The Incidence of Deficit Finance with Imperfect Capital Markets.

• Author: Ben-Gad, Michael

Michael Ben-Gad [*]

The purpose of this paper is to examine the possible differential welfare implications of deficit finance using a portfolio allocation model. To analyze the incidence of changing the time path of taxation in an economy with heterogeneous agents, I develop a two-period, general equilibrium extension of work done previously to analyze the effects of taxation on risk-taking at the individual level. Constraints on short sales of assets are introduced, and fiscal policy, changing the timing of taxation, will indirectly determine which of these constraints bind as well as alter relative tax burdens. Changes in the timing of a flat-rate tax will also alter equilibrium asset returns, and because preferences are such that agents differ in their tolerance of risk, a Pareto frontier can be derived over a range of different levels of deficit finance.

1. Introduction

   During the last 20 years there has been a considerable change in the way that economists view deficit finance. Whereas once researchers focused on the efficacy of deficit finance as an instrument of short-term countercyclical policy, today much of the attention, particularly of public finance economists, focuses on its longer-term redistributive effects across generations. Many scholars, including Diamond (1965), Yotsuzuka (1987), and Woodford (1990), have demonstrated that under certain circumstances, increases in deficit finance can be Pareto improving. Nonetheless Auerbach, Gokhale, and Kotlikoff (1991) have argued that recent fiscal policy in the United States has shifted the tax burden increasingly away from the elderly and toward members of younger cohorts in a way that is hard to justify on efficiency grounds. Similar work in other industrialized countries has found a similar trend. By contrast, within the large body of deficit finance literature, very little attention has been paid to the potential i ntragenerational redistribution of welfare that may result from changes in fiscal policy.

   Similarly, there is an extensive literature comparing the intragenerational incidence of different tax regimes. This type of research (Fullerton and Rogers 1993; Kasten, Sammartino, and Toder 1994) measures the welfare gains and losses, for members of different income classes, of shifting the tax burden between different types of economic activities. What this literature does not address is the potential redistributive consequences of deficit finance--the intragenerational incidence of shifting the payment of a given tax from one period to the next.

   This paper analyzes a two-period, portfolio choice model with imperfect capital markets to demonstrate that changes in the timing of a tax can redistribute welfare intragenerationally among agents with heterogeneous levels of initial wealth. These welfare changes are not driven by shifts in the relative tax burden. Instead, changes in fiscal policy induce changes in equilibrium asset returns that have differential effects on the agents in the economy. Finally, this paper will demonstrate that the different agents' policy preferences over the amount of deficit finance in the initial period are not necessarily monotonic in wealth.

   The first work on the effects of taxation on portfolio choice was done by Domar and Musgrave (1944. The focus of this work was the effects of loss offsets on risk-taking at the level of the private individual. Mossin (1968) and Stiglitz (1969) extended this work to a model that includes agents with a general expected utility function within a two-state stochastic endowment economy. As in Domar and Musgrave, the focus of this work was the effects of government policy on an individuals' choices of assets in an economy in which the gross returns on these assets are fixed.

   To analyze changes in the timing of taxation, this paper will use a two-period general equilibrium extension of the Mossin--Stiglitz model. To study the incidence of such changes, a government budget constraint is explicitly included. In this model, asset returns are endogenously determined and change with government policy. Market imperfections, constraints on short-selling of assets, are also introduced.

   For reasons of moral hazard, adverse selection, or simply the higher likelihood that individuals will default, most people cannot borrow at the same rate of interest as the government or execute short sales of equities costlessly. [1] This limits their ability either to leverage their portfolios or to insure completely against all uncertainty. Fiscal policy, changing the timing of taxation, will indirectly determine which of the constraints on asset holdings bind, as well as alter relative tax burdens. However, the most important effect on welfare will come not from the small changes in the amounts of taxes paid, but rather from the effects of alternative fiscal policies on asset prices. In the presence of imperfect capital markets, if preferences are such that agents differ in their tolerance of risk, changes in the time path of a flat-rate tax will alter equilibrium asset returns, and produce a Pareto frontier over different levels of deficit finance.

   During the last quarter century, United States fiscal policy has undergone considerable upheaval--the long post war decline in the debt burden was halted during the mid-1970s and the debt climbed considerably during the 1980s. Recently, the debt/GDP ratio has once again begun to decline, though its long-term future remains uncertain. More importantly, despite the recent declines in deficit spending, long-term projections of lifetime net tax payments for the members of future generations have remained almost unchanged since Auerbach, Gokhale, and Kotlikoff first introduced their method of generational accounting in 1991. Now as then, baseline fiscal policy appears unsustainable, and absent large cuts in spending, tax rates are likely to rise in the future. This work is a first step toward a sustained examination of the intragenerational incidence of these tax-postponing policies and also provides a possible insight into the type of political equilibria that may perpetuate them.

2. Model

   Consider a closed economy that lasts two periods. Each consumer h [epsilon] H begins period 0 with an endowment of [[k.sup.h].sub.0] units of equities, a unit of which pays a dividend of one unit of consumption in the initial period. After receipt of the dividend, all agents simultaneously choose between the level of initial consumption [[c.sup.h].sub.0] and some portfolio of either government bonds [[b.sup.h].sub.1] or next-period equity holdings [[k.sup.h].sub.1], (net investment in equities is therefore [[k.sup.h].sub.1] - [[k.sup.h].sub.0]), which are exchanged at market prices p and q, respectively. In the second period, there are two different states, one in which the equity pays a dividend [d.sub.1]([s.sub.1]) in second-period consumption [[c.sup.h].sub.1]([s.sub.1]) and another in which the dividend is [d.sub.1]([s.sub.2]) in second-period consumption [[c.sup.h].sub.1]([s.sub.2]) (I will assume that [d.sub.1]([s.sub.2]) [greater than] 1 [greater than] [d.sub.1]([s.sub.1])). By contrast, the governmen t bond is risk free and pays one unit of consumption in either state during the second period. The total number of people in this economy is normalized to one, and so aggregate consumption is equal to one in the initial period and, depending on the state, to [d.sub.1]([s.sub.r]), [gamma] [epsilon] {1, 2} in period 1.

   In each period and every state, the government consumes a fixed amount G, which it finances by a sequence of flat rate taxes [{[[tau].sub.0], [[tau].sub.1]([[S.sub.r])}.sub.r[epsilon][1,2]] on consumption (in this economy, there is aggregate risk and since the intertemporal government budget constraint must ultimately balance, the tax rate is also state dependent and inversely related to the performance of the equities).

   Each consumer h maximizes two-period expected utility

   [max.sub.[c.sup.h]] {[U.sup.h]([[c.sup.h].sub.0] + [pi][beta][U.sup.h]([[c.sup.h].sub.1]([s.sub.1])) + (1 - [pi])[beta][U.sup.h]([[c.sup.h].sub.1]([s.sub.2]))} [MATHEMATICAL EXPRESSIONS NOT REPRODUCIBLE IN ASCII] h [epsilon] H (1)

   subject to the budget constraints

   [[c.sup.h].sub.0] = q([[k.sup.h].sub.0] - [[k.sup.h].sub.1]) - [[pb.sup.h].sub.1] + [[k.sup.h].sub.0] / 1 + [[tau].sub.0] [MATHEMATICAL EXPRESSIONS NOT REPRODUCIBLE IN ASCII] h [epsilon] H (2)

   [[c.sup.h].sub.1]([s.sub.r]) = [[b.sup.h].sub.1] + [[k.sup.h].sub.1]d([s.sub.r])/ 1 + [[tau].sub.1]([s.sub.r]) r [epsilon] {1,2} [MATHEMATICAL EXPRESSIONS NOT REPRODUCIBLE IN ASCII] h [epsilon] H. (3)

   The government's budget constraints are

   G = [[tau].sub.0] [[sigma].sub.h[epsilon]H] [[c.sup.h].sub.0] + p [[sigma].sub.h[epsilon]H] [[b.sup.h].sub.1] (4)

   G = [[sigma].sub.h[epsilon]H] [[b.sup.h].sub.1] = [[tau].sub.1]([s.sub.r]) [[sigma].sub.h[epsilon]H] [[c.sup.h].sub.1]([s.sub.r]) r [epsilon] {1,2}. (5)

   Finally, markets clear for each period and every state of the world:

   [[sigma].sub.h[epsilon]H] [[c.sup.h].sub.0] + G = [[sigma].sub.h[epsilon]H] [[k.sup.h].sub.0] (6)

   [[sigma].sub.h[epsilon]H] [[c.sup.h].sub.1]([s.sub.r]) + G = d([s.sub.r]) + G = d([s.sub.r]) [[sigma].sub.h[epsilon]H] [[k.sup.h].sub.1] r [epsilon] {1,2} (7)

   [[sigma].sub.h[epsilon]H] [[k.sup.h].sub.1] = [[sigma].sub.h[epsilon]H] [[k.sup.h].sub.0] (8)

   Because we prefer to remain in the realm of a two-state economy, only two linearly independent assets are necessary to ensure the completeness of markets. The terms bonds and equities are metaphors, and the variables [b.sub.1] and [k.sub.1] could easily be interpreted to include cash and savings accounts in the case of the former and a range of high-risk investments in the case of the latter.

   PROPOSITION 1. If a fixed level of government expenditure is financed at least in part by debt, then in a two-period endowment economy with perfect capital markets, the prices of both assets decrease with the size of the deficit.

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