Optimal Monetary Policy using a VAR

In this paper we propose a new way to formulate optimal policy based on a quadratic intertemporal welfare function where the dynamic constraint is based on a VAR model of the economy which we call the PVAR method. We argue that the VAR under control should not be derived simply by replacing the VAR equation for the policy instruments by an optimal control rule because this alters the stochastic structure of the VAR. Instead, one should first transform the VAR in order to condition the non-policy variables on the policy instruments, then use the resulting sub-system as the dynamic constraint, and finally construct the VAR under control by combining this sub-system with the resulting optimal policy rule. In this way the original stochastic structure of the VAR is retained. In comparing the two approaches we explain the theoretical advantages of the PVAR over the standard method and we illustrate the methods by examining the formulation of optimal monetary policy for the US. We suggest that since the whole process is easily automated, the PVAR method may provide a useful benchmark for use in real time against which to compare other, probably far more labour intensive, policy choices.