A Time-Varying Parameter Model of A Monetary Policy Rule for Switzerland. The Case of the Lucas and Friedman Hypothesis

This paper is an empirical research of a monetary policy rule for a small open economy model, taking Switzerland as a case-study. A time-varying parameter model of a monetary policy reaction function is proposed to integrate various trade-offs to be made about various macroeconomic variables -- inflation, the output gap and the real exchange rate gap. The Kalman filter estimations of the time-varying parameters shows how rational economic agents combine past and new information to make new expectations about the state variables. The uncertainty created by the time-varying parameter model, and estimated by the conditional forecast error and conditional variance, is decomposed into two components, the uncertainty related to the time-varying parameters and the uncertainty related to the purely monetary shock. Most of the monetary shock uncertainty comes from the time-varying parameters and not from the pure monetary shock. The Lucas and Friedman hypotheses about the impact of uncertainty on output are revisited, using a conditional variance to test them. Both hypothesis are confirmed, using the one-step ahead conditional variance of the monetary shock. An inverse relation between the magnitude of the response on output to the nominal shock and the variance of this shock is found, as Lucas had predicted. Moreover, there is a direct negative impact of uncertainty which reduces output in the long-term.