On-the-job search and precautionary savings

TLDR: In this article, the authors developed and estimated a model of on-the-job search in which risk averse workers choose search effort and can borrow or save using a single risk free asset.

Abstract: In this paper I develop and estimate a model of on-the-job search in which risk averse workers choose search effort and can borrow or save using a single risk free asset. I derive the implications for optimal savings behavior in this environment and relate this to the frictions that characterize the endogenous earnings process implied by on-the-job search. Savings behavior depends in a very intuitive way on the rate at which offers are received, the rate at which jobs are destroyed, and a worker’s current rank in the wage distribution. The implication is that workers, who are identical in terms of preferences and opportunities, have substantially different savings behavior depending on their history and current position in the wage distribution. The mechanism that generates the substantial differences in savings behavior in the model is the dynamic of the “wage ladder” resulting from the search process. There is an important asymmetry between the incremental wage increases generated by onthe-job search (climbing the ladder) and the drop in income associated with job loss (falling off the ladder). The behavior of workers in low paying jobs is primarily governed by the expectation of wage growth, while the behavior of workers near the top of the distribution is driven by the possibility of job loss. The distributions of earnings, wealth and consumption implied by the model (suitably aggregated) align reasonably well with the data, with the notable exception of implying substantially less concentration of wealth among the richest one percent of the population. In this paper I develop and estimate a model of on-the-job search in which risk averse workers choose search effort and can borrow or save using a single risk free asset. I derive the implications for optimal savings behavior in this environment and relate this to the frictions that characterize the endogenous earnings process implied by on-the-job search. Savings behavior depends in a very intuitive way on the rate at which offers are received, the rate at which jobs are destroyed, and a worker’s current rank in the wage distribution. The implication is that workers at different point in the wage distribution have substantially different savings behavior, resulting in wealth dispersion that is much greater than earnings dispersion. The mechanism that generates the high degree of wealth dispersion in the model is the dynamic of the “wage ladder” resulting from the search process. There is an important asymmetry between the incremental wage increases generated by on-the-job search (climbing the ladder) and the drop in income associated with job loss (falling off the ladder). This feature of the model generates differential savings behavior at different points in the earnings distribution. The behavior of workers in low paying jobs is primarily governed by the expectation of wage growth, while the behavior of workers near the top of the distribution is primarily driven by the possibility of job loss. The wage growth expected by low wage workers, combined with the fact that their earnings are not much higher than unemployment benefits, causes them to dissave. As a worker’s wage increases, the incentive to save increases: the potential for wage growth declines and it becomes increasingly important to insure against the large income reduction associated with job loss. The fact that high wage and low wage workers have such different savings behavior leads to a wealth distribution that is much more unequal 1

Figures

Figure 2: Empirical Earnings Distributions: White Males, 1978–2002

Figure 6: Estimated Offered and Accepted Wage Distributions

Figure 5: Likelihood contribution of a typical individual

Figure 7: Lorenz Curves for Wealth: Model and Data

Table 1: Summary Statistics.

Table 2: Model Parameters

Full text

On-the-Job Search and Precautionary Savings: Theory
and Empirics of Earnings and Wealth Inequality
∗
Jeremy Lise
†
Queen’s University
Version of January 13, 2006
Abstract
In this paper, I develop and estimate a model of the labor market that can account for both the
inequality in earnings and the much larger inequality in wealth observed in the data. I show
that an equilibrium model of on-the-job search, augmented to account for saving decisions
of workers, provides a direct and intuitive link between the empirical earnings and wealth
distributions.
The mechanism that generates the high degree of wealth inequality in the model is the
dynamic of the “wage ladder” resulting from the search process. There is an important asym-
metry between the incremental wage increases generated by on-the-job search (climbing the
ladder) and the drop in income associated with job loss (falling off the ladder). The behavior
of workers in low paying jobs is primarily governed by the expectation of wage growth, while
the behavior of workers near the top of the distribution is driven by the possibility of job loss.
This feature of the model generates differential savings behavior at different points in the earn-
ings distribution. The wage growth expected by low wage workers, combined with the fact
that their earnings are not much higher than unemployment benefits, causes them to dis-save.
As a worker’s wage increases, the incentive to save increases: the potential for wage growth
declines and it becomes increasingly important to insure against the large income reduction
associated with job loss. The fact that high wage and low wage workers have such differ-
ent savings behavior generates an equilibrium wealth distribution that is much more unequal
than the equilibrium wage distribution. I estimate the structural parameters of the model by
simulation-based methods using the 1979 youth cohort of the NLSY. The estimates indicate
that the micro-level search and savings behavior—estimated from the dynamics of individ-
uals’ labor market histories and wealth accumulation decisions—aggregates to replicate the
cross-sectional inequality in earnings and wealth for this cohort.
∗
I am grateful for the advice and support of Shannon Seitz and Allen Head. I have also benefited from discussions
with Tom Crossley, Chris Ferrall, Jean-François Houde, Susumu Imai, Kenneth Judd, James MacKinnon, Krishna
Pendakur, Katsumi Shimotsu, Randy Wright, seminar participants at Queen’s University, Simon Fraser University,
and the 2005 Chicago-Argonne Institute on Computational Economics. Financial support from the Social Sciences
and Humanities Research Council of Canada (SSHRC) is appreciated.
†
Phone: (613) 533-2292, E-mail: lisej@econ.queensu.ca, Web: http://www.econ.queensu.ca/students/lise

1 Introduction
In this paper I provide a framework that accounts for both employment transitions and savings
behavior at the micro-level and the joint distribution of wealth and earnings at the aggregate level.
I do so by developing and estimating an equilibrium search model with saving, where the joint
distribution of wealth and earnings is the equilibrium outcome from a labor market characterized
by informational frictions and the possibility of job destruction.
Labor markets are characterized by a surprisingly large degree of wage dispersion across work-
ers, even within narrowly defined markets. This leads to earnings inequality which is large, and
exists even within groups of observationally similar individuals. Accompanying the large disper-
sion in wages is an even larger dispersion in wealth. In industrialized countries, wealth is much
more unequal than earnings. The distribution of wealth is characterized by a long right tail; a very
large amount of wealth is held by a small fraction of individuals. Many households, and in some
countries the majority of households, never accumulate much private wealth. The primary chal-
lenge for any theory of wealth inequality is to simultaneously produce the low median wealth and
the very long right tail.
1
Although wealth dispersion is not usually considered a labor market feature, it is the cumu-
lative result of decisions made by individuals who live in an environment characterized by lots
of wage dispersion and lots of job turnover, both in terms of transitions between employment
and unemployment, and also in terms of transitions between jobs. There are numerous theories
for why earnings are so unequal, all relying on ex ante productivity differences across workers.
2
Mortensen (1990) and Burdett and Mortensen (1998) provide an alternative model of earnings dis-
persion, primarily aimed at addressing the question “Why are similar workers paid differently?”
This framework focuses on differences in firm productivity and recruiting or wage policies com-
bined with informational frictions that make it costly for workers to become fully informed about
the wage policies of all firms. This framework, generally referred to as the Burdett-Mortensen
model, is attractive because it provides a unified theory of job turnover and earnings inequality,
even when workers are ex ante identical.
3
Search models of the labor market provide a rigorous
1
The empirical regularities of income inequality have been documented by Gottschalk and Smeeding (1997) for
OECD countries and by Budría Rodríguez, Díaz-Giménez, Quadrini, and Ríos-Rull (2002) for the United States.
Davies and Shorrocks (2000) outline the stylized facts for wealth inequality.
2
See Neal and Rosen (2000) for an overview.
3
Mortensen (2003) provides a complete development of the Burdett-Mortensen model, including many extensions

yet tractable framework for addressing questions of the dynamics associated with labor market
experiences, including individual workers’ wage dynamics and wage dispersion.
4
In this paper I
demonstrate that search models are also well suited to analyzing workers’ (precautionary) savings
behavior and the resulting wealth inequality.
The mechanism that generates the high degree of wealth inequality in the model is the dynamic
of the “wage ladder” resulting from the search process. There is an important asymmetry between
the incremental wage increases generated by on-the-job search (climbing the ladder) and the drop
in income associated with job loss (falling off the ladder). The behavior of workers in low paying
jobs is primarily governed by the expectation of wage growth, while the behavior of workers
near the top of the distribution is driven by the possibility of job loss. This feature of the model
generates differential savings behavior at different points in the earnings distribution. The wage
growth expected by low wage workers, combined with the fact that their earnings are not much
higher than unemployment benefits, causes them to dis-save. As a worker’s wage increases, the
incentive to save increases: the potential for wage growth declines and it becomes increasingly
important to insure against the large income reduction associated with job loss. The fact that high
wage and low wage workers have such different savings behavior generates an equilibrium wealth
distribution that is much more unequal than the equilibrium wage distribution.
I estimate the structural parameters of the model by simulation-based methods using the 1979
youth cohort of the National Longitudinal Survey of Labor Market Experience (NLSY79). This
data is particularly well suited for my purposes as it contains weekly observations on the labor
market status and wages of individuals from 1978 through 2002. From 1985 onward, with the
exception of 1991, observations on assets are recorded at each interview date. I use simulation-
based estimation to deal with the fact that wealth, which is a state variable, is only observed
at irregularly spaced interview dates, and that unemployment and job durations rarely coincide
exactly with these observations. Sampling data from the simulated model at the same frequency
that the actual data was collected addresses this problem. Given estimates for the model from the
micro observations on individual labor market histories and asset levels, I compare the distributions
of earnings and wealth implied by the model with the those in the data. The wealth distribution
which make the framework well suited to empirical analysis of labor markets.
4
A recent survey of search theory is provided by Rogerson, Shimer, and Wright (2005). A survey of the empirical
search literature is provided by Eckstein and van den Berg (2003).
2

implied by the model matches the data almost exactly.
This paper contributes to the recent literature that attempts to account for wealth inequality,
such as Krusell and Smith (1998) and Castañeda, Díaz-Giménez, and Ríos-Rull (2003). Both
of these papers study wealth inequality within a framework of ex ante identical individuals who
behave optimally in the face of uninsurable idiosyncratic shocks to income. They find that it is
difficult to jointly reconcile the individual income dynamics with aggregate income and wealth
inequality. Krusell and Smith find that the fit to wealth inequality can be improved dramatically if
heterogeneity in the rate of time preference is used. Small differences in the rate of time preference
across individuals results in large differences in savings behavior. Castañeda, Díaz-Giménez, and
Ríos-Rull adopt an alternative approach. Instead of using an income process estimated from the
data, they target the Lorenz coordinates for income and wealth inequality, and let the income
dynamics be whatever is necessary to generate the observed inequality. As a result, the model can
replicate the income and wealth distributions found in the data, but the dynamics of the model’s
income process do not have a direct empirical counterpart. Here, I adopt a different approach.
I estimate the dynamics of the income process within an equilibrium labor search model, and
aggregate up earnings and wealth to check whether the inequality in earnings and wealth from the
model replicates that observed in the data. This exercise requires the model to fit both the dynamics
of individual labor market histories and the cross-sectional implications for the distribution of
earnings and assets. The model is successful on both fronts.
This paper is also related to the literature on search models that include a savings decision.
5
This literature has been primarily concerned with the effect of an individual’s wealth level on his
search effort or reservation wage decision. My contribution is to fully develop a theory for optimal
savings in this environment, and to show that the parameters characterizing the frictions in the
labor market have a direct and intuitive interpretation in the workers’ optimal savings decision,
and imply that wealth will be much more unequal than earnings.
The remainder of the article is organized as follows. Section 2 presents the economic environ-
ment and develops the optimal search and savings decisions of workers. This section also explores
5
This literature included the original theoretical contribution on risk aversion and reservations wages by Danforth
(1979), and the recent contributions of Acemoglu and Shimer (1999), Costain (1999), Browning, Crossley, and Smith
(2003), Lentz (2005), Lentz and Tranæs (2005), and Rendón (2006). Direct empirical support for a positive correlation
between wealth levels and unemployment durations is provided by Bloemen and Stancanelli (2001), Alexopoulos and
Gladden (2002), and Algan, Chéron, Hairault, and Langot (2003).
3

the mechanism relating labor market frictions to the joint distribution of wages and assets. Sec-
tion 4 details techniques used to numerically solve the model. Section 5 describes the data and
subsample used for the estimation, and presents a descriptive look at the data, highlighting the
correlations that relate to important implications of the model. Estimation issues and a strategy for
identification of the model parameters using simulation based estimation methods are presented in
Section 6. Estimation results, and the quantitative implications of the model, are presented in Sec-
tion 7. Section 8 concludes and provides directions for further research. All proofs and extended
derivations are provided in the Appendix.
2 The Economy
In this section, I present an equilibrium search model in the spirit of Burdett (1978), Burdett and
Mortensen (1998), and Christensen, Lentz, Mortensen, Neumann, and Werwatz (2005). The model
is extended to include risk-averse workers who face incomplete markets and the inability to fully
insure consumption streams. The introduction of assets induces an endogenous distribution of
search intensity that is a function of the joint distribution of wages and assets. The firm side of the
problem and the equilibrium conditions remain largely intact from Burdett and Mortensen, where
firms are characterized by continuous heterogeneity in productivity as developed in Bontemps,
Robin, and van den Berg (2000) and summarized in Mortensen (2003).
2.1 The Environment
Time is continuous and there is no aggregate uncertainty. Within a well-defined labor market,
workers are homogeneous in terms of productivity. Workers are ex ante identical, but will differ ex
post due to differing labor market histories. Firms are assumed to differ ex ante by productivity.
6
A labor market is characterized by a continuum of workers with unit mass. Workers are risk averse
and derive utility from consumption and disutility from the effort of searching for a new job. It
is assumed that workers know the stationary wage offer distribution but cannot observe the wage
policy of all firms; they only observe the wage offer of the firm they contact. Unemployed workers
contact firms randomly at a rate that is increasing in search effort. Employed workers contact firms
6
Firm heterogeneity is an essential component for obtaining an equilibrium wage distribution with the characteris-
tics of an empirical wage distribution.
4

Frequently asked questions

Q1. What have the authors contributed in "On-the-job search and precautionary savings: theory and empirics of earnings and wealth inequality∗" ?

In this paper, I develop and estimate a model of the labor market that can account for both the inequality in earnings and the much larger inequality in wealth observed in the data. As a worker ’ s wage increases, the incentive to save increases: the potential for wage growth declines and it becomes increasingly important to insure against the large income reduction associated with job loss. 

Q2. What are the future works in "On-the-job search and precautionary savings: theory and empirics of earnings and wealth inequality∗" ?

I show that in a labor market characterized by informational frictions and the possibility of job destruction, workers with different wages will exhibit very different savings behavior ; indeed they will behave as if they have heterogeneous discount rates. Considering the good fit of both the micro-level and aggregate features of the data, the estimated structural model can be used to quantify the effects of counter-factual experiments—such as changes in unemployment benefits—on search effort and savings decisions of individuals, and on the aggregate levels of unemployment and wealth inequality. This implies that where the lines are close together, the slope of the density is very steep, and conversely, the slop is flatter the further apart are the contour lines. Formal statistical tests for the equality of the Lorenz curves can be undertaken using the procedures developed in Davidson and Duclos ( 2000 ). 

Q3. What is the way to make the wage search model consistent with the empirical shape of the wage?

The addition of firm heterogeneity can make the equilibrium search model consistent with the empirical shape of the wage distribution. 

Q4. What is the key to generating heterogeneity in savings?

15The key to generating heterogeneity in savings is that expected gains and losses in income are not symmetric, and differ according to the current wage. 

Q5. What is the advantage of modeling endogenous search effort rather than using a separate contact rate?

The advantage of modeling endogenous search effort rather than using a separate contact rate when unemployed and employed is that the model implies that both unemployment and job durations are increasing in current assets, with job durations also increasing in the current wage, afeature that turns out to be empirically relevant. 

Q6. How much is the minimum necessary level of consumption for low educated men?

The minimum necessary level of consumption is estimated to be equivalent to approximately $590 per month for low educated and $770 per month for high educated. 

Q7. What is the effect of the introduction of assets on the search intensity?

The introduction of assets induces an endogenous distribution of search intensity that is a function of the joint distribution of wages and assets. 

Q8. What is the effect of on-the-job search on the inequality in wealth?

The success of the model in matching the inequality in wealth is largely attributable to the effect on savings behavior of the wage ladder induced by on-the-job search. 

Q9. what is the flow value of being unemployed with assets a?

The flow value of being unemployed with assets a is given by the utility flow from consumption u(c) less the disutility of search effort e(s) plus the expected change in the value of unemployment. 

Q10. What is the main issue that needs to be overcome in the estimation strategy?

The fact that assets are only partially observed, at irregularly spaced interview dates, is the main issue that needs to be overcome in the estimation strategy. 

Q11. What is the way to estimate the structural model?

Considering the good fit of both the micro-level and aggregate features of the data, the estimated structural model can be used to quantify the effects of counter-factual experiments—such as changes in unemployment benefits—on search effort and savings decisions of individuals, and on the aggregate levels of unemployment and wealth inequality. 

Q12. What is the advantage of using the asset level to the current spell?

This has the advantage of removing the endogeneity of the asset level to the current spell, but comes at the cost of losing a lot of data, and hence a lot of precision. 

Q13. How do you test the hypothesis that the distributions in 1998 and 2002 are equal?

Using a Kolmogorov-Smirnov test for the equality of two distributions, The authordo not reject the null hypothesis that the distributions in 1998 and 2002 are equal, while The authordo reject this hypothesis for any other pair of years. 

Q14. What is the probability of transiting to a better paying job?

The probability of transiting to a better paying job is given by the product of the job contact rate λ, search effort as a function of assets and the wage s(a, w), and the probability that a contacted firm is paying a higher wage F (w) (equal to one when unemployed). 

Q15. What is the way to estimate the BurdettMortensen model?

Robin, and van den Berg (1999, 2000) derive and estimate the BurdettMortensen model with continuous heterogeneity in firm productivity.