A model of the optimal allocation of government expenditures

• Author: Simon Fan,Pierre Pestieau,Yu Pang
• DOI: http://doi.org/10.1111/jpet.12416
• Published date: 01 August 2020
• Date: 01 August 2020

J Public Econ Theory. 2020;22:845–876. wileyonlinelibrary.com/journal/jpet © 2019 Wiley Periodicals, Inc.

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845

Received: 2 October 2018

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Accepted: 31 October 2019

DOI: 10.1111/jpet.12416

ORIGINAL ARTICLE

A model of the optimal allocation of

government expenditures

Simon Fan

1

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Yu Pang

2

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Pierre Pestieau

3,4,5

1

Department of Economics, Lingnan

University, Tuen Mun, Hong Kong

2

School of Business, Macau University of

Science and Technology, Taipa, Macau

3

Department of Economics, University of

Liège, Liège, Belgium

4

CORE, Louvain‐la‐Neuve, Belgium

5

Toulouse School of Economics,

Toulouse, France

Correspondence

Yu Pang, School of Business, Macau

University of Science and Technology,

Taipa 999078, Macau.

Email: ypang@must.edu.mo

Abstract

Government expenditures can be used for various socio-

economic objectives, including public education, con-

sumption of public goods and services, and social

protection. This paper analyzes the optimal allocation of

public expenditures among these competing functions. We

establish an overlapping generations model with hetero-

geneous individuals in which the government optimally

chooses income tax, transfer payment, educational spend-

ing, and public consumption. Our model characterizes the

transitional dynamics and the steady state of each function

with and without a pay‐as‐you‐go intergenerational

contract. We also conduct a simulation illustrating that

the presence of an intergenerational contract may raise

public consumption and social welfare in the steady state.

KEYWORDS

government spending, individual heterogeneity, public consumption,

public education

JEL CLASSIFICATION

H20; H31; H50

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INTRODUCTION

Large‐scale public expenditures are a widespread phenomenon in industrialized economies. In

2016, general government spending amounted to 37.8% of the gross domestic product in the

United States, 39% in Japan, and about 50% in many European countries (OECD, 2018).

Government’s massive involvement in market economies serves redistributive, allocative, and

regulatory purposes, which effectively mitigate income inequality, provide public goods and

services, and promote sustainable development (Barr, 1992; Musgrave, 1959). For instance, the

Nordic model, which features a blend of socialist values and free market capitalism, is usually

perceived to have succeeded in advancing equity, efficiency, and well‐being (Pestieau &

Lefebvre, 2018; Stiglitz, 2015).

Government spending has a variety of socioeconomic objectives. Table 1 lists the government

expenditure breakdown by 10 functions, and reports their percentage shares of total expenditures

in several European countries between 2012 and 2016. In each country, the largest share is

devoted to social protection, mainly in the form of income‐redistribution programs that transfer

wealth to the poor. Schooling is also an important target of public funds: most of these

governments appropriate around 10% of their expenditures to establish and maintain the state

education systems. The other eight functions, including health care, public services, economic

affairs (e.g., infrastructure construction and supply of water and electricity), environmental

protection, and so forth fit generally into the category of consumption of public goods and

services. Public consumption accounts for half of government spending in almost every country.

Based on the classifications used in Table 1, we categorizegovernment expenditures into three

main divisions—public education, social protection, and consumption of public goods and

services. Educational expenditure provides twobenefits: first, it facilitatesthe formation of human

capital of the future generation, allowing altruistic parents to benefit from their children’s

improved quality; second, it promotes social mobility, which helps lower wage inequality of

future generations. The provision of public goods and services directly enhances people’s welfare.

As economic progress improves the living standard, households want more public consumption,

which is complementary to their private consumption (Ganelli & Tervala, 2009). Transfers to the

poor not only raise social welfare by the law of diminishing marginal utility (e.g., Boadway &

Keen, 2000) but also address the public concern over income inequality and long‐term economic

development (De la Croix & Doepke, 2003, 2004; Fleurbaey, 2008, 2009).

To the extent that various categories compete for resources under the fiscal budget

constraint, an intriguing question arises as to how government spending can be optimally

allocated between them? The analysis of the optimal allocation of government spending has

deep roots in economics, going back at least to Samuelson (1954). Existing literature on public

finance concentrates on one or two categories. For example, Docquier, Paddison, and Pestieau

(2007) and Del Rey and Lopez‐Garcia (2013) study the optimal levels of education and pension

provided by a welfare‐maximizing government; other studies include Possen and Slutsky

(1980), Meltzer and Richard (1981), Glomm and Ravikumar (1992, 1997), Boadway and

Marchand (1995), Kaganovich and Zilcha (1999), Del Rey and Lopez‐Garcia (2016). This paper

develops a more comprehensive profile covering social protection, public education, public

consumption, and intergenerational mobility.

We establish an overlapping generations model in which the government chooses income taxes/

transfers and expenditures on education and public consumption. In our model, there are two types

of individuals—the skilled and the unskilled—whose income levels are positively related to their

labor skill. Addressing individual heterogeneity allows us to probe into the redistributive function of

government spending. Moreover, an individual’s skill plays a vital role in shaping her children’s

quality, as a number of empirical studies have demonstrated that parental background is critical to

an individual’s achievement (e.g., Becker, 1991; De la Croix & Michel, 2002). Therefore, even if

individuals’net incomes tend to be equalized after taxes/transfers, the effect of skill heterogeneity

on children’s human capital formation persists.

We start our analysis with the case in which each generation care about their own utility and

do not make any wealth transfer to the previous generation. Our analysisshows that in the steady

state educational expenditure increases with the learning efficiency of skilled workers’children

and the wage differential but decreases with thefertility rate. Also, under some configuration, the

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FAN ET AL.

TABLE 1 Government expenditure by function (% of total expenditure): 2012–2016 average

Belgium Denmark France Germany Greece Italy Netherlands Spain UK

Social protection 36.3 43.3 43.0 42.8 37.6 41.7 36.5 38.9 37.9

Education 11.6 12.6 9.6 9.6 8.2 7.9 11.8 9.1 11.6

Health 14.2 15.5 14.2 15.9 9.3 14.1 17.8 13.7 17.3

General public services 15.4 13.7 11.5 14.1 18.6 17.3 10.9 14.9 11.4

Economic affairs 12.7 6.4 9.4 7.2 13.7 8.0 8.9 11.3 7.2

Public order and safety 3.3 1.8 2.9 3.5 3.8 3.8 4.2 4.5 4.6

Defence 1.6 2.2 3.1 2.4 4.4 2.4 2.5 2.1 5.0

Environment protection 1.8 0.8 1.8 1.4 2.7 1.8 3.3 1.9 1.8

Recreation, culture and religion 2.3 3.2 2.4 2.2 1.3 1.5 3.2 2.6 1.7

Community amenities 0.7 0.5 2.1 0.9 0.5 1.4 0.9 1.1 1.6

Source: Eurostat (accessed on July 25, 2018). Government expenditures are decomposed into 10 broad functions based on the classification of the functions of government (COFOG) used in

the European regime of National Accounts (ESA, 2010). Figures are calculated as a simple average based on the available data for the most recent 5 years.

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