Key classical macroeconomic hypotheses specify that permanent changes in nominal variables have no effect on real economic variables in the long run. The simplest “long-run neutrality” proposition specifies that a permanent change in the money stock has no long-run consequences for the level of real output. Other classical hypotheses specify that a permanent change in the rate of inflation has no long-run effect on unemployment (a vertical long-run Phillips curve) or real interest rates (the long-run Fisher relation). In this article we provide an econometric framework for studying these classical propositions and use the framework to investigate their relevance for the postwar U.S. experience. Testing these propositions is a subtle matter. For example, Lucas (1972) and Sargent (1971) provide examples in which it is impossible to test long-run neutrality using reduced-form econometric methods. Their examples feature rational expectations together with short-run nonneutrality and exogenous variables that follow stationary processes so that the data generated by these models do not contain the sustained changes necessary to directly test long-run neutrality. In the context of these models, Lucas and Sargent argued that it was necessary to construct fully articulated behavioral models to test the neutrality propositions. McCallum (1984) extended these arguments and showed that lowfrequency band spectral estimators calculated from reduced-form models were also subject to the Lucas-Sargent critique. While these arguments stand on firm logical ground, empirical analysis following the Lucas-Sargent prescriptions has not yet yielded convincing evidence on the neutrality propositions. This undoubtedly reflects a lack of consensus among macroeconomists on the appropriate behavioral model to use for the investigation.