EQUILIBRIUM SEARCH AND TAX CREDIT REFORM

• Date: 01 November 2017
• DOI: http://doi.org/10.1111/iere.12245
• Published date: 01 November 2017
• Author: Andrew Shephard

INTERNATIONAL

ECONOMIC

REVIEW

November 2017

Vol. 58, No. 4

EQUILIBRIUM SEARCH AND TAX CREDIT REFORM∗

BYANDREW SHEPHARD1

University of Pennsylvania, U.S.A.

An empirical equilibrium job search model with wage posting is developed to analyze the impact of U.K.

tax reforms. The model allows for a rich characterization of the labor market, with hours responses, accurate

representations of the tax and transfer system, and both worker and firm heterogeneity. The British Working

Families’ Tax Credit and contemporaneous reforms are predicted to increase employment, with equilibrium

effects found to be relatively modest. The model is used to assess the impact of alternative policies, with

equilibrium effects shown to become important as the generosity of tax credits is increased.

1. INTRODUCTION

Over the past two decades, earned income tax credit programs have grown substantially in the

United Kingdom, the United States, and many other countries.2These programs are typically

motivated by a desire from policy makers to increase labor market participation among target

groups and to alleviate in-work poverty. Although the effect of these policies on labor supply

has been studied extensively, much less is known regarding the equilibrium impact of these

policies.3The objective of this article is to develop an empirical equilibrium job search model

that provides us with an appropriate framework to consider these issues. I first apply it in

my analysis of a series of U.K. tax reforms that included the Working Families’ Tax Credit

(WFTC) reform, which considerably increased the generosity of in-work support for families

with children (see Brewer, 2001), and then in my analysis of tax credit design more generally.

This article contributes to the literature on the impact and design of tax credit policies,

but starts from the premise that labor markets may be characterized by considerable search

∗Manuscript received December 2014; revised May 2016.

1I am indebted to Jean-Marc Robin for his extensive advice and support. I thank Chris Flinn and anonymous referees

for comments that have greatly improved this article. I am also grateful to Richard Blundell, Kirill Evdokimov, Guy

Laroque, Costas Meghir, Morten Ravn, participants on the Review of Economic Studies Tour, and numerous seminar

participants for useful comments. Material from the Quarterly Labour Force Survey is crown copyright and has been

made available by the Office for National Statistics through the Economic and Social Data Service. Crown copyright

material is reproduced with the permission of the Controller of HMSO and the Queen’s Printer for Scotland. The Office

for National Statistics and the Economic and Social Data Service bear no responsibility for the analysis or interpretation.

Please address correspondence to: Andrew Shephard, 522 McNeil Building, Department of Economics, University of

Pennsylvania,3718 Locust Walk, Philadelphia, PA 19104,U.S.A. Phone: 215-898-7408. E-mail: asheph@econ.upenn.edu.

2See Hotz and Scholz (2003) for EITC in the United States and Blundell and Hoynes (2004) for the British Working

Families’ Tax Credit and its predecessors.

3Recent studies by Azmat (2006), Leigh (2010), and Rothstein (2008, 2010) have examined the economic incidence

of tax credit programs and provide evidence that suggests that as tax credit entitlement is expanded, gross wages are

reduced.

1047

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

and Economic Research Association

1048 SHEPHARD

frictions (see, e.g., van den Berg and Ridder, 2003).4The presence of labor market frictions

may have important equilibrium implications for our understanding of programs like WFTC. In

particular, if firms set wages, then these frictions bestow them with some degree of monopsony

power. If labor supply were to increase following such reforms, firms may respond by lowering

wage offers, in which case the effective transfer to eligible families is reduced, while noneligible

families may become worse off if they are competing within the same labor market. Conversely,

the increased labor supply may induce firms to increase their recruiting intensity. In terms of

both evaluation and program design, an understanding of the quantitative importance of these

equilibrium effects is essential.

The equilibrium job search literature allows us to capture these and other effects in a dynamic

and imperfectly competitive economy that is characterized by search frictions. Competition

between firms is the fundamental determinant of wages, with the extent of this competition

limited by the presence of search frictions. In the spirit of Burdett and Mortensen (1998), I

consider a model with ex ante wage posting: Firms set wages before meeting potential workers,

which workers then either accept or reject.5I advance this literature in several dimensions, with

the model developed here designed to reflect some key features of the U.K. labor market and

to allow for the possibility of rich equilibrium effects following reforms such as WFTC.

At a methodological level, this article contributes to the empirical equilibrium job search liter-

ature by developing a wage-posting model with wage–hours packages, accurate representations

of the tax and transfer system, and both observed and unobserved worker and firm heterogene-

ity. The article most closely related is the on-the-job search model presented in Bontemps et al.

(1999), which this article builds upon. As in their model, I allow for continuous distributions of

firm productivity and worker leisure flows, but make an important methodological contribution

by relaxing the assumption that the arrival rate of job offers is independent of employment

status. Although conceptually simple, relaxing this assumption in models with both unobserved

worker and firm heterogeneity has previously been considered intractable in the literature (see,

e.g., van den Berg, 1999).6As will become clear, allowing for heterogeneity in worker leisure

flows is important, as it provides the main mechanism through which policies such as tax reforms

induce nondegenerate labor supply responses. To allow for the possibility of richer equilibrium

responses, I additionally allow firms to choose a level of recruiting intensity so as to increase

their meeting rate with workers independent of the posted wage. This provides a framework

that then allows the job offer arrival rates to be endogenized at the macroeconomic level by

complementing the model with aggregate matching functions. I then prove a new important

theoretical invariance result regarding the extent to which certain assumptions on the recruiting

cost function actually matter for my counterfactual simulations.

As I describe in the following section, both WFTC and its predecessor were only available to

families with children. To investigate possible differential impacts to the tax reforms, and to also

4Blundell et al. (2011) study the same tax reforms that I focus on in this article. They present evidence of important

announcement effects on the employment decisions of single parents (employment increasing between the announce-

ment and implementation of the program), which is consistent with the presence of significant labor market frictions

existing for this group. I describe other evaluations of Working Families’ Tax Credit in Subection 5.3.

5Manning (2003) argues that although wage posting is not always appropriate, it provides a good characterization of

wage determination in many settings. This is likely to be particularly true when focusing on low-skilled labor markets,

as in this article. Hall and Krueger (2008) present recent U.S. survey evidence that suggests that although other forms

of wage formation are also important, wage posting is much more prevalent in less skilled occupations (see also the

discussion in Manning, 2003, chapter 5). Other papers have examined the impact of similar policies with alternative

forms of wage determination; Lise et al. (2005) simulate the effect of a wide scale implementation of the Canadian

Self-Sufficiency Project in a model with ex post worker–firm bargaining.

6As we shall see in Section 3, the overidentifying restriction in Bontemps et al. (1999) simplifies the analysis, as it

implies that the optimal strategy of nonemployed workers is independent of the equilibrium wage offer distribution.

This restriction led to a poor fit of the duration data in their application, as empirically job offer arrival rates for

nonemployed workers are often estimated to exceed that of the employed. Furthermore, under this overidentifying

restriction they found that the dispersion in leisure flows was not an important determinant of the variation in individual

wages. These findings contrast with my later results.

EQUILIBRIUM SEARCH AND TAX CREDIT REFORM 1049

explain differences in labor market outcomes, I make a further methodological contribution by

incorporating further dimensions of worker heterogeneity. Both the tax and transfer system and

the key worker parameters may all potentially vary with observable demographic characteristics,

and I demonstrate how the type of semiparametric estimation procedure used in simpler job

search models can be extended to this much richer environment. In contrast to the segmented

markets approach adopted by van den Berg and Ridder (1998), I will allow workers of all

types to operate within the same labor market. It is this feature that allows workers who are

not eligible for tax credits to be indirectly affected by them through changes in the optimal

strategies of firms.

The U.K. labor market has a high prevalence of part-time work, particularly among women

with children. As noted above, the presence of children is a central eligibility requirement for

receipt of tax credits. These features motivate me to incorporate hours of work into the model.

Although the use of the canonical labor supply model may be pervasive, there is a body of

empirical work that challenges the view that individuals are able to freely choose their hours

of work at a fixed hourly wage.7I allow for both part-time and full-time jobs by developing a

multisector model and throughout this article maintain the assumption that jobs sequentially

arrive as wage–hours packages.

The level of generality here means that the model is analytically intractable. Nonetheless,

I show that the model remains empirically tractable by demonstrating how the type of three-

step seminonparametric estimation technique proposed by Bontemps et al. (1999, 2000) in the

context of much simpler environments can be adapted to the considerably richer multisector

framework that I consider here. I estimate the model using U.K. Labour Force Survey (LFS)

data shortly before WFTC was introduced. I show that the estimated model is successful in

explaining prereform differences in employment states and distributions of wages as well as

labor market transitions. Using the estimated parameters, I then simulate the impact of actual

tax reforms and later compare my results to postreform data. I find that the introduction of

WFTC, together with the contemporaneous changes to the tax and transfer system, increased

employment for most groups, with single parents experiencing the largest employment increase.

My main simulations suggest that although equilibrium considerations do play a role in these

reforms, the changes in labor market outcomes are dominated by the direct effect of changing

job acceptance behavior.

My estimated model is shown to reproduce the most important features of the data and

to generate labor supply reform responses that are consistent with numerous studies. This

performance provides the basis for a series of exercises that are concerned with the design of tax

credits. First, I consider the impact of extending the generosity of WFTC and demonstrate that

as maximal tax credit awards are increased, equilibrium effects become much more important.

Second, I develop a framework for considering the optimal design of tax credits under a revenue

constraint. I focus on practically implementable reforms that completely nest the actual U.K.

tax, transfer, and tax credit systems. My analysis points toward a reformed tax credit system,

with tax credit entitlement extended further up the income distribution. Again, I show the

importance of equilibrium considerations.

The remainder of the article proceeds as follows. In the next section, I describe the WFTC

reform, as well as the contemporaneous changes to the U.K. tax and transfer system. In Section 3,

I outline the theoretical model that I use to study tax reforms and describe the optimal strategies

of firms and workers. Section 4 introduces my data, discusses identification and the estimation

procedure, and presents the main estimation results. In Section 5, I then use my estimated model

to simulate the impact of actual tax reforms, whereas Section 6 is concerned with the design of

tax credits. Finally, Section 7 concludes.

7See, for example, Altonji and Paxson (1988) and Dickens and Lundberg (1993). Blundell et al. (2008) studied the

impact of a series of in-work benefit reforms in the United Kingdom during the 1990s and found that the positive effect

on hours worked was largely driven by women who changed their job.