Monetary policy and PID control

Abstract

We show that many currently popular monetary policy rules fall structurally within a class of robust industrial control known as proportional-integral-differential, or PID, control. From this identification we propose a general class of PID-based monetary policy rules that include as limiting cases the original Taylor rule as well as lagged and forward-looking extensions of thereof. The effectiveness of parsimonious extensions of the Taylor rule are consistent with the well-known effectiveness and parsimony of PID control. We find that for the same reason encountered in other PID control applications—noisy data—most monetary policy rules fall in the proportional-integral subset of PID control known as PI control. We estimate both PID and PI monetary policy rules using the historical analysis approach of Taylor and compare the performance of our PI rule to other policy rules using a recently-developed macroeconomic-model comparison methodology. A key feature of PID control is its remarkable effectiveness for systems where the equations of motion are not known. Thus, PID-based rules both link monetary policy with a tradition of practical control in the absence of known dynamical equations and provide baseline rules for monetary policy in the face of macroeconomic model uncertainty.