Proportional income tax and the Ricardian equivalence in a non-expected utility maximizing model.

• Author: Basu, Parantap

1. Introduction

   A number of papers have examined the issue whether the Ricardian equivalence holds in a world where tax is proportional to future labor income. Barro [2] and Tobin [16] discuss deviations from Ricardian equivalence arising from the interaction between individual income uncertainty and tax policy. Following the same line of reasoning as Chen [5], Barsky, Mankiw and Zeldes [3] as well as Kimball and Mankiw [10] make a persuasive argument that in an environment where future labor income is uncertain, the marginal propensity to consume out of a deficit financed tax cut is significantly positive if future taxes are proportional to income. Their argument is that future taxes provide insurance to consumers by reducing the variance of after tax future income. Such an insurance which Barsky, Mankiw, and Zeldes [3] call "risk-sharing effect" reduces the precautionary saving of the consumer, thus boosting current consumption.

   The purpose of this paper is to reexamine this risk-sharing hypothesis and the issue of debt non-neutrality using a nonexpected utility maximizing framework. My analysis builds on recent advances in the representation of non-expected utility functionals which enable us to disentangle risk aversion from intertemporal substitution in consumption. I use a hybrid non-expected utility preferences a la Weil [17], which is isoelastic in intertemporal substitution but exponential in risk preference. The benefit of using this class of non-expected utility functionals is that it admits an analytical solution which is difficult to obtain in the existing permanent income models [18]. Aside from its analytical tractability, this formulation of the preference also helps us to have a useful decomposition of the effect of a deficit financed tax cut into "income" and "information" effects. The risk-sharing effect of a deficit financed tax cut discussed by Barsky, Mankiw, and Zeldes [3] depends on the relative strengths of the aforementioned two effects.

   Our results show that the above risk-sharing effect is quantitatively small for a plausible range of risk aversion and intertemporal substitution. The marginal propensity to consume out of a deficit financed tax cut is considerably lower than the Keynesian consumption propensity proposed by Barsky, Mankiw, and Zeldes [3]. This means that the Ricardian equivalence may be a reasonable approximation even when income tax is proportional This conclusion runs contrary to that of Barsky, Mankiw, and Zeldes [3], and Kimball and Mankiw [10]. The reason for the difference in result is due to the fact that Barsky, Mankiw, and Zeldes [3] and Kimball and Mankiw [10] use expected utility functionals. By assuming expected utility maximization, such a framework imposes a severe restriction on two inherently unrelated preference parameters, namely risk aversion and intertemporal substitution in consumption. The nonexpected utility maximizing approach enables us to understand the separate roles played by these two preference parameters by making the utility function, path dependent.(1) The specific nonexpected utility functional that I employ here admits a closed form solution for the marginal propensity to consume out of a deficit financed tax cut. The pay-off to this analytical tractability is that we can identify the separate roles played by risk aversion and intertemporal substitution in consumption in determining the quantitative importance of the risk-sharing effect on consumption caused by a deficit financed tax cut.

   A few caveats about the use of nonexpected utility functionals in the present context are in order. It is important to note that the central point of this paper is to examine the quantitative significance of the risk sharing caused by deficit financed tax cut in an environment where future tax is not lump-sum but proportional in nature. In order to accomplish this task, it is crucially important to use a choice theoretic framework which disentangles risk aversion from intertemporal substitution. This exercise does not necessarily invalidate the theoretical literature on Ricardian equivalence which widely uses an expected utility maximizing framework. A number of theoretical results about the effect of deficit financed tax cut on consumption when taxes are lump sum in nature are robust to the specification of the utility function. For example, Blanchard [4] uses an expected utility maximizing framework to establish a theoretically robust result that Ricardian equivalence appears as a special case when agent's life horizon approaches infinity. Evans [6] estimates a discrete time version of Blanchard's model [4] with cross country data and concludes that consumers are unlikely to be Ricardian. Since Blanchard [4] assumes future taxes are lump-sum in nature, the issue of risk-sharing effect caused by deficit financed tax cut does not arise there.

   The rest of the paper is organized as follows. In the next section the model is laid out and comparative statics are undertaken. In section III, I report some simulation results based on the analytical solution from the model. Section IV ends with concluding comments.

2. The Model

   I consider a two period model similar to Barsky, Mankiw, and Zeldes [3]. All individuals are identical ex ante except for the expost realization of labor income in the second period of their life. Each agent works in both periods and supplies one unit of labor in each period. Income earned from work in the second period is uncertain. Each individual can borrow or lend at a gross risk free interest rate R. The government cuts taxes and issues bonds to finance the deficit in the first period. In the second period, a tax on labor income is imposed to pay off the debt.

   The intertemporal consumption opportunity facing the consumer can be summarized by the following budget equation:

   [Mathematical Expression Omitted]

   where [C.sub.1] = consumption in the first period, [Mathematical Expression Omitted] = second period consumption, T = tax rebate, [Y.sub.1] = first period income, [Mathematical Expression Omitted] = second period labor income, [Tau] = income tax rate and ~ stands for the random nature of the second period consumption and income.

   Notice that the government provides each individual with a tax cut in the first period and makes sure to raise enough tax revenue to repay the debt in the second period. In other words, the government sets the tax rate [Tau] in such a way that the total tax revenue per person exactly equals the debt per person which means:

   [Tau][[Mu].sub.2] = RT (2)

   where

   [Mathematical Expression Omitted].

   Each agent maximizes the following nonexpected utility functional:

   [Mathematical Expression Omitted]

   where [Mathematical Expression Omitted] =...