Abstract
It is well-known that Ordinary Least Squares (OLS) yields inconsistent estimates if applied to a regression equation with lagged dependent variables and correlated errors. Bias expressions which appear in the literature usually assume the exogenous variables to be non-stochastic. Due to this assumption the numerical sizes of these expressions cannot be determined. Further, the analysis is mostly restricted to very simple models. In this paper the problem of calculating the asymptotic bias of OLS is generalized to stationary dynamic regression models, where the errors follow a stationary ARMA process. A general bias expression is derived and a method is introduced by which its actual size can be computed numerically.
Similar content being viewed by others
References
Dhrymes, Phoebus J. (1981): Distributed lags: problems of estimation and formulation. 2. rev. edn. Amsterdam: North-Holland.
Flynn, Brian James and Westbrook, Daniel M. (1984): Small-sample properties of estimators of a regression equation with a lagged dependent variable and serial correlation. ASA: Proceedings of the Business and Economic Statistics Section, 1984, 653–658.
Gourieroux, Christian and Monfort, Alain (1997): Time Series and Dynamic Models. Cambridge University Press.
Griliches, Zvi (1961): A note on serial correlation bias in estimates of distributed lags. Econometrica 29 (1), 65–73.
Hannan, E.J. (1970): Multiple Time Series: New York: Wiley.
Hatanaka, M. (1974): An efficient estimator for the dynamic adjustment model with autocorrelated errors. Journal of Econometrics, 2, 199–220.
Hong, Dun-Mow and L'Esperance, Wilford L. (1973): Effects of autocorrelated errors on various least squares estimators: A Monte Carlo study. Communications in Statistics, 2, 507–523.
Inder, Brett A. (1987): Bias in the ordinary least squares estimator in the dynamic linear regression model with autocorrelated disturbances. Communications in Statistics B, 16 (3), 791–815.
Jekanowski, Mark D. and Binkley, James K. (1996): Lagged dependent variables and serially correlated errors: Which estimators can we trust? ASA: Proceedings of the Business and Economic Statistics Section, 1996, 237–242.
Lütkepohl, Helmut (1993): Introduction to Multiple Time Series Analysis, 2nd edn. Berlin: Springer.
Maddala, G. S. and Rao, A. S. (1973): Tests for serial correlation in regression models with lagged dependent variables and serially correlated errors. Econometrica 41, 761–774.
Maeshiro, Asatoshi (1980): Small sample properties of estimators of distributed lag models. International Economic Review, 21 (3), 721–733.
Maeshiro, Asatoshi (1987): OLS as an estimator of a dynamic model with ARMA errors. JASA: Proceedings of the Business and Economic Statistics Sec., 638–642.
Maeshiro, Asatoshi (1990): Peculiar bias properties of the OLS estimator when applied to a dynamic model with autocorrelated disturbances. Communications in Statistics A, 19 (4), 1185–1204.
Maeshiro, Asatoshi (1996): Teaching regressions with a lagged dependent variable and autocorrelated disturbances. Journal of Economic Education, 27, 72–84.
Maeshiro, Asatoshi (1999): A lagged dependent variable, autocorrelated disturbances and unit root tests—peculiar OLS bias properties—a pedagogical note. Applied Economics, 31, 381–396.
Mittnik, S. (1990): Computation of theoretical autocovariance matrices of multivariate autoregressive moving average time series; Journal of the Royal Statistical Society B, 52, 151–155.
Phillips, P.C.B. and Wickens, M.R. (1978): Exercises in econometrics, vol. 2. Oxford: Phillip Allan.
Pierce, D.A. (1970): Rational distributed lag models with autoregressivemoving average errors. Proceedings of the Business and Economic Statistics Section of the American Statistical Association, 591–596.
Sargent, Thomas J. (1968): Some evidence on the small sample properties of distributed lag estimators in the presence of autocorrelated disturbances. Review of Economics and Statistics, 50, 87–95.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stocker, T. On the asymptotic bias of OLS in dynamic regression models with autocorrelated errors. Statistical Papers 48, 81–93 (2007). https://doi.org/10.1007/s00362-006-0317-8
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s00362-006-0317-8