Are \"deep\" parameters stable? the Lucas critique as an empirical hypothesis

For years, the problems associated with the Lucas critique have loomed over empirical macroeconomics. Since the publication of the classic Lucas (1976) critique, researchers have endeavored to specify models that capture the underlying dynamic decision-making behavior of consumers and firms who require forecasts of future events. By uncovering \"deep\" structural parameters that characterize these fundamental behaviors, and by explicitly modeling expectations, it is argued one can capture the dependence of agents' behavior on the functions describing policy. However, relatively little effort has been devoted to testing the empirical importance of this critique. Can one find specifications that are policy-invariant? This paper develops a set of tests for small macroeconometric models, especially those used for monetary policy analysis, and implements them on a set of models used extensively in the literature. In particular, we attempt to test the robustness of optimizing versus non-optimizing models to changes in the monetary policy regime. In this paper we present evidence that shows that some forward-looking models from the recent literature may be less stable that their better-fitting backward-looking counterparts.