MEDIAN UNBIASED ESTIMATION OF COEFFICIENT VARIANCE IN A TIME-VARYING PARAMETER MODEL

This article considers inference about the variance of coefficients in time-varying parameter models with stationary regressors. The Gaussia n maximum likelihood estimator (MLE) has a large point mass at 0. We t hus develop asymptotically median unbiased estimators and asymptotical ly valid confidence intervals by inverting quantile functions of regre ssion-based parameter stability test statistics, computed under the co nstant-parameter null. These estimators have good asymptotic relative efficiencies for small to moderate amounts of parameter variability. W e apply these results to an unobserved components model of trend growt h in postwar U.S. per capita gross domestic product. The MLE implies t hat there has been no change in the trend growth rate, whereas the upp er range of the median-unbiased point estimates imply that the annual trend growth rate has fallen by 0.9% per annum since the 1950s.