For a VAR with drifting coefficients and stochastic volatilities, the authors present posterior densities for several objects that are of interest for designing and evaluating monetary policy. These include measures of inflation persistence, the natural rate of unemployment, a core rate of inflation, and "activism coefficients" for monetary policy rules. Their posteriors imply substantial variation of all of these objects for post WWII U.S. data. After adjusting for changes in volatility, persistence of inflation increases during the 1970s then falls in the 1980s and 1990s. Innovation variances change systematically, being substantially larger in the late 1970s than during other times. Measures of uncertainty about core inflation and the degree of persistence covary positively. The authors use their posterior distributions to evaluate the power of several tests that have been used to test the null of time-invariance of autoregressive coefficients of VARs against the alternative of time-varying coefficients. Except for one test, they find that those tests have low power against the form of time variation captured by our model. That one test also rejects time invariance in the data.