Optimal Dynamic Taxation, Saving and Investment

In many recent papers macro-economic models have been developed to study the dynamic evolution of the economy in order to analyze dynamic effects of fiscal policy (e.g. Hall (1971), Brock and Turnovsky (1981), Abel and Blanchard (1983), Judd (1985) and Van de Klundert and Peters (1986)). Aim of these papers is to investigate the incidence of different tax rates such as a tax on profits, a sales tax, a wage tax or a consumption tax with the help of optimal control theory. However, in these kinds of models the tax rates are given exogenously.In this paper we deal with this problem by a more normative approach. We are concerned with optimal dynamic taxation, where the government wants to maximize the utility of a representative consumer (e.g. Turnovsky and Brock (1980)) and tries to choose its tax rate in such a way that this objective is maximized. Moreover, we assume that the government takes into account the way that the firm and consumer will react on its tax policy, while the firms and the consumers takes the decision of the other as given. So, the government behaves as the leader in an open-loop Stackelberg equilibrium (e.g. Basar and Olsder (1982)). However, as pointed out by Kydland and Prescott (1977) and Calvo (1978) such an optimal policy may be time-inconsistent. Once the current is history, the effect of policies on behavior in that period are of little or no interest. Therefore, we are concerned with two possible solutions. The first solution, which is the formal outcome of an open-loop Stackelberg equilibrium of game between government, consumers and firms, is only credible, if there is commitment or if there are reputational forces. The second solution, which correspons to a Nash-Cournot equilibrium is time-consistent, but yields a lower value of steady-state utility. In this paper we show that this problem of time-consistency depends on the kind of tax rates the government chooses.Our approach builds on Abel and Blanchard’s (1983) macro-economic market model, which describes intertemporal choice of consumers and firms in a free market economy. Abel and Blanchard use this framework to analyze the dynamic effects of fiscal policy. We extend the Abel and Blanchard model by modelling optimal government’s behavior and give some rules for the optimal choice of tax policy. It is shown that there only will be time-inconsistency, if the government chooses profit or sales tax to finance their expenditures. Wage and consumption tax cannot be source for time-inconsistency, which gives an incentive to implement these taxes.