EFFICIENT LEARNING AND JOB TURNOVER IN THE LABOR MARKET

• DOI: http://doi.org/10.1111/iere.12233
• Published date: 01 August 2017
• Date: 01 August 2017

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 3, August 2017

EFFICIENT LEARNING AND JOB TURNOVER IN THE LABOR MARKET∗

BYFEI LIAND XIWENG1

University of North Carolina at Chapel Hill, U.S.A; Peking University,China

This article nests a continuous-time learning model `

ala Jovanovic (Journal of Political Economy 92 (1984),

108–22) into a directed on-the-job search framework. We prove that the socially efficient allocation is separable,

that is, the workers’ value functions and optimal controls are independent of both the distribution of workers

across their current match qualities and the unemployment rate. We characterize the dynamics of job transitions

in the efficient allocation. Furthermore, when the matching technology is linear, our numerical results show that

increasing the vacancy creation cost and the speed of learning have ambiguous effects on the unemployment

rate and aggregate job transition.

1. INTRODUCTION

This article nests a continuous-time learning model `

ala Jovanovic (1984) into a directed on-

the-job search framework. In our model, each worker–firm pair gradually learns its unknown

match quality based on cumulative output. The unknown match quality follows a two-point

distribution: It is either high or low. Search is directed in the sense that a worker knows the

terms of trade offered by different firms before choosing where to apply for a job, as in Moen

(1997) and Acemoglu and Shimer (1999). Based on the unidimensional posterior belief about

the match quality, a worker decides if and where to search on the job.

Due to the ex post heterogeneous performance of matches, any nontrivial allocation in-

evitably generates a time-varying distribution of matches over the ex post qualities. In general,

each individual’s optimal decision may depend on this time-varying distribution. As a result,

previous studies mainly analyze the steady state where the distribution is constant over time.2

In a recent pioneering paper, Menzio and Shi (2011) developed a discrete-time framework with

directed on-the-job search and aggregate productivity fluctuation. They showed that the unique

socially efficient solution is separable, in the sense that it does not depend on the time-varying

distribution. As the efficient allocation can be implemented by a decentralized market equilib-

rium if firms and workers can sign complete contracts, their technique allows for equilibrium

analysis of the dynamics of job-to-job transitions.

The current article can be viewed as a continuous-time analog of Menzio and Shi (2011)

with Gaussian learning. Similar to Menzio and Shi (2011), the efficient allocation depends on

neither the distribution of the quality of current matches nor unemployment rate. Consequently,

∗Manuscript received April 2013; revised March 2016.

1We thank the associate editor, Guido Menzio, whose comments have significantly improved the quality of the

article. We also thank Naoki Aizawa, Benjamin Lester, Kenneth Burdett, Jan Eeckhout, Hanming Fang, Chao Fu,

Manolis Galenianos, Nils Gornemann, Kyungmin Kim, Ricardo Lagos, George Mailath, Giuseppe Moscarini, Peter

Norman, Theodore Papageorgiou, Andrew Postlewaite, Moritz Ritter, Robert Shimer, Can Tian, Gabor Virag, and

Pierre-Olivier Weill. Any remaining errors are ours. Weng also acknowledges financial support from the National

Natural Science Foundation of China (Grant No. 71303014) and Guanghua Leadership Institute (Grant No. 12-02), as

well as support from the Spanish Ministry of the Economy and Competitiveness (Project ECO2012-36200) and the Key

Laboratory of Mathematical Economics and Quantitative Finance (Peking University), Ministry of Education, China.

Please address correspondence to: Fei Li, Department of Economics, University of North Carolina Chapel Hill, NC

27599-3305. Phone: +1 919-966-3710. Fax: +1 919-966-4986. E-mail: lifei@email.unc.edu.

2See Burdett and Mortensen (1998) as an example.

727

C

(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

728 LI AND WENG

the planner’s problem can be decomposed into two parts. The planner decides where to send

unemployed workers to search for jobs. For employed workers, the planner gradually learns

the quality of their matches and decides when to separate them and where each worker should

search on the job. Since employed workers are allowed to search on the job, the planner is able

to replace an unpromising match with a new one without suffering the inefficient delay during

job-to-job transition caused by search frictions.

We fully characterize the efficient allocation. When the belief about the quality of a match

being high is large enough, the planner prefers to maintain the match, so it is inefficient to send

the worker to search on the job or separate the match. When the belief is low enough, the planner

immediately separates the match by ending the worker’s employment. In the case where the

belief is intermediate, it is efficient to replace the current match with a new one but inefficient

to destroy the current match; thus, the worker is assigned to search on the job so that the

current match will be destroyed only if a new match is formed. More precisely, the job-finding

rate is decreasing in the quality of the employed worker’s current match because the benefit

of job-to-job transition rises as the quality of the current match becomes less promising. Like

Jovanovic (1984) and Moscarini (2005), our model can explain a number of robust empirical

observations on individual turnovers such as the hump-shaped relationship between tenure and

the hazard rate of separation.

We also analyze a parameterized example of the model with linear matching technology. This

example has a closed-form solution of the planner’s efficient allocation and the corresponding

ergodic stationary distribution of match quality and unemployment rate. We numerically study

the effects of changing the vacancy creation cost and the individual learning speed. Remarkably,

we find that (1) reducing the vacancy creation cost has an ambiguous effect on the unemployment

rate in the presence of learning, (2) the rate at which employed workers move into unemploy-

ment (the EU rate) changes nonmonotonically as the cost of vacancy creation declines, and

(3) although improving the speed of learning monotonically enhances the unemployment rate,

it has a nonmonotonic impact on the the rate at which workers move from one employer to

another (the EE rate).

Our main contribution is to establish the separability of the efficient allocation in a continuous-

time directed on-the-job search model with Gaussian learning.3In Menzio and Shi (2011),

the problem is formulated in discrete time, and the separability result is proved by using a

contraction mapping argument. However, such an argument does not work in a continuous-

time model. We therefore develop a different way to prove the separability result. This approach

can also be applied to other similar settings. For example, Eeckhout and Weng (2015) consider

an application of this technique to a setting with unemployment learning.4

Our second contribution is to investigate the role of learning in an equilibrium economy.

To the best of our knowledge, Moscarini (2005) is the first paper that integrates a Jovanovic-

(1984) like learning model into an equilibrium search framework.5Our model is different

from that of Moscarini (2005) in the following aspects: First, Moscarini (2005) assumes that

an employer’s on-the-job search decision is a yes-or-no choice, which allows him to model

the firm’s problem as a simple stopping-time problem.6However, the model cannot explain

the heterogeneous job-finding rate among different employed workers engaged in on-the-job

3Shi (2009) also considers a continuous-time directed search model and proves that the equilibrium is block recursive

(separable). However, the proof in Shi (2009) can ensure neither the uniqueness nor the efficiency of the equilibrium.

4Another potential application is to introduce multiple occupations. For example, Papageorgiou (2014) considers a

two-sector model where each worker learns his comparative advantage in each sector and decides which sector to work

in. However, due to technical difficulties, this article cannot allow directed on-the-job search.

5Gonzalez and Shi (2010) also develop an equilibrium learning model with directed search. In their model, all

matches are homogeneous, but over time a worker learns his job-finding ability, which is production irrelevant.

6Strictly speaking, in Moscarini (2005), workers do not actively search on the job. New jobs arrive randomly, and

workers passively choose whether to accept the new job. Although one can add search intensity into Moscarini (2005),

the complications arising from his setting as the problem is no longer a stopping-time problem; the value and policy

functions cannot be solved explicitly in general as Moscarini (2005) did.