Public goods, voting, and growth

• Date: 01 December 2019
• Author: Kirill Borissov,Joseph Hanna,Stéphane Lambrecht
• DOI: http://doi.org/10.1111/jpet.12404
• Published date: 01 December 2019

J Public Econ Theory. 2019;21:1221–1265. wileyonlinelibrary.com/journal/jpet © 2019 Wiley Periodicals, Inc.

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Received: 25 April 2017

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Accepted: 12 September 2019

DOI: 10.1111/jpet.12404

ORIGINAL ARTICLE

Public goods, voting, and growth

Kirill Borissov

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Joseph Hanna

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Stéphane Lambrecht

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1

Department of Economics, European

University at St. Petersburg, St.

Petersburg, Russia

2

EA 1384‐IDP‐Institut du Développement

et de la Prospective, Université

Polytechnique Hauts‐de‐France,

Valenciennes, France

Correspondence

Kirill Borissov, Department of

Economics, European University at

St. Petersburg, 6/1A Gagarinskaya Street,

St. Petersburg, Russia 191187.

Email: kirill@eu.spb.ru

Abstract

We study a parametric politico‐economic model of

economic growth with productive public goods and

public consumption goods. The provision of public

goods is funded by a proportional tax. Agents are

heterogeneous in their initial capital endowments,

discount factors, and the relative weights of public

consumption in overall private utility. They vote on the

shares of public goods in gross domestic products

(GDP). We propose a definition of voting equilibrium,

prove the existence and provide a characterization of

voting equilibria, and obtain a closed‐form solution for

the voting outcomes. Also we introduce a “fictitious”

representative agent and interpret the outcome of voting

as a choice made by a central planner for his benefit.

Finally, we undertake comparative static analysis of the

shares of public goods in GDP and of the rate of

balanced growth with respect to the discount factors and

the preferences for public consumption. The results of

this analysis suggest that the representative‐agent

version of our model is capable of capturing the

interaction between many voting heterogeneous agents

only if the heterogeneity is one‐dimensional.

KEYWORDS

growth, intertemporal choice, public goods, voting

JEL CLASSIFICATION

O41; D72; D91; H41

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INTRODUCTION

Public intervention is one of the key factors explaining differences in economic growth patterns

among countries in the world. The role of governments and government expenditures in the

growth process has been at the heart of many theoretical and empirical contributions.

There are two alternative approaches to deal with public intervention in the economy:

Either a social planner is assumed to look for an optimal solution and policy instruments

are then designed to decentralize this solution or policy decisions are assumed to be the

outcome of a political process inside which policy makers and/or voters interact. As far as

economic growth is concerned, both efficiency issues and equity issues can be dealt with in

both approaches.

In this paper, we propose a parametric politico‐economic model of economic growth with

productive public goods that increase private production possibilities and public consumption

goods that contribute to private utility. The government levies a proportional tax on the

consumers’income, which funds the provision of public goods. We assume logarithmic

preferences, the Cobb–Douglas production function and full depreciation of capital. Unlike the

vast majority of the literature, in our model agents are heterogeneous not only in their initial

endowments of private capital, but also in their discount factors and preferences for public

consumption goods.

At each time period, agents vote on two shares and hence the policy space is two‐

dimensional. Therefore, generically a Condorcet winner fails to exist. To overcome this

difficulty, following Kramer (1972) and Shepsle (1979), we assume that agents vote separately

on the two shares within the same period. They cast their vote on each share assuming that the

other share has been settled. A solution is consistent if the pair of shares obtained through that

procedure is self‐supporting in a Nash‐like manner.

We propose a definition of voting equilibrium, prove the existence of voting equilibria,

provide their characterization, and obtain a closed‐form solution for the voting outcomes,

which do not depend on the initial distribution of private capital and expectations. It follows

that if at each time the shares of public goods in gross domestic products (GDP) are determined

by voting, then they are constant over time.

Also we introduce a “fictitious”representative agent and interpret the outcome of voting in

our model as a choice made by a central planner for his benefit. Finally, we undertake

comparative static analysis of the shares of public goods in GDP and of the rate of balanced

growth with respect to the discount factors and the preferences for public consumption. Some

outcomes of this analysis in the general case of many agents are somewhat different from the

outcomes in the case of a representative agent. They show that the representative‐agent version

of our model is a reasonable approximation of the general case with many heterogeneous voting

agents only if the heterogeneity is one‐dimensional.

At first glance it would seem impossible to propose a consistent voting procedure if the

uniqueness of a competitive equilibrium cannot be guaranteed for some policies. It turns out

that this is not the case. We show that under some additional assumption about agents’beliefs it

is possible to generalize the voting procedure in a consistent way to the case where the

uniqueness of competitive equilibria is not ensured and that the outcome of this generalized

voting procedure is the same as in the case of uniqueness.

The structure of the paper is as follows. Section 2 provides a short literature review. Section 3

presents the main building blocks describing the production technology, the government

spending and the agents’preferences. Section 4 provides a preliminary analysis of competitive

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equilibria assuming that the shares of public goods in GDP are given. It studies the existence

and uniqueness of an intertemporal equilibrium and the key characteristics of a balanced‐

growth equilibrium for given shares. Section 5 endogenizes the shares of public goods through a

voting procedure and describes the outcome of voting under the assumption that for any public

policy the competitive equilibrium is unique. Finally Section 6 extends the analysis to the case

where the uniqueness is not ensured. Section 7 concludes.

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LITERATURE REVIEW

Government expenditures on goods and services are traditionally classified as productivity‐

enhancing or utility‐enhancing. Barro (1990), Barro and Sala‐i‐Martin (1992), Glomm and

Ravikumar (1994a), and many others study the optimal level of government expenditures

when they take the form of public production services (see de Haan & Romp, 2007, for a

recent survey of empirical literature; Irmen & Kuehnel, 2009, for a survey of theoretical

literature). Other contributions study the role of public investment to alleviate fixed costs

associated with production and responsible of poverty traps: Dechert and Nishimura (1983)

for the study of nonconvexities due to fixed costs and recently Le Van, Saglam, and Turan

(2016) for an analysis of lock‐ins to underdevelopment caused by the lack of core

infrastructure (road, rail, power supply, and so forth). Bianconi and Turnovsky (1997),

Devereux and Wen (1998), and others study the more conventional case in which

government expenditures take the form of utility‐enhancing public services that provide

direct utility to households. Some analyses have included both aspects of public spending

(see, e.g., Baier & Glomm, 2001; Baxter & King, 1993; Chang, 1999; Chen, 2006;

Economides, Park, & Philippopoulos, 2011; Marrero, 2010). In the vast majority of papers

on economic growth with public intervention the shares of government expenditures are

either exogenous or chosen by a benevolent planner.

The political‐economy literature describes collective choice mechanisms and explains

how fundamentals (preferences and technologies) together with political institutions

determine political outcomes. Glomm and Ravikumar (1994b) and Koulovatianos and

Mirman (2004, 2005) consider infinite‐horizon economies where public sector investments

and public consumption goods are financed by income taxes. They endogenize the provision

of public goods through majority voting. In their models, households can differ only with

respect to their initial endowments of private capital. However, this heterogeneity does not

lead to any disagreement in voting. All agents vote unanimously. In Park and

Philippopoulos (2003) households also can differ only with respect to initial capital

endowments.

In our paper, in addition to heterogeneity in initial endowments, we introduce heterogeneity

in discount factors and preferences for public consumption goods. Heterogeneity in discount

factors exists for a number of reasons, differences in life expectancy, health, family background,

and so forth, and is well documented (for a survey, see Frederick, Loewenstein, & O’Donoghue,

2002). Recent results of Hübner and Vannoorenberghe (2015) and Dohmen, Enke, Falk,

Huffman, and Sunde (2015) show that average patience explains a considerable fraction of the

between‐country variation in growth and income. Patience varies not only between countries,

but also within countries. According to Dohmen et al. (2015), between‐country variance

accounts for about 13.5% and within‐country variation for about 86.5% of total variation.

Another source of heterogeneity in our model stems from the weight attached to public

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