This paper proposes a simple benchmark for monetary policy. Assuming the true model of the economy is unknown, it is based on an unrestricted vector autoregression (VAR). The key result is that instead of deriving optimal policy using the original VAR equations as the constraint, when no restriction is placed on the correlation structure of the VAR disturbances, the constraint should be formed from a transformation of the VAR. This method is applied to the USA, 1964–2009. Significant welfare gains are found compared with actual policy and using a Taylor rule. Incorporating a zero interest rate lower bound lowers output and inflation.