The Scarring Effect of Recessions:
A Quantitative Analysis∗
Christopher Huckfeldt †
New York University
JOB MARKET PAPER
This version: January 12, 2014
[VIEW CURRENT VERSION ]
Abstract
What accounts for the persistent negative outcomes associated with job loss during a
recession? Standard models of equilibrium unemployment are unable to explain the
large and cyclical present value costs of job loss. I study a model of business cycles
with equilibrium unemployment and two key ingredients: specific human capital and
the presence of some “dead-end” jobs, where production requires no specific human
capital input. In response to a negative aggregate shock, firms direct job creation
towards workers with higher human capital, leaving workers who would search for
skill-intensive employment during expansions to search for low-skill jobs. As a result,
workers displaced from higher paying jobs are more likely to be persistently reallocated
to lower paying employment, generating large present value earnings losses. In the
baseline calibration, the model is able to capture 75.1% of the average present value
cost of job loss and 34.2% of the cyclicality. Workers at the lower end of the human
capital distribution are subject to the highest and most cyclical present value losses,
consistent with recent empirical findings that lower income workers are more exposed to
persistent negative earnings risk during recessions. The model is also able to generate
an extended period of below-trend output following a recession.
∗
†
I am endebted to Gianluca Violante, Mark Gertler, and Edouard Schaal for their support and discussions.
chris.huckfeldt@nyu.edu
1
Introduction
What accounts for the high and persistent cost associated with job loss during recessions?
The tepid pace of job creation and accompanying difficulty of finding re-employment are
only first in a long list of woes faced by newly unemployed job-seekers during a recession.
Bils (1985) finds that the wages of job changers are more cyclical than the wages of workers
who maintain continuous employment, implying that job-losers who manage to find reemployment during a recession experience significant wage reductions relative to their previous jobs. Not only do re-employed job-losers face immediately lower wages, but the wages of
within these jobs recession do not recover along with the aggregate economy. Beaudry and
DiNardo (1991) and Hagedorn and Manovskii (2010) document the persistent effect of the
aggregate state of the economy at the time of job creation on subsequent wages. High-wage
industries are observed to hire more-skilled workers during recessions, implying that the
marginally less skilled are systematically directed into lower paying industries (McLaughlin
and Bils, 2001; Deveraux, 2002). Finally, jobs found during recessions do not last as long
as jobs found during expansions: Bowlus (1995) finds that job tenure is decreasing in the
unemployment rate at the time of job creation.
While the various components comprising the cost of job loss have been studied in isolation, there has only recently been an attempt to quantify the entire cost of job displacement
in terms of total lifetime earnings losses. Davis and von Wachter (2011) use Social Security earnings data to compute the counterfactual earnings streams that displaced workers
would have received had they not been subject to job loss. The authors find that relative
to the value of continued employment, displaced workers experience 11.0% discounted value
earnings losses during expansions and 18.6% earnings losses during recessions. Such high
losses speak not only to the immediate loss of earnings associated with unemployment and
reduced wages upon re-employment, but also to the loss of future income growth that would
have been realized absent displacement. Job loss leaves in an indelible mark on workers that
depresses future earnings growth, and never more so than during recessions.
Davis and von Wachter test the ability of several recent models of equilibrium unemployment to generate present value costs of job loss on par with what they compute from the
data. From the Hall and Milgrom (2008) model of credible bargaining, they compute present
value costs that range from 1.14% during expansions to 1.42% during recessions. This is per-
2
haps not surprising, as the credible bargaining model does not feature wage dispersion, and
so the cost of job loss is confined to lost earnings during unemployment. The Burgess and
Turon (2008) job-ladder model does feature equilibrium wage dispersion, however, where
workers realize higher wages both across and within jobs during uninterrupted periods of
employment. Even still, the Davis and von Wachter compute costs from the model ranging
from 2.44% during expansions to just 2.71% during recessions. Both of the models are of
a recent vintage of labor market models that are successful at accounting for the volatility of aggregate unemployment; but clearly, something additional is needed to account for
individual-level earnings dynamics across the business cycle.
In an effort to explain the magnitude and the cost of job displacement, I study a model of
business cycles and equilibrium unemployment with two additional key ingredients: specific
human capital a là Ljungvist and Sargent (1998) and the presence of “dead-end”, low-skill
employment. Agents in the model are either employed in skill-intensive jobs, where output
is proportional to specific human capital; or in skill-neutral jobs, where output requires no
skill-input. Workers in skill-intensive jobs accumulate human capital faster than workers in
skill-neutral jobs, while workers in unemployment are subject to human capital depreciation.
Firms are able to direct their recruitment efforts specifically towards a worker’s level of
human capital when attempting to fill either type of job. The search incentives of workers and
a free entry condition for job creation will generate an endogenous minimum skill requirement
for the creation of skill-intensive jobs. Only skill-intensive jobs are created for workers with
human capital above the minimum skill threshold; likewise, only skill-neutral jobs are created
for workers with human capital below the minimum-skill threshold.
In response to a negative aggregate productivity shock, firms creating skill-intensive jobs
recover less of the fixed costs associated with job creation; as a result, the minimum skill
requirement for skill-intensive jobs increases, directing more workers to search for skill-neutral
jobs. This, and greater human capital depreciation associated with longer unemployment
durations, leaves displaced workers who would search for skill-intensive employment during
an expansion to search for skill-neutral jobs. As a result, workers displaced from higherpaying skill-intensive jobs are more likely to be reallocated to lower paying skill-neutral jobs,
experiencing large and persistent earnings losses, as in the data.
In section 2, I present the basic ingredients of the model, including the equilibrium
definition. I also show that the model has a block-recursive structure which simplifies its
3
computation dramatically. In section 3, I discuss the model calibration and the identification
of key structural parameters. Many of the model-generated moments depend on the equilibrium distribution of workers across employment states and human capital; as such, most of
the parameters are calibrated internally using a minimum-distance criterion. To assess the
performance of the model, I evaluate how well it is able to match the unconditional present
value cost of job loss; and the cyclical change in the cost of job loss. The discounted present
value cost of job loss in the model depends crucially on the parameters dictating the process
for skill loss in unemployment. Using data from the Displaced Workers Supplement of the
Current Population Survey, I target the model to match the empirical mean and 90th percentile relative wage loss of displaced workers on their first job spell out of unemployment.
Hence, I restrict the identification of parameters that influence the long-term effects of job
displacement using cross-sectional variation in short-term post-displacement outcomes.
In section 4, I discuss the results. In the baseline calibration, the model is successfully
able to match 75.1% of the average cost of job loss and 34.2% of the cyclicality. I show that
workers at the left tail of the human capital distribution – the region of the minimum skillrequirement – experience the highest and most cyclical cost of job displacement, consistent
with recent empirical findings that lower-income workers are most exposed to persistent
negative earnings risk during recessions (Guvenen, Ozkan, and Song, 2013). Furthermore,
recessions shift mass from the middle of the skills distribution to the bottom while leaving
the upper tail intact.
To quantify the various channels in my model, I calibrate a simple model without human
capital dynamics and another second model with human capital dynamics but without the
skill-neutral sector. I show that the full model outperforms the simplified model; and that,
in particular, the presence of the skill-neutral sector is critical for generating any cyclicality
in the cost of job loss. I analyze the aggregate implications generated by human capital
dynamics and the skill-neutral sector. I show that the presence of the skill-neutral sector
generates slow recoveries of aggregate output in response to a negative productivity shock.
Section 5 concludes.
4
2
2.1
Model
Setting
The model is set in discrete time with an infinite horizon. There is a unit measure of
agents on the unit interval. Agents have linear preferences over the consumption good,
suffer no disutility of labor, and discount the future by a factor β < 1. Agents are either
unemployed, employed in a skill-neutral job, or employed in a skill-intensive job. In addition
to employment status, agents are differentiated by their endowment of human capital, h ≥ h.
A cumulative distribution function λ gives the measure of workers over a particular level
of human capital and employment state. Agents have geometric lifespans: each period a
fraction ν of workers die and a fraction ν are born into unemployment.
There are two aggregate state variables: an aggregate component of productivity, Z, and
the distribution of workers across human capital and employment states, λ. Z takes on finite
values and evolves according to a first-order Markov chain. The distribution of workers across
skill and employment states is discussed below. Human capital is the individual worker’s
state variable and evolves according to the employment status of the worker.
2.2
Production and wages
Production occurs within one-person firms. There are two production parameters: an aggregate component, Z; and a worker-specific component, h. Skill-neutral firms employing a
worker with skill h operate a production technology to produce output yL that only depends
on the value of aggregate productivity:
yL (h, Z) = Z.
Skill-intensive firms operate a production technology that is linear in worker human capital
and aggregate productivity:
yH (h, Z) = Zh.
The worker’s human capital evolves over the lifetime of the match, introducing within-match
variation in the output of skill-intensive firms. Although matches accommodate variation in
the worker human capital, the type of job is fixed; i.e., a skill-neutral job cannot be converted
5
into a skill-intensive job. Workers who have accumulated human capital while employed in
a skill-neutral job must find a new skill-intensive vacancy to switch job types.
The wage wL (h, Z) received by a worker in a skill-neutral job does not vary by the
aggregate state or the human capital input of the worker:
wL (h, Z) = ϑ
(1)
The wage wH (h, Z) received by a worker in a skill-intensive job varies with the human capital
input but not the aggregate state:
wH (h, Z) = ϑh.
(2)
Hence, wages are completely unresponsive with respect to changes in aggregate productivity,
as in Hall (2005) and Shimer (2013). Firms retain the difference between output and wages
as profit. The parameter ϑ can be interpreted as one minus the profit share of firms.
2.3
Search and matching
Workers must be matched with firms in order to produce. A large number of firms post
vacancies to attract workers. Matching markets are specific to (i) the job-type, skill-neutral
or skill-intensive; and (ii) the required level of human capital. By assumption, markets
are segmented by human capital, in that workers are constrained to search in submarkets
indexed by their endowment of human capital. For a given level of human capital, however,
search is directed; workers choose whether to search for either skill-neutral or skill-intensive
employment, and firms account for the optimal search decision of workers when deciding
where to post vacancies. As will be shown later, the structure of the firm and worker
problems imply that only one type of job opening, skill-neutral or skill-intensive, will be
visited by workers searching from unemployment.
Given the wage structure, workers are never presented with an incentive to search on-thejob for a job of the same type. However, workers in skill-neutral jobs may search on-the-job
for skill-intensive employment. As will be shown, workers in skill-intensive jobs never have
an incentive to search for skill-neutral employment, and hence never search on the job.
Given an aggregate component of productivity Z and worker distribution λ, the number
6
of vacancies in the submarket for skill-neutral jobs is υL (h, Z, λ) and the total number of
searchers is given by sL (h, Z, λ), where
sL (h, Z, λ) = uL (h, Z, λ),
(3)
and uL (h, Z, λ) is the measure of unemployed workers of skill h given the aggregate state of
the economy. The number of vacancies in the submarket for skill-intensive jobs is υH (h, Z, λ)
and the number of searchers is given by sH (h, Z, λ), where
sH (h, Z, λ) = uH (h, Z, λ) + γnL (h, Z, λ).
(4)
Here, the measure of searchers comprises unemployed workers and workers in skill-neutral
jobs who search on-the-job with exogenous search efficiency γ.
The total number of new hires, or matches, generated within a submarket each period is
expressed as mi (h, Z, λ), i = L, H, and determined by a constant returns to scale matching
function:
mi (h, Z, λ) = φi si (h, Z, λ)σ υi (h, Z, λ)1−σ , i = L, H.
(5)
Note that while the shape parameter, σ, is the same in skill-neutral and skill-intensive
markets, the matching function efficiency is allowed to vary. The job-finding probability for
a worker with human capital h searching for a job of type i, when the aggregate state is Z
and λ, is given by
mi (h, Z, λ)
, i = L, H.
(6)
pi (h, Z) =
si (h, Z, λ)
Similarly, the vacancy-filling probability for a vacancy of type i and skill h, when the aggregate state is given by Z and λ, is
qi (h, Z) =
mi (h, Z, λ)
.
υi (h, Z, λ)
The relevant quantity for determining the job-finding and vacancy-filling probabilities within
a submarket is given by the ratio of vacancies to searchers, the “market tightness” ratio:
θi (h, Z) =
υi (h, Z, λ)
, i = L, H.
si (h, Z, λ)
7
(7)
While the measure of searchers and vacancies depends on the distribution of workers across
employment states and human capital, contact rates and labor market tightness ratios are
independent of λ. As will be shown, the entry decision of firms that determines equilibrium
market tightness is independent of λ. This independence is inherited through the market
tightness schedules and implies that all value functions are independent of the distribution
of workers. This property is similar to the “block recursivity“ concept of Menzio and Shi
(2010, 2011).
In general, either a skill-neutral or skill-intensive submarket will be open for a specific level
of human capital, but not both. There is an endogenous minimum skill requirement h∗ (Z)
for forming skill-intensive matches that depends on the aggregate component of productivity.
Unemployed workers with h < h∗ (Z) will search in skill-neutral markets; unemployed workers
with h ≥ h∗ (Z) will search in skill-intensive markets. As will be shown, the minimum skill
requirement will negatively co-vary with the aggregate state and will be jointly determined
by the endogenous search decision of workers and free-entry conditions for firms posting
vacancies in the skill-neutral and skill-intensive submarkets.
2.4
Human capital dynamics
Human capital lies in a finite set H. Newborn workers draw an initial value of human capital
from a distribution function F with support over the entire set H. Human capital for existing
agents evolves according to their employment status, as summarized in Table 1. New values
of human capital are revealed at the beginning of each period.
Workers in unemployment face two sources of human capital risk: obsolescence and
gradual depreciation. With probability ξ, a worker who enters the period with human
capital h finds her skills rendered obsolete, and the worker must draw a new value of human
capital h0 from a distribution F o (·; h), defined as
1
F (h0 ; h) =
F (h)
o
Z
h
dF (h0 )dh0 .
(8)
h
Hence, workers draw from a distribution constructed from the initial distribution for newborn workers with upper support at the beginning-of-period level of human capital. Note
that the construction of the distribution ensures that workers never gain skill from an obso-
8
Table 1: Human capital dynamics by employment status
Employment status of worker
Skill-intensive
Skill-neutral
Unemployed
∆h increase
πH
πL
0
Probability of . . .
∆h decrease obsolescence
0
0
0
0
πU
ξ
lescence shock; and that agents with higher h face higher expected losses from obsolescence.
Immediately after the realization of the obsolescence shock (and within the same period),
the worker faces a probability πU of losing a quantity ∆h of human capital. Note that the
realization of both events are independent. A worker who experiences an obsolescence shock
faces the same probability πU of losing a quantity ∆h of human capital as a worker who does
not experience an obsolescence shock.
Workers in skill-intensive jobs steadily accumulate human capital. Each period, a worker
in a skill-intensive job faces a probability πH that her endowment of human capital increases
by a quantity ∆h. A worker in a skill-neutral job also accumulates human capital, but
at a slower rate than a worker in a skill-intensive job. Each period, the worker has a
probability πL < πH of accumulating a quantity ∆h of human capital. Hence, workers
in skill-neutral jobs can eventually accumulate enough human capital to qualify for skillintensive employment.
The two sources of human capital depreciation are meant to capture different types of
human capital risk. The gradual process of depreciation governed by πU captures the loss
of skills that accompany disuse. The obsolescence probability, ξ, captures the risk that
accumulated skills are no longer relevant to current production techniques. An unemployed
computer programmer loses skill as she spends less time programming; but also is subject to
the risk that the skills she has are no longer relevant, as other computer programmers who
are employed adopt new programming languages and conventions. Similarly, a machinist’s
skills may be attached to the vintage of his workplace tools. While employed, a machinist
is exposed to the latest vintage of machine tools, whereas an unemployed worker skills are
attached to the vintage of tools associated with his last job.
9
2.5
Timing
The timing within the model is divided into three sub-periods. In the first sub-period, the
new value of aggregate productivity Z is revealed, along with new values of human capital
among agents. Workers are endogenously and exogenously separated from existing matches.
A fraction ν of workers die and a corresponding fraction 1 − ν are born. In the second
sub-period, firms post vacancies and workers search. In the third and final sub-period, new
and existing matches produce.
2.6
Worker and firm value functions
Agents maximize the present discounted value of consumption. Workers have two non-trivial
decision problems: first, workers in skill-neutral matches who have accumulated sufficient
human capital may find it optimal to quit into unemployment to search for a skill-utilizing
job. Second, and more importantly, employed and unemployed workers decide whether to
search in the skill-neutral or skill-utilizing submarkets. For workers with low values of human
capital, this will be a trivial decision: given the fixed costs associated with posting a vacancy,
a firm will never find it profitable to post a skill-intensive vacancy for her level of human
capital, rendering the probability of finding a skill-intensive job zero. For an intermediate
region, however, firms will be able to recover the fixed costs of vacancy-posting from future
profit flows as long as the probability of attracting a new hire is sufficiently high. For firms
to face a high vacancy filling rate, it must be the case that the ratio of searchers to vacancies
is relatively high, implying a low probability for workers to find a job. Workers will thus face
a trade-off of higher job-finding probabilities in skill-neutral markets with higher expected
wage flows in skill-intensive markets. The point at which workers find it optimal to search
in skill-intensive submarkets will determine the minimum skill threshold, h∗ (Z).
The value functions of workers and firms are written from the perspective of the third
sub-period, after the realization of aggregate and human capital shocks, match separation,
and search and matching.
10
2.6.1
Workers
Let U (h, Z) be the value of a worker of skill h in unemployment when the aggregate component of productivity is Z.1 Further, let UH (h, Z) be the value to a worker with skill h of
searching in the skill-intensive market when the aggregate component of productivity is Z;
and let UL (h, Z) be the corresponding value of searching in the skill-neutral market. Then,
and
Ui (h, Z) = pi (h, Z)Ei (h, Z) + 1 − pi (h, Z) U (h, Z) i = L, H
(9)
0
0
0
0
U (h, Z) = b + (1 − ν)βE max UL (h , Z ), UH (h , Z ) ,
(10)
L,H
subject to the evolution of h0 and Z 0 . The parameter b is the flow utility of not working.
Workers discount the future by the probability of surviving into the next period, (1 − ν), and
by the discount factor, β. Expectations are taken with respect to the exogenous processes
for the aggregate component of productivity and human capital. Once the updated values of
aggregate productivity and the worker’s own human capital are realized, the worker directs
her search decision to either the skill-neutral or skill-intensive market by comparing the
values UL (h, Z) and UH (h, Z). These values are determined by the equilibrium job finding
rates in the relevant submarkets, pL (h, Z) and pH (h, Z), along with the value of employment
in skill-neutral and skill-intensive jobs, to be discussed below. From this, we determine the
minimum skill requirement when the aggregate state is Z:
h∗ (Z) = min{h | UH (h, Z) ≥ UL (h, Z)}.
(11)
As well be shown, the job-finding probabilities for skill-intensive jobs are increasing in h,
while the job-finding probabilities for skill-neutral jobs are decreasing in h. The benefit from
working in a skill-intensive job is similarly increasing in h. Thus, an individual with higher
human capital faces a higher probability of working in the skill-intensive sector and a higher
return to finding a skill-intensive job.
Let EL (h, Z) be the value of employment in a skill-neutral job for worker with human
1
In theory, the value of an unemployed worker could also depend on the distribution of workers across
human capital and employment states, λ. The assumption of directed search eliminates λ as a state variable
in decisions of workers and firms, and hence I suppress it writing value functions.
11
capital h when the aggregate component of productivity is Z. Then,
n
EL (h, Z) = wL + (1 − ν)βE dL (h0 , Z 0 )U (h0 , Z 0 ) + γpH (h0 , Z 0 ) 1 − dL (h0 , Z 0 ) EH (h0 , Z 0 )
o
+ 1 − γpH (h0 , Z 0 ) 1 − dL (h0 , Z 0 ) EL (h0 , Z 0 ) .
(12)
A worker in a skill-neutral job earns a period wage of wL .2 There are three events that can
occur in the next period: (i ) the worker will separate from the match into unemployment
with probability dL (h, Z); (ii ) given no match destruction, the worker will search on-thejob and find a skill-intensive job; (iii ) and absent both match destruction and successful
on-the-job search, the worker remains matched with her current firm.
The separation probability dL (h, Z) reflects that the worker may endogenously decide
to leave her current match to search for a skill-intensive match from unemployment. The
separation probability can thus be expressed as

1
dL (h, Z) =
δ
L
if U (h, Z) ≥ EL (h, Z)
,
(13)
otherwise
where δL ∈ (0, 1) is the exogenous separation probability specific to skill-neutral matches.
As will be made clear, a firm never has incentive to separate from either a skill-neutral or
skill-intensive match.
A worker’s separation and on-the-job search depends in part on her level human capital, h, relative to the minimum human capital required to find a skill-intensive job from
unemployment, h∗ (Z). Workers in skill-neutral jobs always start with h < h∗ (Z), but onthe-job human capital accumulation may result in the worker’s human capital evolving to
some h0 such that h0 > h∗ (Z); or a change in aggregate productivity to Z 0 > Z may imply
h∗ (Z) < h < h∗ (Z 0 ). In either case, the worker has the choice to search for a skill-intensive
job while still employed or to separate and search from unemployment. Whether the worker
decides to separate or search on-the-job depends on the relative value of U (h, Z) to EL (h, Z),
determined by the efficiency of search from unemployment, γ. In particular, if γ = 1, so
that search on-the-job is as efficient as search from unemployment, workers will never en2
Since wages in skill-neutral jobs do not depend the aggregate state or a worker’s human capital endowment, I hereafter suppress them from the notation.
12
dogenously separate from skill-neutral jobs. Note that for workers with a value of human
capital below h? (Z), the issues of endogenous separation decision and search on-the-job will
be moot, as there will be no active submarkets for skill-intensive employment available.
We now consider the value of a skill-intensive worker. Let EH (h, Z) be the value of
employment in a skill-intensive job. Then,
n
o
EH (h, Z) = wH (h) + (1 − ν)βE δH U (h0 , Z 0 ) + (1 − δH )EH (h0 , Z 0 )
(14)
A worker in a skill-intensive job receives a wage wH (h) that increases with her human capital
input, but does not vary with the aggregate state. Aside from continued human capital
appreciation, a worker employed in a skill-intensive job can look forward to one of two
events: exogenous separation, with probability given by the exogenous parameter δH ; or
continued employment, with probability 1 − δH .
2.6.2
Firms
The value of a skill-neutral firm employing a worker of skill h when the aggregate state is Z
is given by JL (h, Z), where
n
o
JL (h, Z) = Z − wL + (1 − ν)βE 1 − dL (h0 , Z 0 ) 1 − γpH (h0 , Z 0 ) JL (h0 , Z 0 ) ,
(15)
subject to the evolution of h0 and Z 0 . Note that, although period output is independent
of the worker’s human capital, the probability of match dissolution is not. For low values
of the aggregate component of productivity, the minimum hiring standard h∗ (Z) increases,
and skill neutral firms will post vacancies to attract workers with values of human capital
who would otherwise be searching for skill-intensive jobs. The skill-neutral firm knows that,
should the aggregate state increase and the worker’s human capital is above the minimum
skill standard, the worker will either quit or search on-the-job for skill-intensive employment.
Hence, the value of a skill neutral firm is decreasing in the skill endowment of its worker.
This will manifest as decreasing job-finding rates in human capital for skill-neutral workers.
Observe that the problem of “over-qualified” workers in skill-neutral jobs will be present
even for matches where worker’s human capital is below the minimum skill threshold for any
value of the aggregate state. Such workers have a constant probability πL that their skills
13
increase by a single unit. Hence for high values of the aggregate state when h∗ (Z) decreases,
such workers also have higher expected exit rates. The cyclicality of match destruction
among skill-neutral matches will decrease the overall cyclicality of skill-neutral job creation.
The value of a skill-intensive firm is given by JH (h, Z) and is determined by the following:
n
o
0
0
JH (h, Z) = Zh − wH (h) + (1 − ν)βE (1 − δH )JH (h , Z ) ,
(16)
subject to the evolution of h0 and Z 0 . Skill-intensive firms produce output Zh and pay a
wage wH (h), retaining the remainder as profits. The match continues into the following
period if the worker does not die and if the match is not exogenously separated. Given the
structure of the wage bill, it is straightforward to see that the value of a skill-intensive firm
is increasing in h.
2.7
Free entry and market segmentation
Firms must pay a period cost κL to post a vacancy in a skill-neutral sub-market and a cost
κH to post a vacancy in a skill-intensive sub-market. As is typical in search and matching
models, free entry drives the value of posting a vacancy in any market to zero, and we derive
the following complementary slackness conditions:
κi
≥ Ji (h, Z), θi (h, Z) ≥ 0, i = L, H
qi (h, Z)
(17)
In active submarkets, the cost κi of posting a vacancy for a job of type i is equal to expected
value associated with posting a vacancy, qi (h, Z)Ji (h, Z). In inactive submarkets, I assume
that θi (h, Z) = 0, so that the job-finding probability is equal to zero and the vacancy
filling probability is equal to one, following Menzio and Shi (2010). The vacancy filling
probabilities, qi (h, Z), are decreasing functions of market tightness, θi (h, Z), and hence can
be used to determine job-finding probabilities at each submarket.
2.7.1
Equilibrium market segmentation
In equilibrium, unemployed workers of skill h will only search for a single type of job given the
value of aggregate productivity, skill-neutral or skill-intensive. The segmentation of human
capital sub-markets into job types and the values of labor market tightness across human
14
capital sub-markets are jointly determined by equations (11) and (17). Although the equilibrium bifurcation of the human capital space into search for skill-neutral and skill-intensive
jobs is governed by a set of interdependent equations, the forces dictating equilibrium can
be understood quite simply.
First, consider the value of a skill-intensive firm in equation (17) with i = H. The value
of the firm is proportional to the period profit flows, which are strictly increasing in h. Given
aggregate productivity Z, there exists a point h(Z) such that
JH (h) < κH ∀ h ≤ h(Z).
(18)
Skill-neutral firms will have a natural incentive to open vacancies for h ≤ h(Z), as period
profits of a skill-neutral firm do not depend on human capital.
For values of h just above h(Z), the value of JH (h, Z) will be very low. In order to satisfy
the zero-profit condition, the firm will have to have a high vacancy filling rate qH (h, Z),
implying that job-finding rates will be low. Given the low job-finding rates associated with
searching for a skill-intensive vacancy, a worker might prefer to search in a skill-neutral
submarket with a higher job-finding rate. Depending on the trade-offs embodied in the
workers directed search problem, either h? (Z) > h(Z), so that the worker chooses not to
search for skill-intensive jobs from unemployment even while firms would otherwise have
an incentive to post skill-intensive vacancies; or h? (z) = h(Z), so that unemployed workers
search for skill-intensive jobs at the minimum profitable h for firms.
2.8
Equilibrium
The equilibrium for this economy is given by a (i ) a list of value functions, JL , EL , JH , EH ,
and U ; (ii ) a separation policy for workers in skill-neutral matches, dL (h, Z); (iii ) a minimum
skill threshold, h∗ (Z); (iv ) a market tightness schedule for skill neutral sub-markets, θL (h, Z);
(v ) a market tightness schedule for skill-intensive sub-markets, θH (h, Z); (vi ) a distribution
of workers across human capital and employment states, λ; and (vii ), an aggregate law of
motion, G, such that, (a) given the labor market tightness schedules θL (h, Z) and θH (h, Z),
h? (Z) describes the optimal search policy of an unemployed worker, dL (h, Z) is the optimal
quit policy of a worker in a skill-neutral match, and U (h, Z), EL (h, Z), and EH (h, Z) are
the associated value functions; (b), given h∗ (Z) and dL (h, Z), θL (h, Z) and θH (h, Z) give the
15
optimal vacancy posting decision for firms, and JL (h, Z) and JH (h, Z) are the associated
value functions; and (c), the aggregate law of motion G is consistent with the exogenous
laws of motion for h and Z, policy functions dL (h, Z) and h? (Z), labor market tightness
schedules θL (h, Z) and θH (h, Z); and the distribution of workers across human capital and
employment states, λ.
3
Calibration
I choose a weekly calibration to capture the high rate of job finding in the United States. I
calibrate the model to match a combination of aggregate statistics and moments related to
individual-level labor market outcomes. Many of these moments depend on the endogenous
distribution of workers across human capital and employment states.3 As such, only a
small subset of parameters are calibrated outside of the model; the rest are calibrated by
repeatedly simulating the model and using a minimum-distance criterion to minimize the
distance between data moments and model simulated counterparts.
3.1
Externally calibrated parameters
There are seven parameters that are calibrated outside the model. These include the process
for aggregate labor productivity; the discount rate, β; the flow value of leisure, b; the worker
death probability, ν; and the bounds for the human capital grid, h and h. For the aggregate
labor productivity process, I adopt the parameters used in Hagedorn and Manovskii (2008)
for weekly data, setting the persistence parameter ρZ = 0.9895 and innovation parameter
σZ = 0.0034. I discretize the productivity with a three-state Markov chain using the Rouwenhorst method, which has demonstrated high accuracy for approximating highly persistent
processes (Rouwenhorst, 1995; Kopecky and Suen, 2010). I set the discount rate β to 0.9992,
corresponding to annual risk free rate of about 5%. I set the value of home production b
3
For example, the parameter determining human capital accumulation within a skill-intensive job should
be consistent with average annual wage growth. But average annual wage growth is a weighted average
of wage growth of workers continuously employed in skill-intensive jobs, whose wage increases reflect the
accumulation of specific human capital; workers continuously employed in skill-neutral jobs, whose wage
does not vary; workers displaced from skill-intensive to skill-neutral jobs, who experience wage losses; and
workers who transition from skill-neutral to skill-intensive jobs, who experience a wage increase. These
outcomes depend on an entire range of parameter values.
16
to 0.4. This is a controversial parameter in the literature on the quantitative properties
of the Diamond-Mortensen-Pissarides model of equilibrium unemployment (Shimer, 2005;
Hagedorn and Manovskii, 2008). In my model, it is completely inconsequential, as wages are
completely rigid with respect to aggregate productivity.
As opposed to other models of on-the-job search and labor flows, only a small subset
of workers in this model are able to search on-the-job: those in skill-neutral employment
who have high enough human capital to qualify for skill-intensive employment, either due
to human capital accumulation or a change in the aggregate state that lowers the minimum
hiring requirement. Hence, I am unable to follow the typical strategy of calibrating the
efficiency of on-the-job search to match employment-to-employment job flows. Given the
atypical role of on-the-job search in my model, I simply set γ equal to one, so that search
efficiency on the job is equal to search efficiency from unemployment. Note that this precludes
endogenous separation of skill-neutral workers to search for skill-neutral employment from
unemployment, so all separation in the model will be exogenous. I further set δL = δH to
match a monthly EU transition rate of 0.026.
The probability of worker death is ν = 0.00048, corresponding to an average 40-year labor
market career. There are 75 equispaced points in the human capital grid. The maximum
and minimum values of human capital h and h so that significant masses in the ergodic
distribution do not accumulate at the endpoints of the human capital distribution. I set ∆h,
the quantity of human capital lost due to skill depreciation in unemployment and gained
due to skill appreciation in employment, to ∆h = h − h /(NH − 1).
3.2
Internally calibrated parameters
I simulate the model to match a variety of moments describing unemployment and employment flows, individual wage growth, and features of the wage distribution. There are as
many parameters as there are targeted moments, so the model is exactly identified. The list
of targeted moments and the model generated counterparts are given in Table 3.2.2. The
resulting parameter values are given in Table 5. Three parameters in particular are central
to the model’s ability to capture the present value of job loss measure from the data: (1)
the weekly probability of losing a quantity ∆h of human capital, πU ; (2) the obsolescence
probability, ξ; and (3), the posting cost in the skill-intensive market, κH . These parameters
17
Table 2: Externally calibrated parameters
Parameter
ρZ
σZ
β
b
γ
δH (= δL )
ν
h
h
Description
persistence parameter of productivity
standard deviation of productivity
discount factor
value of leisure
efficiency of on-the-job search
match survival prob.
death probability
human capital upper bound
human capital lower bound
Value/Source
0.9895, HM (2008)
0.0034, HM (2008)
0.9992, 5% interest rate
0.4, see text
1.0, see text
0.0053, monthly EU rate
4.8 ×10−4 , 40 year career
6.1
0.95
(and the empirical moments used to achieve identification) merit separate discussion.
3.2.1
Dispersion in outcomes following job displacement
Within a given period, human capital loss can be either small, due to gradual depreciation; or
large, due to obsolescence. But changes in human capital only matter for earnings through
the worker’s type of employment. Workers displaced from skill-intensive to skill-neutral
jobs experience larger immediate relative wage losses than workers reallocated within skillintensive or skill-neutral jobs.
The combination of small and large human capital losses, together with transitions from
skill-intensive to skill-neutral jobs, generates heterogeneity in immediate wage outcomes. But
these parameters dictating these occurrences – πU , ξ, and κH – are also crucial for generating
large present value losses. Absent a reasonable mass of workers around the skill-requirement
h∗ (Z), most human capital depreciation shocks will not induce a transition to low-skill jobs,
and hence not reduce future growth in earnings and large present value losses.4 But moreover,
without the obsolescence shock ξ, only unemployed workers within close enough proximity to
h∗ (Z) will risk being displaced to a skill-neutral job and are exposed to persistent earnings
losses following job displacement.
4
Note that κH dictates immediate wage losses from displacement by determining the minimum level of
human capital for which a firm is willing to create a skill-intensive vacancy; and thus, also determines the
ratio of the minimum observed wage at a skill-intensive job to the wage at a skill-neutral job.
18
Table 3: Relative wage losses upon reemployment, displaced workers
Occupation transition
All
Stayers
Switchers
Average ∆w
−0.0522
−0.0135
−0.0735
90th pct ∆w
−0.5273
−0.4291
−0.6197
Source: CPS Displaced Workers Supplement, 1984-2012
The connection between the dispersion of immediate wage losses and present value losses
immediately suggests a calibration strategy. I calibrate the parameters ξ, πU , and κH to
match statistics measuring average wage change following displacement, 90th percentile wage
losses, and average wage losses conditional on occupation changes. Hence, the calibration is
disciplined by identifying parameters that generate large present-value income losses from
cross-sectional dispersion in wage loss and post-displacement occupation flows.
To study post-displacement wage and employment outcomes, I use the Displaced Worker
Supplement (DWS) to the Current Population Survey, following a long literature studying
the cost of job displacement in the United States (e.g., Farber, 2004). The DWS has been
administered biennially since 1984 in either January or February of the relevant year. Workers are asked whether they have recently been terminated for reasons unrelated to individual
performance or voluntary separation, such as a firm closing, a shift being abolished, or insufficient work. The survey records the date of job loss, nature of the lost job, and the
associated weekly earnings. The survey records how many jobs the worker has held since the
displacement episode, and for the subset of workers also in the monthly outgoing rotation
subsample, it is possible to compare current to previous earnings to compute earnings losses
associated with job displacement.
In constructing my sample, I restrict my attention to workers who have successfully made
full-time to full-time transitions and who are employed in the private sector for both jobs. I
also isolate workers who report current wages from the first job since the initial displacement.
For each year of the survey, I calculate the mean and the 90th percentile proportional wage
change, and then I average over years. I also calculate the statistics separate for workers who
19
stay in the same occupation (“stayers”) and job-changers who switch occupations (“switchers”). To the extent that occupation reflects the skill input of a job, displaced workers in
the data who switch occupations following a job displacement are more likely to have undergone a diminution to the skill requirement of their work, corresponding to a transition of
“skill-intensive” to “skill-neutral” employment in the model.
The statistics from the data are given in Table 3. I find an average wage loss of −5.22%
and a 90th percentile loss of −52.74%. The immediate proportional wage losses associated
with job displacement are clearly more modest than the net present-value costs estimated
by Davis and von Wachter, revealing that the bulk of earnings losses from job displacement
occur through persistently stagnant future wages. Yet the 90th percentile losses are indeed
quite substantial and reveal the extent of diversity in post-displacement experiences.
Of the workers in my sample, a striking percentage have switched occupations in the first
job after the displacement episode: 64.5 %. Occupation stayers suffer far less negative wage
changes following displacement: on average, stayers realize a wage change −1.35% to that
of −7.35 among switchers.
In the calibration procedure, I simulate the model and administer a model-analogue
to the DWS, recording the mean wage changes; 90th percentile wage losses; and relative
wage losses of job-type switchers versus stayers. Average wage losses will reflect the gradual
component of human capital loss associated with the parameter πU , whereas 90th percentile
wage losses will be associated with the earnings losses of displaced workers who experience
larger skill loss due to an obsolescence shock. Relative wage losses of occupation switchers
versus stayers reflects the value of κH ; a higher value implies a higher h∗ (Z), and hence a
higher average wage among skill-intensive workers.
I compute the best-fit weekly probability of skill obsolescence while in unemployment or
skill-neutral employment of 0.086. The weekly probability of losing a unit of human capital is
0.125, implying that the average unemployed worker loses 2.07% of their stock human capital
over 4 week period of continuous unemployment. The calibrated value of κH is 23.1368.
3.2.2
Other parameters
The cyclicality of the minimum hiring requirement directly relates to the volatility of unemployment and job creation. As is widely known, both wage rigidity and a small profit share
are required to generate empirically plausible unemployment volatility (Shimer, 2005; Hall,
20
Table 4: Internally targeted moments
Moment
Mean wage change following displacement
90th percentile wage loss following displacement
Average wage loss occupation switchers/stayers
Relative volatility of unemployment
Monthly UE rate
Average wage growth
Experience premium, > 5 years experience
P90-P10 log wage residuals, < 5 years experience
Wage distribution, p90/p50
Wage distribution, p50/p25
Target
−0.05
−0.644
1.258
5.150
0.420
0.013
1.350
0.963
2.122
1.452
Model output
−0.05
−0.504
1.134
5.298
0.456
0.013
1.340
0.715
1.904
1.541
2005). A literature has emerged to study models which are able to endogenously generate
wage rigidity and sufficiently volatile unemployment (Hall and Milgrom, 2008; Gertler and
Trigari, 2009). In this paper, I do not attempt to endogenously account for the volatility
of unemployment, and hence I calibrate the firm profit share, 1 − ϑ, to match unemployment volatility. The cyclicality of job finding will vary across skill-neutral and skill-utilizing
markets, and hence this parameter must be calibrated within the model.
Note that I rely on different moments of the wage distribution to help identify different
parameters in the calibration. While these moments are correlated, and hence no single
moment uniquely identifies a single parameter, it is possible to understand the identification
of certain parameters by focusing the role played by one or two moments in particular.
I use the monthly transition rate from unemployment to employment (from Menzio and
Shi, 2011) and the 90-50 wage ratio to identify the matching efficiency parameters for the
skill-neutral and skill-intensive labor markets, φL and φH . Wage dispersion in the upper
ends of the wage distribution is only generated from continuous human capital accumulation
of workers within skill-intensive jobs. If job-finding rates in skill-intensive jobs are too low,
unemployment generated from exogenous separation rates will put too much of a drag on
the process of within-individual skill-accumulation, and hence shrink the 90 − 50 wage ratio.
On the other hand, if φH is too high, unemployment episodes will be short and do little to
hold back the process of human capital accumulation, expanding the 90 − 50 ratio too much.
I similarly use the 50 − 25 wage ratio to identify the skill accumulation process for low-
21
Table 5: Internally calibrated parameters
Parameter
Labor market:
ϑ
κH
φH
φL
Human capital:
µnb
σnb
πH
(52 · πH · ∆h)/h̄H
πL
(52 · πL · ∆h)/h̄L
πU
(4 · πU · ∆h)/h̄U
ξ
Description
Value
One minus profit share
Vacancy posting cost (skill-intensive)
Matching efficiency (skill-intensive)
Matching efficiency (skill-neutral)
Human capital initial distribution, mean
Human capital initial distribution, standard deviation
Weekly probability of human capital increase
(skill-intensive)
Annual percent human capital accumulation
no separation (skill-intensive)
Weekly probability of human capital increase
(skill-neutral)
Annual expected human capital accumulation
no separation (skill-neutral)
Weekly probability of human capital decrease
(unemployment)
Four-week percent human capital loss
(continuous unemployment)
Obsolescence probability
0.9319
23.1368
0.2634
0.0955
0.7872
0.1475
0.0216
3.60%
0.0113
8.00%
0.1545
2.93%
0.0510
skill workers. Workers in skill-neutral jobs can only move to skill-intensive jobs through the
process of on-the-job skill accumulation dictated by πL or through cyclical variation in the
minimum skill requirement. If πL is too low, it takes too long for workers in skill-neutral jobs
to obtain the necessary human capital to progress into skill-intensive employment, increasing
the proportion of the workforce in skill-neutral jobs and hence decreasing the 50 − 25 wage
ratio. I compute πL = 0.0113, implying that the average worker in a skill-neutral job
increases her stock of human capital by 8.00% during a year of continuous employment.
Human capital accumulation in skill-intensive jobs is identified from average annual increase in wages across workers. I estimate a Mincer wage regression from the 2000 U.S.
Census with a quartic in potential experience. From the estimated coefficients, I compute
the average annual growth in wages for each year of accumulated experience to be 1.4%
22
Figure 1: Initial and stationary distribution of workers over human capital
0.14
stationary distribution
initial distribution
0.12
Density
0.1
0.08
0.06
0.04
0.02
0
1
2
3
4
5
Human capital (h)
6
7
8
9
over a 40-year career. I compute πH = 0.0216, implying that the average worker in a
skill-intensive job increases her stock of human capital by 3.60% over a year of continuous
employment. Observe that while workers in skill-intensive jobs accumulate human capital
at a higher rate than workers in skill-neutral jobs, workers in skill-neutral jobs experience a
greater percentage increase in human capital over a year of uninterrupted employment. This
is because workers in skill-neutral jobs possess have less human capital on average: 1.292
units, compared with 3.671 units for workers in skill-intensive jobs.
In the model, I use a discretized log-normal distribution for the initial distribution of
human capital. To identify the mean, I match the relative wages of workers with greater
than five years of experience to the wages of workers with less than five years of experience.
I calculate the empirical moment from the 2000 U.S. Census. For the standard deviation,
I match the difference in the 90th percentile and 10th percentile among workers with less
23
than 5 years of potential job experience from the log wage residuals generated by a Mincer
wage regression using the same data. The best-fit mean and standard deviation parameters
are 0.7872 and 0.1475, respectively.
Figure 1 compares the initial and ergodic distributions of workers over human capital.
The initial distribution and the ergodic distribution share roughly the same mode, but the
ergodic distribution has more mass over upper values of human capital: the average value
of human capital in the economy is 3.222, compared to 2.621 among newborn workers. In
interpreting Figure 1 and statistics from the initial distribution, one must take into account
that newborn agents begin life in unemployment, where they are subject to shocks that erode
their endowment of human capital. Hence, the average human capital of newborn workers
is higher than the average human capital of workers employed for the first time.
The relation of the initial distribution to the ergodic distribution is important for understanding the role of obsolescence shocks. Recall that worker with human capital h hit by an
obsolescence shock draws a new value of human capital from a distribution constructed from
the initial distribution with upper support h and normalized to integrate to one. Hence,
workers with higher human capital expect to lose more human capital when they experience
an obsolescence shock.
Finally, the model generates a small fraction of workers in skill-neutral jobs. In the
ergodic distribution, roughly 4.7% of workers are in unemployment; 17.0% of workers are
employed in skill-neutral jobs; and 78.3% of workers are employed in skill-intensive jobs.
Skill-intensive workers thus account for 82.2% of the employed population.
4
Results
To compute the discounted present cost of job loss implied by the model, I formulate auxiliary
value functions that exclude flow utility of leisure. Specifically, equation (10) is replaced by
n
o
Ũ (h, Z) = (1 − ν)βE max ŨL (h0 , Z 0 ), ŨH (h0 , Z 0 ) ,
24
(19)
and Ũ (h, Z) is replaced in the equations for the value of employment and the continuation
values of searching in skill-neutral and skill-intensive labor markets:
ŨL (h, Z) = pL (h, Z)ẼL (h, Z) + 1 − pL (h, Z) Ũ (h, Z)
(20)
ŨH (h, Z) = pH (h, Z)ẼH (h, Z) + 1 − pH (h, Z) Ũ (h, Z)
(21)
n
ẼL (h, Z) = wL + (1 − ν)βE dL (h0 , Z 0 )Ũ (h0 , Z 0 ) + γpH (h0 , Z 0 ) 1 − dL (h0 , Z 0 ) ẼH (h0 , Z 0 )
o
0
0
0
0
0
0
+ 1 − γpH (h , Z ) 1 − dH (h , Z ) Ũ (h , Z )
(22)
n
o
ẼH (h, Z) = wH (h) + (1 − ν)βE δH Ũ (h0 , Z 0 ) + (1 − δH )ẼH (h0 , Z 0 )
(23)
I now have a series of Bellman equations that express the value of expected wage flows.
The cost of job displacement for an individual in a job of type i with human capital h when
the aggregate component of productivity is Z is the difference of the pre-displacement value
and the post-displacement value relative to the pre-displacement value.
Ci (h, Z) =
Ẽi (h, Z) − Ũ (h, Z)
.
Ẽi (h, Z)
(24)
To calculate the average, I integrate (24) over the conditional distribution of workers over
human capital and job type given that a worker is employed and the aggregate state is Z.
Let µ(L|h, Z) be the probability that an employed worker is in a skill-neutral job given that
the worker’s human capital is h and the aggregate component of productivity is Z; and let
λE (h|Z) be the conditional distribution of employed workers across human capital. Then the
cost of job displacement when aggregate productivity is Z can be expressed as the following:5
C(Z) =
Z µ(L|h, Z)CL (h, Z) + 1 − µ(L|h, Z) CH (h, Z) dλE (h|Z).
H
Table 6 compares the empirical costs of job loss with those computed in the model. The model
does fairly well at capturing the magnitude of the cost of job loss. Davis and von Wachter
calculate the average cost of job loss to be 11.9% of the value of continued employment. In
the model, the average cost of job loss compared to continued employment is 8.94%, roughly
5
Note that Davis and von Wachter compute the 20-year expected cost of job displacement, whereas
individuals in my model live an expected 40 years. Given that I am studying a stationary economy and the
long time-frame associated with Davis and von Wachter’s measure, the difference is negligible.
25
Table 6: Cost of job loss, data and model
Present value cost of job displacement, expansion
Present value cost of job displacement, recession
Average cost of job loss
Percent increase, recessions over average
(1)
Data
(2)
Model
(3)
% explained
11.0%
18.6%
11.9%
56.3%
7.59%
10.66%
8.94%
19.27%
–
–
75.10%
34.22%
75.10% of the value from the data. The model does slightly worse at capturing the cyclicality
in the cost of job loss. The percent increase in the cost of job loss during recession compared
with the average over aggregate states is 19.27% in the model, compared to 56.3% in the
data, so the model captures around 34.22% of the cyclical variation in the data.
How does the addition of human capital dynamics and dead-end jobs improve the model’s
ability to match the magnitude and cyclicality in the present value cost of job loss? In the
next sections, I show how variation in job-finding rates and minimum hiring rates reallocates
workers to the skill-neutral sector. I then explain how variation in the minimum hiring
standard manifests in the cyclicality of the distribution of workers over human capital and
in the distribution of the present value cost of job displacement across human capital. Finally,
I analyze the relative performance of the full model against a model with no human capital
dynamics; and against a model with no skill-neutral employment.
4.1
Cyclicality of the minimum hiring standard and distributional
implications
Figure 2 plots job-finding probabilities over human capital sub-markets for recessions and
expansions. The vertical lines at the minimum skill requirements h∗ (ZE ) and h∗ (ZR ) demarcate job-finding probabilities for skill-neutral jobs (to the left) and skill-intensive jobs
(to the right). Accordingly, both schedules of job-finding rates have a discontinuity at the
skill-standard for the respective aggregate state. During recessions, firms pay the same fixed
cost of posting a vacancy and see expected period profits decline, as output decreases while
26
Figure 2: Job finding rates, expansions and recessions
0.35
Job finding probability
0.3
h*(ZE)
0.25
h*(ZR)
0.2
0.15
0.1
0.05
recession
expansion
1
2
3
4
5
6
Labor markets by human capital (h)
7
8
9
wages stay the same. Hence, firms begin posting vacancies at a higher level of human capital, h∗ (ZR ) = 1.93. The sub-markets between h∗ (ZE ) and h∗ (ZR ) are characterized by
skill-utilizing vacancies during expansions; and skill-neutral vacancies during recessions.
Note that, for a given aggregate state, job finding rates are increasing in human capital
for h ≥ h∗ (Z) and declining in human capital for h < h∗ (Z). For skill-intensive firms,
period profits are increasing in h and the firm’s discount rate does not vary in h. Hence,
for greater levels of human capital, the firm faces a higher expected return for posting a
vacancy. The free entry condition for submarkets with a higher h accommodates greater
vacancy posting and a higher ratio of vacancies to job searchers, θH (h, Z). A higher value
of θH (h, Z) decreases the vacancy filling probabilities and increases job-finding probabilities.
27
During expansions, the ratio of the maximum to minimum job finding probability is 5.26,
indicating substantial heterogeneity in the probability of finding a skill-utilizing job across
levels of human capital.
Job-finding rates in skill-neutral markets decline markedly with human capital. Although
profit flows in skill-neutral jobs do not vary with h, workers with higher human capital will
search on-the-job when a favorable shift in the aggregate state decreases the minimum skill
requirement or when the worker has accumulated enough human capital over the course of
his job tenure to search for a skill-intensive job. This means that skill-neutral firms apply
a lower discount factor to matches with a higher h, so that the present value of the job to
the firm decreases in human capital. Hence, if a worker is displaced from a skill-intensive
match and has human capital just below the minimum skill-threshold, that worker faces a
lower job-finding rate than she will after her human capital has sufficiently depreciated. This
increases the cost of job displacement relative to a model with a single type of job.
What are the implications in the cyclical variation of the minimum skill threshold and
job-finding rates for the distribution of workers? Figure 3 gives the equilibrium distribution
of employed workers over human capital for recessions and expansions. Once again, the
minimum skill-requirement for each aggregate state is indicated by a vertical line. Recessions
move a substantial mass of workers from the middle of the distribution to the bottom of the
distribution.6
Figure 4 shows the distribution of the cost of displacement across human capital for
recessions and expansions. We see a somewhat surprising result: the workers who face
the highest present value cost of job displacement are not high skilled workers, who are
presumably exposed to the greatest immediate losses from job displacement, but rather
middle-skill workers, particularly those with values of human capital around the minimum
skill requirement for the given aggregate state. For both recessions and expansions, there is a
notable spike in the cost of displacement in the region around the minimum hiring standard.
For this population of workers, job loss is predictive of future losses.
Consider the case of recessions. In a recession, the cost of job displacement sharply
increases as h approaches h∗ (ZR ) from the right. Workers in this region are predominately
6
There is a noticeable dip in the distribution function for recessions around the region of the minimum
skill threshold, h∗ (ZR ). Recall that job-finding rates in skill-neutral jobs are declining as h approaches
h∗ (ZR ) from the right. This is the cause of the dip.
28
Figure 3: Distribution of workers over human capital
0.045
expansion
recession
0.04
0.035
Density
0.03
0.025
0.02
h*(ZE)
0.015
h*(ZR)
0.01
0.005
0
1
2
3
4
5
Human capital (h)
6
7
8
9
employed in skill-neutral jobs during recessions and can expect to either accumulate enough
skills while employed to search for skill-intensive jobs; or will be able to search for skillintensive employment when the aggregate state switches. Thus, their value of continued
employment is high. Unemployed workers in this region will have to search for skill-neutral
jobs, and will face very low job-finding rates until their skills fall significantly, as discussed
earlier. Note that the cyclicality of the cost of job-loss is particularly high in the region
about h∗ (ZR ), more than doubling in value from expansions to recessions.
Hence, the model endogenously generates greater counter-cyclical persistent earnings
risk for workers at the left tail of the human capital distribution. This model outcome is
consistent with the empirical findings of Guvenen, Ozkan, and Song (2013), who show that
29
Figure 4: Present value cost of job displacement by human capital
Percent loss relative to continued employment
0.25
0.2
0.15
0.1
0.05
h*(ZE)
h*(ZR)
0
1
2
expansion
recession
3
4
5
Human capital (h)
6
7
8
9
workers at the left tail of the earnings distribution are more subject to persistent negative
earnings shocks during recessions.
Outside the region of the spike, the cost of job-displacement initially rises with h, but then
gradually decreases. The increase in the cost of job loss reflects that higher skilled workers
face greater expected human capital loss if subject to an obsolescence shock. The decrease in
cost occurs because job-finding probabilities are increasing in human capital, and so higher
skilled workers spend less time in unemployment and are less exposed to the possibility of
obsolescence. As h increases, the effect of the job-finding rate in reducing unemployment
spells dominates the possibility of higher expected losses, and the present value cost of job
loss falls.
30
4.2
Comparison of nested models
How much do human dynamics and the presence of “dead-end” jobs contribute to the cost of
job loss? To answer this question, I study two reduced versions of the full model. In the first
model, human capital is fixed for individuals (i.e., skills do not evolve in response to labor
market outcomes) and all jobs are skill-intensive. I recalibrate the parameters governing the
initial human capital distribution to match features of the U.S. earnings distribution. The
second model features identical human capital dynamics to the full model, but there is no
skill-neutral sector. I calibrate the second model to the same set of moments as I calibrate
the full model. Results are given in Table 7.
The model without skill dynamics and skill-neutral jobs is unable to explain the magnitude of the cost of job loss: the average cost of job loss is just 1.02% the value of continued
employment. While the cost of displacement increases 6.7 percentage points during recessions in the data, the cost only increases by 0.24 percentage points in the model without
skill dynamics. Hence, the model captures only 8.59% of the cost of job loss in the data;
and can only explain 4.01% of the increase in the cost of job loss during recessions. Given
that workers in the model without human capital dynamics recover their full wages upon
re-employment, the cost of job loss entirely reflects the lack of earnings during the period
of unemployment. The increase in the cost of job loss during recessions only reflects the
increase in unemployment durations due to decreased job creation.
The model with skill dynamics but no skill-neutral sector does a better job at matching
the magnitude of the cost of job loss. The average cost of job loss is 6.53% of continued
employment, accounting for 54.83% of the increase in the data; and increases to 7.86% of
continued employment during recessions, matching 21.87% of the increase in the data. The
second model is still calibrated to match average and 90th percentile wage losses, so displaced
workers will find re-employment at lower wages; and workers with longer unemployment
durations are likely to lose a greater quantity of skill. But note that the average present
value cost of displacement in the model, 6.53%, is only slightly above the targeted mean
wage loss targeted in the model, 5.22%. Once a displaced worker is reemployed, his process
of skill-accumulation is no different for a worker of the same skill but no history of job
displacement. Hence, the model has difficulty generating the full cost of job displacement.
The model without a skill-neutral sector also does better at generating cyclicality in the
present value cost of job displacement. Workers displaced during recessions have higher
31
Table 7: Model comparisons
(1)
Data
Present value
cost, average
Present value
cost, recession
Difference,
recession vs. average
Percent average
cost explained
Percent recession
increase explained
(2)
No skill
dynamics
(3)
No skillneutral jobs
(4)
Full model
11.9
8.59
6.53
8.94
18.6
1.27
7.86
10.66
6.7
0.24
1.33
1.72
100.0
8.59
54.83
75.10
100.0
4.01
21.87
28.23
unemployment durations and can expect greater skill loss. But once employed, the process
of skill accumulation is unaffected by the worker’s history of displacement.
The full model does better then the model without skill-neutral jobs, explaining 37.04%
more of average cost of job-loss; and 29.08% more of the cyclicality in the cost of job loss. The
full model generates persistence in post-displacement employment outcomes to the extent
that workers are reallocated to skill-neutral jobs. Workers who resume post-displacement
employment in skill-neutral jobs face a lower rate of skill accumulation. But moreover, note
that while only one type of job vacancy is posted for a given level of human capital and a
given aggregate state, there is a distribution of workers across job-types within a value of
human capital. Hence, the process of reclaiming lost earnings does not just occur though
regaining lost skills, but also in the successful transition from unemployment to a skill-neutral
job to a skill-intensive job. This process is more extensive and more sensitive to aggregate
fluctuations than the process represented in the model with only skill dynamics.
In addition to the cyclicality in post-displacement outcomes generated from the process
of regaining skills, the full model generates more cyclicality because a greater proportion of
32
Table 8: Aggregate statistics
y
Relative St. Dev.
Autocorrelation
Correlation with y
1.00
0.87
1.00
Relative St. Dev.
Autocorrelation
Correlation with y
1.00
0.76
1.00
n
u
υ
θ
U.S. Economy, 1964:01-2005:01
0.60
5.15
6.30
11.28
0.94
0.91
0.91
0.91
0.78
−0.86
0.91
0.90
0.27
0.77
0.88
Model Economy
5.30
5.27
0.77
0.48
−0.89
0.55
8.35
0.71
0.92
displaced workers find re-employment in skill-neutral jobs when the aggregate state of the
economy is bad. Two forces work in this direction. First, as in the economy with only skilldynamics, longer unemployment durations translate to greater skill loss, and hence workers
are more likely to be reallocated to skill-neutral employment. Second, the cyclicality of the
minimum hiring threshold means that more workers are resume employment in a skill-neutral
job. A third and more minor force is that job-finding rates in the skill-neutral sector are
sharply decreasing in human capital.
4.3
4.3.1
Aggregate implications
Short run
To assess the aggregate implications of the model, I take quarterly averages over weekly
quantities simulated from the model. I HP-filter the data using the normal smoothing parameter. In the model, I generate large welfare costs of job loss through a cyclical process of
persistently reallocating workers to less productive jobs. The standard deviation of filtered
output is 0.02, well within the normal range, implying that the welfare cost of job displacement generated within the model is not an artifact of implausibly high output volatility.
Table 4.3.1 gives aggregate statistics of some key aggregate quantities, including output,
wages, unemployment, and employment from the U.S. data and the model. The relative
33
volatility of unemployment with respect to output matches the data fairly well, but note
that this was a calibration target. Otherwise, the persistent of output and unemployment
from the model are a little bit under their empirical counterparts, but not by too much. The
model misses the volatility of employment, but this is not surprising, given that the model
entirely abstracts from the participation margin.
4.3.2
Medium run
The model has some additional channels that may work towards generating medium-frequency
variation in output. During recessions, there is a downward shift in the distribution of workers over human capital. Given the slow recovery of human capital in the model, the distribution should be a slow moving state variable that does immediately revert to the ergodic
distribution following a negative productivity shock. To investigate this property of the
model, I study the impulse response of output and unemployment to a negative 3.4 percent
shock to productivity.7 I compare the full model to the model without human capital dynamics studied in the previous section. Given that I am studying the role of the distribution
of workers on aggregate output, I compute a global approximation to the impulse response,
simulating each model 1500 times in response to the negative aggregate shock and taking
averages. The impulse responses are given in Figure 5.
The role of the slow-moving human capital distribution is dramatically clear in the impulse response of output. Output in the economy without human capital dynamics makes
a full recovery within 28 quarters. At 28 quarters in the full model, however, output is still
down 1.39% from the ergodic mean. Output in the full model initially has a sharp recovery
until about 15 quarters after the shock, at which point it reverts to a slower recovery path.
Clearly, the output recoveries implied by the full model are somewhat extreme. But
they provide a basis for understanding the aggregate welfare costs of cyclical human capital
destruction. Galı̀, Smets, and Wouter (2012) document that the economics recoveries following recessions since the early 1990s that have been characterized as “jobless recoveries” for
their slow rate of employment recovery have featured equally slower rates of output growth.
As documented by Jaimovich and Siu (2012), these periods also coincide with the onset of
skill-biased technological change and the growth of employment in low-skill jobs.
7
The lowest value of productivity on my grid is 3.4% below the ergodic mean for productivity.
34
Figure 5: Impulse responses
Output
0
Percent change
−0.005
−0.01
−0.015
−0.02
−0.025
−0.03
no human capital dynamics
full model
−0.035
10
20
30
40
50
Quarters
60
70
80
90
100
Unemployment
no human capital dynamics
full model
Percent change
0.15
0.1
0.05
0
10
5
20
30
40
50
Quarters
60
70
80
90
100
Conclusion
In an effort to explain the large and cyclical present value cost of job loss, I have studied
a model of equilibrium unemployment and business cycles with on-the-job human capital
accumulation and “dead-end” employment. In response to an aggregate shock, firms direct
job creation towards workers with more skill, forcing displaced workers who would otherwise
search for skill-intensive jobs to search for skill-neutral jobs. The counter-cyclical increase
in hiring standards and greater skill-depreciation from higher unemployment durations generates greater cyclicality in the present value cost of job loss.
The calibrated model is able to account for 75.1% of the average cost of job loss across
aggregate states and 34.2% of the cyclicality, compared to just 21.9% of the average cost
and 12.4% of the cyclicality in the most successful of models surveyed by Davis and von
35
Wachter (2012). I explore the distributional implications of my model, and I show that
recessions move a mass of middle-skill workers to the lower end of the skill distribution; and
furthermore, workers at the lower end of the human capital distribution are subject to the
highest and most cyclical costs of job displacement.
The model also speaks to the phenomena of “slow recoveries”. A recession shifts the
distribution of human capital towards the origin, generating a persistent output gap as
output in the economy slowly converges to potential output through the gradual process of
individual skill accumulation.
The model features an explicit connection between the cyclicality in the skill content of
new jobs and the recovery of economy aggregates. In this context, skill-biased technological
change could be interpreted as an increase in the probability of skill obsolescence. Going
forward, I plan to see whether the model calibrated to fit data prior to the onset of skill-biased
technological change will generate as slow a recovery in aggregate output.
36
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