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

Essays in Honor of Peter C. B. Phillips

ISBN: 978-1-78441-183-1

ISSN: 0731-9053

Publication date: 21 November 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

Acknowledgements

Acknowledgments

We thank an anonymous referee and Tom Fomby for their helpful comments.

Citation

Bao, Y., Ullah, A. and Zhang, R. (2014), "Moment Approximation for Least-Squares Estimator in First-Order Regression Models with Unit Root and Nonnormal Errors", Essays in Honor of Peter C. B. Phillips (Advances in Econometrics, Vol. 33), Emerald Group Publishing Limited, Bingley, pp. 65-92. https://doi.org/10.1108/S0731-905320140000033003

Publisher

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Emerald Group Publishing Limited

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