A Life-Cycle Model ofTrans-Atlantic Employment Experiences
Sagiri Kitao

Lars Ljungqvist

Thomas J. Sargent∗

December 12, 2015

Abstract
To understand trans-Atlantic employment experiences since World War II, we build
an overlapping generations model with two types of workers whose different skill acquisition technologies affect their career decisions. Search frictions affect short-run
employment outcomes. The model focuses on labor supply responses near beginnings
and ends of lives and on whether unemployment and early retirements are financed
by personal savings or public benefit programs. Higher minimum wages in Europe
explain why youth unemployment has risen more there than in the U.S. Higher risks
of human capital depreciation after involuntary job destructions cause long-term unemployment in Europe, mostly among older workers, but leave U.S. unemployment
unaffected. Increased probabilities of skill losses after involuntary job separation interact with workers’ subsequent decisions to invest in human capital in ways that generate
the age-dependent increases in autocovariances of income shocks observed by Moffitt
and Gottschalk (1995).

Key words: Heterogeneity, search frictions, experience, human capital, disutility of work,
aging, job tenure, unemployment duration, hazard rate, early retirement, earnings volatility,
autocovariance of income shocks, unemployment benefits, job protection, minimum wage.

∗
Kitao: Keio University (email: sagiri.kitao@gmail.com); Ljungqvist: Stockholm School of Economics and
New York University (email: lars.ljungqvist@hhs.se); Sargent: New York University and Hoover Institution(email: thomas.sargent@nyu.edu).

1

1

Introduction

Before the 1970s, unemployment rates were significantly lower in Europe than in the U.S.,
but after the 1970s, Europe suffered persistently higher unemployment than the U.S. These
aggregate outcomes conceal important differences over life cycles of European and American workers. Figure 1 displays the unemployment rate and the employment-to-population
ratio at different ages for men in France and the U.S. in 1970 and 2004.1 We include theemployment-to-population ratio because many workers who collect government provided
disability insurance and early retirement payments are probably unemployed rather thanunable to work (see OECD (2003, chap. 4)). Most macro-labor analyses of trans-Atlantic
employment experiences in the tradition of matching models (e.g., Mortensen and Pissarides(1999)) and also in frictionless representative household models (e.g., Prescott (2005)) ignore
life cycle dynamics.
This paper constructs a heterogeneous-agent life-cycle model that fits cross-time andcross-continent differences in employment by age while preserving a string of quantitative
successes achieved by earlier macro-labor studies. Our model makes contact with data onlife-cycle profiles of asset holdings, consumption, and earnings as well as age-dependent flows
into and out of unemployment.2 It does this while incorporating mechanisms from earlier
work by Mortensen and Pissarides (1999) and Ljungqvist and Sargent (2008) that portray
situations in which government-imposed layoff costs that suppress frictional unemployment
can offset some of the unemployment increases caused by generous unemployment benefits.
To explain trans-Atlantic employment outcomes, this paper extends Ljungqvist and Sargent’s (1998, 2008) studies of the consequences of microeconomic ‘turbulence’. Bertola and
Ichino (1995) and Ljungqvist and Sargent (1998) argued that the outbreak of high European unemployment around 1980 was connected to Gottschalk and Moffitt’s (1994) findingthat the instability of earnings of U.S. workers increased between the 1970s and the 1980s.
Bertola and Ichino (1995) interpreted greater earnings instability as reflecting more volatile
local demand shocks and showed how a rigid wage and high layoff costs in Europe would
lead to higher unemployment in a model with homogeneous workers. In contrast, Ljungqvist
and Sargent (1998, 2008) imputed some increased earnings variability to shocks to workers’
1
See also Rogerson (2006) who reports the employment-to-population ratio for both men and womenin the U.S. and several European countries in 2003. Except for Italy with its lower female labor market
participation, the same picture emerges as in our figure 1 where the prime-age European population of age
30 through 50 has very similar participation rates to those of the U.S. population.
2
For two related life-cycle models of unemployment, see Hairault et al. (2010) and Low et al. (2010) who
attribute elevated old-age unemployment to benefit programs that are available only to older workers.

2

human capital and showed how generous unemployment benefits in Europe would generatehigh long-term unemployment among workers who had lost human capital after their mostrecent layoff. Instead of Ljungqvist and Sargent’s learning-by-doing technology, the present
analysis includes Ben-Porath’s (1967) human capital acquisition technology, and shows how
turbulence generates age-dependent increases in autocovariances of income shocks like those
documented by Moffitt and Gottschalk (1995).
Our models of economies on the two sides of the Atlantic ocean share common demographics, preferences, and technologies for production, job market search, and human capitalacquisition. Of these primitives, we assume that only the human capital acquisition technology changed over time and that it changed in the same way on both the two sides of theAtlantic ocean, in particular, that it deteriorated between what we call tranquil times (before
the 1970s) and turbulent times (after the 1970s) in the sense that there was an increased
risk of losing more human capital at times of involuntary job destruction. This is our notionof an increase in turbulence. We compute distinct steady states in tranquil and turbulent
times. Differences in government policy are the only causes of differences in outcomes acrossthe two continents in these steady states. We hold taxation, social security, unemployment
insurance, and job protection policies constant across time, but make them differ systematically across continents: most importantly, in Europe, unemployment insurance is of longer
duration and job protection is stronger. The minimum wage is assumed never to bind in
the U.S. and not in Europe prior to the 1970s. But we make the European minimum wage
binding after the 1970s for workers with low education and experience.
Our primitives rest on two pillars that support ‘time-averaging’ models: (1) indivisibilities in labor supply, and (2) time separable preferences that express a distaste for volatileconsumption. By dropping the employment lotteries and complete markets that had beena microfoundation for macroeconomic models that determined a fraction of the populationthat was randomly assigned to work each period (see Prescott (2005)), time-averaging models
eliminate an aspect of macro models that labor economists disliked. Time-averaging models replace those fractions of people randomly assigned to work with fractions of lives that
individual workers choose to work.3 At interior solutions for career length, a time-averaging
3

Abstracting from productivity shocks and human capital in an indivisible-labor complete-market modelin continuous time, Ljungqvist and Sargent (2006) showed that, holding the workers’ preferences fixed, thesame labor supply elasticity would emerge if the employment lotteries and complete markets were withdrawn
and instead individual workers were forced to confront the indivisible labor choice by choosing fractions of
their lifetimes to work while trading a single risk-free asset to smooth their consumption over time. As a
discussant, Prescott (2006a) welcomed the abandonment of employment lotteries, and proceeded to revise his
earlier Nobel lecture (Prescott (2005)) by adding a new section on “The Life Cycle and Labor Indivisibility”

3

model like ours would exhibit the same high labor supply elasticity at the extensive margin
that an employment lotteries model would at an employment-population ratio less than one.
The reason that labor supply turns out not to be highly elastic in our model in tranquil times,
either in the U.S. or in Europe, is that our calibration puts workers at a corner solution forcareer length that is generated by an official retirement age.4 That corner solution explains
why in tranquil times our model generates similar employment outcomes in Europe and the
U.S. despite higher taxes and more generous benefits in Europe.
Ljungqvist and Sargent (2014, sec. 4) describe conditions that in a time-averaging modelcause workers to shorten their careers by privately financing early retirement after a permanent negative earnings shocks. In the model of this paper, human capital losses in turbulent
times conclude careers in Europe because of the incentives provided by publicly financed
long-term unemployment and early retirement programs that are available in Europe but
not in the U.S. The conjunction of increased turbulence and the outbreak of high European
unemployment enable us to identify and calibrate a key parameter in our framework – thedisutility of work.
The remainder of this paper is organized as follows. Section 2 previews key forces in
the model and how we use them to calibrate parameters. Section 3 describes the model
environment in detail. Bellman equations are specified in section 4. Section 5 explains thecalibration of the model, and section 6 reports on the outcomes of the analysis. Concluding
remarks are offered in section 7.

2

Key forces and calibration strategy

The following two subsections describe sources of workers’ heterogeneous lifetime labor market experiences and how a decomposition of the parameter space guides our calibration of themodel via simulated moments. These descriptions identify interactions among forces thatallow the model to capture trans-Atlantic employment experiences after World War II andalso yield auxiliary implications that line up well with observations on lifetime consumption
and asset profiles, the turnover of workers and jobs, and the changing dynamics of individual
earnings data.
in a second edition (Prescott (2006b)), in which he extends the Ljungqvist and Sargent (2006) analysis toinclude a particular intensive margin in workers’ labor supply.
4
See Ljungqvist and Sargent (2014, sec. 6) for a time-averaging analysis of implicit tax wedges in pension
systems that can cause heterogeneous agents to stop working at the same official retirement age.

4

2.1

Heterogeneities

A constant population consists of overlapping generations of heterogeneously situated workers who randomly survive from period to period and live at most T periods. The presenceof an indivisibility makes a person work either full time or not at all in a given period. As
in the Lucas and Prescott (1974) island model, a worker must search for ‘the labor market’.
Once there, he earns a competitively determined wage per unit of the effective labor that
he had acquired by investing in human capital, but subject to a transitory earnings shock.
When not working, a person either enjoys leisure full time or searches for the labor market
at a disutility-causing intensity of his choice. A worker passes through three phases: (1) aphase of youthful inexperience characterized by an environment with a high job destruction
rate and frequent changes of jobs at productivities drawn from a McCall (1970) style offer
distribution; (2) a mature phase as an experienced worker who confronts a lower rate ofjob destruction than he had while he was “inexperienced” and who now has access to ahuman capital acquisition technology in the style of Ben-Porath (1967); and (3) a phase of
mandatory retirement that starts at age T n + 1 < T . The worker can choose not to work
during phases (1) and (2). If he withdraws from the labor market permanently, we say that
he retires before the mandatory retirement age. There are two ways that workers who are
unemployed and workers who retire early support themselves. Workers save by acquiring asingle risk-free financial asset. Accumulations of this asset are one way to finance consumption during retirement and other times when the worker is not supplying labor or is sufferingtransitory negative earnings shock while employed. Payments from the government in theform of unemployment compensation and social security retirement benefits are anothersource of funds. Workers are heterogeneous. Ex ante, there are two types of workers, highand low, that we think of as high school only and college graduates, respectively. They are
distinguished by the probability distributions of potential productivities that they face andalso by the parameters of their Ben-Porath human capital acquisition technologies. Workers’ decisions to acquire human capital in the face of these technologies contribute realistic
differences in profiles of labor earnings and financial assets across our two types of workers. Ex post heterogeneity is generated by luck in drawing random numbers that determine(1) job search outcomes, (2) times taken to become an experienced worker, (3) transitory
earnings shocks while employed, (4) job destruction, and (5) extraordinary human capitaldepreciation at times of involuntary job loss.
One-worker firms are randomly paired with workers in the labor market in each period.
All active firms pay the competitively determined wage per efficiency unit of labor and rent
5

capital. Idiosyncratic productivities that follow a Markov process make firms heterogeneous
ex post. A firm can be created by incurring a startup cost. Firms exit because they receive
exogenous destruction shocks or because their productivities fall below an optimal reservation
productivity. By imposing a job destruction tax, the government influences the reservation
productivity and through it the layoff rate and productivity distribution of active firms.

2.2

Calibration with simulated moments

We first parameterize government policies: tax rates on labor and capital, unemployment
insurance, social security systems, minimum wages and layoff costs. We base our parameterization on official statistics and commonly accepted estimates. When the literature reveals
disagreements about magnitudes, we err on the conservative side by understating policy
differences across continents. For example, while assuming no layoff tax in the U.S., wecalibrate a European layoff tax at only three months of low-type workers’ average earnings.
For given government policies, we find that outcomes change smoothly in response to
perturbations of all parameters except one that measures the disutility of work. Except
for that disutility parameter, other parameters mainly affect one equilibrium outcome while
having only minor effects on other outcomes. This structure of the model guides our approach to calibrating it. Fixing the disutility that a worker suffers when supplying labor, wesequentially iterate over parameters that determine: (i) agents’ decisions to consume, supply
labor, and accumulate financial assets and human capital; (ii) firms’ decisions to hire andfire workers. We eventually calibrate the disutility of work in a third stage.
We initialize our calibration procedure with a value for the disutility of work. It must
be set low enough that in the absence of human capital losses, in both Europe and the U.S.
workers do not want to retire before the mandatory retirement age.
In the first stage, we treat firms’ layoff rates as if they were fixed, deferring fitting
those layoff rates to the second stage. Given that caveat, we calibrate the model of the
U.S. in tranquil times. The subjective discount rate and parameters of the job search andhuman capital technologies and of the layoff rate are determined by targeting observations
on durations of unemployment spells, earnings profiles, asset holdings, and numbers of jobs
held over a lifetime. (The aggregate unemployment rate is a function of the average durationof unemployment and the inflow into unemployment, as implied by rates of job churning.)
For Europe, we import the technology parameters and the subjective discount rate fromthe calibration of the U.S. model; but not the layoff rate. Unemployment was lower in6Europe than in the U.S. during what we identify as the tranquil decades of the 1950’s and1960’s, a difference mechanically accounted for by a lower inflow rate into unemployment inEurope along with similar average durations of unemployment in Europe and the U.S. (See
Layard et al. (1991)). For Europe, our calibration target is a layoff rate that generates a
tranquil-times unemployment rate 1.5 percentage points lower than in the U.S.
In the second stage, the distribution of human capital for workers who have found ‘thelabor market’ from the first calibration stage together with any government imposed layoff
tax and the idiosyncratic productivity process determine firms’ reservation productivity thatin turn implies a layoff rate for that economy. Since our first calibration stage has alreadyidentified the U.S. and European layoff rates to be fit, we use those two layoff rates ascalibration targets when parameterizing a common idiosyncratic productivity process forfirms in both the U.S. and Europe. Given that calibrated productivity process, a European
layoff tax equal to three months of low-type workers’ average earnings explains the suppressedlayoff rate in Europe which in turn implies a European unemployment rate that is 1.5
percentage points lower than the unemployment rate in the U.S. with its zero layoff tax.
In the third stage, we jointly calibrate the value of the disutility of work and the stochastic
process for shocks to human capital of displaced workers in turbulent times. Here thecalibration targets are, first, to capture that European unemployment more than doubles
in turbulent times, and, second, to reproduce Gottschalk and Moffitt’s (1994) observationof increased earnings volatility in the U.S. On the one hand, too low a disutility of work
could generate such a high European unemployment rate only if the shocks to earnings weremuch larger than observed. On the other hand, too high a disutility of work would make
European unemployment respond too much to human capital losses, meaning that we could
fit the dramatic increase of European unemployment only by assuming counterfactually small
increases in shocks to earnings.

3

Environment

The gross interest rate 1 + r is exogenous. As described in section 5, one key steady state iscalibrated so that the people in the model hold half of the economy’s physical capital.

7

3.1

Worker activities, search and human capital technology

In each period, there arrives a new cohort of agents who are alive for at most T periods.
Agents of age t < T face a probability mt of surviving until next period. Conditional on
surviving, an agent is of working age during her first T n < T periods of life but cannot work
during her remaining T − T n periods. T n + 1 is a mandatory retirement age. A worker
can choose to retire earlier. An unemployed agent of working age has access to a searchtechnology like one posited by Alvarez and Veracierto (2001). By expending a search efforts ∈ [0, 1], an agent finds ‘the’ centralized labor market next period with probability S(s) if
she is experienced, and with probability S̃(s) if she is inexperienced. All workers go throughan initial phase of ‘inexperience’ before entering a later phase of ‘experience’. The type ofjob a worker encounters depends on whether she is in the first or second phase of her labormarket career.
There is ex ante heterogeneity because two types of workers i = H, L are differentiatedaccording to (1) when they are inexperienced, the probability distribution Gi (n̂) of effective
units of labor from which they draw jobs, and (2) when they are experienced, an initiallevel ho,i and the parameters of a skill acquisition stochastic matrix Hin (h, h̄; ℓ) that governs
stochastic transitions from human capital h to human capital h̄. To operate that skill
acquisition technology, an experienced worker needs to be employed.
An inexperienced agent of type i who finds the labor market draws a job offer to supplyn̂ effective units of labor from a probability distribution Gi (n̂). If the offer is accepted,
effective units of labor remain constant as long as the agent retains the job and does not
become experienced. For the sake of brevity, we refer to it as a worker’s ‘job’ but, as will
become clear in section 3.3, it would be more accurate to call it a worker’s ‘spell in thelabor market’. At the end of a period, after working but before workers have chosen theirconsumption rates, nature separates inexperienced workers from jobs with probability λ̃, andfirms choose to destroy other jobs with probability q. If a job survives, an inexperienced
agent faces a probability π that she becomes experienced and enters the second phase of her
career. Next, agents whose jobs have not been destroyed decide whether to keep their jobs
or to quit and search for new ones next period. The effective units of labor supplied by anagent who just became experienced and did not quit are n̂(ho,i , l), where ho,i is the initialhuman capital of an agent of type i, that will remain with her for the rest of her working
life, and l is the time that the agent devotes to acquiring additional human capital.5
5The phase of ‘inexperience’ captures the job churning by young workers observed by Neal (1999) who
formulated a search model in which a worker’s productivity is the sum of two components – a career match

8At the end of a period after working but before consumption decisions are made, naturedestroys jobs held by experienced agents with probability λ ≤ λ̃ and firms destroy more withprobability q.6 If a job survives and the worker does not quit, an employed experienced agent
chooses how much time l ∈ [0, 1] to spend on human capital acquisition next period. The
agent’s effective units of labor supply, n̂(h, l) = h(1 − l), declines in l. By allocating l unitsof time in a period, she acquires a type-dependent probability Hin (h, h̄; l) that her humancapital at the end of the period is h̄. But before it is used in production, with probability
λ, an employed agent experiences a job destruction event chosen by nature, and then her
end-of-period human capital is subject to yet another transition probability Hiλ (h̄, h′ ).
When supplying n̂ effective units of labor, a worker is subject to an i.i.d. earnings shockθ with probability distribution Θ(θ) that makes her labor supply become n = θ n̂ in that
period, which we call her efficiency units of labor. A worker’s decision to supply labor istaken before θ is realized.

3.2

Preferences

We assume that preferences are separable between consumption and leisure,
E0

T
X
t=0



β t log ct − Bt ,with Bt ∈ {B u (s), B},(1)

where we have adopted a logarithmic form that would be consistent with balanced growth if
there were technological progress. The disutility of effort includes both a disutility of search
and a job match. At the beginning of a period, a worker can draw new values of both components, or
she can retain her career and draw only a new job. The optimal career-job strategy has a worker focus onfinding a suitable career before searching for an ideal job. While this theory generates churning, it does not
explain lengths of employment spells during that process because values of careers and jobs are known assoon as they are drawn. One way to embellish the environment would be to incorporate learning like Pries
and Rogerson (2005). For tractability, Pries and Rogerson assume that successive observations of a worker’s
output is the sum of a true underlying match quality and a uniformly distributed i.i.d. random noise, sothat learning takes a simple “all-or-nothing” form. Unfortunately, that tractability comes at the price of an
unrealistically large variation in output. For example, in Pries and Rogerson’s preferred parameterization of
two possible match qualities, bad and good, the corresponding ranges of realized outputs, not reported intheir paper, are [−2.46, 4.46] and [−1.56, 5.36], respectively, where realizations in the disjoint set perfectly
reveal the true match quality and others are uninformative. Given the problematic nature of these models
for quantitative analysis, we opted for our hard-wired representation of the phase of inexperience. We expectthat similar outcomes would emerge from a more fully specified model with features drawn from Neal (1999)
and Pries and Rogerson (2005).
6
Compared to experienced workers, we subject inexperienced workers to an additional risk of job separation, (λ̃ − λ) ≥ 0, in order to induce additional job churning in the initial phase of inexperience.

9

when unemployed B u (s) that is increasing in s; and a disutility of work B. The disutility ofwork has no intensive margin since our agents can work either full time or not at all.

3.3

Production technology

The production technology is the same as in Ljungqvist and Sargent (2007) except that
we alter the process that randomly matches workers with firms. Ljungqvist and Sargent(2007) assumed that jobs newly created by firms are matched randomly with workers who
have just found the centralized labor market, but that ongoing firm-worker matches continue
until they are broken by a worker’s either quitting or dying or by a firm’s decision to end ajob. To facilitate analysis, in this paper we assume that all pre-existing ‘job sites’, including
both newly created and continuing ones, are randomly re-matched with workers who findthemselves in the centralized labor market. A process randomly matches a firm job sitewith someone drawn from the pool of workers present in the centralized labor market. The
firm pays that randomly drawn worker a competitively determined wage times that worker’s
particular supply of efficiency units of labor. There are no ‘jobs’ in the sense of long-term
relationships between particular firms and particular workers. Instead, to a worker a ‘job’
refers to her current spell in the centralized labor market, while to a firm a ‘job’ is an ongoingprofitable employment opportunity that is occupied over time by different people who varyrandomly in both their skill and experience levels.
We have designed our environment to confront firms with interesting job creation anddestruction decisions, and workers with interesting search and quitting decisions, while also
allowing an equilibrium wage to equate an aggregate demand with an aggregate supply of
efficiency units of labor. Our specification is in the spirit of Lucas and Prescott (1974)
and Alvarez and Veracierto (2001), who invented manageable environments in which workers search but a unique wage rate per efficiency unit of labor is nevertheless determined
competitively.
Incurring a startup cost µ allows a firm to create a job next period with productivity
level z = zinitial . The productivity level after that is generated by a Markov transition kernelZ(z, z ′ ). At the end of a period, nature exogenously destroys jobs with probability λ; thenfirms can choose to terminate other jobs.
A firm’s production function is
F (z, k, n) = z k α n1−α ,10with α ∈ (0, 1),(2)

where z is a job-specific productivity level, k is physical capital that depreciates at the rate
δ, and n is efficiency units of labor supplied by the worker filling the job.
The timing of events is as follows. At the end of a period, a fraction λ of all jobs is
randomly and exogenously destroyed. Next, firms with surviving jobs observe productivity
levels and choose whether to terminate jobs or to produce at the new productivity levelnext period. This decision is taken before knowing the identity of the worker who will
fill a particular job next period. That means that all firms choose the same reservation
productivity level z̄ and that the population of firms terminates a fraction q of jobs thatsurvived after the exogenous probability λ termination shock. Next period, all remaining
jobs and newly created jobs are randomly assigned to workers present in the centralizedlabor market. Firms observe their workers’ efficiency units of labor and then rent amountsof capital that maximize profits. Workers receive a competitively determined wage rate w
per efficiency unit of labor, which ensures that all workers in the central labor market are
employed and that newly created jobs expect to break even.
Firms and workers are both affected by the exogenous job destruction rate λ. At theend of a period, a fraction λ of all firms’ jobs are randomly destroyed, and a fraction λ ofall employed workers are randomly separated from the centralized labor market. Similarly,
firms’ endogenous destruction of jobs at a rate q generates that same fraction of forced
separations from the centralized labor market among employed workers. In contrast, workers
who quit have no direct impacts on firms since firms’ jobs are randomly matched in eachperiod with remaining workers and newcomers in the centralized labor market. Similarly
the additional exogenous separation rate among inexperienced workers, (λ̃ − λ) ≥ 0, has nodirect consequences for firms.

3.4

Government policies

The government’s labor market policy consists of three programs. First, workers who are
exogenously or endogenously laid off by firms are entitled to unemployment benefits for dmax
periods. During that entitlement period, a function Γ(e) maps lost earnings e, excluding any
transitory earnings shock θ, into benefits that are paid until the worker either finds a newjob or retires. Second, firms pay a job destruction tax Ω for each job that they choose toterminate. Third, the government imposes a ‘minimum wage’, or more precisely, a minimum
earnings level emin, excluding any transitory earnings shock θ.
The government taxes labor earnings including unemployment benefits at a rate τn and11interest earnings at a rate τk . Labor earnings are also subject to the payroll (social security) tax at rate τp . Social security benefits of ǫ are paid to retirees who have reached the
mandatory retirement age T n + 1. All accidental bequests are collected by the government.
The difference between revenues from taxation and accidental bequests, and payments for
unemployment benefits and social security benefits is spent on public consumption X.7

4

Bellman equations

Tables 1 and 2 show states, decisions, and value functions for several classes of agents. An
inexperienced worker bears a tilde on her value function and has state a, γ, d, t when she
is unemployed and a, n̂, t when she is employed, where a denotes her assets, γ her pastearnings-related unemployment compensation, d her elapsed duration of unemployment (thistracks UI benefits eligibility of limited duration), t her age, and n̂ her effective units of labor.
Value functions of experienced workers bear no tilde’s and have state a, h, t when employed
and a, h, γ, d, t when unemployed, where h denotes a worker’s human capital level. Agentsof age t > T n are retired, and have state a, t.
For notational simplicity, let Ao (x), An (x, n) and Au (x, γ) denote assets, including acurrent period’s net-of-tax income, of a retired agent, an employed agent and an unemployedagent, respectively. These assets can be consumed or saved in the current period. They arefunctions of an agent’s savings x last period, an employed agent’s labor supply in efficiency
units n, and an unemployed agent’s unemployment benefits γ:
Ao (x) = [1 + (1 − τk )r] x + ǫ ,

4.1

(3)

An (x, n) = [1 + (1 − τk )r] x + (1 − τn − τp ) w n ,(4)

Au (x, γ) = [1 + (1 − τk )r] x + (1 − τn ) γ .

(5)Retired people

The value function for a retired agent is
V o (a, t) = max {log(c) + βmt V o (Ao (a − c), t + 1)} ,csubject to(6)c ∈ [0, a] .

7
Our calibration strategy is to match tax rates and benefits and to let X be a residual. Hence, thecomputation of an equilibrium involves no loop to impose the government budget constraint.

12Policy function co (a, t) describes the optimal level of consumption.

4.2

Experienced workers

The value function of an experienced agent of type i = H, L who has accepted an employment
opportunity for next period is
Vin (a, h, t)



X
X
n
′
= max
log(c)
+
βm
−B
+
Θ(θ
)
Hin (h, h̄; l′ )
t
′
c,l

θ′

h̄
 X
· λ
Hiλ (h̄, h′ )Viu (An (a − c, θ′ n̂(h, l′ )), h′ , Γ(wn̂(h, l′ )), 1, t + 1)h′+(1 − λ)qViu An (a − c, θ′ n̂(h, l′ )), h̄, Γ(wn̂(h, l′ )), 1, t + 1n
+(1 − λ)(1 − q) max Vin An (a − c, θ′ n̂(h, l′ )), h̄, t + 1 ,Viusubject to

n

′



′

A (a − c, θ n̂(h, l )), h̄, 0, 1, t + 1


o

, (7)

c ∈ [0, a] , l′ ∈ [0, 1 − emin /(wh)] .

Policy functions cni (a, h, t) and li (a, h, t) give optimal levels of consumption in the current
period, and time spent on human capital accumulation in the next period, respectively.
The value function for an experienced unemployed agent is
Viu (a, h, γ, d, t)



= max
log(c) + βmt −B u (s′ )c,s′nS(s′ ) max Vin (Au (a − c, γ ′ ), h, t + 1) ,Viu (Au (a − c, γ ′ ), h, γ ′ , d + 1, t + 1)o
+ 1 − S(s′ ) Viu (Au (a − c, γ ′ ), h, γ ′ , d + 1, t + 1)
subject toc ∈ [0, a] , s′ ∈ [0, 1] , γ ′ =

(



(8)

γ, if d < dmax ;0, if d ≥ dmax .

Policy functions cui (a, h, γ, d, t) and si (a, h, γ, d, t) give optimal levels of consumption in thecurrent period, and time spent on job search in the next period, respectively.
In period T n − 1, the agent would optimally set l′ = 0 if employed and s′ = 0 if unemployed, and all the continuation value functions in Bellman equations (7) and (8) would be13

replaced by V o (An (a − c, θ′ n̂(h, l′ )), t + 1) and V o (Au (a − c, γ ′ ), t + 1), respectively.

4.3

Inexperienced workers

The value function of an inexperienced type i agent who has accepted an employment opportunity for next period isṼin (a, n̂, t)X= max log(c) + βmt −B n +Θ(θ′ )c′θ· [λ̃ + (1 − λ̃)q]Ṽiu (An (a − c, θ′ n̂), Γ(wn̂), 1, t + 1)n+(1 − λ̃)(1 − q) π max Vin (An (a − c, θ′ n̂), ho,i , t + 1),oViu (An (a − c, θ′ n̂), ho,i , 0, 1, t + 1)n+(1 − π) max Ṽin (An (a − c, θ′ n̂), n̂, , t + 1),
o
u
n
′
Ṽi (A (a − c, θ n̂), 0, 1, t + 1)

subject to(9)c ∈ [0, a] .

Policy function c̃ni (a, n̂, t) tells optimal consumption.
The value function for an inexperienced unemployed agent isṼiu (a, γ, d, t)





= max
log(c) + βmt −B u (s′ )
c,s′

n
X

′
′
+S̃(s )Gi (n̂ ) I wn̂′ ≥ emin max Ṽin (Au (a − c, γ ′ ), n̂′ , t + 1) ,n̂′oṼiu (Au (a − c, γ ′ ), γ ′ , d + 1, t + 1)

 u u
′
′
′
+I wn̂ < emin Ṽi (A (a − c, γ ), γ , d + 1, t + 1)


 u u
′
′
′
+ 1 − S̃(s ) Ṽi (A (a − c, γ ), γ , d + 1, t + 1)

subject toc ∈ [0, a] , s′ ∈ [0, 1] , γ ′ =14(γ, if d < dmax ;0, if d ≥ dmax .

(10)

where I(·) is an indicator function that is equal to one if the statement in parentheses istrue and zero otherwise. Policy functions c̃ui (a, γ, d, t) and s̃i (a, γ, d, t) give optimal levelsof consumption in the current period and time spent on job search in the next period,
respectively.
If the agent is still inexperienced in period T n − 1, she would optimally set s′ = 0 if
unemployed, and all the continuation value functions in Bellman equations (9) and (10) arethen replaced by V o (An (a − c, θ′ n̂), t + 1) and V o (Au (a − c, γ ′ ), t + 1), respectively.

4.4

Firms

The value functions of an existing firm with the productivity level of z aren hioV f (z) = max En Ṽ f (n, z) , −Ω ,no 1−λXṼ f (n, z) = max z k α n1−α − wn − (r + δ)k +Z(z, z ′ )V f (z ′ ).
k
1+r ′

(11)
(12)

z

Associated with the solution to an existing firm’s optimization problem is a reservation
productivity z̄ that satisfies
hif
En Ṽ (n, z̄) = Ω.

(13)

The break-even condition for starting a new firm is
µ=

h
i
1
En Ṽ f (n, zinitial ) .
1+r

(14)

In a stationary equilibrium, firms that are exogenously destroyed or that choose to exit are
replaced by new firms that enter with initial productivity level of zinitial .

5

Calibration

The annual net interest r is set equal to 4%, which is a common value in macroeconomic
analyses (see e.g. Cooley (1995)).8 The stationary population consists of 70% low-type
8

The model period is bi-monthly but in this section on calibration, we will explicitly refer to annual rates
and probabilities. With some slight abuse of notation, we continue to use variables such as the interest rater even though these are expressed at a bi-monthly frequency in the rest of the paper.

15

workers and 30% high-type workers.
Following the overview of our three calibration stages in section 2.2, we first report theparameter values of government policies in section 5.1, the only primitives that differ acrossthe two model economies of Europe and the U.S., respectively. The parameters of the firstcalibration stage and any observations targeted are described in section 5.2 that pertains
to a simple life-cycle model, and in section 5.3 that refers to labor market transitions. In
addition to the parameterization of primitives, the first stage generates layoff rates that need
to be consistent with firms’ optimization in the second calibration stage, which determine theparameterization of the production technology in section 5.4. Finally, section 5.5 identifies
the disutility of work and the process for human capital loss in turbulent times, i.e., thethird calibration stage.

5.1

Government policies

The unemployment insurance benefit Γ(e) amounts to a replacement rate of 60% of lastearnings e in both the U.S. and Europe, but the benefit is capped by a ceiling γ that is set
at 50% of average earnings in the U.S., and at 100% of average earnings in Europe. The
maximum duration of unemployment insurance dmax is 6 months in the U.S. but of unlimited
duration in Europe.9
Europe has a job destruction tax Ω equivalent to three months of low-type workers’
average earnings, but in the U.S. there is none. In the U.S. there is never a binding minimum
wage. In Europe, the minimum wage does not bind in tranquil times, but we make it bindin turbulent times. In our indivisible-labor model, that binding European minimum wageis represented as a level of minimum earnings emin equivalent to 50% of average earnings in
Europe. Dolado et al. (1996) report that minimum wages in most European countries areabout 50-70% of average earnings compared to about 33% in the U.S.
The labor income tax rate τn is set to 15% for the U.S. and 30% for Europe, while thesocial security payroll tax rate τp equals 10% on both continents. The total tax rates onlabor income of 25% and 40% in the U.S. and Europe, respectively, are in line with the9
While unemployment insurance is typically of limited duration, Layard et al. (1991) emphasize thatfurther benefits are often available in Europe for an indefinite period after unemployment compensation has
been exhausted. Hunt (1995) describes the German policy in 1983 when unemployment compensation (‘Arbeitslosengeld’) replaced 68% of an unemployed worker’s previous earnings and could be collected for at most
12 months. After those benefits were exhausted, means-tested unemployment assistance (‘Arbeitslosenhilfe’)
paid a replacement rate of 58% for an indefinite period. For additional evidence on generous replacement
rates and long benefit durations in Europe, see Martin (1996), who also considered housing benefits.

16

estimates of effective tax rates across OECD countries in Mendoza et al. (1994). The tax
rate on capital τk is set to 15% in both the U.S. and Europe.
The social security benefit ǫ is equivalent to 40% of average earnings in the U.S. and 50%
in Europe. The constant benefit implies a progressive replacement rate. According to theOECD study of Queisser and Whitehouse (2006), the average gross replacement rate in the
U.S. for an individual with the average earnings is 38.6%, while it is 28.1% and 49.6% forindividuals with twice and half the average earnings, respectively. The replacement rates arein general higher in Europe. The average gross replacement rate is 52.9% in France, 45.8%
in Germany and 78.8% in Italy.
Recall that public consumption X is determined residually from the government budget
constraint.

5.2

A simple life cycle model

To attain the target that the agents in the U.S. model own 50% of the aggregate capitalstock in tranquil times, we set the subjective annual discount factor β = 0.981. Our calibration target is motivated by the fact that the 5% wealthiest U.S. households have claims
on about half of U.S. wealth (see e.g. Budrı́a Rodrı́guez et al. (2002)). We seek to model
determinants of the remaining half of total wealth that is held by the agents in the model
because our framework does not capture various mechanisms that have been identified ascontributing to high degrees of wealth concentration, such as entrepreneurship and intergenerational transfers (see e.g. Cagetti and De Nardi (2008) for a survey of the literature). The
disutility of work is set to B = 0.22, based on calibration targets to be laid out in section
5.5. Age-dependent survival probabilities mt are taken from the life tables of Bell and Miller(2005).
Workers who are experienced can spend time ℓ to accumulate human capital according
to the skill acquisition stochastic matrix Hin (h, h̄; ℓ) that governs stochastic transitions fromskill level h to skill level h̄ for a worker of type i, whose initial endowment of human capitalis ho,i . The stochastic matrix is deduced from a deterministic Ben-Porath technology ht+1 =ht + Ai (ht lt )ν that we calibrate at an annual frequency as follows. The curvature parameteris set to ν = 0.8 so that it falls in the range of estimates in the applied labor literature,e.g., see Heckman et al. (1998) whose assumption of no human capital depreciation we also
adopt. We then target the difference in earnings between the two types of workers (noncollege and college graduates) at ages 25 and 50: in particular, an entry-level earnings ratio17

of 1.6 between high- and low-type workers at age 25, and subsequent earnings growth of 60%
and 110% between ages 25 and 50 for the low type and the high type, respectively. Afternormalizing ho,L = 1, our calibration results in parameter values ho,H = 1.79, AL = 0.049,
and AH = 0.066. Appendix A describes how we map this technology into the stochastic
matrix Hin (h, h̄; ℓ).
The idiosyncratic labor productivity shock θ is distributed log-normally, log θ ∼ N(0, σθ2 ).
The variance σθ2 is set at 0.04, which lies in the range of micro estimates for the transitory
components of earnings shocks, see e.g. Heathcote et al. (2010) and Guvenen (2007).

5.3

Labor market transitions

A major labor market transition is from an inexperienced to an experienced worker. Conditional on working, that happens at an annual probability of π = 0.33, i.e., it takes on
average three years to become experienced. The probability distribution Gi (n̂) of effective
units of labor from which inexperienced workers draw jobs, is taken from Ljungqvist andSargent (2008), i.e., a normal distribution with a mean of 0.7 and a variance of 0.02 that has
been truncated to the unit interval [0, 1] and then normalized to integrate to one. But ina twist that helps make contact with data, we splice together the earnings of inexperienced
and experienced workers of each type i so that the resulting earnings profiles in figure 4.a aresmooth. This is accomplished by multiplying the productivity draws from Gi (n̂) by ρho,i ,where ho,i is the initial level of human capital for a newly experienced worker and ρ adjusts
the scale of the effective units of inexperienced workers and is set at 0.9. The result is thatearnings tend to increase smoothly as agents move from inexperience to experience (despite
the time allocated to human capital investment and its negative effect on current earnings
that will be initiated once workers become experienced).
The search technology and disutility for finding the labor market is taken from Alvarezζuand Veracierto (2001). Search effort s ∈ [0, 1] yields a disutility B u (s) = B (1−s)ζ −1 , and asu

in Alvarez and Veracierto (2001), we adopt the parameter value ζ = 0.98. We set B = −Bζ,
so that the disutility of maximum search intensity is the same as the disutility of working.
Following Alvarez and Veracierto (2001), the probability of finding the job market is linear
˜ for inexperienced workers.
in search effort: S(s) = ξs for experienced workers and S̃(s) = ξs
The parameters ξ = 0.666 and ξ˜ = 0.764 are calibrated so that the model matches the average
unemployment duration of 3 months for both experienced and inexperienced workers.
Jobs are destroyed either by nature or by firms’ decisions. We set nature’s annual job

18

destruction rate to λ = 0.03, and proceed to determine the added job destruction rate qchosen by firms as if it also were a fixed parameter in the first calibration stage. Specifically,in line with observations of Hall (1982) we seek to target around six jobs held on average overthe 40-year period for age bracket 25-64, and another average of three jobs over the initial
five years for age bracket 20-24. The higher turnover at the beginning of careers is attainedby the extra layoffs that nature imposes on inexperienced workers, λ̃ − λ. Our calibrationTRyields the parameter value λ̃ = 0.123 and firms’ layoff rate qUS= 0.118 for the U.S. economy
in tranquil times, where the latter will be rationalized in the second calibration stage whenparameterizing the stochastic process for firms’ productivities.
Given the above targets of a 3-month average duration of unemployment for all workers, and around nine jobs held on average over a lifetime, the implied U.S. unemployment
rate in tranquil times is 5.4%. Our calibration target for Europe in tranquil times is an
unemployment rate that is lower by 1.5 percentage points. Since the historical record is thatdurations of unemployment were similar across the Atlantic in tranquil times, we ‘calibrate’TR
European firms’ layoff rate to be qEU= 0.049, or more exactly, this is a second target to berationalized in the second calibration stage when parameterizing the stochastic process forfirms’ productivities that will prevail on both sides of the Atlantic.
Another major labor market transition arises in turbulent times when nature’s job destruction is associated with the risk of extraordinary human capital loss. The distributionof human capital h′ for such a laid-off worker, as encoded in the transition probabilities
Hiλ (h̄, h′ ), is the left half of a normal distribution, with the range starting at the lowest
possible human capital ho,i and ending at the worker’s human capital before the layoff h̄.
Specifically, the truncated distribution, indexed by the variance σλ2 of the underlying normal
distribution, is obtained as follows. We take the left side of a normal distribution that isconfined to and centered on the unit interval. The truncated distribution is normalized tointegrate to one, and is the same for every experienced worker who is laid off due to nature’s
job destruction. For each such laid-off worker, we merely rescale the range of the described
distribution so that it starts with ho,i and ends at that particular worker’s human capitalh̄ before the layoff. In tranquil times, the variance of the underlying normal distribution iszero, since there is no loss of human capital. In turbulent times, the variance of the underlying distribution is set to σλ2 = 0.306, based on calibration targets to be laid out in section
5.5.1010

For our parameterization based on an underlying normal distribution with a mean at the worker’s humancapital before the layoff h̄, and then using the truncated left half of that distribution with a range starting at
ho,i , the maximum degree of turbulence is bounded by a uniform distribution over that range. When opting

19

5.4

Production technology

We adopt a standard parameterization of a firm’s production function: a capital share of
α = 0.33 and an annual depreciation rate of δ = 0.06. Regarding a firm’s job-specific productivity level z, we follow Mortensen and Pissarides (1994) who in a continuous-time model
assume that the process that changes the idiosyncratic productivity is Poisson with arrival
rate pz , and when there is a change, the new value z is drawn from a fixed distribution. Analogously, our Markov transition Z(z, z ′ ) at a bi-monthly frequency is as follows. Next period’s
productivity z ′ remains unchanged at value z with probability 1 − pz . With probability pz ,a new productivity is drawn from a normal distribution having mean 0.5 and variance σz2that has been truncated to the unit interval [0, 1] and then normalized to integrate to one.
In contrast to Mortensen and Pissarides (1994), who set pz and σz to match job creation
with data reported for U.S. manufacturing by Davis and Haltiwanger (1992), our calibration
targets come from the first calibration stage where we matched the average number of jobs
held by a worker over her working age.11
We calibrate the two parameters pz and σz to fit our targeted layoff rates for the U.S.
and Europe in tranquil times. The solid line in figure 2 depicts all combinations of (pz , σz )for which the reservation productivity of U.S. firms is such that their annual layoff rate isTR
qUS= 0.118. The family of dashed lines describe Europe, where each dashed line is drawn
for a different job destruction tax. Starting from below the seven dashed lines represent a
job destruction tax equivalent to 0, 1, 2, 3, 4, 5 and 6 months of low-type workers’ average
earnings, respectively. Analogous to the solid line, each dashed line with its particular job
destruction tax depicts all combinations of (pz , σz ) for which the reservation productivity
TRof European firms is such that their annual layoff rate is qEU= 0.049. The intersectionof the dashed line in the middle (that corresponds to a job destruction tax equivalent to 3
months of low-type workers’ average earnings) and the solid line, at (pz , σz ) = (0.070, 0.053)
and marked by a bullet, rationalizes both targeted layoff rates for the U.S. and Europe,for even higher turbulence, we can achieve that by shifting the mean of the underlying normal distribution
to ho,i , and then using the truncated right half of that distribution with a range ending at h̄. Successively
reducing the variance of that underlying distribution generates further increases in turbulence, and maximum
turbulence is attained at a zero variance which would mean that Hiλ (h̄, ho,i ) = 1, so that all job destruction
by nature is associated with 100% loss of accumulated human capital, i.e., any worker experiencing job
destruction induced by nature ends up with her initial endowment ho,i .
11While we do not seek to match job destruction data, our calibration target for the U.S. annual layoffTRrate (due to jobs being destroyed by nature or by firms’ decisions in our model), λ + (1 − λ)qUS= 0.144,is yet close to Davis and Haltiwanger’s (1992) reported gross job destruction rate of 11.3% per year in the
U.S. manufacturing sector over the 1972 to 1986 period.

20

respectively.
New jobs are created at a startup cost µ equivalent to three months of low-type workers’
average earnings in the U.S. economy in tranquil times, and the productivity of a new job
is zinitial = 0.5.

5.5

Disutility of work and turbulence

The parameter space in figure 3 is the disutility of work B and an index for the parameterization of extraordinary human capital loss in turbulent times. Specifically, the latter index
is the average percentage loss of accumulated human capital implied by the calibration oftransition probabilities Hiλ (h̄, h′ ).12 We have superimposed on that parameter space two setsof isoquants – a family of downward-sloping curves pertaining to the attainment of specific
European unemployment rates in turbulent times, and a set of horizontal lines pertaining to
the attainment of specific percentage increases in the permanent variance of U.S. labor earnings between tranquil and turbulent times, in the way analyzed by Gottschalk and Moffitt(1994).
Each downward-sloping curve shows combinations of the disutility of work and the index
for turbulence that generate a specific European unemployment rate in turbulent times.
Starting from the left side those isoquants go from 7% to 20% European unemployment in
turbulent times. Since our calibration target is 10%, we select the fourth isoquant fromthe left side. As can be seen, an unemployment target can be attained for practically any
disutility of work if we make offsetting changes in the degree of turbulence. A higher disutilityof work makes European workers more prone to bail into publicly funded unemployment, so
we must reduce the degree of turbulence in order not to overshoot the specific unemployment
rate at a given isoquant. On the right side of the figure there are vertical shaded regionsthat indicate problems for our underlying calibration of the model in tranquil times. In
particular, when moving to the right of the first vertical line, the higher value of disutility
causes higher European unemployment already in tranquil times and hence, the calibration
target of a European unemployment rate that is 1.5 percentage points lower than that of
the U.S. is no longer met. When crossing the second vertical line to the right, European
unemployment in tranquil times is even higher than that of the U.S. And after the third
12
Note that the percentage loss is expressed in terms of accumulated human capital, excluding the endowment ho,i that constitutes a lower bound for human capital. Hence, the highest possible loss is 100% andimplies that any worker who suffers job destruction by nature would fall down to her initial endowment ho,i .
The associated transition probabilities Hiλ (h̄, h′ ) would equal one for h′ = ho,i , and zero otherwise.

21

vertical line, the European unemployment rate in tranquil times exceeds 10%. We conclude
that explaining low European unemployment in tranquil times implies upper bounds on thedisutility of work.13
As further discussed in section 6.2, we compute permanent and transitory componentsof earnings in the U.S. model economy. Each horizontal line in figure 3 shows combinationsof the disutility of work and the index for turbulence that generate a specific percentage increase in the permanent variance between tranquil and turbulent times for high-type workers.
Starting from below, those isoquants represent increases of 25%, 50%, 75% and 100%, respectively. The reason that the isoquants are perfectly horizontal is that U.S. workers areat a corner solution for career length – they retire at an official retirement age – and hence,
perturbations in the disutility of work do not affect outcomes. Since Gottschalk and Moffitt(1994) report on observed increases of around 40% in the permanent variance, we pick theparameter values at the bullet point in figure 3, where the permanent variance of earnings
increases by 36% for high-type workers (and by 27% for low-type workers, not shown).
While our calibration ensures that European unemployment will rise to 10% in turbulent
times, and that the U.S. economy will experience some earnings dynamics reminiscent ofGottschalk and Moffitt (1994), questions remain about what the model has to say about any
differences in outcomes over individuals’ life cycles. We turn to these next.

6

Outcomes

Table 7 shows how our model fits aggregate labor market outcomes across the Atlantic ocean
in the post-World War II era. As in the data, the unemployment rate was significantly
13

In figure 3, we retain the parameterization from earlier calibration stages and only vary the disutilityof work B and the stochastic process for human capital loss in turbulent times. So when varying B, why
do we not need to recalibrate the entire model to ensure that the targets of the earlier two calibration
stages are still met? The reason is that we initialized the calibration procedure with a value of the disutilityof work (B = 0.22) that is low enough so that workers are at a corner solution for career length at the
mandatory retirement age, which makes the outcomes of the first two calibration stages almost invariant to
the particular choice of such a low value of B. To show that to be the case, we have recalibrated the entire
model for alternative values of B ∈ {0.10, 0.15, 0.20, 0.25} and found that the parameterization in the firsttwo calibration stages are indeed virtually unchanged and as a result, they all generate isoquants for 10%
European unemployment in turbulent times that lie on top of the one drawn in figure 3 for B = 0.22. But
when choosing too high a disutility of work, e.g. B = 0.30, that invariance no longer holds, and it is especiallythe parameterization of the stochastic process for firms’ productivities that change – the calibration procedureseeks to balance off the occurrence of publicly funded early retirement in Europe already in tranquil times
by lowering the layoff rate of firms. Since such high values of B generate counterfactual outcomes of early
retirement in tranquil times and cannot attain the two targets in the third calibration stage, we do not
pursue that shaded part of the parameter space in figure 3 any further.

22lower in Europe as compared to the U.S. in tranquil times (before the 1970s), but thatchanged dramatically after the 1970s when European unemployment more than doubled
while the U.S. unemployment rate remained virtually unchanged. A mechanical explanation
for Europe having a lower unemployment rate in the pre 1970s tranquil times was its lower
inflow rate into unemployment while the average duration of unemployment was similar on
both sides of the Atlantic. A mechanical explanation for the outbreak of high unemployment
in Europe during the post 1970s turbulent times was a drastic increase in the average durationof unemployment while the inflow rate remained low and below that of the U.S., where notmuch changed across tranquil and turbulent times.
These aggregate statistics conceal worker heterogeneities that are critical for understanding our theory of trans-Atlantic employment experiences. To provide a background for ouranalysis of individual dynamics that are set off by turbulence, section 6.1 reports life-cycle
outcomes implied by our model in tranquil times; in turbulent times those same dynamics
characterize lives of those workers who choose to work until the mandatory retirement age.
Comparing tranquil and turbulent times, section 6.2 examines how the dynamics of individuals’ earnings change, and section 6.3 probes beneath the aggregate unemployment outcomesof table 7 to study individual experiences across different ages and education levels. All of
our inquiries produce outcomes that are strikingly similar to the data.

6.1

U.S. outcomes in tranquil times

Figure 4 shows life-cycle profiles of earnings (panel a) and assets holdings (panel b) of U.S.
low-type and high-type workers, respectively. The solid lines describe model outcomes andthe dashed/dotted lines depict data. The earnings data refer to full time male workers
from the U.S. Census in 2006, and the asset data are from the Survey of Consumer Finance(SCF) in 2004, depicting household holdings of financial and non-financial assets net of debt
such as housing loans and other lines of credit. High-type (low-type) workers correspond tocollege (non-college) graduates in the data, and in the case of asset holdings, the sample does
not include the top 5% of households, for reasons explained in section 5. Model outcomes
resemble data in figure 4, as do the life-cycle profiles of consumption in figure 5. (See e.g.
Gourinchas and Parker (2002).)
The model’s upward-sloping earnings profiles are driven by workers who have by becoming
experienced have acquired access to the Ben-Porath human capital technology. Figure 6
displays life-cycle profiles of average human capital (panel a) and associated investments

23

measured as the fraction of time a worker devoted to human capital accumulation (panelb). Thanks to past achievements in this strand of research, our succeess in matching theearnings profiles of figure 4 could be anticipated. For the record, note that earnings are
increasing not only because an older worker has more human capital but also because she
gradually reallocates time away from human capital accumulation and toward selling theservices of already accumulated human capital. That underlying investment calculus will
be central in the next section when we study age-dependent changes in autocovariances ofindividual earnings induced by increased turbulence.
The heightened job churning of young workers during the inexperience phase introduces
a concavity in the life-cycle profile of the average number of jobs held at different ages infigure 7 – a shape that roughly conforms with observations, e.g., see Hall (1982). This higher
rate of inflow of inexperienced workers into unemployment gives rise to the elevated youth
unemployment depicted by the dashed line in figure 8.a. That confirms a common mechanicalexplanation for why the youngest group of workers experience higher unemployment rates
across time periods and across countries.
Figure 8 shows that U.S. unemployment outcomes in turbulent times closely resemble
those in tranquil times: the unemployment rate (dashed lines) are virtually the same acrosstranquil times (panel a) and turbulent times (panel b). This pattern prevails despite thefact that higher human capital losses in turbulent times alter individual earnings dynamics,
to which we turn next.

6.2

U.S. earnings dynamics in turbulent times

Since laid off workers are entitled to unemployment benefits for a maximum of 6 months in
the U.S., the eruption of turbulence does not cause unemployment to change very much in
the U.S. Instead, at our parameterization of the disutility of work, laid off American workers
who experience losses of human capital choose to return to work at diminished earnings
rather than to enter privately financed early retirement. We now use artificial earnings data
to examine whether our model exhibits the kind of earnings dynamics observed by Gottschalkand Moffitt (1994) and Moffitt and Gottschalk (1995). It makes sense to study the two types
of worker separately. We start by focusing on the high type.
Using the U.S. model economy in tranquil and turbulent times, respectively, we generate
artificial versions of Gottschalk and Moffitt’s PSID panels for 1970–78 and 1979–87, respectively. Applying their method for decomposing each panel’s earnings into permanent and24transitory components delivers figures 9.b and 10.b as our counterparts to their figures 2 and
4 (reproduced here in our figures 9.a and 10.a). Evidently, our representation of turbulence
spreads the distributions of both components of the Gottschalk-Moffitt decompositions in
the directions that they observed. There are differences in the ranges of the distributions.
That the distribution of permanent earnings in figure 9.b spans a smaller range than do theGottschalk-Moffitt data is not surprising. Our artificial panel contains an ex-ante homogeneous group of college graduates, while the PSID used by Gottschalk and Moffitt comprises
a diverse group of American males with different educational backgrounds. It is also noteworthy that the increased earnings variability in the more turbulent period in our figure
10.b occurs at lower standard deviations than Gottschalk and Moffitt’s. In this respect,
the increase in economic turbulence in our parameterization for the 1980’s falls short of thechanges observed in U.S. data. That was also true in the simpler frameworks of Ljungqvist
and Sargent (1998, 2008).
The corresponding figures for low-type workers are very similar. That might not be
too surprising since our calibration of the model brings similar percentage increases in thevariances of permanent earnings for both types of worker, which in turn comes from targetingthe percentage increases in actual variances observed by Gottschalk and Moffitt (1994). It issensible for us to consider low-type and high-type workers separately because merging themwould result in a bimodal distribution of permanent variances. An increase in turbulence
would have ambiguous effects on the variance of that blended distribution: not only would
the tails gather mass but the valley between the two peaks of the bimodal distribution wouldchange.
To illustrate forces at work, consider the following unanticipated shock to American
workers in tranquil times. For a large number of randomly drawn employed workers in
different age groups, let each worker experience a loss of human capital that decreases her
earnings by 10 percent. Simulate their subsequent earnings until the mandatory retirementage; compare those paths to what their earnings would have been in the absence of thoseshocks to human capital. Outcomes of that experiment for high-type workers appear infigure 11. The nearer a worker is to the official retirement age, the lower is her propensity
to invest in human capital in order to make up for the loss of human capital.
After our experiment in figure 11, one might not be surprised to learn that the artificial
panel data from the U.S. model economy imply increases between tranquil and turbulent
times in autocovariances of earnings of older workers, as reported in table 8. In fact, ourresults conform closely with the earnings dynamics documented by Moffitt and Gottschalk25

(1995), who conclude that between the 1970s and 1980s, there has been “an increase incovariances . . . larger for the older age groups and for the low-order covariances.” The percentage changes in autocovariances in our simulated data resemble theirs, as can be inferredfrom figure 12 that reproduces Moffitt and Gottschalk’s (1995) figure 1(d) that depicts how
autocovariances by lag order in age group 45–54 evolve over the years.
In the U.S. model economy, turbulence primarily leaves its mark on earnings dynamics,
not on unemployment. Things are different for people living inside the European model
economy.

6.3

European unemployment experiences

A government imposed job destruction tax that suppresses the layoff rate and frictional
unemployment causes the unemployment rate to be lower in Europe in tranquil times. Figure
13 shows that without that tax, unemployment in Europe would be higher than in the U.S.
,primarily due to higher unemployment benefits in Europe. At our calibration of a job
destruction tax equal to three months of low-type workers’ average earnings, the European
unemployment rate is 1.5 percentage points lower than that of the U.S. From the historical
record, the President’s Committee to Appraise Employment and Unemployment Statistics(1962), appointed by President John F. Kennedy, confirmed the reliability of statistics thatindicated significantly lower unemployment rates in Europe in the 1950s. That led the
Deputy Commissioner of the Bureau of Labor Statistics to suspect high costs of laying off
workers in Europe to be the cause.14 Because a job destruction tax lowers unemployment
by reducing the layoff rate, our model economy reproduces the observations of longer job
14

Deputy Commissioner Robert J. Myers (1964, p. 180–181) wrote:“One of the differences [between the U.S. and Europe] lies in our attitude toward layoffs. The
typical American employer is not indifferent to the welfare of his work force, but his relationshipto his workers is often rather impersonal. The interests of his own employers, the stockholders,tend to make him extremely sensitive to profits and to costs. When business falls off, he soon
begins to think of reduction in force . . .
In many other industrial countries, specific laws, collective agreements, or vigorous public opinion protect the workers against layoffs except under the most critical circumstances. Despite
falling demand, the employer counts on retraining his permanent employees. He is obliged tofind work for them to do. . . .
These arrangements are certainly effective in holding down unemployment.”

For an analysis of why there is a strong presumption that job destruction taxes reduce unemployment insearch models and in matching models in which firms are only liable to pay the tax for the workers they
have chosen to hire, but not after merely encountering job seekers who are not hired, see Ljungqvist (2002).

26

tenures and therefore, on average, fewer jobs held by a European worker over her lifetime
than by a U.S. worker, as shown in figure 7.
To appreciate why European unemployments rates explode in turbulent times, we examine an experienced worker’s decision rule for job search intensity in tranquil times. In
addition to her type, the state variables of an unemployed worker are her assets, human capital, last earnings (as a determinant of unemployment benefits) and age, but not the length ofpresent unemployment spell, since there is no maximum duration of unemployment benefits
in Europe. For an unemployed person who owns the average wealth level and is entitled tobenefits based on average earnings in her age group, figure 14 depicts the optimal searchintensity as a function of age and ‘human capital loss,’ i.e., how much her human capital
falls below the average level in her age group as measured by accumulated human capital,
excluding the endowment ho,i that constitutes a lower bound for human capital. The solidline is a contour for full search intensity, below which an unemployed worker chooses thehighest search intensity. Between the solid and dashed lines, the optimal choice is an interior solution for search intensity; there is a corner solution above the dashed contour line forzero search intensity.15 Figure 14 shows that a high-type worker (panel b) is more resilient
to a human capital loss, choosing a higher search intensity than would a corresponding lowtype worker (panel a). The explanation for this is twofold. First, Ljungqvist and Sargent(2014, sec. 3) show in a learning-by-doing framework that, off corners, the more elastic isan earnings profile to accumulated working time, the longer is a worker’s career. We haveverified that an analogous result holds in the present framework: in particular, if we relax
the mandatory retirement age, a high-type worker with her more productive Ben-Porath human capital technology would choose a longer career than a corresponding low-type worker.
Second, unemployment benefits are computed as a replacement ratio of last earnings but
are subject to a maximum benefit level, which means that the effective replacement rate ishigher for low-type workers because her benefits are based on lower incomes and therefore
less likely to be restricted by the maximum benefit level. For these two reasons, a low-type
worker is more prone to become discouraged after losing human capital and to choose a lower
search intensity than would a high-type worker of the same age after the same percentage
loss of human capital. Fortunately, there are no extraordinary human capital losses in tranquil times, so the European unemployment rates in figure 8.a are practically the same across15

The non-monotonicities of the negatively sloped contour lines in figure 14 are due to our discretizationof the state space. In computations with finer grids, we obtained smoother contour lines with smaller
non-monotonicities and confirmed that the computed equilibrium does not change much with finer grids.

27

low- and high-type workers of the same age (not shown in the figure).
It is useful to decompose European unemployment outcomes in turbulent times into twoparts – first without and then with a restrictive minimum wage. If there is no minimum
wage, the economic forces at work can be gleaned from figure 14, since those tranquil times
decision rules in will be largely the same in turbulent times. Based on that figure, we would
not expect to see any major increase in unemployment among workers of age 40 and younger
because they are choosing high search intensities regardless of any human capital losses.
While they potentially stand to lose considerable amounts of human capital since most of
the investments are completed by age 40 in figure 6, they also have more than half of theirworking lives ahead of them until they reach the official retirement age of 65. In our model
economy, these relatively young workers are inclined to take a new start in the labor market
after any unfortunate loss of human capital. The decision rules in figure 14 show that anincreasing number of workers exercise the option to bail into generous unemployment benefits
as they age. This is indeed the outcome in figure 15.a where unemployment by age starts
gradually to increase after age 40 as compared to tranquil times in figure 8.a. In table 9,
older age groups in Europe experience increasing average durations of unemployment anda larger fraction of long-term unemployed among the unemployed of an age group. (ForEurope in table 9, compare the two columns Tranquil and Turbulent⋆ , where the asterisk
indicates no minimum wage.)
The introduction of a restrictive minimum wage in Europe affects only low-type workers
at the beginning of their careers, as can be seen in figure 15 by comparing turbulent times
without a minimum wage (panel a) and with a minimum wage (panel b). After summing
the weighted unemployment rates of low- and high-type workers in figure 15.b, we arrive at
the European unemployment rate by age in turbulent times in figure 8.b (solid line). Overa life-cycle, the obstruction associated with the minimum wage is a transient phenomenon:
prime-age European workers suffer no higher unemployment rates than do prime-age American workers. The end-of-career elevated unemployment is a very different issue. As notedby OECD (2003, chap. 4), some of these workers might be found in government provided
disability insurance and early retirement programs, but they are actually unemployed rather
than unable to work. Having said that, our European model economy serves the majority ofworkers well. Those (1) who are not unduly impacted by the minimum wage, and (2) who do
not suffer untimely human capital losses and them become induced by generous benefits towithdraw into early retirement will lead lives like they would have had if times had remained
tranquil. In portraying the distribution of years out of work over an individual’s working age,28

figure 16 provides a perspective on how different European workers were affected by living
in turbulent instead of tranquil times. Despite a thicker tail to the right with more than
five years out of work, the majority of Europeans in turbulent times are idle less than twice
the mean of 1.9 years in tranquil times. The U.S. distributions (not shown) are practicallyunchanged over time. They resemble the European distribution in tranquil times but somewhat shifted to the right with a mean of 2.6 years out of work over an individual’s working
age, due to the higher rates of job churning in the U.S. (see figure 7).

7

Concluding remarks

Our heterogeneous-agent life-cycle model extends a line of research about how observed
increases in labor earnings variability contributed to an outbreak of persistently higher unemployment in Europe after the 1970s. After incorporating key components of earlier studies
into the present framework and adopting standard parameterizations from related macroeconomic analyses, we have confirmed predictions of those earlier papers and gone on to derive
additional implications that are also born out by data. A brief overview of this line of inquiry helps us to appreciate the forces at work in our present framework and to describe
challenges that remain for macro-labor studies in general, and for analyses of trans-Atlantic
employment experiences in particular.
In Ljungqvist and Sargent’s (1998, 2008) extensions of a McCall (1970) style searchmodel, risk-neutral workers maximize expected present values of lifetime labor earnings andunemployment benefits while accumulating human capital through learning by doing. Since
benefits are a fraction of last earnings, their choices of high reservation wages and low searchintensities make laid-off agents who suffer large losses of human capital prone to become
long-term unemployed. Ljungqvist and Sargent (2008) extended the theory by modifying
two assumptions. In order to study life-cycle dynamics and how layoff costs can suppress
frictional unemployment and thereby explain why Europe had lower unemployment thanthe U.S. in tranquil times, they replaced (i) perpetual youth and and a constant probabilityof retiring, and (ii) a drawn wage (per unit of human capital) staying constant over theduration of an accepted job with (i’) stochastic aging that send workers through age classes
until retirement, and (ii’) occasional new wage draws at a continuing job. Those two newfeatures remain central to our present model.
Ljungqvist and Sargent (2006) compared their turbulence theory to Prescott’s (2005)
attribution of low European employment to high tax rates. That inquiry proceeded in two29

parts, and its implications are central to the present paper. First, when including Europeanstyle benefits within Prescott’s employment lotteries model, Ljungqvist and Sargent (2006)
reverse the puzzle that Prescott had set out to study, namely, why Europeans work solittle, became the opposite one: putting generous benefits into that employment lotteriesmodel with its high labor supply elasticity causes employment to plummet far more thanwhat Prescott had observed and hence, the puzzle now becomes why Europeans work somuch. Second, as summarized in footnote 3, it turns out that employment lotteries are notnecessary, because a similar high labor supply elasticity emerges in a time averaging model
when career lengths are at interior solutions. Thus, our present analysis balances these forcesby moving workers on and off corner solutions associated with an official retirement age.
Our analysis incorporates the turbulence mechanism within an environment that also
includes important features and outcomes that researchers from various traditions will recognize: changes in unemployment rates and incidences of long-term unemployment acrossage and education square well with post-World War II outcomes; life-cycle profiles of consumption and asset holdings are in line with the evidence; the Ben-Porath human capital
technology is parameterized in a standard way and hence, earnings profiles conform with earlier estimates; and if earnings data is simulated from our model and then sent to Gottschalkand Moffitt (1994) with the instruction that it pertains to two distinct groups of high school
only and college graduates, respectively, it might pass as an addition to their empirical data.
Moreover, by incorporating a Ben-Porath human capital technology that way we do implies
age-dependent increases in autocovariances of income shocks, finding that makes contact
with the empirical study of Moffitt and Gottschalk (1995).
Our work in this paper illustrates what we see as constructive developments in macrolabor today. Discarding an aggregation theory based on empirically dubious employment
lotteries in favor of a time-averaging life-cycle framework brings macroeconomic work closer
to a longstanding tradition in labor economics based on the life-cycle model. That is progressbecause it facilitates constructive exchanges between macro and labor researchers who havecome to opposite conclusions about magnitudes of labor supply elasticities. The life-cycle
framework promises to focus macroeconomic researchers’ attention on the microeconomic
observations about lifetime labor supply, observations ignored when the lotteries model prevailed among macroeconomists. That can spur research that might lead to the labor supply
elasticity accord foretold by Ljungqvist and Sargent (2011). As emphasized by Rogerson
and Shimer (2011, p. 690),“There is potentially a lot of useful information in the disaggregated data that30

may help to distinguish competing theories. . . . we note two findings here: unemployment differences are particularly pronounced among younger workers, while
employment differences are particularly pronounced both for younger and older(but not prime-aged) workers. More generally, incorporating differences in age,gender and skill level may be useful for distinguishing theories of labor market
outcomes. . . . Kitao et al. [present paper] is a recent example that moves in thisdirection.”
Our model sends inexperienced workers through a phase of job search during which they
suffer exogenous job losses at higher rates than they will later in life. They draw productivities from a McCall (1970) style offer distribution. Working allows a youth stochasticallyto “become experienced”, which means moving to a second phase in which the worker acquires access to a Ben-Porath human capital technology. Hard wired into our model, thephase of inexperience generates outcomes observed early in careers. It helps us meet two
challenges to explaining the increase in European youth unemployment. First, since young
workers have little human capital to lose, our turbulence dynamics cannot explain higher
youth unemployment. Second, because the returns to becoming experienced are large in ourframework, it requires a substantial friction somehow to hinder young workers from starting
their careers. We take that friction to be a binding European minimum wage after the 1970s.
That minimum wages are higher in Europe than the U.S. is beyond dispute, but there isdisagreement about the implications of that fact for employment.
To illustrate opposing opinions about the employment effects of minimum wages, we return to France in figure 1 as our representative of Europe. Using data for 1990-1998 fromthe French Labor Force Survey, Abowd et al. (2000) find strong negative effects on future
employment probabilities of workers whose current real wage falls between the current real
minimum wage and a future increased real minimum wage. Using the same data source forthe year 1981–1989, Dolado et al. (1996) assemble similar evidence for negative employment
effects of the minimum wage but suggest that the business cycle could be a confounding
factor. They proceed to discuss observations and explanations that point in different directions before concluding that “French evidence suggests that the substantial rise in the SMIC
[minimum wage] to the mid-1980s had no adverse effect on employment” (Dolado et al.
1996, p. 343). Both of these papers mention the growing importance of publicly funded programs that either combine education with work or provide low-wage subsidized employment.
Abowd et al. (2000) declare that their study excludes workers whose participation in suchprograms have earned them legal exemption from the minimum wage. After noting the dra31

matic growth in coverage of those programs from 8000 participants in 1976 to about 900,000
in 1993, along with an OECD report stating that the average wage for French teenagers in1987 actually fell below the SMIC, Dolado et al. (1996, p. 338) go on to say that “this should
be taken not as evidence that the SMIC is set at a very high rate, but as an indication that
the SMIC is not the effective minimum wage for these workers.” That conclusion puzzles
us because if we were to include those complications in our model, it would certainly beevidence of too high a minimum wage. The frictions involved when firms and workers seek
to win exemptions or employment subsidies might help explain why the average durationof unemployment rose from 3.3 months to 7.5 months for the youngest age group in our
European model economy after the minimum wage became binding.
Our model of trans-Atlantic employment experiences contains two independent building
blocks – effective minimum wages in Europe and increased turbulence on both sides of theocean. Our model imputes detrimental employment effects to those high European minimum
wages while confirming robustness of earlier turbulence theory of European unemployment
and then confirming that turbulence in the present extended framework brings additional
forces that improve fits to observations on earnings dynamics. The empirical evidence that
we take as the tell-tale signs for an increase in our notion of economic turbulence sincethe 1970s continues to accumulate – from Katz and Autor’s (1999) demonstration that
Gottschalk and Moffitt’s (1994) findings are robust across a variety of studies and data
sets to Kambourov and Manovskii’s (2008) documenting that there occurred a substantial
increase in occupational and industry mobility in the U.S. over the period 1968–1997.

32

A

Skill acquisition technology

For a given state of human capital ht at the beginning of a period year and a choice lt ofinvestment in human capital, the deterministic Ben-Porath technology ht+1 = ht + Ai (ht lt )ν
would tell us ht+1 should be at the end of the year. We have to adapt that outcome because
we discretize the state space by insisting that h lie on one of the 20 grids of human capital.
We design stochastic transition matrices that guarantee that the mathematical expectationof ht+1 is the outcome predicted by the deterministic Ben-Porath technology ht+1 = ht +Ai (ht lt )ν . For example, suppose that ht is 1.0 (grid point number 1) and that ht+1 = 1.2 isimplied by plugging a particular choice of lt into the deterministic Ben-Porath technology;
and suppose that the two nearest grid points are grid point number 1 = 1.0 and grid point
2= 2.0. Then conditional on being at grid 1 today we would set the transition probabilityof going to grid point 2 tomorrow to p(1, 2) = 0.2, and similarly we would set p(1, 1) = 0.8.
To compute the transition matrix under our bi-monthly frequency, we guess and iterate.
First of all, we make sure that agents do not want to travel more than one grid point over a
period of one year (this is just to simplify computations). For each state, choice pair ht , lt ,we first guess that the probability of staying at the current grid in the next period (in twomonths) is p̄. We can then compute recursively the expected human capital in each period
up to the beginning of the next year, that is, in 6 model periods, or 12 months. We check if it
coincides with what it should be according to the deterministic Ben-Porath technology, andadjust p̄ until we achieve the right value. We search in this way for all ht , lt combinations tocompute the entire transition matrix Hin (ht , ht+1 ; lt ).

33

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37

Table 1: States and decisions
Variable

Meaningitworker type (low or high)
age

a
c

assetsconsumptionsγ
dsearch intensity
UI benefits
elapsed duration of unemploymenthlhuman capital
investment in human capitalnn̂θefficiency units of labor (θn̂)
effective labor (before earnings shock)worker earnings shockzkfirm productivity shockphysical capital

Table 2: Value functions
Value function

phase of life

decisionsṼiu (a, γ, d, t)Ṽin (a, n̂, t)

inexperienced, unemployedinexperienced, employedc, a′ , sc, a′Viu (a, h, γ, d, t) experienced, unemployedVin (a, h, t)
experienced, employed
V o (a, t)old, retiredc, a′ , sc, a′ , lc, a′V f (z){operate, exit}, k

firm

38

Table 3: Government policies
Description

U.S.

Europedmax
Γ(e)UI maximum duration
UI with previous earnings e

6 months
60% replacement

unlimited
60% replacementγΩmaximum UI
job destruction tax

50% avg. earnnone

100% avg. earn
3mos of low-type earneminminimum wage

none

τn

labor tax rate

15%

50% avg. earn but only
in turbulent times
30%

τp
τk

social security tax rate
capital tax rate

10%
15%

10%
15%

ǫ
X

social security benefits
public consumption

40% avg. replacement
residual

50% avg. replacement
residual

Table 4: Parameters of a simple life-cycle model (annual frequency)
Parameter

Description

Value

Preferences, demographics and interest rateβsubjective discount factor

0.98141Bmtr

disutility of work
survival prob. at age t
net real interest rate

0.22
Bell and Miller (2005)
0.04

Human capital technology
νAi

Ben-Porath curvature parameter
Ben-Porath multiplicative parameter

0.8
AL = 0.04924, AH = 0.06616

ho,i
Hin (h, h̄; l)initial human capital
Ben-Porath discretization: transition
prob. h ⇒ h̄, given investment lho,L = 1.0,
ho,H = 1.78507
see Appendix A

Θ(θ)

prob. dist. of worker earnings shocklog θ ∼ N(0, 0.04)

39

Table 5: Parameters for labor market transitions
Parameter

Description

Value

Search disutility and technology
ζ
B
ξ
ξ˜

u

search disutility curvature parameter

0.98

search disutility multiplicative parametersearch technology parameter (experienced)−0.22 · 0.98 = −B ζ
0.66584

search technology parameter (inexperienced)

0.76410

Probabilities of job terminationλ(λ̃ − λ)prob. of exogenous job destruction
prob. of additional exogenous job separation for0.03 (annual)
0.09253 (λ̃ = 0.12253)q

inexperienced workers
prob. of firms destroying jobs

endogenous

Career phase of inexperienceπ
Gi (n̂)prob. of becoming experienced
prob. dist. of effective labor n̂, from which an
inexperienced worker of type i draws

0.33 (annual)n̂ ∼ N(0.7, 0.02) andrange truncated to [0, 1]

Human capital loss upon exogenous job destruction
Hiλ(h̄, h′ )prob. of h′ for worker with beginning-of-period h̄,
deduced from left half of truncated normal dist.,

σλ2 = 0 (tranquil)

where underlying distribution is N(h̄, σλ2 ))σλ2 = 0.3059 (turb.)

Table 6: Parameters of production technology
Parameter

Description

Value

α

capital share in prod. function

0.33

δ
µ
zinitial

capital depreciation rate
startup cost for a new job
productivity of a new job

0.06 (annual)
3mos of low-type earn
0.5Z(z, z ′ )transition prob. for productivity:
random draw with prob. pz

pz = .069550

at which z ′ ∼ N(0.5, σz2 ) andrange truncated to [0, 1]

σz = 0.05344

40

Table 7: Unemployment outcomesU.S.

EuropeTranquil

Turbulent

Tranquil

Turbulent

Unempl. rate (percent)
Unempl. duration (months)†

5.39
3.00

5.45
3.01

3.90
3.21

9.99
12.93

Inflow rate (percent)⋆
Outflow rate (percent)⋆

3.41
66.6

3.45
66.5

2.16
62.8

2.22
23.2

†

Cross-sectional average duration of all spells in progress⋆
At bi-monthly model frequency

Table 8: Percentage increase between tranquil and turbulent times in autocovariances ofannual earnings at different lag orders for high-type workers in the U.S.
Lag
order

Age group
25–34 35–44 45–54

1–4

5.4

25.3

54.1

5–9
10–15

2.6
3.0

15.0
5.3

39.4
23.4

Table 9: Unemployment duration and long-term unemployment by age in Europe.
Unempl. duration(months)⋆

Long-term unempl.
(percent of unempl.)

Age

Tranquil

Turbulent

Turbulent⋆

Tranquil

Turbulent

Turbulent⋆

20-29

3.29

7.51

3.31

0.51

16.42

0.50

30-39
40-49
50-59

3.17
3.01
2.99

6.20
7.58
17.34

3.42
8.11
19.13

0.37
0.17
0.14

11.61
16.13
47.94

0.69
18.36
51.53

60-

3.35

26.36

29.16

0.29

63.77

66.61

All

3.21

12.93

14.70

0.40

31.40

33.55

Without the minimum wage
41

1970

2004

Figure 1: Male unemployment and employment-population rates (in percent) by age inFrance and the U.S., respectively, in 1970 (left panel) and 2004 (right panel). Source: OECD(by courtesy of Robert Shimer).

42

Standard deviation

0.15

0.1

0.05

0
2

4

6

8
10
Arrival rate (%)

12

14

16

Figure 2: Isoquants for firms’ layoff rates as functions of the productivity process, defined by
the bi-monthly arrival rate of shocks (pz ) and the standard deviation (σz ). The solid line is
the isoquant for a U.S. annual layoff rate of 11.8%. The family of dashed lines are isoquants
for a European annual layoff rate of 4.9%, given different job destruction taxes. Startingfrom below, the dashed lines represent taxes from 0 to 6 months of low-type workers’ average
earnings, respectively.

average loss of skills (%)

100

80

60

40

20

0
0.05

0.1

0.15

0.2
0.25
disutility B

Figure 3: See section 5.5.
43

0.3

0.35

70

10

60
Wealth in $10,000

Earnings in $10,000

12

8
6
4
2
0
20

50
40
30
20
10

30

40
Age

50

0
20

60

30

40

50

60

70

80

90

Age

(a) Earnings(b) Assets

Figure 4: Earnings (panel a) and assets (panel b) as a function of age in the U.S. The solidlines describe outcomes in the model and the dashed lines depict U.S. data, where the upper(lower) pair of a solid and a dashed line refer to high-type (low-type) workers who correspondto college (non-college) graduates in data.

7

Consumption in $10,000

6
5
4
3
2
1
0
20

30

40

50

60

70

80

90

Age

Figure 5: Consumption as a function of age in the U.S. The solid line is high-type workers
and the dashed line is low-type workers.

44

3

0.5

0.4
2.5
0.3
2
0.2
1.5
0.1

1
20

30

40
Age

50

0
20

60

30

(a) Human capital

40
Age

50

60

(b) Investments

Figure 6: Human capital (panel a) and investments in human capital (panel b) as a functionof age in the U.S. in tranquil times. The solid line is high-type workers and the dashed line
is low-type workers.

Average number of jobs held

10

8

6

4

2
U.S.
Europe
0
20

30

40
Age

50

60

Figure 7: Workers’ average number of jobs held at different ages in tranquil times. The solidline is Europe and the dashed line is the U.S

45

35

30

30
Unemployment rate (%)

Unemployment rate (%)

35

25
20
15
10
5
0

25
20
15
10
5

25

30

35

40

45
Age

50

55

60

0

65

25

(a) Tranquil times

30

35

40

45
Age

50

55

60

65

(b) Turbulent times

Figure 8: Unemployment rates as a function of age. The solid line is Europe and the dashedline is the U.S in tranquil times (panel a) and in turbulent times (panel b).

30
Tranquil
Turbulent

25

25
20

20
15
Percent

15
10

10
5

5

0
−2

0
−1.5

−1

−0.5
0
0.5
Mean of log annual earnings

11.5(a) Data

−0.4

−0.2
0
0.2
Mean of log annual earnings

0.4

0.6

(b) Model

Figure 9: Distribution of permanent earnings in the U.S. The dark bars and the light bars
correspond to tranquil and turbulent times, respectively, as taken from Gottschalk andMoffitt (1994, fig. 2) (panel a) and our model (panel b).

46

40
Tranquil
Turbulent45

35Percent

40
35

30

30

25

25

20

20

15

15

10
10

5
5
0
0

0.2

0.4

0.6
0.8
Standard deviation

1

1.2

1.4

0
0

0.1

0.2
0.3
Standard deviation(a) Data

0.40.5(b) Model

Figure 10: Distribution of standard deviations of individuals’ transitory earnings in the U.S.
The dark bars and the light bars correspond to tranquil and turbulent times, respectively,
as taken from Gottschalk and Moffitt (1994, fig. 4) (panel a) and our model (panel b).
−7−7.5

percentage

−8
−8.5
−9
loss at age 35
loss at age 40
loss at age 45
loss at age 50
loss at age 55

−9.5
−10
−10.5
0

5

10
15
20
years since the shock

25

30

Figure 11: Earnings loss relative to the age-earnings profile for high-type workers in the U.S.
in tranquil times, after a hypothetical one-time loss of human capital that causes an initialdecline in income by 10%. The curves refer to representative samples of the population atage 35, 40, 45, 50 and 55, respectively, for whom the lengths of remaining income data span29, 24, 19, 14 and 9 years, respectively.
47

Figure 12: Empirical log earnings variances and covariances by year and by lag order in age
group 45–54 in the U.S. Source: reproduction of Moffitt and Gottschalk (1995, figure 1(d)).

48

6Unemployment rate (%)

5.5
5
4.5
4
3.5
3
0
1
2
3
4
5
6
Layoff costs (months of low−type worker average earnings)

100

100

80

80
Human capital loss (%)

Human capital loss (%)

Figure 13: Unemployment rate as a function of layoff costs in Europe in tranquil times.
Layoff costs are measured in terms of months of low-type workers’ average earnings.

60

40

20

60

40

20
Search intensity 0
Search intensity 1

0
30

35

40

Search intensity 0
Search intensity 1

45

50

55

0
30

60

Age

35

40

45

50

55

60

Age

(a) Low type(b) High typeFigure 14: Optimal search intensity of the average low-type worker (panel a) and high-type
worker (panel b) in Europe in tranquil times, as a function of age and ‘human capital loss’.
The agent is assumed to hold the average wealth level and to be entitled to benefits basedon average earnings in her age group. The search intensity is plotted for different levels ofhuman capital below the average level in her age group, where the difference between thesenumbers is interpreted as her ‘human capital loss’. The solid (dashed) line is the contour
curve for full (zero) search intensity.
49

35

35
Low−type
High−type

30
Unemployment rate (%)

Unemployment rate (%)

30
25
20
15
10
5
0

Low−type
High−type

25
20
15
10
5

25

30

35

40

45
Age

50

55

60

65

0

25

(a) Without minimum wage

30

35

40

45
Age

50

55

60

65

(b) With minimum wage

Figure 15: Unemployment rates as a function of age in Europe in turbulent times without
a minimum wage (panel a) and with a minimum wage (panel b). The solid line is high-type
workers and the dashed line is low-type workers.

0.09
Tranquil
Turbulent

0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0

5
10
Number of years out of work

15

Figure 16: Distribution of number of years out of work over an individual’s working age inEurope. The dashed line is tranquil times and the solid line is turbulent times.

50