DYNAMIC CONTRACTS WITH WORKER MOBILITY VIA DIRECTED ON‐THE‐JOB SEARCH

• Published date: 01 November 2016
• DOI: http://doi.org/10.1111/iere.12202
• Author: Kunio Tsuyuhara
• Date: 01 November 2016

INTERNATIONAL ECONOMIC REVIEW

Vol. 57, No. 4, November 2016

DYNAMIC CONTRACTS WITH WORKER MOBILITY VIA DIRECTED

ON-THE-JOB SEARCH∗

BYKUNIO TSUYUHARA1

University of Calgary, Canada

This article proposes a model with dynamic incentive contracts and on-the-job search in a frictional labor market.

The optimal long-term contract exhibits an increasing wage–tenure profile. With increasing wages, worker effort also

increases with tenure. These two features imply that the probabilities of both voluntary and involuntary job separation

decrease with both job tenure and the duration of employment. Given these results, workers experience differing

labor market transitions—between employment, unemployment, and across different employers—and the equilibrium

generates endogenous heterogeneity among ex ante homogeneous workers.

1. INTRODUCTION

This article proposes a model with dynamic incentive contracts and on-the-job search in

a frictional labor market. Employment relationships are generally long term (Farber, 2010).

Nevertheless, workers frequently move between jobs as well (Nagyp´

al, 2008). Given these two

important characteristics of the labor market, the main purpose of this article is to provide new

insights into how work incentive within a long-term employment relationship interacts with

worker mobility in the labor market.

The model in this article has several important features. First, I assume the worker search is

a directed process; that is, the firms offer a contract to attract workers, and the workers direct

their search to a particular job offer.2This assumption enables a clean characterization of the

optimal contract. Second, I assume both employed and unemployed workers are allowed to

search. The job discontinues if the worker leaves for another job, that is, voluntary separation

(quits). In addition, the job output depends on the employed worker’s unobservable effort,

and the job discontinues if the output is “too low,” that is, involuntary separation (layoff). This

endogenous job separation provides an additional work incentive, which evolves over time and

interacts with labor mobility.

There are three key results in this study. First, the firm offers a dynamic wage contract

that is increasing with tenure on the job. The result shows there are two reasons to offer

the increasing wage–tenure contract: (i) to encourage the worker to stay in the firm and (ii) to

provide an incentive to exert effort. The decomposition of wage variation into these two reasons

is consistent with the back-loaded wage contract typically found in on-the-job search models

∗Manuscript received September 2014; revised January 2016.

1This article is based on Chapter 2 of my Ph.D. thesis submitted to the University of Toronto. I am deeply indebted

to Shouyong Shi for his extensive help and encouragement in writing this article. I am grateful to the associate editor,

Guido Menzio, and two anonymous referees for their insightful and detailed suggestions that helped me significantly

improve the article. I also thank Ettore Damiano, Jan Eeckhout, Li, Hao, Gueorgui Kambourov, Philipp Kircher, Nobu

Kiyotaki, Matt Mitchell, Robert Shimer, Henry Siu, Scott Taylor, Trevor Tombe, Randy Wright, and conference and

seminar participants at the University of Calgary, Toronto, Osaka, and Vanderbilt University, Econometric Society

(Tokyo and Barcelona), RMM, SAET (Faro), and SED (Istanbul and Cyprus) for helpful comments and suggestions at

various stages of this article. Financial support from Shouyong Shi’s Bank of Canada Fellowship and Canada Research

Chair and from Ettore Damiano’s SSHRC grant is acknowledged. Please address correspondence to: Kunio Tsuyuhara,

Universityof Calgary, 2500 UniversityDrive, Calgary, Alberta, T2N 1 N4, Canada.E-mail: kunio.tsuyuhara@ucalgary.ca.

2Acemoglu and Shimer (1999a, 1999b) and Moen (1997) are early applications of directed search in the labor market.

Deracroix and Shi (2006) develop a model of directed search on the job.

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(2016) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1406 TSUYUHARA

(Burdett and Coles, 2003; Shi, 2009) and in efficiency wage models (Lazear, 1981; Lazear and

Moore, 1984). The second result is that the labor market can be divided into two segments: (i)

the competitive segment, where the wage increases for both retention and incentive reasons;

and (ii) the monopsonistic segment, where no firms enter to compete for the employed worker

but the wage still increases due to the incentive reason. Finally, the third result is that, with

increasing wages, worker effort also increases with tenure, which decreases the probability of

layoffs. Since increasing wage itself decreases the probability of quits over time, the optimal

contract implies the probabilities of both quits and layoffs decrease with tenure. As a result,

workers experience differing labor market transitions—between employment, unemployment,

and across different employers—and endogenous heterogeneity among ex ante homogeneous

workers emerges.

The theory described in this article is based on two important studies. On the one hand, the

dynamic contracting problem in this model is similar to the model of repeated moral hazard in

Spear and Srivastava (1987). I follow their recursive contracting approach and solve the firm’s

optimal contracting problem in an equilibrium framework. On the other hand, the analysis of

dynamic contracts with directed on-the-job search in this article closely follows that of Menzio

and Shi (2010). The main addition of this article to Menzio and Shi (2010) is the moral hazard

problem of a worker’s effort. In this extended environment, I prove the existence of a block

recursive equilibrium (BRE) where the individual firm’s contracting problem and worker’s job

search problem do not depend on the distribution of workers in equilibrium.3Although this

article does not consider aggregate and idiosyncratic shocks, the result shows how Menzio and

Shi (2010) analysis can incorporate a richer contractual environment.4

There is growing literature on asymmetric information in search theoretic labor market

models.5Moen and Ros´

en (2011) and Zaharieva (2010) analyze employed worker unobservable

effort and a contracting problem in a competitive search framework. This article is different

from these studies in considering dynamic wage contracts and on-the-job search. By neglecting

to consider these aspects, these studies preclude the interaction between the dynamic incentive

problem and worker mobility in the labor market. Other recent studies include Moen and

Ros´

en (2006) analyzing an efficiency wage contracting problem in a random search framework

and Guerrieri et al. (2009) and Carrillo-Tudela and Kaas (2015) analyzing adverse selection

problems.

Relational contracting models show that a long-term relationship acts as a self-enforcing

mechanism to maintain incentives.6In a closely related article, Board and Meyer-Ter-Vehn

(2015) analyze the effect of on-the-job search in a competitive labor market. However, even

with on-the-job search, the lack of commitment on the firm’s side in their model implies the

optimal contract that pays a constant wage for the duration of the match. Therefore, their model

is unable to capture the dynamics of work incentive on the job and the resulting implications

on wage, productivity, and job turnover.

2. LABOR MARKET WITH SEARCH FRICTION AND MORAL HAZARD

2.1. Preferences and Technology. There is a continuum of infinitely lived workers with a

unit measure and a continuum of firms whose measure is determined by competitive entry.

All workers and firms are ex ante homogeneous. Time is discrete and indexed by t. Workers

cannot save or borrow against their future income. In each period, a worker consumes ωt=wt,

wage income if employed, or ωt=b, unemployment benefit if unemployed. Unemployment

3Following the original contribution by Shi (2009), Menzio and Shi (2010) establish the notion of BRE with on-the-job

search in a stochastic environment.

4Other applications of the BRE include Gonzalez and Shi (2010) and Menzio et al. (2013).

5Burdett and Mortensen (1980) is one of the original theoretical contributions. They extend the theory of job

search to include implicit contracts and develop a consistent theory of labor market equilibrium. Cao and Wang (2013)

empirically investigate contracting problems in a dynamic search model.

6See especially MacLeod and Malcomson (1998) for related macroeconomic implications.