In this paper we model and explain US macroeconomic outcomes subject to the discipline that monetary policy is set optimally. Exploiting the restrictions that come from optimal policymaking, we estimate the parameters in the Federal Reserve's policy objective function together with the parameters in its optimization constraints. For the period following Volcker's appointment as chairman, we estimate the implicit inflation target to be around 1.4% and show that policymakers assigned a significant weight to interest rate smoothing. We show that the estimated optimal policy provides a good description of US data for the 1980s and 1990s.