Monetary Uncertainty and Investment in an Optimizing, Rational Expectations Model with Income Taxes and Government Debt

Abstract

THE EFFECT OF MONETARY GROWTH on an economy's investment has long been of interest to economists, and monetary growth models provide a convenient tool for the analysis of this question. The standard optimizing growth model postulates that money is injected into the private sector through transfer payments which typically either are of lump sum form or are proportional to wealth, income, or money holdings. (See, for example, Brock (1974), Calvo (1979), Fischer (1979), and Gertler and Grinols (1982).) In these models monetary changes are tied directly to changes in subsidy or tax rates, and greater expected money growth generally either has no effect on investment or increases it through a Tobin (1965) effect. In this paper we analyze the effects that a stochastic monetary policy has on investment in an economy with individual optimization, rational expectations, and a government which makes expenditures and finances them through borrowing, money creation, and proportional income taxes. With such a formulation, money can be injected into the private sector through government purchases and open market operations as well as through transfers, and the link between money growth and subsidy or tax rates is weakened or nonexistent. We assume that the nominal income tax rates are constant over time. Given tax rates and (stochastic) government consumption, the stochastic monetary growth rule followed by the government induces a stochastic government debt policy. The effects that changes in the stochastic monetary growth rate have on investment depend on the nature of the depreciation deduction and on the relationship between the coefficient of relative risk aversion and the tax rate on production income. When depreciation deductions are based on historical costs, an equilibrium is unique so long as the coefficient of relative risk aversion is greater than the tax rate applicable to production income. In this case an increase in the mean rate of money growth decreases equilibrium investment while a mean preserving spread in the money growth rate increases investment. Given Friend and Blume's (1975) finding that the coefficient of relative risk aversion is substantially greater than one, this seems to be the empirically relevant case. If the coefficient of relative risk aversion is less than the tax rate on production income, multiple equilibria are possible, and the effects on investment of changes in the stochastic money growth rate are generally indeterminate. When depreciation deductions are based on replacement costs, investment is independent of the stochastic money growth rate. The paper is organized as follows. Section 2 develops the optimization problem of the representative individual when depreciation deductions are based on historical costs. Section 3 describes the behavior of the government and develops the rational expectations equilibrium for this economy. Section 4 examines the effects on investment of changes in the stochastic money growth rate. Section 5 briefly reconsiders the model when depreciation deductions are based on replacement costs.