Disinflation with Simple Interest Rate Rules in Forward vs. Backward-Looking Models

This paper analyses the mechanics of simple interest rate rules for two models----one with backward and the other with forward looking, rational expectations. The approach is to consider policy when faced with a specific task reducing inflation in a stabilizing manner. The two models are: (i) the expectations-augmented Phillips curve and (ii) the Phelps-Taylor overlapping nominal contracting model with rational expectations. The size and timing of output effects of disinflation depend not only on the parameters of a policy rule that has the Federal funds rate react to deviations of inflation and output from targeted paths, but also on its smoothness and on the timing of the disinflation path. In the forward-looking staggered contracting model, an output expansion occurs only if the inflation target is phased in over time; a recession results if the Fed smooths the nominal interest rate; and a recession followed by a boom occurs, if the Fed slowly phases in disinflation using an interest rate smoothing rule. In the backward-looking expectations-augmented Phillips curve model, disinflation leads to recessions of varying severity, depending on policy parameters. In general, smoother interest rate rules do not imply lower sacrifice ratios, nor do policies that delay implementation of the lowered inflation target. Non-smoothed interest rate rules are preferable because stability is less sensitive to the calibration of parameters. If policy smoothes the funds rate, stable disinflation is accompanied by prolonged output (and inflation) oscillations that mimic business cycles, if reactions to output are too small. All results are derived analytically, but illustrations based on simulations of the relevant, calibrated rational expectations models are also presented