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A Comparison of First-Difference and Forward Orthogonal Deviations GMM

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  • Robert F. Phillips

Abstract

This paper provides a necessary and sufficient instruments condition assuring two-step generalized method of moments (GMM) based on the forward orthogonal deviations transformation is numerically equivalent to two-step GMM based on the first-difference transformation. The condition also tells us when system GMM, based on differencing, can be computed using forward orthogonal deviations. Additionally, it tells us when forward orthogonal deviations and differencing do not lead to the same GMM estimator. When estimators based on these two transformations differ, Monte Carlo simulations indicate that estimators based on forward orthogonal deviations have better finite sample properties than estimators based on differencing.

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  • Robert F. Phillips, 2019. "A Comparison of First-Difference and Forward Orthogonal Deviations GMM," Papers 1907.12880, arXiv.org.
    • Handle: RePEc:arx:papers:1907.12880
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    References listed on IDEAS

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    5. Phillips, Robert F., 2019. "A numerical equivalence result for generalized method of moments," Economics Letters, Elsevier, vol. 179(C), pages 13-15.
    6. Kazuhiko Hayakawa, 2009. "First Difference or Forward Orthogonal Deviation- Which Transformation Should be Used in Dynamic Panel Data Models?: A Simulation Study," Economics Bulletin, AccessEcon, vol. 29(3), pages 2008-2017.
    7. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
    8. Cheng Hsiao & Qiankun Zhou, 2017. "First difference or forward demeaning: Implications for the method of moments estimators," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 883-897, October.
    9. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
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