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IV, GMM or likelihood approach to estimate dynamic panel models when either N or T or both are large

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  • Hsiao, Cheng
  • Zhang, Junwei

Abstract

We examine the asymptotic properties of IV, GMM or MLE to estimate dynamic panel data models when either NorT or both are large. We show that the Anderson and Hsiao (1981, 1982) simple instrumental variable estimator (IV) or maximizing the likelihood function with initial value distribution properly treated (quasi-maximum likelihood estimator) is asymptotically unbiased when either N or T or both tend to infinity. On the other hand, the QMLE mistreating the initial value as fixed is asymptotically unbiased only if N is fixed and T is large. If both N and T are large and NT→c (c≠0,c<∞) as T→∞, it is asymptotically biased of order NT. We also explore the source of the bias of the Arellano and Bond (1991) type GMM estimator. We show that it is asymptotically biased of order TN if TN→c (c≠0,c<∞) as N→∞ even if we restrict the number of instruments used. Monte Carlo studies show that whether an estimator is asymptotically biased or not has important implications on the actual size of the conventional t-test.

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  • Hsiao, Cheng & Zhang, Junwei, 2015. "IV, GMM or likelihood approach to estimate dynamic panel models when either N or T or both are large," Journal of Econometrics, Elsevier, vol. 187(1), pages 312-322.
    • Handle: RePEc:eee:econom:v:187:y:2015:i:1:p:312-322
    DOI: 10.1016/j.jeconom.2015.01.008
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    7. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
    8. Peter C.B. Phillips, 2014. "Dynamic Panel GMM with Near Unity," Cowles Foundation Discussion Papers 1962, Cowles Foundation for Research in Economics, Yale University.
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    3. Carbajal-De-Nova, Carolina, 2017. "A proposed method to estimate dynamic panel models when either N or T or both are not large," MPRA Paper 93100, University Library of Munich, Germany, revised 02 Sep 2017.
    4. Dhaene, Geert & Jochmans, Koen, 2016. "Bias-corrected estimation of panel vector autoregressions," Economics Letters, Elsevier, vol. 145(C), pages 98-103.
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    7. Pua, Andrew Adrian Yu & Fritsch, Markus & Schnurbus, Joachim, 2019. "Large sample properties of an IV estimator based on the Ahn and Schmidt moment conditions," Passauer Diskussionspapiere, Betriebswirtschaftliche Reihe B-37-19, University of Passau, Faculty of Business and Economics.
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    11. Cheng Hsiao & Qiankun Zhou, 2016. "Asymptotic distribution of quasi-maximum likelihood estimation of dynamic panels using long difference transformation when both N and T are large," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 675-683, November.
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    More about this item

    Keywords

    IV; MLE; GMM; Asymptotic bias; Large N; T;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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