Expected Inflation and Interest Rates in a Multi‐asset Model: A Note

Abstract

This paper analyzes the effect of expected inflation on nominal interest rates, in a theoretical model with money and two different bond types. The inclusion of three assets instead of the usual two causes the effect of expected inflation on the interest rates to deviate from unity. Depending on the sizes of the wealth and interest rate effects on the various asset demands, the effect of expected inflation could even be negative. Several special cases are also considered, and the implications for the interpretation of empirical results are discussed. THE PROFESSION HAS SHOWN a continuing strong interest in the effect of expected inflation on interest rates, both from a theoretical and an empirical perspective. Fisher's [6]original hypothesis was that there should be a one-forone effect, so that expected inflation has no effect on the ex ante real interest rate. Numerous researchers have failed to find that strong an empirical effect on nominal rates, however, and some have expressed puzzlement over this empirical result. (The empirical literature includes [1, 2, 3, 5, 6, 10, 13, 14] and numerous others.) Theoretical models generally consider a short-run situation in which the real rate of return on financial assets is free to deviate from the marginal product of capital. The simplest possible such macro model, with IS, LM, and vertical aggregate supply curve equations, generates the Fisher result that dr/dir-the effect of expected inflation -r on the nominal interest rate r-equals unity. But there are several possible modifications to this model which can drive the value of dr/dir either up or down. First, the Mundell [12] effect states that the presence of a real balance effect on consumption depresses the value of dr/dir. Second, the Phillips effect [9, 10] states that a nonvertical aggregate supply curve depresses dr/d7r. Third, Levi and Makin [10] showed that if the level of expected inflation influences inflation uncertainty, and if inflation uncertainty in turn affects the parameters of any behavioral function, then this channel alters the value of dr/dir. And finally, the Darby [4] effect states that the presence of a tax on nominal interest income magnifies dr/dir. Recently, Carmichael and Stebbing [3] argued that bonds might be closer substitutes for money than for anything else, so expected inflation might have a