Wealth Accumulation, On the Job Search, and Inequality

52 Pages·2016·0.59 MB·English

Wealth Accumulation, On the Job Search, and
Inequality
Gaston Chaumont Shouyong Shi
(cid:3)
Pennsylvania State University
This Version: April 30, 2016
Abstract
Using a model of directed on-the-job search in the labor market we analyze the equilibrium interactions
betweenwealthaccumulationandlaborsearchdecisionsofworkers. Theobjectiveofthepaperistounderstand
how workers hedge against income risk generated by search frictions by choosing savings and searching for
di⁄erentjobs. Inthemodelworkersareendogenouslyheterogeneousintheirearningsandwealthlevel. Thejob
search decision implies a trade-o⁄for workers in equilibrium: they can search for jobs that pay low wages and
face a high job-(cid:133)nding probability or they can search for jobs that pay high wages and face a low job-(cid:133)nding
probability. Demand for assets is driven by precautionary motives due to the risk of a decrease in earnings.
It is also assumed that wealth level cannot be lower than a certain borrowing limit. This model is used to
assess quantitatively the e⁄ects of wealth accumulation on job search decisions and the resulting wage and
wealth distribution.in the steady state. Our main quantitative (cid:133)ndings are the following. The wealth e⁄ect on
job search decisions cannot generate a very large frictional wage dispersion while at the same time matching
employmenttransitionrates. Weobtainamean-minratioof1.087. However,asmallwagedispersionisableto
spanasigni(cid:133)cantlylargerwealthdispersion. Moreover,themodelisabletoreproducesomefactsofthewealth
distribution observed in the data.
1 Introduction
Since the seminal contributions of Diamond (1981), and Mortensen and Pissarides (1994)
there have been a large number of studies that analyze the labor market implications of
Corresponding author: [email protected]
(cid:3)
1
job search and its dynamics. Search models capture the existence of unemployment in
equilibrium and introduce income risk for workers associated with job loss or with (cid:133)nding
a new job. Hence, these models permit an analysis of how wealth accumulation and labor
search interact.
Understanding the interactions between labor search and wealth accumulation is impor-
tant for analyzing how individuals hedge income risk coming from search frictions. Also it
permits studying how search friction a⁄ect the equilibrium wage and wealth distribution.
There are mainly, three ways to smooth consumption over time: (i) by buying and selling
contingent assets (or getting insurance) in the case that enough markets are available in the
economy; (ii) by accumulating and dis-accumulating wealth in the case that there is not
a complete set of contingent assets available; and/or (iii) by matching with jobs that are
somehow associated with lower levels of income risk, provided there exists some instrument
to do it. Assuming away the possibility of perfectly insuring against income risk through
contingent assets, wealth accumulation and job search decisions are the main instruments
that workers can use to smooth consumption. Hence, there is a potential for important
interactions between these two choices.
There is evidence in recent literature that suggests a non negligible interaction between
these two variables. For example, Chetty (2008) reports that individuals that receive large
(cid:135)ows of income when they lose their jobs (i.e., severance payments) stay longer periods of
time in the unemployment pool. In addition, Herkenho⁄, Phillips, and Cohen-Cole (2015)
show that the ability to borrow signi(cid:133)cantly increases unemployment duration. There is also
evidence of a signi(cid:133)cant positive relationship between wealth and unemployment duration
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for European economies. Algan, Cheron, Hairault, and Langot (2003), Bloemen and Stan-
canelli (2001), and Lentz and Tranaes (2005) provide evidence for France, Netherlands, and
Denmark, respectively. Theseandotherrecentpapersintheliterature, suggestthatthelevel
of wealth of an individual might be an important determinant of the job search behavior.
Notice also that, allowing for assets accumulation permits analyzing the e⁄ects of labor
market frictions and job search decisions on the distribution of wealth. As reported by
Budria, Diaz-Gimenez, Quadrini, and Rios-Rull (2002), the U.S. economy is characterized
by a wealth distribution that is possitively skewed, that shows a short and fat left tail,
and a long and thin right tail. The Gini coe¢ cient for weallth is 80%, meaning that this
distribution is very unequal accross households in the U.S. economy. How much of it can be
accounted by labor market dynamics is a question that has not yet been carefully adressed.
The objective of this paper is to study how wealth a⁄ects labor search behavior of work-
ers and how this behavior a⁄ects the distribution of wages and wealth in equilibrium. To
accomplish these goals, we set up a model of directed on-the-job search in the labor market.
In the model, (cid:133)rms post di⁄erent types of contracts that o⁄er di⁄erent levels of wages, and
hence, provide di⁄erent expected lifetime utility to workers (value). As it is explained in
more detail later, each of these type of contracts are o⁄ered in a di⁄erent submarket. On the
other side of the labor market, workers decide which of these submarkets to visit in order
to apply for a job. To emphasize the interactions between job search decisions and wealth
accumulation, we assume that workers are identical in all dimensions except in their level of
assets holdings and their current situation on the labor market. The size of worker popula-
tion is (cid:133)xed while the number of (cid:133)rms in each submarket is determined by competitive entry
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(after paying an entry cost). In equilibrium, submarkets with a lower value for the workers
will provide a higher value for the (cid:133)rms and will be visited by a larger number of (cid:133)rms. As
a consequence, workers who visit submarkets that provide them with a lower value will face
a higher probability of obtaining the job.
In addition to their search decision, risk averse individuals choose every period their level
of consumption and savings subject to a borrowing limit. In this context, the level of asset
holdings and submarket choice interact as follows. For individuals with high level of wealth,
labor income risk is not very signi(cid:133)cant because they are able to smooth consumption by
deccumulating assets. Hence, they prefer to visit submarkets where the wage rate is high
but where they face a lower probability of getting the new job. On the other hand, for those
individuals with asset levels closer to the borrowing limit, consumption smoothing is a very
importantissue. Asaconsequence, theywill (cid:133)nditoptimal toapplyforanewjobthato⁄ers
a lower wage rate but that is associated with a higher probability of actually getting the job.
This mechanism can qualitatively reproduce the fact that unemployed workers with higher
levels of wealth or access to credit access spend more time unemployed before (cid:133)nding their
next job. In our model, the mechanism behind is that those individuals with higher levels
of wealth will apply for better paid jobs that at the same time are associated with a lower
probability of being hired. As a result, the unemployment duration of wealthy individuals
will be longer than that of individuals with low levels of wealth.
Using the setup brie(cid:135)y outlined above, we intend to provide a quantitative answer of how
the distribution of wealth a⁄ects job search decisions of di⁄erent individuals and how these
search decisions can produce di⁄erent wealth and earnings distributions in the steady state.
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We analyze numerically how much wealth dispersion can be generated within the model in
steady state and what implications it has on consumption dispersion in the population.
In addition to studying the interactions between wealth and job search decisions, we are
also interested in analyzing the quantitative implications of the model in terms of frictional
wage dispersion, i.e. the dispersion in wages among homogenous individuals. In a recent
paper, Hornstein, Krusell, and Violante (2011) pointed out that standard textbook search
models can only account for a very small frictional wage dispersion when they are calibrated
to the U.S. data and, in particular, the job-(cid:133)nding rate of unemployed workers. They pro-
pose a new measure of wage dispersion, the mean-min ratio. We explore the quantitative
implications of our model in terms of the mean-min ratio. Workers are endogenously het-
erogenous in wealth and the current wage. By a⁄ecting wage decisions, wealth may generate
extra wage dispersion, in addition to the one generate by search frictions.
The main quantitative (cid:133)ndings are as follow. The e⁄ects of wealth on job search behavior
alonecannotgenerateaverylargefrictionalwagedispersionwhileatthesametimematching
employment transition rates. We obtain a mean-min ratio in wages of 1:087. Although there
is an important interaction between wealth level and job search decisions for individuals
with low levels of wages, these low levels of wages are not o⁄ered in equilibrium. Hence, the
mass of individuals for whom the level of wealth is an important determinant of job search
decisions is a relatively small fraction of the population.
However, a small dispersion in wages is able to span a large dispersion in wealth. The
baseline calibration yields a Gini coe¢ cient in earnings equal to 6% and a Gini coe¢ cient
in wealth equal to 27%. Even though these numbers are still small compared to the 61%
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and 80% respectively observed in the data, a Gini of 27% for wealth is a strikingly high
number given that our model abstracts from heterogeneity in worker skills and job types.
That is, by only introducing heterogenous initial conditions of workers in terms of their state
in the labor market and their asset holdings we can account for one third of the total wealth
inequality in the U.S. economy.
Moreover, the model is able to reproduce the shape of the wealth distribution observed
in the data, which has been hard to account for in the previous labor search literature (see
Lise (2013), for example). Additionally, we conduct some robustness checks of the results.
In terms of wage dispersion, on-the-job search is quantitatively very signi(cid:133)cant, as pointed
out by Hornstein et al. (2011). Not allowing for on-the-job search reduces frictional wage
dispersion almost to zero. In that case, we obtain a mean-min ratio of 1:023, which is
consistent with the results in Krusell, Mukoyama, and Sahin (2010). In addition, although
the Gini coe¢ cient in wealth is robust to changes in interest rates, the shape of the wealth
distribution depends considerably on the interest rate.
Certainly, this paper is not the (cid:133)rst attempt in the literature to analyze the interaction
between wealth accumulation and the job market. However, most of the literature has fo-
cused on the interactions between wealth accumulation and search e⁄ort and/or e⁄ort on the
job. Forexample, inrelatedstudies, LentzandTranaes(2005)andLentz(2009)analyzehow
wealth a⁄ects unemployed workers(cid:146)e⁄ort to search for a new job, and what the optimal level
ofunemploymentinsuranceiswhenthee⁄ectofwealthonsearche⁄ortistakenintoaccount.
However, since their environment does not allow for on-the-job search, the equilibrium has
a single wage rate, which makes the environment not appropriate for studying the impact
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of asset holdings on wage dispersion. In other papers that analyze incentive problems when
individual can accumulate wealth, e.g. Werning (2002) and Kocherlakota (2004), the focus
is on analyzing how hidden savings a⁄ect unemployment insurance possibilities in a context
of moral-hazard.
Previous work in the literature has also added wealth in a model with labor search and
matching frictions to analyze the dynamics of labor market and capital investment over
the business cycle. However, most of these papers make speci(cid:133)c assumptions to eliminate
households(cid:146)income risk generated by labor search frictions. For example, Merz (1995) and
Shi and Wen (1999) assume that households are composed by a continuum of individuals
and that each individual only cares about the household(cid:146)s utility. Hence, idiosyncratic risks
associated with labor search frictions are completely smoothed within a household. Another
example is Andolfatto (1996) who assumes that there exist perfect insurance markets to
smooth matching risk.
A more closely related paper is Krusell et al. (2010), who study the interactions between
wealth accumulation and job market outcomes. They integrate a model of precautionary
savings with income shocks in the style of Bewley (1977), Huggett (1993), and Aiyagari
(1994) with a standard Diamond-Mortensen-Pissarides model. Our environment di⁄ers from
Krusell et al. (2010) in several aspects. First, we allow for on-the-job search which intro-
duces additional volatility in the income process, making the interactions between wealth
accumulation and job search decisions richer. Second search is directed in our model but
undirected in Krusell et al. (2010). Directed search is consistent with the (cid:133)ndings by Hall
and Krueger (2008) that point out that 84 percent of white, male, non-college workers re-
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port to either "know exactly" or "had a pretty good idea" about how much their current
job would pay from the beginning of the application process. In addition, directed search
simpli(cid:133)es the analysis and computation. The resulting equilibrium is block recursive, as (cid:133)rst
de(cid:133)ned by Shi (2009), which has the feature that individuals decisions do not depend on
aggregate distribution of workers across individual states. Hence, we can compute the equi-
librium exactly, rather than relying on the approximated aggregation algorithms in Krusell
et al. (2010). In addition, this allows us to precisely calculate dynamics outside of the steady
state and compare transitions from one state to another.
Another closely related paper is Lise (2013), who sets up a partial equilibrium model
of on-the-job search in which job o⁄ers are randomly drawn from a (cid:133)xed known stationary
distribution. A major di⁄erence between our model and Lise (2013) is that in our setup
job search is directed. This di⁄erence is important for understanding how wealth a⁄ects
search decisions. In particular, in Lise (2013), since job o⁄ers arrive at random from a (cid:133)xed
distribution and there is no option value of remaining unemployed, the reservation wage
of unemployed workers is equal to home production and, hence, is independent of wealth.
In our model instead, unemployed workers with lower wealth are more urged to (cid:133)nd a job
and, hence, choose to search for relatively low wages that are easier to get. This creates a
potentially important interaction between wealth and job search decisions that should be
taken into account in the analysis. As an example of how this di⁄erence is relevant, in Lise
(2013), both a rich individual with a high wage that just lost his job and a poor individual
that has been unemployed for several periods could accept an o⁄er from the same job. In
contrast, in our environment, the individual with low levels of wealth will search for a job
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in a submarket that o⁄ers a low wage relative to the individual with a large stock of assets
who would search in a submarket where a higher wage is o⁄ered. This e⁄ect can introduce
further dispersion in the distribution of wealth and earnings, and might be a useful channel
to explain why U.S. earnings and wealth distribution show long and thin right tails. It is
important to remark then, that a big part of the in(cid:135)uence of wealth accumulation on job
search decisions is due the e⁄ects of assets holdings of unemployed workers.
Finally, this paper is related to Herkenho⁄(2015). Although the spirit of his model and
ours is similar, the objects of analysis are di⁄erent. He uses a directed search model to
study how the access to credit card impacts unemployment duration and job recoveries after
recessions. He focuses on o⁄-the-job search and only conducts some exercises allowing for
on-the-job search in an appendix. In contrast, we study how wealth distribution interacts
withjobsearchdecisions andare particularlyinterestedinthecase thatallows foron-the-job
search. As noticed by Hornstein et al. (2011), on-the-job search can increase frictional wage
dispersion.
The paper is organized as follows. In section 2 we introduce the environment. Section
3 presents individuals(cid:146)optimal decisions and market tightness. In section 4, we de(cid:133)ne a
recursive competitive equilibrium and a block recursive equilibrium in this environment.
Section 5 presents the computational strategy. Section 6 contains quantitative results and
section 7 concludes. Appendix A shows the algorithm used to compute the model and
Appendix B contains counterfactual exercises.
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2 The Environment
2.1 Workers, Firms and Matching
Time is discrete and lasts forever, t = 0;1;:::. There is a measure of risk averse workers with
utilityineachperiodbeinggivenbyU : R+ R,whereU0(c) (0; )andU00(c) ( ;0)
! 2 1 2 (cid:0)1
c R+, and U0(0) = . In each period a worker is endowed with an indivisible unit of
8 2 1
labor. So, a worker is in either full employment or unemployment. In addition, workers(cid:146)
time preference parameter is given by (cid:12) (0;1).
2
In reward for their work, an employed workers is paid a remuneration ! W [!;!(cid:22)],
2 (cid:17)
while an unemployed worker produces an output (cid:135)ow of b 0. In addition, workers can
(cid:21)
accumulate assets a R, which provide a net return r, determined in competitive markets
2
and taken as exogenous in this model. We assume that (cid:12)(1+r) < 1 in order to have
existence of an equilibrium in a context with precautionary savings.1 Assets holdings are
assumed to be bounded in the set A = [a;a(cid:22)]. It might seem arbitrary to assume an upper
bound for wealth and bounds for the space of wages but it can be established that if bounds
are chosen appropriately, this is with no loss of generality.
So, all workers arehomogeneous except forthreedimensions that fullycharacterizethem:
(i) they can be employed or unemployed, (ii) their current level of earnings (labor earnings
or home production), and (iii) their level of wealth.
Job search is directed. Workers can choose to search for a job in a continuum of submar-
1As shown by Aiyagari (1994), when individuals face some income risk and they have some borrowing
limit, precausinary savings motives could induce agents to accumulate in(cid:133)nite wealth if (cid:12)(1+r) < 1 does
not hold. Hence, an equilibrium condition in such an environment is that (cid:12)(1+r)<1.
10