Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models
An approximation to order T−2 is obtained for the bias of the full vector of least-squares estimates obtained from a sample of size T in general stable but not necessarily stationary ARX(1) models with normal disturbances. This yields generalizations, allowing for various forms of initial conditions, of Kendall’s and White’s classic results for stationary AR(1) models. The accuracy of various alternative approximations is examined and compared by simulation for particular parameterizations of AR(1) and ARX(1) models. The results show that often the second-order approximation is considerably better than its first-order counterpart and hence opens up perspectives for improved bias correction. However, order T−2 approximations are also found to be more vulnerable in the near unit root case than the much simpler order T−1 approximations.
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Volume (Year): 56 (2012)
Issue (Month): 11 ()
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- Broda, Simon & Paolella, Marc S. & Carstensen, Kai, 2007.
"Bias-adjusted estimation in the ARX(1) model,"
Munich Reprints in Economics
19992, University of Munich, Department of Economics.
- repec:exe:wpaper:99/06 is not listed on IDEAS
- MacKinnon, James G. & Smith Jr., Anthony A., 1998.
"Approximate bias correction in econometrics,"
Journal of Econometrics,
Elsevier, vol. 85(2), pages 205-230, August.
- James G. MacKinnon & Anthony A. Smith, Jr., . "Approximate Bias Correction in Econometrics," GSIA Working Papers 1997-36, Carnegie Mellon University, Tepper School of Business.
- James G. MacKinnon & Anthony A. Smith Jr., 1995. "Approximate Bias Correction in Econometrics," Working Papers 919, Queen's University, Department of Economics.
- Mackinnon, J.G. & Smith, A.A., 1996. "Approximate Bias Correction in Econometrics," G.R.E.Q.A.M. 96a14, Universite Aix-Marseille III.
- Sawa, Takamitsu, 1978. "The exact moments of the least squares estimator for the autoregressive model," Journal of Econometrics, Elsevier, vol. 8(2), pages 159-172, October.
- Vinod, H.D. & Shenton, L.R., 1996. "Exact Moments for Autor1egressive and Random walk Models for a Zero or Stationary Initial Value," Econometric Theory, Cambridge University Press, vol. 12(03), pages 481-499, August.
- Glenn D. Rudebusch, 1990.
"Trends and random walks in macroeconomic time series: a re-examination,"
Finance and Economics Discussion Series
139, Board of Governors of the Federal Reserve System (U.S.).
- Rudebusch, Glenn D, 1992. "Trends and Random Walks in Macroeconomic Time Series: A Re-examination," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 661-80, August.
- Dufour, J.M. & Kiviet, J.F., 1995.
"Exact Tests in Single Equation Autoregressive Distributed Lag Models,"
Cahiers de recherche
9549, Universite de Montreal, Departement de sciences economiques.
- Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, vol. 80(2), pages 325-353, October.
- Dufour, J.M. & Kiviet, J.F., 1995. "Exact Tests in Single Equation Autoregressive Distributed Lag Models," Cahiers de recherche 9549, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Maekawa, Koichi, 1983. "An Approximation to the Distribution of the Least Squares Estimator in an Autoregressive Model with Exogenous Variables," Econometrica, Econometric Society, vol. 51(1), pages 229-38, January.
- Jan F. Kiviet & Garry D.A. Phillips, 1998. "Degrees of freedom adjustment for disturbance variance estimators in dynamic regression models," Econometrics Journal, Royal Economic Society, vol. 1(RegularPa), pages 44-70.
- Hadri, Kaddour & Phillips, Garry D. A., 1999.
"The accuracy of the higher order bias approximation for the 2SLS estimator,"
Elsevier, vol. 62(2), pages 167-174, February.
- Hadri, K. & Phillips, G.D.A., 1999. "The Accuracy of the Higher Order Bias Approximation for the 2SLS Estimator," Discussion Papers 9906, Exeter University, Department of Economics.
- Tsui, Albert K. & Ali, Mukhtar M., 1994. "Exact distributions, density functions and moments of the last squares estimator in a first-order autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 17(4), pages 433-454, May.
- Kadane, Joseph B, 1971. "Comparison of k-Class Estimators when the Disturbances are Small," Econometrica, Econometric Society, vol. 39(5), pages 723-37, September.
- Grubb, David & Symons, James, 1987. "Bias in Regressions With a Lagged Dependent Variable," Econometric Theory, Cambridge University Press, vol. 3(03), pages 371-386, June.
- Russell Davidson & James G. MacKinnon, 1985. "Testing Linear and Loglinear Regressions against Box-Cox Alternatives," Canadian Journal of Economics, Canadian Economics Association, vol. 18(3), pages 499-517, August.
- Kiviet, Jan F. & Phillips, Garry D. A. & Schipp, Bernhard, 1995. "The bias of OLS, GLS, and ZEF estimators in dynamic seemingly unrelated regression models," Journal of Econometrics, Elsevier, vol. 69(1), pages 241-266, September.
- Tanizaki, Hisashi, 2000. "Bias correction of OLSE in the regression model with lagged dependent variables," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 495-511, October.
- Nankervis, J. C. & Savin, N. E., 1988. "The exact moments of the least-squares estimator for the autoregressive model corrections and extensions," Journal of Econometrics, Elsevier, vol. 37(3), pages 381-388, March.
- Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
- Jan F. Kiviet & Garry D. A. Phillips, 2005. "Moment approximation for least-squares estimators in dynamic regression models with a unit root *," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 115-142, 07.
- Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, edition 1, number 9780198774488, December.
- Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
- Kiviet, Jan F. & Phillips, Garry D.A., 1993. "Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable," Econometric Theory, Cambridge University Press, vol. 9(01), pages 62-80, January.
- Kiviet, Jan F. & Phillips, Garry D. A., 1994. "Bias assessment and reduction in linear error-correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 215-243, July.
- Bao, Yong, 2007. "The Approximate Moments Of The Least Squares Estimator For The Stationary Autoregressive Model Under A General Error Distribution," Econometric Theory, Cambridge University Press, vol. 23(05), pages 1013-1021, October.
- Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
- Emma M. Iglesias & Garry D. A. Phillips, 2008. "Finite Sample Theory of QMLE in ARCH Models with Dynamics in the Mean Equation," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(4), pages 719-737, 07.
- Orcutt, Guy H & Winokur, Herbert S, Jr, 1969. "First Order Autoregression: Inference, Estimation, and Prediction," Econometrica, Econometric Society, vol. 37(1), pages 1-14, January.
- Tanaka, Katsuto, 1983. "Asymptotic Expansions Associated with the AR(1) Model with Unknown Mean," Econometrica, Econometric Society, vol. 51(4), pages 1221-31, July.
- Magnus, J.R., 1978. "The moments of products of quadratic forms in normal variables," Other publications TiSEM 17c77a44-1789-4cf4-a382-a, Tilburg University, School of Economics and Management.
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