Dynamic Instrument Rules Based on Time Varying Coefficients Vector Autoregressive Modeling and Forecast-Based Monetary Policy

This paper proposes a method to construct monetary instrument rules whose coefficients are time varying. We refer the instrument rules as the dynamic instrument rules. Our approach is a statistical and practical tool for the central bank to achieve some specified targets. The dynamic instrument rules consist of two elements: (1) time varying coefficients vector autoregressive modeling (time varying VAR) with the vector of control variables and (2) linear quadratic dynamic programming. The coefficients of time varying VAR are assumed to change gradually (this assumption is widely known as smoothness priors of the Bayesian procedure), and they are estimated by the Kalman filer. Based on the estimated time varying VAR and linear quadratic dynamic programming, the dynamic instrument rules are derived in each period for achieving the targets. Our approach is convenient and effective for the practitioners in the central bank when they are unaware of the true model of the economy. However, it is not based on the theory of the economic agents who have rational expectations. In our empirical analyses, we show the effectiveness of our approach by applying it to the inflation targeting of the United Kingdom and the nominal growth rate targeting of Japan. Furthermore, we emphasize that the optimal monetary policy must be forecast-based because there exist lags of monetary policy. Our method realizes a forecast-based policy. Additionally, we find that the coefficients of time varying VAR change in response to the changes of monetary policy