Phillips Curves, Expectations of Inflation and Optimal Unemployment over Time

Readers of my article on optimal over time1 will recognize its principal theme to be the following. Among all alternative equilibrium states of steady anticipated or deflation, all with the same steady unemployment rate, there exists a state with an algebraic anticipated rate that is optimal. But, by virtue of the immediate postulated gains from over-employment-from employment in excess of the equilibrium level-and the immediate postulated losses from under-employment, social time preference plays a critical role in determining each day's optimal level of aggregate demand and thereby the ultimate steady rate of algebraic that society will asymptotically settle for. The higher the rate of time preference, the more does this asymptotic algebraic rate exceed the statically optimal rate and the greater is the present optimal level of aggregate demand. If the current rate of inflation exceeds the asymptotic rate of algebraic inflation, then the optimal aggregate demand policy will produce transient (vanishing) underemployment and thus a rate of below expectations. If the current expected rate of is below the asymptotic rate of algebraic inflation, then the optimal fiscal policy aims for transient overemployment and algebraic in excess of expectations. It is odd that Mr. Williamson, in his Comment, 2 should find a deflationist moral in this even-handed theme. My article rejected the conventional approach to the choice of aggregate demand, which takes expectations as exogenous or irrelevant, not any conventional conclusion about the merits of inflationary policies. One conclusion of the model is that a society with the requisite time preference can rationally opt for over-employment, unexpectedly high and its aftermath of high steady in the eventual future equilibrium. Even the statically optimal rate of algebraic inflation-in my formulation this is the maximum rate of algebraic consistent with full liquidity or monetary efficiency-might be one of mild if the real rate of interest is small enough. The interesting variation on this dynamic model that Williamson proposes would, loosely speaking, make more deflation worse than less deflation on the other side of the static optimum. There are