In this paper we investigate the comparative properties of empirically-estimated monetary models of the U.S. economy. We make use of a new data base of models designed for such investigations. We focus on three representative models: the Christiano, Eichenbaum, Evans (2005) model, the Smets and Wouters (2007) model, and the Taylor (1993a) model. Although the three models differ in terms of structure, estimation method, sample period, and data vintage, we find surprisingly similar economic impacts of unanticipated changes in the federal funds rate. However, the optimal monetary policy responses to other sources of economic fluctuations are widely different in the different models. We show that simple optimal policy rules that respond to the growth rate of output and smooth the interest rate are not robust. In contrast, policy rules with no interest rate smoothing and no response to the growth rate, as distinct from the level, of output are more robust. Robustness can be improved further by optimizing rules with respect to the average loss across the three models.