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

In: Essays in Honor of Peter C. B. Phillips

Author

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  • Yong Bao
  • Aman Ullah
  • Ru Zhang

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.

Suggested Citation

  • Yong Bao & Aman Ullah & Ru Zhang, 2014. "Moment Approximation for Least-Squares Estimator in First-Order Regression Models with Unit Root and Nonnormal Errors," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 14, pages 65-92, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:aecozz:s0731-905320140000033003
    DOI: 10.1108/S0731-905320140000033003
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    Cited by:

    1. Yong Bao & Aman Ullah, 2021. "Analytical Finite Sample Econometrics: From A. L. Nagar to Now," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 17-37, December.

    More about this item

    Keywords

    Unit root; nonnormal; moment approximation; C22; C20; C13;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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