Public Input Competition under Stackelberg Equilibrium: A Note

• Published date: 01 December 2015
• DOI: http://doi.org/10.1111/jpet.12124
• Date: 01 December 2015
• Author: YONGZHENG LIU,JORGE MARTINEZ‐VAZQUEZ

PUBLIC INPUT COMPETITION UNDER STACKELBERG

EQUILIBRIUM:ANOTE

YONGZHENG LIU

Renmin University of China

JORGE MARTINEZ-VAZQUEZ

Georgia State University

Abstract

This paper examines the Stackelberg equilibrium for pub-

lic input competition and compares it with the noncooper-

ative Nash equilibrium. Given two asymmetric regions, we

show that under the Nash equilibrium the more productive

region tends to spend more on public input, which results

in this region attracting more capital than the less produc-

tive region. The comparison of the two equilibria reveals

that the leader region obtains a first-mover advantage under

the Stackelberg setting. This suggests that if regions interact

with each other sequentially as in the Stackelberg equilib-

rium, then the regional disparity that is due to the hetero-

geneity of productivity is likely to be mitigated or enlarged,

depending on which region performs the leadership role in

the competition process.

1. Introduction

The past several decades have witnessed a growing interest in the study

of how competition for capital influences governments’ choices of fiscal

Yongzheng Liu, School of Finance, China Financial Policy Research Center,Renmin Uni-

versity of China, Beijing, China (yongzheng.liu@ruc.edu.cn). Jorge Martinez-Vazquez,

International Center for Public Policy, Georgia State University, Atlanta, USA (jorge-

martinez@gsu.edu). We would like to thank two anonymous referees, James Alm, Sally

Wallace, Yongsheng Xu, and seminar participants at the 67th Congress of the Interna-

tional Institute of Public Finance (IIPF) for their comments and helpful suggestions. This

research was supported for Liu by the Program for New Century Excellent Talents in Uni-

versity (NCET-13-0573) of the Ministry of Education of China and for Martinez-Vazquez by

the Spanish Ministry of Economy and Competitiveness under project No. ECO2012-37572.

Received March 31, 2014; Accepted April 3, 2014.

C2014 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 17 (6), 2015, pp. 1022–1037.

1022

Public Input Competition 1023

policies. The standard argument, which originates in the fundamental work

of Zodrow and Mieszkowski (1986) and Wilson (1986), has been that compe-

tition through taxation leads to inefficiently low tax rates. On the contrary, if

competition is conducted through the use of public input that enhances the

productivity of private capital, an overemphasis on that policy is commonly

expected to emerge (Keen and Marchand 1997; Bayindir-Upmann 1998;

Bucovetsky 2005).1Despite providing valuable insights into the nature of

competition among governments, these results have been generally obtained

under a noncooperative game framework in which competing units move

simultaneously. However, as challenged by Wang (1999) and Kempf and

Rota-Graziosi (2010), the relevance of the noncooperative hypothesis for the

study of fiscal competition has not yet been established in reality.2Relaxing

this hypothesis to investigate a scenario in which competition is conducted

in a sequential game framework, both studies show that the downward pres-

sure on tax rates is indeed less strong than predicted in the standard tax

competition analysis—in large part that is due to the property of strategic

complementarity of tax rates across the competing units. More specifically,

when the competing units follow a sequence of moves in setting their tax

rates, the second moving region (the “Stackelberg follower”) will increase its

tax rate if it observes a higher level of tax rate chosen by the first moving re-

gion (the “Stackelberg leader”); the leader anticipates this and consequently

increases its tax rate. As a result, the selected tax rates in both regions in the

Stackelberg equilibrium are higher than that in the noncooperative Nash

equilibrium.

This paper adds to this literature by asking whether the different

outcomes implied by the varied game settings for tax rate setting can

be generalized to the case of competition through public input. More

specifically, we investigate the Stackelberg equilibrium for public input com-

petition and compare it with the noncooperative Nash equilibrium. For

simplicity and tractability, our model assumes: (i) that regions that are

heterogeneous in productivity compete for mobile capital by providing a

productivity-enhancing public input; and (ii) that the capital tax rate is co-

ordinated by the social planner and so it is no longer a policy instrument

1Numerous subsequent works have extended and refined these arguments in a variety

of directions. See Dembour (2008) for a survey of the literature on competitive location

policies. For surveys of the tax competition literature in general, see Wilson (1999) and

Wilson and Wildasin (2004).

2Due to the complexity of the strategic interaction of competing units, it has indeed never

been clarified in the literature which game setting, either simultaneous or sequential, is

a better approximation of reality. In some cases, it is conceivable that the smaller regions

make their strategic responses after they observe the actions chosen by the larger regions.

In other cases, the difference between core versus periphery regions may also translate

into strategic asymmetries. The empirical literature, on the other hand, does provide some

evidence on the presence of Stackelberg-type leaders in tax competition across regions and

countries (e.g., Altshuler and Goodspeed 2002; de Mello 2008).