Most of the literature estimating DSGE models for monetary policy analysis assume that policy follows a simple rule. In this paper we allow policy to be described by various forms of optimal policy - commitment, discretion and quasi-commitment. We find that, even after allowing for Markov switching in shock variances, the inflation target and/or rule parameters, the data preferred description of policy is that the US Fed operates under discretion with a marked increase in conservatism after the 1970s. Parameter estimates are similar to those obtained under simple rules, except that the degree of habits is significantly lower and the prevalence of cost-push shocks greater. Moreover, we find that the greatest welfare gain sfrom the 'Great Moderation' arose from the reduction in the variances in shocks hitting the economy, rather than increased inflation aversion. However, much of the high inflation of the 1970s could have been avoided had policy makers been able to commit, even without adopting stronger anti-inflation objectives. More recently the Fed appears to have temporarily relaxed policy following the 1987 stock market crash, and has lost, without regaining, its post-Volcker conservatism following the bursting of the dot-com bubble in 2000.
