The 1970s and early 1980s witnessed two main approaches to the analysis of monetary policy. The first is the early new classical approach of Lucas, based on the assumptions of rational expectations and market clearing. The second is the atheoretical econometrics of Sims's VAR program. Both have developed: the new classical approach has been enriched through various accounts of price stickiness, cost of adjustment or alternative expectational schemes; the original VAR program has developed into the structural VAR program. This paper clarifies the relationship between these two programs. Based on work of Cochrane (1998), it shows that the typical method of evaluating unanticipated, unsystematic monetary policy is correct only if the conditions necessary for Lucas's policy-ineffectiveness proposition hold, while recent methods for evaluating systematic monetary policy violate Lucas's policy-noninvariance proposition ("the Lucas critique"). The paper shows how to construct and estimate (using regime changes) a model in which some agents form rational-expectations and others follow rules of thumb. In such a model, monetary policy actions can be validly decomposed into systematic and unsystematic components and valid counterfactual experiments on alternative systematic monetary-policy rules can be evaluated.