Improved variance estimation of maximum likelihood estimators in stable first-order dynamic regression models

In dynamic regression models conditional maximum likelihood (least-squares) coeffi cient and variance estimators are biased. From expansions of the coeffi cient variance and its estimator we obtain an approximation to the bias in variance estimation and a bias corrected variance estimator, for both the standard and a bias corrected coeffi cient estimator. These enable a comparison of their mean squared errors to second order. We formally derive suffi cient conditions for admissibility of these approximations. Illustrative numerical and simulation results are presented on bias reduction of coeffi cient and variance estimation for three relevant classes of first-order autoregressive models, supplemented by effects on mean squared errors, test size and size corrected power. These indicate that substantial biases do occur in moderately large samples, but these can be mitigated substantially and may also yield mean squared error reduction. Crude asymptotic tests are cursed by huge size distortions. However, operational bias corrections of both the estimates of coeffi cients and their estimated variance (for which we provide software) are shown to curb type I errors reasonably well. ∗corresponding author Nanyang Visiting Professor at the Division of Economics, School of Humanities and Social Sciences, Nanyang Technological University, 14 Nanyang Drive, Singapore 637332 ([email protected]; +65 65921535); Emeritus Professor of the Amsterdam School of Economics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands ([email protected]). † Cardiff Business School, Aberconway Building, Colum Drive, CF10 3EU, Cardiff, Wales, UK ([email protected]).