Improved Variance Estimation of Maximum Likelihood Estimators in Stable First-Order Dynamic Regression Models
AbstractIn dynamic regression models conditional maximum likelihood (least-squares) coefficient and variance estimators are biased. From expansions of the coefficient variance and its estimator we obtain an approximation to the bias in variance es- timation and a bias corrected variance estimator, for both the standard and a bias corrected coefficient estimator. These enable a comparison of their mean squared errors to second order. We formally derive sufficient conditions for admissibility of these approximations. Illustrative numerical and simulation results are presented on bias reduction of coefficient and variance estimation for three relevant classes of ?rst-order autoregressive models, supplemented by e¤ects on mean squared er- rors, 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 esti- mates of coefficients and their estimated variance are shown to curb type I errors reasonably well.
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Bibliographic InfoPaper provided by Nanyang Technolgical University, School of Humanities and Social Sciences, Economic Growth centre in its series Economic Growth centre Working Paper Series with number 1206.
Length: 47 pages
Date of creation: Jun 2012
Date of revision:
higher-order asymptotic expansions; bias correction; efficiency gains; lagged dependent variables; finite sample moments; size improvement;
Other versions of this item:
- Kiviet, Jan F. & Phillips, Garry D.A., 2014. "Improved variance estimation of maximum likelihood estimators in stable first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 424-448.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-01-07 (All new papers)
- NEP-ECM-2013-01-07 (Econometrics)
- NEP-ETS-2013-01-07 (Econometric Time Series)
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