Moment Approximation for Least-Squares Estimator in First-Order Regression Models with Unit Root and Nonnormal Errors

Advances in Econometrics, 2014, vol. 33, 65-92.

Posted: 27 Feb 2016

See all articles by Yong Bao

Yong Bao

Purdue University

Aman Ullah

University of California, Riverside (UCR) - Department of Economics

Ru Zhang

University of California, Riverside (UCR)

Date Written: February 25, 2014

Abstract

An extensive literature in econometrics focuses on finding the exact and approximate first and second moments of the least-squares estimator in the stable first-order linear autoregressive model with normally distributed errors. Recently, Kiviet and Phillips (2005) developed approximate moments for the linear autoregressive model with a unit root and normally distributed errors. An objective of this paper is to analyze moments of the estimator in the first-order autoregressive model with a unit root and nonnormal errors. In particular, we develop new analytical approximations for the first two moments in terms of model parameters and the distribution parameters. Through Monte Carlo simulations, we find that our approximate formula perform quite well across different distribution specifications in small samples. However, when the noise to signal ratio is huge, bias distortion can be quite substantial, and our approximations do not fare well.

Keywords: Unit root, nonnormal, moment approximation

JEL Classification: C22, C20, C13

Suggested Citation

Bao, Yong and Ullah, Aman and Zhang, Ru, Moment Approximation for Least-Squares Estimator in First-Order Regression Models with Unit Root and Nonnormal Errors (February 25, 2014). Advances in Econometrics, 2014, vol. 33, 65-92. , Available at SSRN: https://ssrn.com/abstract=2738115

Yong Bao (Contact Author)

Purdue University ( email )

Department of Economics
West Lafayette, IN 47907
United States

Aman Ullah

University of California, Riverside (UCR) - Department of Economics ( email )

900 University Avenue
4136 Sproul Hall
Riverside, CA 92521
United States
909-787-5037, X1591 (Phone)

Ru Zhang

University of California, Riverside (UCR) ( email )

900 University Avenue
Riverside, CA CA 92521
United States

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