Optimal fiscal policy in a stochastic growth model

Abstract

Although most neoclassical growth models focus on competitive equilibria which are Pareto optimal and ignore the role of government, recent works by Romer [28,29], Judd [20], Baxter and King [S], and Bizer and Judd [7] have shown that government can be introduced into and suboptimal equilibria can be studied in these models as well. Their studies, however, are positive analyses of the effects of fiscal policy in competitive equilibria. The purpose of this paper is to apply Ramsey’s [27] theory of optimal taxation to the normative study of fiscal policy in a stocastic growth model. Ramsey studied a static, representative consumer economy with many goods. In his formulation, a government consumes a fixed amount of these goods, which it purchases at market prices and finances by levying flat-rate excise taxes, prices and quantities are determined in a competitive equilibrium. The government is benevolent, and its objective is to choose the optimal tax rates to maximize the representative consumer’s utility. A number of economists, among them Kydland and Prescott [23], Barro [3], Turnovsky and Brock [31], and Lucas and Stockey [26], have noted that Ramsey’s formulation can be applied to dynamic economies with uncertainty if one reinterprets the goods in static problems as dated, state contingent goods. In this framework, a fiscal policy is a rule which specifies state contingent tax rates and the amount of public debt issue in each date. The optimal fiscal policy is defined as the one which leads to a quantity