Optimal unemployment insurance and redistribution

• Published date: 01 June 2018
• Author: Katherine Cuff,Robin Boadway
• Date: 01 June 2018
• DOI: http://doi.org/10.1111/jpet.12287

Received: 15 October 2016 Accepted: 11 December 2016

DOI: 10.1111/jpet.12287

ARTICLE

Optimal unemployment insurance and

redistribution

Robin Boadway1Katherine Cuff2

1Queen'sUniversity

2McMasterUniversity

RobinBoadway, Economics, Queen's

University,Kingston, K7L 3N6, Canada

(boadwayr@econ.queensu.ca).

KatherineCuff, Economics, McMas-

terUniversity, 1280 Main Street

West,Hamilton, L8S 4L8, Canada

(cuffk@mcmaster.ca).

Weare grateful to the associate editor, Etienne

Lehmann,and two anonymous referees for their

usefulsuggestions. We have also benefited from

commentsby John Burbidge and Jean-Denis

Garon,and by participants in the 50th Annual

Conferenceof the Canadian Economics Asso-

ciation,the 72nd Annual Congress of the Inter-

nationalInstitute of Public Finance, the Joint

Universityof Exeter TaxAdministration Research

Centreand Japanese Public Economics Work-

shopand the XXVIII Annual Congress of the

ItalianSociety of Public Economics. Financial sup-

portfrom the Canada Research Chair Programme

isalso gratefully acknowledged by the second

author.

We characterize optimal income taxation and unemployment insur-

ance in a search-matching framework where both voluntary and

involuntary unemployment are endogenous and Nash bargaining

determines wages. Individuals decide whether to participate as job

seekers and if so, how much search effort to exert. Unemployment

insurancetrades off insurance versus search and participation incen-

tives. We also allow for different productivity types so there is a

redistributive role for the income tax and show that a piecewise lin-

ear wage tax internalizes the macro effects arising from endoge-

nous wages. Type-specific lump-sum taxes and transfers can then

redistribute between individuals of differing skills and employment

states. Our analysis embeds optimal unemployment insurance into

an extensive-margin optimal redistribution frameworkwhere trans-

fers to the involuntarily and voluntarily unemployed can differ,and

nests severalstandard models in the literature.

1INTRODUCTION

Governments engage in both redistribution and social insurance. They redistribute among employedworkers earning

different incomes and those who choose not to work, and they provide unemployment insurance to those unable to

find a job. Optimal redistribution and optimal unemployment insurance have typically been analyzed separately,the

former in models where workers have heterogeneous productivities and the latter in single-productivity settings. In

this paper, we embed optimal unemployment insurance analysis into an optimal income tax model of redistribution.

This entails policy makers making a distinction between transfersto the voluntarily unemployed (nonparticipants) and

the involuntarily unemployed.

There is a large literature on optimal redistribution following Mirrlees (1971), and it has been extended in several

directions. See, for example, the summaries in Banks and Diamond (2010), Boadway (2012), Golosov and Tsyvinski

(2015), and Tuomala(2016). Of relevance for us is the extension to allow for involuntary unemployment due to search

frictions (Hungerbühler, Lehmann, Parmentier, & Van der Linden, 2006; Jacquet, Lehmann, & Vander Linden, 2014;

Journal of Public Economic Theory.2018;20:303–324. wileyonlinelibrary.com/journal/jpet c

2018 Wiley Periodicals,Inc. 303

304 BOADWAYA ND CUFF

Kroft, Kucko, Lehmann, & Schmieder,2016; Lehmann, Parmentier, & Vander Linden, 2011). In these papers, following

Diamond (1980) and Saez (2002), individuals can vary their labor supply only along the extensive margin: theydecide

between searching for work in a job market specific to their productivity and being voluntarily unemployed. Employ-

ment in each job market is determined by a static matching function (see Mortensen, 1977; Pissarides, 1990; and the

survey in Mortensen & Pissarides, 1999), and wages are the outcome of bargaining between each hired worker and a

firm. The government observes wages and chooses wage-specific taxesas well as a common transfer to all voluntarily

and involuntarily unemployed. Workers are risk-neutral, which obviatesthe need for unemployment insurance. The

analysis characterizes the pattern of optimal taxes and transfers, and compares them with those in the absence of

involuntary unemployment. Redistributive taxestake into account their effect both on participation decisions and on

wage setting.

The literature on optimal unemploymentinsurance is also long-standing (Coles & Masters, 2006; Karni, 1999; Topel

& Welch,1980) and has recently been revisited by Chetty (2008). It focuses on the trade-off between insurance against

involuntary unemployment and moral hazard due to search effort when there is no market for unemploymentinsur-

ance and workers may not be able to self-insure because of liquidity constraints. This approach has been extendedby

Landais, Michaillat, and Saez (forthcoming-a) to allow for endogenous wage rates.Unemployment insurance continues

to tradeoff insurance against search incentives, and they show how this trade-off varies over the macroeconomic busi-

ness cycle (Landais, Michaillat, & Saez, forthcoming-b). In addition, the facts that unemployment insurance can affect

the wage rate and that search can be inefficient lead to indirect—or macro—effects that must be taken into consider-

ation. Since all workers are ex ante identical, there is no redistributive motive affecting the choice of unemployment

insurance.

We analyze optimal redistribution and unemployment insurance jointly in a model that includes the main features

of both the above approaches. Weadopt an extensive-margin approach to the labor market augmented by search fric-

tions. Individuals endowed with given productivity decide whether to search for a job at their skill level, and if so how

intensively to search. Workersare risk-averse so value unemployment insurance. There is a perfectly elastic supply of

firms offering jobs at each skill level,and free entry subject to a zero-expected profit constraint determines the number

ofjobs offered. Successful matches are determined by a matching function, and wages are determined by Nash bargain-

ing. The government observeswages and firm–worker output, knows the underlying technology and wage determina-

tion process, and imposes wage-specific and therefore skill-specific taxes on the employed. The skill of those who do

notfind work—the involuntarily unemployed—or who choose not to participate—the voluntarily unemployed—is unob-

servable so transfers to them cannot depend on skill. However,job search activities are observable and consequently,

transfers to the involuntarilyand voluntarily unemployed may differ.

A key insight of our model is to show that it is optimal to use a piecewise linear wage tax that imposes both a

wage-specific marginal tax rate and a wage-specific lump-sum tax. The wage-specific marginal tax rateinternalizes the

various indirect or macro effects that arise through endogenous wages. The lump-sum tax-transfer instruments apply-

ing to the employed, the involuntarilyunemployed, and the voluntarily unemployed can then redistribute and provide

unemployment insurance without having to take into account these indirect effects. We also show how incorporat-

ing a search effort decision gives rise to another incentive margin that the government must take into account when

determining optimal redistribution policy,and how the participation decision affects optimal unemployment insurance.

Unemployment insurance design is not, however,affected by redistribution concerns. These are addressed by taxes

and transfers applying to workersand the voluntarily unemployed.

The remainder of the paper is organized as follows. In the next section, we outline the general model. In Section

3, we solve the government's problem to examine the optimal role of a piecewise linear wage tax and in Section 4 we

characterize the optimal transferpolices for insurance and redistribution purposes. We briefly conclude in Section 5.