Median Unbiased Estimation of Coefficient Variance in a Time-Varying Parameter Model

Abstract

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