This thesis consists of three essays examining the driving forces behind in inflation and unemployment fluctuations in the United States.In the first essay, a time-varying parameter vector auto-regressive model with stochastic volatility and mixture innovations is developed to study the empirical relevance of the Lucas critique for the postwar U.S. economy. Contrary to the Lucas critique, there are large changes at certain points of time in the parameters associated with monetary policy that do not correspond to changes in reduced-form parameters for inflation or the unemployment rate. However, an apparent reduction in the late1980s in the impact of monetary policy shocks on inflation, but not on the unemployment rate, is documented. Relate...