Abstract
This paper builds on this work by deriving explicitly an optimal feedback rule using the same simple structual model of inflation as in the empirical papers cited above. Inflation is generated by a rational expectations-augmented Phillips curve, rather than a Lucas supply function, in which excess demand has the asymmetric effect on inflation described above. Real aggregate demand is determined by the real interest rate and is characterized by a certain degree of persistence. Both supply and demand are subject to stochastic shocks. The monetary instrument controlled by the authorities is the nominal interest rate which, in conjunction with the expected inflation rate, determines the real interest rate. Expectations in the model are rational, i.e., given by the expected value determined by the model.
In addition to the explicit implementation of rational expectations, this paper extends the previous work in this area by deriving optimal feedback rules based on the assumption that the policymaker wishes to minimize the squared deviations of output and inflation from their respective targets. Another feature of this model which distinguishes it from the related literature of time inconsistency (Barro and Gordon, 1983, Goodhart and Huang, 1995, and Svensson, 1995) is that the authorities do not control inflation directly, but can only influence it indirectly through the effect of their instrument on real aggregate demand. This provides both a richer and more realistic characterization of the policy problem.
Based on the optimal feedback rule endogenously derived from the model with an asymmetric Phillips curve, we derive a number of interesting policy implications. One is that the greater the degree of asymmetry, the larger the mean output gap needed to achieve a stable inflation rate, and consequently the greater the incentive for the policymaker to reduce the variability of aggregate demand. More generally, we find that the monetary authority should adjust its instrument according to the relevent policy regime, i.e. the asymmetric relationship between inflation and output sets another contraint (in addition to the commonly observed constraint from the tradeoff of price and output stability in a Lucas supply function model) on the behavior of the authority so that it has less incentive to lower interest rates to stimulate growth, and hence it has less incentive to behave time inconsistently. Although other parameters in the model also influence the effectiveness of this constraint, the primary parameter is the slope of the Phillips curve.