WORKER TURNOVER AND UNEMPLOYMENT INSURANCE

• Published date: 01 November 2018
• DOI: http://doi.org/10.1111/iere.12322
• Date: 01 November 2018

INTERNATIONAL ECONOMIC REVIEW

Vol. 59, No. 4, November 2018 DOI: 10.1111/iere.12322

WORKER TURNOVER AND UNEMPLOYMENT INSURANCE∗

BYSEKYU CHOI AND JAVIER FERN ´

ANDEZ-BLANCO1

University of Bristol, U.K.; Universitat Aut `

onoma de Barcelona, Barcelona GSE,and MOVE,

Spain

This article studies a competitive search model of the labor market with learning about match-specific

productivity in which risk-averse workers factor present and future unemployment risks in their search decisions.

We examine internally efficient equilibrium allocations in which match termination occurs only if the joint value

of a worker–firm pair is negative. Internal efficiency poses a trade-off between present and future risks. Public

insurance provision also affects this trade-off and, hence, worker turnover and job composition. In addition to

unemployment benefits, the implementation of the planner’s allocation requires a negative income tax and a 0

layoff tax.

1. INTRODUCTION

From a job-seeker’s perspective, a job consists of a list of items, including primarily a wage

scheme and an expected duration. Regarding the latter, evidence shows that a large number of

new matches are short-lived in the U.S. economy, which underscores the importance of future

unemployment risks in workers’ search decisions. In Choi and Fern´

andez-Blanco (2017), using

data from the Survey of Income and Program Participation, we document that over 42% of

newly employed workers return to nonemployment within a year, and this transition rate drops

to 25% in the second year. Farber (1999) estimates these rates at 50% and 33%, respectively,

using the National Longitudinal Survey of Youth.

The goal of this article is to analyze the constrained efficiency of equilibrium hires and

separations in a frictional economy with incomplete markets in which present and future unem-

ployment risks are intertwined. Strikingly, the literature has mostly addressed the present and

future risks separately. Regarding the present risks, a number of papers have studied the optimal

design of unemployment insurance (UI). See, e.g., Hopenhayn and Nicolini (1997), Shimer and

Werning (2008), and, closest to ours, Golosov et al. (2013). Regarding employment protection

policies, Blanchard and Tirole (2008) and Cahuc and Zylberberg (2008) show that the rationale

underlying layoff taxes is to make firms internalize the welfare costs of dismissals,2but do not

∗Manuscript received June 2015; revised March 2017.

1Previous versions of the article have circulated under the title “Unemployment Duration and Worker Turnover.”

We thank Jeff Campbell, Melvyn Coles, Jes´

us Fern´

andez-Villaverde, Johannes Gierlinger, Nezih Guner, Joan Llull,

Mart´

ı Mestieri, Espen Moen, Giuseppe Moscarini, Nicola Pavoni, Edgar Preugschat, Jos´

e-V´

ıctor R´

ıos-Rull, Robert

Shimer, Kjetil Storesletten, Marcelo Veracierto, and Ludo Visschers for their feedback. We are also grateful to the

editor Guido Menzio and three anonymous referees as well as numerous participants at the NBER Summer Institute

2014, REDg-Dynamic General Equilibrium Macroeconomics Workshop 2014, Mainz Workshop in Labour Economics

2014, Essex SaM Workshop 2014, SaM Annual Conference 2015, ESSIM 2015, and at various seminars. Sekyu gratefully

acknowledges financial support from the Spanish Ministry of Economy and Competitiveness through grant ECO2012-

32392 and through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2011-0075), and Javier

from the Spanish Ministry of Science and Technology under Grant No. ECO 2013-46395, ECO2015-67602-P from

MINECO/FEDER, UE, and from the Spanish Ministry of Economy and Competitiveness through the Severo Ochoa

Programme for Centres of Excellence in R&D (SEV-2015-0563). Please address correspondence to: Javier Fern´

andez-

Blanco, Dept. Economia i Hist`

oria Econ `

omica, Universitat Aut`

onoma de Barcelona, 08193 Bellaterra, Spain. Phone:

+34 935814626. E-mail: javier.fernandez@uab.cat

2This is also the rationale for an experience-rated UI system. See, e.g., Feldstein (1978) and Wang and Williamson

(2002).

1837

C

(2018) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1838 CHOI AND FERN ´

ANDEZ-BLANCO

consider the effects on job creation. Although both job-creation and job-destruction margins

are considered in Alvarez and Veracierto (2001), jobless workers do not take unemployment

risks into account in the search process.

To this aim, we construct a two-period competitive search model of the labor market, building

on Moen (1997), and model endogenous separations by introducing match-specific productivity

as an experience good.3All firms and workers are ex ante identical. In Period 1, search takes

place: Firms compete for workers by committing to contractual offers, and risk-averse workers

decide what sort of job to search for and the search intensity. Search is directed in the sense

that offers promising a higher employment value attract more applicants. Upon meeting, a firm

and a worker draw a match-specific productivity. This is unobservable in the first period but is

learned in the second period.

The unemployment risks are consumption risks because markets are incomplete, firms can

only make payments to their own employees, and workers cannot self-insure by saving. As

a result, risk-averse workers factor present and future unemployment risks in their search

decisions. In equilibrium, as a result of the competition for workers, risk-neutral firms act

both as employers and insurers of their employees as in the implicit contract literature. See

Baily (1974) and Azariadis (1975). This is due to the difference in the ability to bear risk

between workers and firms. There are two margins through which private markets may respond

to workers’ preferences: a job-creation margin and a match-termination margin. Regarding

Period 1 unemployment risks, many low-wage jobs are posted in equilibrium to increase the

employment chances of job seekers, as in Acemoglu and Shimer (1999).4

We focus on equilibrium allocations in which Period 2 match-termination decisions are inter-

nally efcient, meaning that firms and workers resolve their coordination problems within the

match, and separation occurs if and only if the joint value of the match is negative.5In addition

to being a necessary condition to reach constrained efficiency, we argue that internal efficiency

may result endogenously in equilibrium if either the contracting space is sufficiently wide or if

an efficient negotiation process takes place. As the joint value is increasing in both the wage

and the match-specific productivity, internal efficiency establishes a negative relationship be-

tween the wage and the productivity threshold that makes the joint value equal to 0. Therefore,

job seekers trade off present and future unemployment risks. Moreover, public provision of

insurance affects such a trade-off and, hence, the equilibrium worker turnover.

To study the constrained efficiency of the equilibrium allocation, we compare it with the

social planner’s solution, i.e., the allocation that maximizes the expected discounted utility of

the representative worker subject to the search and information frictions described above. The

planner faces a moral hazard problem, as workers’ search intensity is unobservable. Because of

workers’ risk aversion, the planner attenuates the consumption difference between employment

and unemployment in a way compatible with efficiently providing search incentives. As a result,

the consumption of the unemployed is above their home production, which is their consumption

level in the laissez-faire economy. The equilibrium is constrained inefficient: The consumption

risks are not efficiently covered in the market economy because the sort of insurance markets

offer against those risks makes job creation inefficiently high and match-termination rates

inefficiently low.

We show that the planner’s allocation can be decentralized if a government sets a UI system

funded by lump sum taxes to insure away the consumption risks. Our main result is that the

implementation of the planner’s allocation requires a negative income tax and a 0 layoff tax. The

rationale for this policy result is quite intuitive. The publicly provided insurance crowds out the

private provision of insurance. That is, the equilibrium wage and the productivity threshold both

3The experience feature was first introduced by Nelson (1970), meaning that the quality of a match can only be

assessed by experiencing it. See also Jovanovic (1979).

4As Krishna (2009, Ch. 4.1) argues, this result also holds in first-price auctions, with risk-averse bidders making

higher bids because of the risk of losing.

5Indeed, we borrow the term of internal efficiency from the literature with on-the-job search. See Moen and Ros´

en

(2004) and Menzio and Shi (2011).

TURNOVER AND UNEMPLOYMENT INSURANCE 1839

increase with unemployment benefits as workers play riskier job-search strategies. To incentivize

job creation and discourage match termination, firms must be subsidized, and although such

subsidies could be set in various different forms, the efficient channel in a competitive search

framework is through wages because contractual offers guide workers’ search decisions. We

show that the income tax rate must be such that the subsidy the firm obtains for not terminating

the match is proportional to unemployment benefits. In sharp contrast with the Pigovian tax

found in Blanchard and Tirole (2008), we show that layoff taxes must be 0 because they distort

not only match termination but also job creation in an inefficient way.

It is worth noticing that the publicly provided UI shapes not only worker turnover but also

job composition, as both wages and output per worker increase with UI benefits. These effects

are similar to the ones obtained in Acemoglu and Shimer (1999) and Golosov et al. (2013).6

The former show that a UI scheme induces firms to create more capital-intensive, higher-wage

jobs. In the latter, there are too few risk-averse workers seeking high-productivity jobs, and

unemployment benefits (financed by increasing and regressive income taxes) allow workers to

take riskier strategies in their job search. In our setting, average productivity increases with UI

benefits because the insurance provided by low-productivity jobs is crowded out by the public

provision of insurance.

We extend this normative exercise to an infinite horizon economy and show that these policy

results continue to hold. Then, we calibrate the model to match some salient features of the U.S.

labor market and compute the optimal policy that maximizes a steady-state utilitarian social

welfare function. We find that UI benefits are excessively generous, which is in line with Krusell

et al. (2010). Furthermore, the optimal policy raises worker turnover, total output, output per

worker, and wages relative to the laissez-faire steady-state equilibrium.

Two standard assumptions in the literature on worker turnover are risk-neutral workers

and random search. See, e.g., Jovanovic (1984) and Moscarini (2005). Pinheiro and Visschers

(2014) analyze an economy with random search and wage posting, where firms are ex ante

heterogeneous in their termination rates and risk-neutral workers take into account wages

as well as displacement rates in their offer-acceptance decisions. In the competitive search

framework, Menzio and Shi (2011) model an economy with on-the-job search, aggregate shocks,

and match quality, but with risk-neutral workers. As a result, they find that the constrained

efficient allocation can be decentralized. We deviate from these papers by analyzing the welfare

effects of the interaction between risk aversion and directed search on equilibrium hiring and

separation rates.

The article is organized as follows: Section 2 describes the environment. Section 3 investigates

the constrained efficient allocation. In Section 4, we characterize the market equilibrium and

its welfare properties. The infinite horizon economy is studied in Section 5. The quantitative

analysis is undertaken in Section 6. Finally, Section 7 concludes. All proofs and additional

analysis are postponed to the Appendix.

2. ATWO-PERIOD ECONOMY

The economy lasts for two periods. It is populated by a unit mass of risk-averse workers

and a large continuum of risk-neutral firms. All agents discount Period 2 utility at the factor β.

Workers are ex ante identical and unemployed at the beginning of Period 1.

The worker’s utility function is additively separable in consumption and search intensity,

v(c)−φ(s). The function vis twice continuously differentiable, increasing, and concave in

consumption c. We assume that v(0) =0 and lim

c→0v(c)=∞. Job seekers derive disutility φ(s)

6Output per worker also increases with UI benefits in Marimon and Zilibotti (1999), Acemoglu (2001), and Teulings

and Gautier (2004). Key differences with respect to these papers are their assumptions of risk-neutral workers, random

search, and an exogenous separation rate independent of the match quality. We abstract from job-specific human and

physical capital investments, which would enhance the welfare gains of turnover reducing unemployment benefits.