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Keywords:

  • borrowing constraints;
  • government debt;
  • income inequality;
  • structure-induced equilibrium;
  • voting;
  • D72;
  • H52;
  • H60

ABSTRACT

  1. Top of page
  2. ABSTRACT
  3. I. INTRODUCTION
  4. II. THE MODEL
  5. III. THE POLITICAL EQUILIBRIUM
  6. IV. WELFARE IMPLICATION
  7. V. INCOME INEQUALITY AND BORROWING CONSTRAINT
  8. VI. CONCLUSION
  9. REFERENCES
  10. Supporting Information

We develop a two-period, three-class of income model where low-income agents are borrowing constrained because of capital market imperfections, and where redistributive expenditure is financed by tax and government debt. When the degree of capital market imperfection is high, there is an ends-against-the-middle equilibrium where the constrained low-income and the unconstrained high-income agents favour low levels of government debt and redistributive expenditure; these agents form a coalition against the middle. In this equilibrium, the levels of government debt and expenditure might be below the efficient levels, and the spread of income distribution results in a lower debt-to-GDP ratio.

I. INTRODUCTION

  1. Top of page
  2. ABSTRACT
  3. I. INTRODUCTION
  4. II. THE MODEL
  5. III. THE POLITICAL EQUILIBRIUM
  6. IV. WELFARE IMPLICATION
  7. V. INCOME INEQUALITY AND BORROWING CONSTRAINT
  8. VI. CONCLUSION
  9. REFERENCES
  10. Supporting Information

Conventional wisdom dictates that a higher inequality of income results in a larger redistributive public expenditure and results in a greater issue of government debt that finances redistribution. This theoretical prediction builds on a median-voter framework, in which a higher level of inequality translates into a poorer decisive agent in the political arena, who will then demand greater redistribution (Romer, 1975; Roberts, 1977; Meltzer and Richard, 1981; Krusell and Rios-Rull, 1999) and, thus, greater government debt issue for financing redistribution (Cukierman and Meltzer, 1989).

The empirical evidence, however, does not necessarily support the above-mentioned theoretical predictions. OECD cross-country data show that the volume of redistribution is negatively correlated with income inequality (for example, Gottschalk and Smeeding, 1997; Chen and Song, 2009). The theoretical prediction of inequality and government debt is also controversial. For instance, Belgium, France, and Germany, all located in Continental Europe, show low Gini coefficients and high debt-to-GDP ratios whereas the United Kingdom and the United States, included in the Anglo-Saxon group, show high Gini coefficients and low debt-to-GDP ratios.1 The negative correlation also holds for the sample countries when wage differential is taken as a measure of inequality.2 A negative correlation between inequality and debt-to-GDP ratio is observed for some OECD countries. This indicates that the relationship between inequality and the size of government is not as simple as the standard theory might suggest. The motivation of this paper is to address the gap between conventional wisdom and empirical evidence.

Several theories have been provided to make sense of the above-mentioned puzzles. Examples include political bias towards the rich (Benabou, 2000), the prospect of upward mobility by low-income agents (Quadrini, 1999; Benabou and Ok, 2001; Alesina and La Ferrara, 2005; Arawatari and Ono, 2009), lobbying and campaign contributions by the rich (Rodriguez, 2004; Campante, 2010), voters' preferences for redistribution (Creedy and Moslehi, 2009; Creedy et al., 2010), and borrowing constraints that hit low-income agents (Casamatta et al., 2000; Bellettini and Berti Ceroni, 2007; Cremer et al., 2007). These studies, however, assume that redistributive expenditure is financed only via income tax. In other words, they abstract away government debt as an additional option for financing redistributive expenditure even though government debt is one of the major sources of government revenue in OECD countries.

The purpose of this paper is to consider the relationship between inequality and the size of government debt when voting results in a negative correlation between inequality and redistributive expenditure. In particular, we focus on the role of borrowing constraints (or, equivalently, capital market imperfection) as a source of the negative correlation, and examine how politically determined government debt and expenditure are affected by the degree of capital market imperfection. In addition, we consider the spread of income distribution and examine its impact on the debt-to-GDP ratio in relation to the degree of capital market imperfection.

For the purpose of analysis, we utilize the two-period, three-class of income model of Bellettini and Berti Ceroni (2007). In their framework, redistributive expenditures, such as publicly provided education and investment in infrastructure such as schools, libraries and research institutes are financed through the first-period income tax; the expenditures improve the productivity of all agents in the second period. We introduce government debt as an additional policy option for financing redistributive expenditure into their framework. That is, the redistributive expenditure is financed by the first-period income tax as well as by government debt issue. The debt repayment is financed by the second-period income tax.

Under this extended framework, voters cast a ballot over the first-period income tax, and also over government debt issue. Under this type of voting game, the existence of a Condorcet winner of the majority voting game is not necessarily guaranteed because of the multidimensionality of the issue space (see, for example, Persson and Tabellini, 2000, chapter 2). To deal with this problem, we utilize the concept of a structure-induced equilibrium (Shepsle, 1979). We determine the decisive voter over one issue given the other issue and derive his/her reaction function for each policy issue. We then find the point where the two reaction functions cross; this point corresponds to the structure-induced outcome of the majority voting game.

Our model demonstrates that voting over policy produces two opposing effects on agents via the government expenditure: a negative effect that results in a greater tax burden for financing expenditure and, thus, the utility loss today; and a positive effect that results in an improvement of labour productivity in the second period and, thus, the utility gain in the future. When agents are borrowing unconstrained, they prefer a higher level of government expenditure and, thus, a higher first-period tax and government debt as their first-period income becomes lower. Because of the borrowing, unconstrained agents can reallocate resources freely from the second period to the first period, and they can compensate the utility loss today by the utility gain tomorrow. Therefore, they want to increase government expenditure in order to get the benefit of the second-period labour productivity improvement.

However, the opposite result holds when agents are borrowing constrained. Borrowing-constrained agents prefer lower government debt and expenditure as their first-period income becomes lower. Borrowing-constrained agents are unable to reallocate resources freely from the second period to the first period. Because of this constraint, the utility gain from government expenditure in the future is valued less than the utility loss from government expenditure today for the borrowing-constrained agents. Therefore, they prefer less government expenditure and, thus, lower first-period income tax and debt as their first-period income becomes lower.

Given the above-mentioned feature of the model, we obtain the following three results. First, the type of decisive voter depends on the degree of capital market imperfection. The decisive voter is the middle-income, borrowing-unconstrained agent when the degree of capital market imperfection is low. However, the decisive voter becomes the low-income, borrowing-constrained agent when the degree is high. That is, the economy displays the ends-against-the-middle equilibrium, as in Epple and Romano (1996), where the high- and low-income agents, who favour low government expenditure and debt, form a coalition against the middle who favour high government expenditure and debt.

The second result is that the political equilibrium generally fails to attain efficient allocation. That is, first-period tax, government debt, and expenditure in the political equilibrium are higher or lower than the efficient level depending on either the income level of a decisive voter or the degree of capital market imperfection. In particular, under certain conditions, there exists a critical level of capital market imperfection such that the political equilibrium levels of first-period tax, government debt, and expenditure are below the efficient level when the degree of capital market imperfection is above the critical level. This result implies that countries with less access to capital markets are more likely to attain lower levels of first-period tax, government debt, and expenditure than deemed efficient.

The third result is that the effect of income distribution on the debt-to-GDP ratio depends on the degree of capital market imperfection. In particular, there exists a critical level of capital market imperfection, which is different from that described in the paragraph above, such that the income distribution results in a higher debt-to-GDP ratio when the degree of capital market imperfection is below the critical level, and the standard result a la Cukierman and Meltzer (1989) holds. However, when the degree is above the critical level, the opposite result holds because the decisive voter, who is a borrowing-constrained low-income agent, wants to choose lower government expenditure and debt. That is, there is a negative correlation between inequality and debt-to-GDP ratio when the degree of capital market imperfection is high.

Our analysis and results contribute to the following three strands of literature. The first strand is the literature on inequality and redistribution in the presence of borrowing constraints. Examples are Casamatta et al. (2000), Bellettini and Berti Ceroni (1979), Cremer et al. (2007), and Arawatari and Ono (2011). These studies demonstrate that the decisive voter prefers a lower income tax as his/her income is decreased when he/she is borrowing constrained. Thus, they clarify the role of borrowing constraint in presenting the negative correlation between inequality and the preferred tax for redistribution. However, government debt is abstracted away in these studies. The current paper contributes to the literature by demonstrating how the politically determined size of government debt is affected by income distribution in the presence of borrowing constraints.

The second strand is the literature on tax smoothing and government debt (for example, Barro, 1979; Lucas and Stokey, 1983; Aiyagari et al., 2002). Our model demonstrates that, in an efficient allocation, the tax rates should be equal between two periods, and the size of government debt is adjusted to smooth tax rates across periods. However, the model demonstrates that, in political equilibrium, the first-period tax rate becomes lower or higher than the efficient rate depending on either the income level of a decisive voter or the degree of capital market imperfection. The result suggests that the presence of borrowing constraint might prevent the realization of tax smoothing in the political economy.

The third strand is the literature on the politics of government debt. Although there are many studies that consider how the size of government debt is determined via politics, most of them abstract away the role of income inequality among voters in the determination of government debt. Previous studies instead have focused on the roles of common pool problems (for example, Tabellini, 1986; Velasco, 1999), political instability (for example, Persson and Svensson, 1989; Aghion and Bolton, 1990; Alesina and Tabellini, 1990; Tabellini and Alesina, 1990), altruistic and selfish agents (de Walque and Gevers, 2001), and intergenerational conflict (for example, Song et al., 2012).

An exception is the study of Cukierman and Meltzer (1989), which demonstrates the positive correlation between inequality and government debt: a higher level of inequality results in a greater issue of government debt. However, as mentioned above, empirical evidence suggests that the relationship is not so straightforward: some countries are featured by low inequality and high debt-to-GDP ratio, whereas others are characterized by high inequality and low debt-to-GDP ratio. The current paper demonstrates that there is a negative correlation between inequality and debt-to-GDP ratio when the degree of capital market imperfection is high. The result could provide one possible explanation for the empirical evidence among some OECD countries.

The organization of this paper is as follows. Section 'THE MODEL' introduces the model. Section 'THE POLITICAL EQUILIBRIUM' characterizes political equilibrium. Section 'WELFARE IMPLICATION' compares the political equilibrium with the efficient allocation. Section 'INCOME INEQUALITY AND BORROWING CONSTRAINT' examines the effect of income inequality on the debt-to-GDP ratio. Section 'CONCLUSION' provides concluding remarks. Proofs of Propositions are given in the Supplementary appendix, which is available in a supplementary file on the journal website.

II. THE MODEL

  1. Top of page
  2. ABSTRACT
  3. I. INTRODUCTION
  4. II. THE MODEL
  5. III. THE POLITICAL EQUILIBRIUM
  6. IV. WELFARE IMPLICATION
  7. V. INCOME INEQUALITY AND BORROWING CONSTRAINT
  8. VI. CONCLUSION
  9. REFERENCES
  10. Supporting Information

We consider a small open economy model that is based on Bellettini and Berti Ceroni (1979). Agents live in two periods; they are indexed by their first-period labour productivity inline image, which is also equal to their income. They belong to three income classes (low, middle and high) in terms of their first-period labour productivity, denoted by inline image. The fraction of people in each class is given by inline image with inline image and inline image. The average first-period income, inline image, which is equal to aggregate labour income, is assumed to satisfy inline image; the distribution of the first-period income is right-skewed.

In their first period of life, agents allocate their labour income between consumption and saving. Because of the assumption of a small open economy, the aggregate return on saving is exogenous and equal to inline image. Following De Gregorio (1996) and Bellettini and Berti Ceroni (1979), we assume that, in the first period, agents cannot borrow more than inline image times their after-tax income to finance current consumption. When inline image, agents cannot borrow at all; when inline image, agents can borrow as much as they want. Therefore, the index inline image represents the degree of capital market imperfection. A lower ψ implies a higher degree of capital market imperfection.

Preferences are specified by the following inter-temporal utility function:

  • display math

where inline image and inline image represent consumption of a type-i agent in periods 1 and 2, respectively, and inline image denotes the discount factor. We employ the above-mentioned specification for the tractability of analysis. The role of this assumption will be discussed later.

Labour income in the second period is equal to the agent's labour productivity in that period. Following Bellettini and Berti Ceroni (1979), we assume that a type-i agent's productivity in the second period, defined by inline image, depends on the public expenditure in the first period. In particular, we assume inline image, where inline image is an exogenous parameter, inline image is a coefficient of labour productivity depreciation and G is public expenditure in the first period. The expenditure G increases the productivity of labour of all agents in the second period. Examples of the public expenditure are publicly financed education and public investment in infrastructure such as schools, universities, research institutions, and libraries.

The public expenditure in the first period is financed through linear income taxation and government debt issue. We assume convex costs of collecting taxes in order to avoid corner solutions for the endogenous tax rate. In particular, if inline image is the tax rate in the t-th period, the actual tax revenue in that period is inline image, where inline image is the aggregate labour income (i.e., GDP) in the tth period.3

The government budget constraints in the first and the second periods, respectively, are given by:

  • display math(1)
  • display math(2)

where B denotes government debt issue. In the first period, the revenue from tax and debt issue is used for public expenditure G. In the second period, government debt is paid off by the second-period tax revenue. We assume that the government is not allowed to default.

III. THE POLITICAL EQUILIBRIUM

  1. Top of page
  2. ABSTRACT
  3. I. INTRODUCTION
  4. II. THE MODEL
  5. III. THE POLITICAL EQUILIBRIUM
  6. IV. WELFARE IMPLICATION
  7. V. INCOME INEQUALITY AND BORROWING CONSTRAINT
  8. VI. CONCLUSION
  9. REFERENCES
  10. Supporting Information

At the beginning of period 1, each agent votes over τ1 and B to maximize his/her indirect utility subject to the government budget constraints. The corresponding level of government expenditure is determined via the first-period government budget constraint (1). After that, each agent chooses consumption inline image and inline image to maximize his/her utility subject to individual budget constraints. At the beginning of period 2, the government imposes the tax τ2 to finance the repayment of government debt.

The tax revenue in the second period is solely used to finance debt repayment. This implies that setting B is equivalent to setting τ2. Given this property, we hereafter focus on the political determination of τ1 and τ2, rather than τ1 and B, and consider the following two-stage maximization problem. In the first stage, agents vote over policies to maximize their indirect utility subject to the government budget constraints (1) and (2). In the second stage, given policies, agents choose consumption to maximize their utility subject to individual budget constraints.4

In what follows, we induce the political equilibrium by backward induction. First, we solve the utility maximization problems of the agents (Section 'Economic decisions'). Then, we define the political institution and describe the policy preferences of the agents (Section 'Policy preferences, the political institution, and voting'). Finally, we characterize political equilibrium of the voting game (Section 'Political equilibrium').

III.1 Economic decisions

The utility maximization problem of a type-i agent is as follows:

  • display math(3)

where inline image denotes the saving of a type-i agent. The first and the second constraints are individual i's budget constraints in the first and the second periods, respectively. The third constraint is the borrowing constraint.

In order to solve the problem, suppose first that the borrowing constraint is not binding. The solution to the utility maximization problem yields:

  • display math(4)
  • display math(5)
  • display math(6)

where the superscript u denotes ‘unconstrained’.

We substitute the saving function into the borrowing constraint (3) to obtain the condition where a type-i agent is actually unconstrained in terms of the tax rates τ1 and τ2:

  • display math(7)

This condition states that the borrowing constraint of a type-i agent does not bind when his/her after-tax income is high in the first period and is low in the second period.

Alternatively, suppose that the borrowing constraint is binding; that is, (7) fails to hold. The solution to the utility maximization problem yields:

  • display math(8)
  • display math(9)
  • display math(10)

where the superscript c denotes “constrained”.

III.2 Policy preferences, the political institution, and voting

In the voting stage, agents vote over policies to maximize their indirect utility. In order to set up this maximization problem, we first derive the indirect utility functions in terms of tax rates. For this purpose, we substitute the consumption functions derived in the previous subsection into the utility function inline image and obtain the following:

  • display math

The productivity in the second stage, inline image, depends on the government expenditure G and, thus, on the tax rates τ1 and τ2. In order to write inline image as a function of τ1 and τ2, we define:

  • display math

and rewrite E2 as a function of inline image

  • display math

The variable inline image shows the marginal effect of public expenditure G on the second-period GDP, denoted by E2.

We utilize inline image and inline image to rewrite two government budget constraints (1) and (2) as follows:

  • display math(11)
  • display math(12)

where

  • display math

We impose the following assumption:

Assumption 1. inline image

The inequality condition of inline image ensures that the tax rate in the second period is set within the range (0, 1/2) in equilibrium. Given inline image the term which appears in (11) and (12) is positive as long as inline image. Therefore, the condition of inline image ensures that inline image and inline image hold in equilibrium; otherwise the economy experiences (a) international lending of assets rather than borrowing, and (b) no government expenditure, both of which are not considered in this paper. The inequality condition of inline image also guarantees single-peaked preferences over τ1 and τ2. These roles of Assumption 1 are found in the following analysis.

By using (11), we can present the lifetime income of a type-i agent as a function of tax rates:

  • display math

With the above-mentioned lifetime income, the indirect utility function of a type-i agent becomes:

  • display math(13)

The tax rates τ1 and τ2 are determined by individuals through a political process of majoritarian voting. Because the issue space is bidimensional, the Nash equilibrium of a majoritarian voting game may fail to exist. To deal with this feature, we use the concept of issue-by-issue voting, or structure-induced equilibrium, as formalized by Shepsle (1979). In particular, if preferences are single peaked for each policy issue, a sufficient condition for inline image to be an equilibrium of the voting game is that inline image represents the outcome of majority voting over τ1 when the other dimension is fixed at inline image, and vice versa. In Appendix A.1, it is shown that preferences are indeed single-peaked along every dimension of the issue space.

We can now solve the problem in the voting stage. A type-i agent chooses τ1 to maximize his/her indirect utility given inline image and he/she chooses τ2 to maximize his/her indirect utility given τ1. The threshold level of capital market imperfection for a type-i agent, denoted by inline image, is derived by substituting his/her preferred pair of tax rates into condition (7). The following proposition states policy preferences of agents.

Proposition 1. The most preferred policy by a type- i agent satisfies:

  • display math
  • display math(14)

where inline image is given by:

  • display math

Proof. See Appendix A.2.

For each type of i, there is a threshold level of capital market imperfection, denoted by inline image. When the degree of imperfection is higher, such that inline image, any agent belonging to class i is borrowing constrained. The threshold level inline image becomes higher as the productivity in the first period becomes lower: inline image. That is, an agent belonging to a lower class is more likely to be borrowing constrained.

The degree of capital market imperfection critically affects the preferences over policy. In order to understand the role of capital market imperfection, we first consider its impact on the preference over the government expenditure financed by the first-period tax and debt. On the one hand, raising the government expenditure decreases the utility today through an increase in the first-period tax burden. On the other hand, raising the government expenditure, financed by an increase in the first-period tax and debt issue, increases the utility in the future through an improvement in labour productivity. Therefore, the most preferred first-period tax and debt are determined to equate negative and positive effects at a margin.

When a type-i agent is borrowing unconstrained, he/she can choose inline image and inline image that attain the maximum of utility. His/her preferences over inline image and inline image follow the standard result in the literature of the political economy of redistribution (Romer, 1975; Roberts, 1977; Meltzer and Richard, 1981; Cukierman and Meltzer, 1989): a richer agent prefers lower tax and debt issue. However, when he/she is borrowing constrained, he/she cannot reallocate income freely from the second period to the first period. Given this limitation, the utility gain in the future is less valued than the utility loss today. Therefore, a constrained agent prefers a lower level of government expenditure and, thus, lower first-period tax and debt as he/she becomes poorer.

The positive correlation between income and the preferred policy levels for constrained agents is crucial in the following analysis. The positive correlation between income and the preferred tax rate (or government expenditure) has already been shown by Bellettini and Berti Ceroni (1979). One of the contributions of this paper is to show that the positive correlation also holds between income and the preferred level of public debt; constrained agents prefer a lower first-period tax rate and lower public debt as they become poorer.

The mechanism behind the abovementioned result is as follows. First, given other variables, a lower preferred tax rate yields a lower level of government expenditure, a lower level of second-period labour productivity, and thus a smaller second-period tax base. This result comes from the assumption of a linear relationship between government expenditure and second-period productivity. Second, given the second period tax rate which is independent of the first-period tax rate, a smaller tax base implies smaller tax revenue in the second period. Third, because government bonds are repaid by the second-period tax revenue, the smaller tax revenue allows the government to issue smaller amounts of government bonds in the first period. Therefore, there is a positive correlation between income and the preferred level of government debt for constrained agents.

Voters' preferences over the second-period tax rate are unaffected by types and capital market imperfection. This property depends on the specification of the second-period productivity, inline image. The second-period productivity inline image is linearly related to government expenditure G. This implies that maximizing inline image with respect to inline image is equivalent to maximizing G with respect to inline image. Because G is unaffected by types and capital market imperfection, as shown in (11), the choice of inline image is independent of them. This result also holds true as long as preferences are characterized by a constant inter-temporal elasticity of substitution (see Appendix A.3).5, 6

The preferred levels of government expenditure and public debt by a type-i agent are derived by substituting inline image and inline image into the government budget constraints (11) and (12). The preferred levels satisfy the following properties. First, inline image and inline image are affected by the degree of capital market imperfection when a type-i agent is borrowing constrained. Second, inline image is linearly related to inline image because inline image holds from (11) and (12), and inline image is independent of the type of an agent and is simply given by inline image.

The abovementioned results still hold when we alternatively assume sequential voting. In sequential voting, voting in the first stage is divided into two substages: voting over the first-period tax rate first, and then voting over the second-period tax rate. We solve this two-stage maximization problem by backward induction. As observed in the indirect utility function given in (13), the choice of the second-period tax rate is independent of the first-period tax rate due to the specification of the second-period productivity; every agent prefers inline image, which is equivalent to that chosen in issue-by-issue voting. We substitute inline image into the indirect utility function and maximize it with respect to τ1. Then we obtain the preferred first-period tax rate in sequential voting, which coincides with that in issue-by-issue voting.

The following corollary states how the policy preferences of agents are affected by capital market imperfection when agents are borrowing constrained.

Corollary 1.
  1. inline image, inline image, and inline image.
  2. inline image and inline image at inline image.

Proof. See Appendix A.4.

Figure 1 illustrates how voters' preferences over policies (τ1 , G, B) are affected by the degree of capital market imperfection, denoted by ψ. When they are borrowing unconstrained, their choice of τ1, G and B is independent of capital market imperfection. However, when they are borrowing constrained, their choice depends on the degree of capital market imperfection. A lower ψ implies that they are more constrained. In order to relax the constraint, they prefer a lower first-period tax rate and, thus, prefer a lower level of government expenditure.

image

Figure 1. The most preferred policies for a type-i agent.

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III.3 Political equilibrium

Based on the characterization of voting behaviour of each type of agent, we now consider the determination of structure-induced equilibrium policies via majority voting. The second-period tax rate is given by inline image because all types of agents prefer this rate. Given inline image, the equilibrium first-period tax rate is given by the most preferred τ1 by the median voter. The equilibrium levels of government expenditure and debt are then given by the preferred levels by the median voter over τ1.

In order to determine the median voter over τ1, we introduce the critical level of the first-period income, inline image, defined by:

  • display math

Direct calculation leads to:

  • display math

When the first-period productivity of a type-i agent is high such that inline image, inline image always holds for a type-i agent. In other words, he/she is borrowing unconstrained for any degree of capital market imperfection of inline image. He/she has enough income in the first period that is beyond the critical level inline image and, thus, can choose a combination of consumption and saving that does not hit the borrowing constraint from the viewpoint of utility maximization. In contrast, an agent might be borrowing constrained for a low ψ if inline image holds. In order to reduce a set of possible political equilibria, we impose the following assumption with respect to inline image.

Assumption 2. inline image.

Assumption 2 ensures that type-h agents are never borrowing constrained. Therefore, given the properties of preferred first-period tax rate, demonstrated in Proposition 1 and Corollary 1, the decisive voter will be a type-l or a type-m agent. The following proposition determines the decisive voter, contingent on the degree of capital market imperfection.

Proposition 2. The decisive voter over τ1 is a borrowing-constrained type- l agent if inline image and a borrowing-unconstrained type- m agent if inline image where:

  • display math

Political equilibrium policies, inline image, are given by:

  • display math

Proof. See Appendix A.5.

Figure 2 illustrates the political equilibrium policies inline image, inline image and inline image. As demonstrated in the figure, the identity of the median voter depends on the degree of capital market imperfection, denoted by ψ: a higher ψ means a lower degree of capital market imperfection. When an agent is less likely to be borrowing constrained, such that inline image, the decisive voter becomes the type-m agent who is borrowing unconstrained. Their preferred policies lie between those by type-l and type-h agents. However, when an agent is more likely to be borrowing constrained, such that inline image, there is an ends-against-the-middle equilibrium: the decisive voter is the borrowing-constrained, type-l agent. He/she prefers a lower tax rate and, thus, lower levels of government expenditure and debt than the type-m agent because of the strict financial constraint. The policies preferred by the borrowing-constrained type-l agent lie between those by type-m and type-h agents.

image

Figure 2. The bold curves show equilibrium policies.

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IV. WELFARE IMPLICATION

  1. Top of page
  2. ABSTRACT
  3. I. INTRODUCTION
  4. II. THE MODEL
  5. III. THE POLITICAL EQUILIBRIUM
  6. IV. WELFARE IMPLICATION
  7. V. INCOME INEQUALITY AND BORROWING CONSTRAINT
  8. VI. CONCLUSION
  9. REFERENCES
  10. Supporting Information

In this section, we evaluate the political equilibrium in terms of efficiency. Following Bellettini and Berti Ceroni (1979), we focus on the set of policy variables that maximize the present discounted value (PDV) of aggregate disposable income. We compare it with the political equilibrium policies and investigate under what condition the political equilibrium results in an excess burden of tax and debt.

The PDV of aggregate disposable income, denoted by I, is given by:

  • display math

that is,

  • display math

The first term on the right-hand side is the aggregate disposable income in the first period, and the second term is the present value of the aggregate disposable income in the second period.

The first-period tax rate τ1 has two competing effects on PDV of aggregate disposable income. An increase in τ1 creates a negative effect via a decrease in the first-period after-tax income, and a positive effect via an increase in the government expenditure devoted to education. A social planner chooses τ1 to equate these two competing effects at a margin. The second-period tax τ2 also has two competing effects via the second-period after-tax income and government expenditure. The planner chooses τ2 to equate these two competing effects at a margin.

Let inline image denote the efficient tax rates that maximize the PDV of aggregate disposable income, and inline image denote the corresponding levels of government expenditure and debt, respectively. The efficient tax rates inline image andinline image are derived by setting inline image and inline image, respectively:

  • display math

The planner chooses the same tax rates between the two periods in order to smooth tax burdens over periods. The corresponding levels of government expenditure and debt are calculated by substituting inline image andinline image into the government budget constraints:

  • display math

A noteworthy feature is that the second-period tax rate in the political equilibrium is efficient: inline image. In order to understand the mechanism behind this result, we focus on the term related to τ2. In the political equilibrium, the decisive voter j chooses τ2 to maximize his/her second-period after-tax income, given by:

  • display math

In contrast, in the efficient allocation, the planner chooses τ2 to maximize the aggregate second-period after-tax income, given by:

  • display math

The objective functions are different between the two problems. However, the terms related to τ2 are equivalent between the two problems; both are given by inline image. This is because the government expenditure G, given in (1), enters into these two objective functions in a linear fashion. Therefore, we can obtain the efficient second-period tax rate in the political equilibrium.

The efficiency generally fails to hold as regards τ1, G and B. The following proposition demonstrates the conditions for which the political equilibrium levels of τ1, G and B are higher or lower than the efficient levels.

Proposition 3.
  1. Suppose that inline image holds. Then,
    • display math
  2. Suppose that inline image holds. Then,
    • display math
  3. Suppose that inline image and inline image hold. Then,
    • display math
    where:
    • display math

Proof. See Appendix A.6.

Figure 3 illustrates the result in Proposition 3. In order to provide the interpretation of the result in Proposition 3, we focus on the first-period tax rate because the properties of government expenditure and debt are qualitatively similar to those of the first-period tax rate. After describing the efficiency of the first-period tax rate, we discuss the efficiency of debt issue in relation to the previous studies.

image

Figure 3. (a) The case of inline image. (b) The case of inline image. (c) The case of inline image and inline image.

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In the current framework, efficiency requires the same tax rates between the two periods in order to smooth the tax burden across periods. However, the political equilibrium realizes a lower or a higher first-period tax rate than the efficient one depending on either the income level of a decisive voter or the degree of capital market imperfection.

To confirm this argument, consider first the case of a low degree of capital market imperfection such that inline image: an unconstrained middle-income agent becomes the decisive voter. He/she prefers a lower first-period tax rate than the efficient one when his/her income is high such that inline image; otherwise, he/she prefers a higher tax rate. Therefore, the decisive voter's income level affects the efficiency of the political-equilibrium first-period tax rate when he/she is borrowing unconstrained.

Next, consider the case of a high degree of capital market imperfection such that inline image: the decisive voter is the constrained low-income agent. As demonstrated in Section 'Policy preferences, the political institution, and voting', a constrained agent prefers a lower tax rate as the degree of imperfection is increased. This implies that a further imperfection improves tax smoothing when the preferred tax rate by the decisive voter is initially higher than the efficient one, while it prevents tax smoothing when the preferred tax rate is initially lower than the efficient level. Therefore, the degree of capital market imperfection determines the degree of difference from the efficient rate when the decisive voter is borrowing constrained.

Given the discussion so far, we can now state that the political equilibrium does not necessarily result in an overissue of public debt in the current framework. Previous studies have generally shown that the politics results in an overissue of public debt because of common-pool problems (Tabellini, 1986; Velasco, 1999) and political instability (Persson and Svensson, 1989; Aghion and Bolton, 1990; Alesina and Tabellini, 1990). In the real world, however, some countries, such as Australia, Korea and New Zealand, do have successful control over the issue of public debt (OECD, 2009). These countries could be viewed as issuing public debt below the efficient level. The result of underissue of public debt in the current framework may provide one possible explanation for these countries.

V. INCOME INEQUALITY AND BORROWING CONSTRAINT

  1. Top of page
  2. ABSTRACT
  3. I. INTRODUCTION
  4. II. THE MODEL
  5. III. THE POLITICAL EQUILIBRIUM
  6. IV. WELFARE IMPLICATION
  7. V. INCOME INEQUALITY AND BORROWING CONSTRAINT
  8. VI. CONCLUSION
  9. REFERENCES
  10. Supporting Information

The analysis so far has demonstrated the political equilibrium policy given the distribution of income. This section takes a step towards changing a situation. In particular, we consider an increase in the initial income of the high type, inline image, coupled with a decrease in the initial income of the low type, inline image.7 We focus on the term inline image, which represents the marginal impact of government expenditure on the second-period GDP. Then, we consider the spread of income distribution, keeping inline image unchanged. Under the inline image-preserving spread of income distribution, the second-period tax rate is unchanged because it is given by inline image. Thus, the specification enables us to concentrate on the decisive voter's choice over the first-period tax τ1 and the government debt B.

Proposition 4. Suppose that the first-period income of the high type, inline image increases and the first-period income of the low type, inline image,decreases, leavinginline imageunchanged. There then exists a critical level ofψ, denoted byinline image, such that the equilibrium debt-to-GDP ratio decreases ifinline image; the equilibrium debt-to-GDP ratio increases ifinline image.

Proof. See Appendix A.7.

The result in Proposition 4 states that the effect of income inequality on the debt-to-GDP ratio depends heavily on the degree of capital market imperfection, denoted by ψ. The spread of income distribution results in a lower debt-to-GDP ratio when the degree of capital market imperfection is high such that inline image. However, it results in a higher debt-to-GDP ratio when the degree is low such that inline image. In order to understand the mechanism behind this result, we present three key results about agents' preferences being affected by the spread of income distribution. Based on the results, we demonstrate illustratively the effect of income distribution on the debt-to-GDP ratio.

First, recall the threshold level of capital market imperfection for a type-j agent (inline image), denoted by inline image (Proposition 1):

  • display math

The threshold level is increased by the spread of income distribution in the following two ways. Given ψ, the spread of income distribution decreases type-inline images labour earnings and, thus, decreases his/her after-tax income. In addition, a decrease in the type-inline images income induces him/her to choose a higher first-period tax rate, which results in a lower after-tax income for every agent as long as the type-l agent is a decisive voter. Because of these two negative effects on the after-tax income, the type-j (inline image) agent, who is initially borrowing unconstrained, could become borrowing constrained. This implies that the range of ψ that makes the type-j agent (inline image) free from borrowing constraint, inline image, becomes narrower as the income inequality becomes higher.

Second, the spread of income distribution produces positive and negative effects on the preferred debt-to-GDP ratio of each agent. The inline image-preserving spread of income distribution increases the first-period GDP, E1, implying an expansion of the tax base in the first period. This gives the decisive voter an incentive to increase government spending and, thus, to issue more public debt. In addition, the type-l agent chooses higher government spending and, thus, a higher level of public debt when he/she is a decisive voter because his/her income is decreased by the spread of income distribution. These are positive effects on the debt-to-GDP ratio. In contrast, an increase in the first-period GDP, E1, makes the debt-to-GDP ratio lower for a given B; this is a negative effect.

When the type-j (inline image or m) agent is borrowing constrained, the positive effect becomes smaller than the negative effect because he/she is unable to freely reallocate resources between the two periods. His/her policy choice results in a lower debt-to-GDP ratio in response to the spread of income distribution. In contrast, the positive effect overcomes the negative effect when he/she is borrowing unconstrained.

Third, under Assumption 2, a type-h agent is always borrowing unconstrained and, thus, prefers a higher inline image in response to the spread of income distribution. However, the preferred level of inline image by a type-h agent is always lower than that by the other two types of agents under Assumption 2. Therefore, the decisive voter is a type-l or type-m agent who prefers a lower inline image between them (Proposition 7).

Based on the above-mentioned three results, we now illustrate changes in preferences over inline image for each type of agent as in Figure 4. The dotted and solid curves in panel (a) depict the type-j agents' choices over inline image before and after the spread of income distribution, respectively. The spread of income distribution increases the threshold level of ψ that distinguishes the type of decisive voter from inline image to inline image. The bold dotted and solid curves in panel (b) depict the decisive voter's choices over inline image before and after the spread of income distribution, respectively. There exists a unique level of ψ, denoted by inline image such that the bold dotted and solid curves cross at this level. Therefore, the range of ψ is divided into four subranges of ψ, as illustrated in Figure 4: inline image, and inline image

image

Figure 4. (a) The dotted and solid curves depict the choice of a type-inline image agent over inline image before and after the spread of income distribution, respectively. (b) The bold dotted and solid curves depict the choice of the decisive voter over inline image before and after the spread of income distribution, respectively.

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image

Figure 5. The bold curve illustrates the type-i's indirect utility as a function of τ1 given τ2. The figure is the case of inline image.

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For inline image the initial decisive voter is a borrowing-constrained, type-l agent, and he/she still remains the decisive voter after the spread of income distribution. His/her choice over policies results in a lower level of inline image in response to the decrease in his/her income. In contrast, for inline image, the initial decisive voter is a borrowing-unconstrained type-m agent. Because of the spread of income distribution, the decisive voter changes from a borrowing-unconstrained type-m agent to a borrowing-constrained type-l agent. The policy choice by the latter results in a lower level of inline image than that by the former, as demonstrated in Figure 4.

For inline image, the initial decisive voter is a borrowing-unconstrained type-m agent. The decisive voter changes from a borrowing-unconstrained type-m agent to a borrowing-constrained type-l agent. The policy choice by the latter results in a higher level of inline image than that by the former as demonstrated in Figure 4. Finally, for inline image the initial decisive voter is a borrowing-unconstrained type-m agent, and he/she still remains the decisive voter after the spread of income distribution. His/her choice over policies results in a higher level of inline image in response to the spread of income distribution.

VI. CONCLUSION

  1. Top of page
  2. ABSTRACT
  3. I. INTRODUCTION
  4. II. THE MODEL
  5. III. THE POLITICAL EQUILIBRIUM
  6. IV. WELFARE IMPLICATION
  7. V. INCOME INEQUALITY AND BORROWING CONSTRAINT
  8. VI. CONCLUSION
  9. REFERENCES
  10. Supporting Information

This paper developed the two-period, three-class of income model with borrowing constraints (i.e., capital market imperfection), and examined the politics of redistributive expenditure financed by tax and government debt. In our framework, a borrowing-unconstrained agent prefers higher government expenditure and debt as his/her first-period income becomes lower because he/she wants to compensate his/her income loss today by redistributive expenditure in the future. However, an opposite result holds for a borrowing-constrained agent: he/she prefers lower government expenditure and debt because his/her income becomes lower due to he/she being unable to make such compensation under borrowing constraints.

We showed the following three results. First, the type of decisive voter depends on the degree of capital market imperfection. In particular, the decisive voter becomes a low-income, borrowing-constrained agent, rather than the middle, when the degree of capital market imperfection is high. The economy displays the ends-against-the-middle equilibrium. Second, the political equilibrium generally fails to attain efficient allocation. In particular, under certain conditions, the political equilibrium attains an underissue of government debt when the degree of capital market imperfection is high.

Third, the spread of income distribution results in a lower debt-to-GDP ratio when the degree of capital market imperfection is high. This is because the decisive voter is a borrowing-constrained low-income agent who wants to choose lower government expenditure and debt. The result implies that there is a negative correlation between inequality and debt-to-GDP ratio when the degree of capital market imperfection is low.

The standard result in the literature of politics and government debt is that (i) the political economy displays an overissue of government debt, and (ii) the spread of income distribution results in a greater issue of government debt. Our analysis and results, therefore, show that the standard result does not hold when the borrowing constraint is considered. More importantly, the result of the negative correlation between inequality and debt-to-GDP ratio could provide one possible explanation for the cross-country evidence among OECD countries.

Several directions for future research are highlighted by our results in this paper. First, we assumed a small open economy where the interest rate is exogenous. This simplifies the analysis and guarantees the analytical treatment of our political game but at the cost of abstracting general equilibrium effects. Second, the default of government debt was not considered in our analysis. Third, we assumed that the second-period productivity is linearly related to government expenditure. This assumption enables us to solve the model analytically, but results in that all types of agents prefer the same rate of the second-period tax. Relaxing these assumptions provides interesting areas for future research.

  1. 1

     Gini coefficients in Belgium, France, and Germany in the mid-2000s were 0.271, 0.270, and 0.298, respectively; debt-to-GDP ratios in those countries in 2005 were 0.957, 0.760, and 0.711, respectively. In contrast, Gini coefficients in the United Kingdom and the United States in the mid-2000s were 0.335 and 0.381, respectively; debt-to-GDP ratios in these countries in 2005 were 0.461 and 0.623, respectively. The source of the Gini coefficients is OECD (2008), and the source of the debt-to-GDP ratio is OECD (2009).

  2. 2

     As a measure of wage differential, we take relative earnings of those who have completed tertiary education as a percentage of earnings of those who have completed upper secondary or post-secondary. A higher percentage implies a higher wage inequality. OECD (2009) reports that relative earnings for age group 25–64 with tertiary education in Belgium, France, Germany, the United Kingdom and the United States in 2006 are 137.0, 157.4, 162.6, 149.2 and 183.4, respectively, for males; and 133.7, 145.8, 153.3, 177.1, and 170.2, respectively, for females. With the evidence of debt-to-GDP ratio shown in footnote 1, we find that a higher wage inequality is associated with a lower debt-to-GDP ratio among the five sample countries except in the case of wage inequality of males in the United Kingdom.

  3. 3

     The assumption of convex costs could be viewed as the reduced form of distortion in the labour market produced by labour–leisure choice (see, for example, Casamatta et al., 2000; Bellettini and Berti Ceroni, 1979; Cremer et al., 2007). The assumption of distortionary taxation is solely to ensure an interior solution to preferred tax rates and otherwise plays no role.

  4. 4

     The second-period tax rate, chosen in the first period, is assumed to be executed without deviation. This assumption implies that the government pre-commits to a certain policy schedule inline image before individuals make decisions on consumption and saving.

  5. 5

     Voters' preferences over the second-period tax rate may be affected by certain types of agents when the specification of the second-period productivity is relaxed. This relaxation could affect the result of the ends-against-the-middle equilibrium. We would like to thank one of the referees for pointing this out. We leave this issue for future work because such a relaxation makes it difficult for us to achieve an analytical solution.

  6. 6

     Under the current specification of the model, all types of agents prefer the same second-period tax rate. This result does not mean that the analysis reduces to a one-dimensional voting problem. To confirm this, recall the first- and the second-period government budget constraints given in (1) and (2), respectively. Substituting the former to the latter, we obtain an inter-temporal government budget constraint given by inline image. The constraint implies that there are three policy variables to be determined via voting: the first-period tax rate, the second-period tax rate, and the level of public debt. The first two are determined via voting; and the rest is determined to satisfy the inter-temporal constraint.

  7. 7

     Assuming a decrease in inline image instead of a decrease in inline image does not qualitatively affect the result shown below.

REFERENCES

  1. Top of page
  2. ABSTRACT
  3. I. INTRODUCTION
  4. II. THE MODEL
  5. III. THE POLITICAL EQUILIBRIUM
  6. IV. WELFARE IMPLICATION
  7. V. INCOME INEQUALITY AND BORROWING CONSTRAINT
  8. VI. CONCLUSION
  9. REFERENCES
  10. Supporting Information
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Supporting Information

  1. Top of page
  2. ABSTRACT
  3. I. INTRODUCTION
  4. II. THE MODEL
  5. III. THE POLITICAL EQUILIBRIUM
  6. IV. WELFARE IMPLICATION
  7. V. INCOME INEQUALITY AND BORROWING CONSTRAINT
  8. VI. CONCLUSION
  9. REFERENCES
  10. Supporting Information

Additional Supporting Information may be found in the online version of this article at the publisher's web site:

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boer12005-sup-0001-supmat.zip93KAppendix A.

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