The Dynamics of Growth and Income Inequality under Progressive Taxation

• Published date: 01 August 2016
• Author: MURAT KOYUNCU,STEPHEN J. TURNOVSKY
• DOI: http://doi.org/10.1111/jpet.12191
• Date: 01 August 2016

THE DYNAMICS OF GROWTH AND INCOME INEQUALITY

UNDER PROGRESSIVE TAXATION

MURAT KOYUNCU

Bogazici University

STEPHEN J. TURNOVSKY

University of Washington

Abstract

This paper develops an endogenous growth model having a progres-

sive income tax structure in which heterogeneous agents, who differ in

terms of their rates of time preference, supply labor elastically. We an-

alyze the dynamic adjustment to an increase in progressivity and show

that the economy will converge to an equilibrium growth path with

nondegenerate distributions of both income and wealth. The role of

the endogeneity of labor supply is emphasized and shown to have a

major impact on the nature of the transitional path, as a result of the

impact of the progressive tax on agents’ work incentives. Our theoret-

ical analysis is supplemented with, and supported by, numerical sim-

ulations, which generally match the empirical evidence rather closely.

We also show that the responses of the different income groups con-

trast sharply from one another so that focusing on the economy-wide

average provides an incomplete picture.

1. Introduction

The effects of taxes on the growth rate and distribution of income is an important and

widely discussed topic. Most of the literature addressing this issue adopts the conven-

tional assumption of flat tax rates (see, e.g., Stokey and Rebelo 1991; Mendoza, Razin,

and Tesar 1994; Domeij and Heathcote 2004; Garc´

ıa-Pe˜

nalosa and Turnovsky 2007,

2011). Since in practice most tax systems in advanced economies exhibit some degree

Murat Koyuncu, Department of Economics, Bogazici University, Bebek, Istanbul TR-34342, Turkey

(mkoyuncu@boun.edu.tr). Stephen J. Turnovsky, Department of Economics, University of Washington,

Seattle, WA 98195 (sturn@uw.edu).

We thank participants of the APET conferences held in Istanbul in June 2010 and in Seattle in July

2014, the ASSET conference held in Alicante in October 2010, the workshop “Advances in Dynamic

Macroeconomics” held in Bolzano in May 2011, and the “RCEA Workshop on Advances in Business

Cycles and Economic Growth Analysis” held in Rimini in May 2011, as well as seminar participants at

the University of Groningen, Bilkent University, and Catolica University, Lisbon, for their comments

on preliminary versions of this paper. The comments of the referees are also gratefully acknowledged.

Koyuncu acknowledges financial support from the European Union Seventh Framework Programme

(FP7/2007–2013) under Grant agreement number 268472 (PROGTAX) and the Bogazici University

Research Fund (BAP) under project number 5601.

Received December 10, 2014; Accepted February 20, 2016.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (4), 2016, pp. 560–588.

560

Dynamics of Growth and Income Inequality 561

of progressivity, it is important to reassess these issues in the context of a progressive tax

structure.

Two approaches to incorporating progressive income taxation into macrodynamic

models can be identified. One strand of literature adopts the incomplete asset markets

framework. In this approach to life cycle economies, heterogeneity arises from unin-

surable idiosyncratic productivity shocks against which progressive taxes act as a partial

insurance mechanism. One important contribution is Casta˜

neda, D´

ıaz-Gim´

enez, and

R´

ıos-Rull (2003), who conclude that endogenous labor supply and progressive income

taxation is crucial in order to account properly for wealth inequality. Several studies

adopt this approach to focus on income tax reforms. More specifically, they assess the

gains in switching from progressive to flat taxes and they evaluate the quantitative ef-

fects of such reforms on the U.S. economy (see, e.g., Caselli and Ventura 2000; Altig et al.

2001; Caucutt, ˙

Imrohoroglu, and Kumar 2003; Conesa and Krueger 2006; ˙

Imrohoroglu,

˙

Imrohoroglu, and Fuster 2008; Kitao 2010).

An alternative approach, adopted by Sarte (1997) and Li and Sarte (2004), assumes

complete asset markets. By introducing a progressive income tax structure, together

with heterogeneous rates of time discount, they avoid the degenerate equilibrium dis-

tribution of income that would otherwise occur with heterogeneous time preferences

alone.1Li and Sarte employ an endogenous growth framework and make two restrictive

assumptions: first that labor is supplied inelastically, and second, they restrict attention

to the equilibrium-balanced growth path. While this provides a natural benchmark, it

clearly does not offer a complete picture of the role of tax progressivity in determining

the growth–inequality relationship.

This study belongs to this second strand of the literature. Its contribution is three-

fold. First, we focus on the more general setup where labor is supplied elastically. This

generalization is important, since the adjustment of labor has been shown elsewhere to

play a crucial role in determining the impact of structural changes on both growth and

inequality, even in the absence of taxes.2But it becomes an even more crucial part of

this process in the presence of a progressive tax structure, with the potentially signifi-

cant impact on work incentives. Indeed, the fact that an increase in the progressivity of

the tax structure has an adverse effect on labor supply is well established empirically,

and confirms the relevance of endogenizing the labor supply.3

Second, we consider the entire dynamic adjustment path, highlighting how its re-

sponse to structural changes is highly dependent upon the flexibility of labor supply,

particularly in the short run. For example, we find that assuming labor to be supplied

inelastically seriously understates the adverse short-run effect of an increase in tax pro-

gressivity on the growth rate of output. Moreover, as our analysis suggests, for plausible

1This degenerate equilibrium in which the most patient agent owns all the wealth was first identified

by Becker (1980).

2For example, Turnovsky and Garc´

ıa-Pe˜

nalosa (2008) using a neoclassical framework show how endog-

enizing the labor supply can reverse the long-run growth–inequality response to a productivity increase

from that obtained when labor is supplied inelastically. In this case, ignoring the response of labor

supply in the adjustment process may be not only quantitatively but also qualitatively misleading!

3For example, Hausman (1981) using U.S. data and Blomquist (1983) and Blomquist, Ekl¨

of, and

Newey (2001) using Swedish data find that higher progressivity reduces hours of work in their stud-

ies. Guvenen, Kuruscu, and Ozkan (2009) reach a similar conclusion in a cross-country study. Koyuncu

(2011) documents how the reduction in progressivity in the United States between the periods 1971

and 1974 and 1986 and 1989 and the increase in progressivity in Germany over the same time period

were associated with an increase in hours worked in the United States and a decline in hours worked

in Germany.