

0.933

0.918

1980 model

Table 10: Output and welfare relative to 1980 in the model with turbulence and with
employment protection
In order to explore the sources of welfare gains brought about by employment protection,
we decompose the welfare gains into two components. The last two rows of Table 10show the results of this decomposition. In the second to last row we display output
and welfare when the firing cost is constrained to only affect the job creation margin,
while firms’ investment in type-A jobs are kept at the value in the 2010 United States
steady state. The lower job creation reduces both welfare and output compared to theunconstrained case. In the last row we display welfare and output when the firing cost is
constrained to only affect the investment in type-A jobs, while the job finding rate is kept
at its baseline value. In this case, both output and welfare are higher compared to theunconstrained case.
It is important to keep in mind that our model only provides for a partial welfare analysis
and does not capture all tradeoffs that are relevant to the introduction of employment
protection measures. First, welfare results are sensitive to assumptions on wage bargaining. The extent to which wage bargaining fails to set efficient incentives for investingin relationship-specific skills is difficult to quantify. Second, our analysis abstracts fromother dimensions that might be relevant for assessing the effect of employment protection
on welfare. For example, Bratti, Conti, and Sulis (2021) argue that excessive employment
protection can also push more workers into temporary contracts and thereby reduce
training. For these reasons, this analysis should be interpreted as identifying a channel
through which employment protection may have beneficial effects, which in a full analysis would have to be weighed against other channels through which excessive protection
may reduce welfare.

44

7Conclusion

There are major differences in employment protection across countries. In Europe,widespread firing restrictions and insider-outsider labor markets protect senior workers
at the expense of their junior and temporary counterparts. Excessive employment protection can lead to well-known negative repercussions, including the high levels of youth
unemployment observed in a number of European countries.
In this paper, we consider a different channel through which certain forms of employment
protection can have potentially beneficial effects. By creating the expectation of longlasting employment relationships, employment protection can facilitate investments byworkers and firms in relationship-specific capital. Employment protection is especiallyvaluable when frequent turbulence shocks threaten to generate inefficient separations
and the destruction of such capital.
We argue that the impact of employment protection on relationship-specific investments
can help explain divergent trends in the college wage premium between countries withtight employment protection such as Germany and countries with low levels of protection such as the United States. When turbulence shocks that temporarily lower the
productivity of worker-firm matches become more frequent, the expected duration of
employment relationships will fall in countries with little employment protection, resulting in less investment in relationship-specific capital. These effects are more pronounced
for less-educated workers, whose skills are more job-specific than those of more educated workers. For this reason, a rise in turbulence raises the college wage premiumin countries such as the United States, but has little impact in countries with greater
employment protection such as Germany. We argue that the employment-protection
mechanism can account for close to half of the divergent trends in the college wage
premium between the United States and Germany. The mechanism is also consistent
with observed trends in job tenure and returns to tenure for more- and less-educatedworkers, as well as the observation that less-educated workers in the United States haveexperienced little growth in real wages in recent decades.
Our work could be extended in different directions. In our analysis, we focus on matchspecific investments that improve the productivity of a given worker-firm pair. One could
also consider more general investments by firms in technologies that are complementary
to workers’ accumulated firm-specific skills. That is, while some firms’ production
technology relies on having experienced workers, other technologies work equally well45with inexperienced workers. In a model of directed technological change along thelines of Acemoglu (2002b), the incentive to develop technologies that work well withexperienced workers would be higher if (because of labor regulation) a firm is more likely
to have many such workers in the future. The direction of technical change in the context
of a search model has previously been considered by Michelacci and Lopez-Salido (2007),
but not from the perspective of the skill premium in the labor market.
In terms of modeling workers’ careers, a natural next step would be to consider aframework that allows for job-to-job transitions and job ladders (as in Moscarini and
Postel-Vinay 2019). Job-to-job transitions do occur in our framework, because workers canquickly find a job after a separation. However, we do not focus on job-to-job transitions
as a source of wage growth. Voluntary job-to-job transitions would naturally interact
with firms’ incentives to invest in the relationship.26
Our employment protection model focuses on blanket protections that apply to all workers and can be interpreted as government regulations. Another potential source of firing
restrictions are unions. It would be interesting to relate the employment-protection mechanism to changes in the reach of unions over time and across countries (see, for example,
Acemoglu, Aghion, and Violante 2001 for an analysis of the role of deunionzation forinequality). However, deunionization does not offer an immediate explanation for theobject of study here, namely the different trends between the United States and Germany, since union coverage has fallen drastically since the 1980s in Germany (Dustmann,
Ludsteck, and Schönberg 2009).
When comparing the skill transferability of more- and less-educated workers, the questionof why college-educated workers have more portable skills is relevant. One possibility isthat portable skills are ultimately linked to a worker’s occupation, and college-educatedworkers have a higher likelihood of being able to continue in the same occupation after alayoff (Kambourov and Manovskii 2009b; Kambourov and Manovskii 2009a; Böhm, vonGaudecker, and Schran 2019).
Lastly, the creation of different types of jobs plays a central role in our theory, and it
would be useful to provide more direct empirical evidence on what characterizes thesejob types. Along these lines, Gregory (2020) uses German data to document heterogeneity
in the steepness of workers’ earnings profiles across firms, which corresponds well withthe two job types in our theory. Bayer and Kuhn (2019) consider the ability to transition26

See Lentz and Roys (2015) for an analysis that integrates job-to-job transitions with the issue of generaljob-specific training.

46

into jobs that involve more responsibility to be an important source of wage growth.
Type-A jobs in our environment could be interpreted as settings were firms make suchtransitions possible. There can also be heterogeneity across jobs in terms of job security(Jarosch 2021, Jung and Kuhn 2018), which would naturally interact with the incentive toinvest in the relationship-specific skills emphasized in our theory. In short, there are many
opportunities for future research on the relationship between employment protection,
investment in relationship-specific skills, and wage inequality in modern economies.

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53

A

Data Appendix

The main data sources for the empirical analysis and the model calibration are the Panel
Study of Income Dynamics for the United States, and the Socio-Economic Panel (SOEP)
for Germany. The PSID is conducted by the Survey Research Center (SRC) at the University of Michigan and can be accessed freely via their website.27 The SOEP is administeredby the German Institute for Economic Research, DIW Berlin. More information on the
SOEP and how researchers can gain access to it is available on the Institute’s website.28
We employ version 31 of the SOEP data set (2016, doi:10.5684/soep.v31).

Panel Study of Income Dynamics The PSID was conducted on a yearly basis between
1968 and 1996, and every two years from 1997 onwards. The structure of the PSID is apanel in which individuals belonging to a PSID family in 1968 are followed over timeas they form a new household or re-join their previous one. We focus on individuals infamilies belonging to the original SRC sample, which is designed to be representative of
the US population.
We focus on male respondents who, at the time of the interview, are identified as theirfamily’s head.29 For consistency with the assumptions on demographics in the model, we
restrict attention to individuals aged 25–64 who declare that they only work for someone
else. Hence, we exclude self-employed individuals and those who answer that they workfor “Both someone else and self.”
We define a single education variable for each individual that corresponds to the maximum reported educational attainment, or the maximum number of years of education.
Workers are classified as having a high-school degree if they report at least 12 but lessthan 16 years of education, and as having a college degree if they report at least 16 yearsof education. We discard individuals with less than 12 years of education. We define realearnings per hour as earnings per hour deflated via the CPI, using 2010 as base year. We
discard observations where the resulting real hourly earnings are below 7.50 2010 dollars,or the total number of hours worked is below 500 or above 5,000 in the last year.
Potential experience is defined as current age minus (years of education + 6). The
27

https://psidonline.isr.umich.edu/default.aspx
https://www.diw.de/en/soep
29
The PSID reports that: “Historically, PSID has used the term Head to refer to the husband in aheterosexual married couple and to a single adult of either sex. Starting in 2017, the term “Reference
Person” replaced “Head.” For more information visit: https://psidonline.isr.umich.edu/Guide/FAQ.aspx.
28

54

employment tenure variable is continuously available starting from 1981. Until 1993,
the information is reported as the number of months with the current employer. From1994 onwards, the information is reported in three separate questions for years, months,
and weeks with the current employer, which must be added to obtain a single tenure
figure. To maintain consistency with the quantitative model, we then adjust the tenure
figure by taking the minimum between the tenure information and age − 25. We discard
observations for which the resulting months of tenure are more than 12 × (age − 16).
All the statistics in the paper are computed using a system of weights that keeps the age
distribution constant in every year to the 1981 distribution.

Socio-Economic Panel The German SOEP has been conducted on a yearly basis since1984. Similarly to the PSID, the SOEP is a longitudinal study that periodically surveys thesame set of families that were interviewed in the original sample. Although there havebeen expansions in the samples in 1990 (East German sample) and in 1994 (immigrantsample), we focus on the original sample, which only includes families originally from
West Germany.
We focus on male respondents aged 25–64 who do not declare themselves to be selfemployed. We infer self-employment from the “generated” variable labeled “STIB Occupational Position.”
The SOEP provides separate variables for college attainment and total years of educationand training. We define a college degree variable for each individual if college completionis reported at some point in the panel. For those who do not report college completion, we
define a unique educational attainment variable for each individual, based on the highest
number of years of education recorded in the panel for that individual. We then generatea high-school degree variable if the individual reports at least 10.5 years of education ortraining. We discard observations that report less than 10.5 years of education or training.
We discard workers who declare less than 20 hours of work per week. We postulate aminimum hourly wage that is equal, in every year, to the 2015 statutory minimum wage
(8.50 euros per hour), discounted by the relative price index.
Starting with the system of individual weights provided by the SOEP for the original
sample, we construct a system of weights that keeps the age distribution constant over
the years to the 1984 distribution, in an analogous manner to the US sample.
55

B

Additional Figures and Tables
Log of hourly wage (ages 45–54)
US (1981-2013)

DE (1984-2013)

0.281***

0.122***(.030)(.021)

0.488***

0.475***(.035)(.053)-.107**-.166***(.048)(.050)

Exper. 3rd degree pol.

yes

yes

Year FEyes

yes# Obs.

7,578

10,137

R2

0.241

0.268

Tenure >= 20
College graduate
Interaction

Notes: Standard errors clustered at individual level in parentheses. For the
PSID, the sample consists of male workers aged 45 to 54 who report between
500 and 5,000 hours worked in a year. For the SOEP, the sample consists of maleworkers aged 45 to 54 who report a minimum of 20 hours worked per week
in the last year. Each column consists of a separate regression of log wages ona year fixed effect, a third-degree polynomial of potential experience, and an
indicator variable for 20 years of tenure or more on the current job. *** p < 0.01,** p < 0.05, * p < 0.1.

Table B.1: Returns to high tenure for college- and less-educated workers in the US (PSID)
and Germany (SOEP).

56

Dependent variable: Log hourly real wage
US (PSID), 1981-2013
High school

Returns to 10 yearsof tenure

Germany (SOEP), 1984-2013

CollegeHigh school

College

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

.129***(.016).121***(.012).060**(.028).002(.021).039*(.021).047***(.016).052(.054)-.053(.037).069**(.032).119***(.024)-.013(.058).100**(.040)

Difference in returns(High school - College)# Obs.

22,45021,88813,422

13,106

28,81428,416

9,329

9,247

Experience (polynomial)

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Year FE

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Individual FE

No

Yes

No

Yes

No

Yes

No

Yes

Notes: Standard errors clustered at individual level in parentheses. For the PSID, the sample consistsof male workers aged 45 to 54 who report between 500 and 5,000 hours worked in a year. For the SOEP,
the sample consists of male workers aged 45 to 54 who report a minimum of 20 hours worked per week
in the last year. The dependent variable is hourly log wages. The explanatory variables include yearsof tenure, years of tenure squared, and an indicator for whether the job started more than one year ago,
instrumented using deviations from the average within the employment spell. Regressions include athird-degree polynomial of potential experience. ***p < 0.01, **p < 0.05, *p < 0.1.

Table B.2: Returns to tenure using the method in Altonji and Shakotko (1987).

57

1
0.9

Cumulative Probability

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1

1.5

2

2.5

3

3.5

4

Human capital after separation
Non-College

College

Figure B.1: Cumulative probability of falling to any skill level h′ after a separation withskill level h = h10 for L (dotted line) and H (solid line) workers.

58

Probability of exog. separation

0.25

0.2

0.15

0.1

0.05

0
2

4

6

8

10

12

14

16

18

20

Years of tenure
1980

2010

Figure B.2: Probability of exogenous separation as a function of tenure for L and H
workers in the 1980 (solid line) and 2010 (dotted line) calibrations.

59

Share of workers

1980

2010

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0
0-4

5-9

10-14

15-19

20-24

25-30

30-34

0
0-4

35-40

5-9

10-14

Years of tenure
Age 25-34 (model)
Age 45-54 (model)

15-19

20-24

25-30

30-34

35-40

Years of tenure
Age 25-34 (data)
Age 45-54 (data)

Age 35-44 (model)
Age 55-64 (model)

Age 35-44 (data)
Age 55-64 (data)

Figure B.3: Distribution of workers by age and years of tenure in the data (dotted lines)
and model (solid line), in the 1980 (left panel) and 2010 (right panel) steady states.

60

Identification of firing cost

Firing cost and tenure

4

0.45

3.5

0.445

3

0.44

2.5

Firing cost

Long-term tenure, 1980

0.455

0.435

2

0.43

1.5

0.425

1

0.42

0.5

0.415

0
0

0.1

0.2

0.3

0.4

0.5

0

Firing cost at tenure = 1

5

10

15

Years of Tenure

Figure B.4: Left panel: Share of Long-term tenure workers in Germany in 1980 as
a function of the firing cost, and share in the data (dotted black line). Right panel:
Calibrated firing cost as a function of years of tenure with current employer.

61

C

Model Computation

In computing the model, we impose a vector of 20 possible values for individual humancapital, h, log-spaced between h1 = 1 and h20 = 20. We discretize the vector of turbulence
shocks, ϵ, as 10 equally spaced values between 0.01 and ϵ̄ = 0.6.
The calibration routine minimizes a loss function defined, for each vector of parametersp, as the sum of the squared differences between the data-generated and the modelgenerated moment:
min L(p) =Xam [Datam − M odelm (p)]2 ,mwhere the weight am is set equal to 10 for the moments that concern the fraction ofworkers with short- and long-term tenure (which is particularly important to match
given our mechanism), and equal to one for the other moments.

62

D

Details on match surplus and wage setting

In this section, we provide detailed expressions for the surplus generated by firm-worker
matches, and for the resulting equilibrium wage. To keep notation as simple as possible, we present these expressions for the case of a match not currently experiencing
a turbulence shock (the case in which the match is experiencing a turbulence shock isanalogous).
The surplus of a match between a firm and a worker of education e, skill level h, andexperience x, in a type-p job of tenure t, is equal to:Spe (x, h, t) = VAe (x, h, t) − Eh′hie′U (x, h ) + Jpe (x, h, t) + Φep (x, h, t),where the expectation Eh′ is taken with respect to the skill loss probabilities Qe (i, j), as
defined in Equations (3) and (4).
If the surplus is positive, the wage is determined by Nash bargaining between the worker
and the firm, with the worker retaining a share α of the resulting surplus:hi
VAe (x, h, t) − Eh′ U e (x, h′ ) = αSpe (x, h, t).
We now have all the ingredients to derive expressions for the equilibrium wage.
In type-A vacancies, the level of effort is not contractible, and is taken as given at thenegotiation stage. Using the Bellman equations defined in Section 4.5 and rearranging
the expression to isolate the wage, we obtainhewA(x, h, t) = ae (x)hz ∗ (x, h, t)2 − β (1 − θ(t))(1 − γ)Eh′ (VAe (x + 1, h′ , t + 1))


i
e
′
e
′
+ (1 − θ(t))γEh′ ,ϵ ṼA (x + 1, h , t + 1, ϵ) + θ(t)Eh′ (U (x + 1, h )) +hi
Eh′ U e (x, h′ ) + αSAe (x, h, t).
Analogously, in type-N vacancies the equilibrium wage can be written as:hewN(x, h, t) = −β (1 − θ(t))(1 − γ)VNe (x + 1, h, t + 1)i
+ (1 − θ(t))γEϵ ṼNe (x + 1, h, t + 1, ϵ) + θ(t)Eh′ U e (x + 1, h′ ) +
h
i
e
′
e
(x, h, t).
Eh′ U (x, h ) + αSN
63There are three caveats that should be noted. First, the firing cost is only relevant forcontinuing matches. That is, when the firm and the workers are first matched, the firing
cost is not part of the surplus and, if the match is not formed (which never happens inequilibrium) the firm is not subject to the firing cost. Second, skill loss only happensin case of separation after the first period of tenure. That is, if a given match does not
result in employment, the worker remains unemployed but is not subject to skill loss.
Third, each worker can only be matched with one firm in each period. If the match is notformed, the worker remains unemployed for that period and cannot be matched withanother firm.

64

E

Robustness of quantitative results

In this section, we discuss robustness of our main results to alternative choices in ourmodel calibration.
E.1

Magnitude of the turbulence shocks

In the main calibration summarized in Table 4 we set the parameter that controls theminimum productivity loss of regular productivity during turbulent times, ϵ̄, to 0.6. This
choice can be interpreted as a normalization, since the model can rationalize the empiricalshare of workers with long-term tenure with multiple combinations of frequencies ofturbulence shocks, γ, and minimum productivity losses, ϵ̄.
To verify that our main results are not driven by this particular choice of ϵ̄, we recalibrate
the model by setting ϵ̄ to a lower (ϵ̄ = 0.4) and higher (ϵ̄ = 0.8) value than our baseline
calibration (ϵ̄ = 0.6). Columns (1) and (3) of Table E.3 summarize the remaining calibrated
parameters in these alternative calibrations. Most parameters are estimated to be very
similar regardless of the choice of ϵ̄. Unsurprisingly, the only exceptions are γ80 and γ10 ,with higher values of ϵ̄ implying lower estimated values of the frequency of turbulence
shocks.
Table E.4 reports the college wage premium in the 1980 and 2010 steady states and in the
counterfactual that isolates the effect of turbulence in the “United States” and “Germany”
economies under the baseline calibration (Panel B) and the alternative calibrations using
a lower (Panel A) and higher (Panel C) values of ϵ̄. All these versions of the model deliver
identical implications of turbulence and labor protection for the college premium.
E.2

Calibrating the model using German SOEP data

The targets of our baseline calibration include, among the other moments, the college
premium by age group in the PSID data for the United States. As discussed in Section
6.3, these moments are critical to pin down our mechanism and are key to understandwhy, as a result of turbulence, the college premium evolves differently in economies withand without employment protection. In particular, a key implication of our mechanismis that the experience-college premium profile should become steeper only in an economy without employment protection. This implication is confirmed by comparing theexperience-college premium profile in the PSID and the SOEP data between 1980 and2010 (Table 9).
65

Parameter

Interpretation

(1)

(2)

(3)

(4)

ϵ̄ = 0.4ϵ̄ = 0.6ϵ̄ = 0.8

SOEP

Panel A: Time-invariant parametersσL

L skill specificity

0.308

0.309

0.308

(0.309)σH

H skill specificity

0.047

0.053

0.053

(0.053)

ψ

Prob. skill upgrade

0.494

0.498

0.500

0.466

η

Pareto initial skills

4.580

4.574

4.570

4.587

Panel B: Time-variant parameters (1980)
Lg80

L productivity growth

0.00050.00040.0003-0.0067

AH
80

Skill bias

1.288

1.286

1.282

1.161

γ80

Prob. turbulence shock

0.014

0.020

0.026

(0.020)θ80 (1)

Prob. separation shock

0.209

0.208

0.209

(0.208)Panel C: Time-variant parameters (2010)∆g10

Change product. growth

0.007

0.007

0.007

0.0001L
νA,10

Share of type-A jobs

0.489

0.513

0.538

1.000

H
νA,10

Share of type-A jobs

0.930

0.950

0.951

0.8514AH
10Skill bias

1.495

1.495

1.500

1.235

γ10

Prob. turbulence shock

0.038

0.053

0.068

(0.053)

θ10 (1)

Prob. separation shock

0.174

0.175

0.175

(0.175)

Table E.3: Calibrated parameter values for the 1980 and 2010 steady states under different
values of ϵ̄ (Columns 1-3) and in the calibration that uses SOEP data (Column 4). Values
in brackets are taken from the baseline calibration (Column 2).
We now verify that the same implication holds true when we use the SOEP data tocalibrate the model and remove the firing cost to generate the “United States” economy.
In performing this alternative calibration, we keep some of the parameters to the baseline
calibration and exclude the corresponding targets from the loss function. In particular, we
use the magnitude of the turbulence and separation shocks, the transferability parameters,
the size of the firing cost, and the parameters controlling the sensitivity of the supply of
type-A vacancies obtained in the baseline calibration, since these parameters are only
well-identified starting from a setting with no employment protection. We postulate ahigher value of workers’ productivity during unemployment (b = 0.4), to reflect the moregenerous unemployment insurance prevailing in the German labor market (Ljungqvist
66College Premium
Setting

No Firing Cost

Firing Cost

“United States”“Germany”

1980

0.32

0.32

2010: turbulence and skill-biased tech. change

0.59

0.46

2010: only turbulence

0.43

0.32

1980

0.32

0.32

2010: turbulence and skill-biased tech. change

0.59

0.47

2010: only turbulence

0.43

0.33

1980

0.32

0.32

2010: turbulence and skill-biased tech. change

0.59

0.47

2010: only turbulence

0.43

0.33

1980

0.38

0.37

2010: turbulence and skill-biased tech. change

0.61

0.39

2010: only turbulence

0.52

0.33

Panel A: ϵ̄ = 0.4

Panel B: ϵ̄ = 0.6

Panel C: ϵ̄ = 0.8

Panel D: SOEP Calibration

Table E.4: The rise in the college wage premium (log difference of average wages) withand without employment protectionand Sargent 2008). We then calibrate the remaining parameters by using SOEP data on
the college premium by age group, on the lifetime wage growth of H-workers, and on
the dispersion of wages at age 25. Column (4) of Table E.3 shows the resulting calibrated
parameters. Starting from this calibration, we then remove the firing cost to generate the“United States” economy in the 1980 and 2010 steady states.
Panel D of Table E.4 shows the college premium in the “United States” and the “Germany”
economy in this alternative calibration. The qualitative pattern of the baseline results
is preserved. However, as expected, in this case the college premium does not increasesignificantly in the “Germany” case, consistently with the observed behavior of thecollege premium in Figure 1. Table E.5 displays the college premium by age group in thisalternative calibration. Consistently with our mechanism, we observe a steepening of the

67

1980
Data

2010

Model

Data

Model
Full

Turb.

Panel A: “United States”
Age 25-34

0.244

0.174

0.408

0.282

0.174

Age 35-44

0.282

0.314

0.541

0.510

0.421

Age 45-54

0.367

0.440

0.645

0.726

0.655

Panel B: “Germany”
Age 25-34

0.157

0.162

0.291

0.219

0.172

Age 35-44

0.308

0.300

0.281

0.341

0.312

Age 45-54

0.412

0.416

0.365

0.423

0.439

Table E.5: College premium by age group in the “United States” (Panel A) and the“Germany” (Panel B) economies in 1980 and 2010 in the calibration using SOEP data.
experience-college premium profile in the “United States” economy (with no employment
protection) but not in the “Germany” economy (with employment protection).

68