When monetary policies are endogenous, the conventional VAR approach for detecting the effect of monetary policies is powerless. This paper proposes to test the implication of monetary policies along a different dimension. That implication is to exploit the policy induced exogeneity of endogenous variables that are the source of monetary non-neutrality. We illustrate the idea by constructing a new Keynesian sticky wage model with capital accumulation and then testing the implications of optimal monetary policies for nominal wages under both complete and incomplete information. Econometric test using post war US data suggests that the nominal wage is exogenous with respect to lagged macro variables. Such exogeneity is consistent with new Keynesian models in which the monetary authority pursues active monetary policy based on information with a lag.