This paper empirically examines how the Fed responds to stock prices and inflation movements, using the forward-looking Taylor rule augmented with the stock price gap. The typical linear policy reaction function has a substantial change after 1991, but lacks the robustness in that the estimation result is sensitive to a minor change of the sample period. To alleviate the problem, we allow for temporary and permanent variations of the reaction coefficients by introducing nonlinearity and a structural break. The time variation of the inflation coefficient shows that the Fed is more aggressive in periods of inflationary pressure. However, unlike the linear model case, we find little evidence of a significant change in the Fed's active response to inflationary pressure after the structural break at 1991:I. We also find a positive response to the stock price change after 1991:I. But the time varying pattern of the response is counter-cyclical to stock price change, which does not support the view that the Fed actively reacts to a stock price bubble.