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A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions

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  • Kruiniger, Hugo

Abstract

In this paper we consider two kinds of generalizations of Lancaster's (Review of Economic Studies, 2002) Modified ML estimator (MMLE) for the panel AR(1) model with fixed effects and arbitrary initial conditions and possibly covariates when the time dimension, T, is fixed. When the autoregressive parameter ρ=1, the limiting modified profile log-likelihood function for this model has a stationary point of inflection and ρ is first-order underidentified but second-order identified. We show that the generalized MMLEs exist w.p.a.1 and are uniquely defined w.p.1. and consistent for any value of ρ≥-1. When ρ=1, the rate of convergence of the MMLEs is N^{1/4}, where N is the cross-sectional dimension of the panel. We then develop an asymptotic theory for GMM estimators when one of the parameters is only second-order identified and use this to derive the limiting distributions of the MMLEs. They are generally asymmetric when ρ=1. One kind of generalized MMLE depends on a weight matrix W_{N} and we show that a suitable choice of W_{N} yields an asymptotically unbiased MMLE. We also show that Quasi LM tests that are based on the modified profile log-likelihood and use its expected rather than observed Hessian, with an additional modification for ρ=1, and confidence regions that are based on inverting these tests have correct asymptotic size in a uniform sense when |ρ|≤1. Finally, we investigate the finite sample properties of the MMLEs and the QLM test in a Monte Carlo study.

Suggested Citation

  • Kruiniger, Hugo, 2018. "A further look at Modified ML estimation of the panel AR(1) model with fixed effects and arbitrary initial conditions," MPRA Paper 88623, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:88623
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    File URL: https://mpra.ub.uni-muenchen.de/88623/1/MPRA_paper_88623.pdf
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    References listed on IDEAS

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    1. Bun, Maurice J.G. & Carree, Martin A., 2005. "Bias-Corrected Estimation in Dynamic Panel Data Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 200-210, April.
    2. Javier Alvarez & Manuel Arellano, 2004. "Robust Likelihood Estimation Of Dynamic Panel Data Models," Working Papers wp2004_0421, CEMFI.
    3. Arellano, Manuel & Bover, Olympia, 1995. "Another look at the instrumental variable estimation of error-components models," Journal of Econometrics, Elsevier, vol. 68(1), pages 29-51, July.
    4. Kruiniger, Hugo, 2013. "Quasi ML estimation of the panel AR(1) model with arbitrary initial conditions," Journal of Econometrics, Elsevier, vol. 173(2), pages 175-188.
    5. Lee, Lung-Fei & Chesher, Andrew, 1986. "Specification testing when score test statistics are identically zero," Journal of Econometrics, Elsevier, vol. 31(2), pages 121-149, March.
    6. Matteo Bottai, 2003. "Confidence regions when the Fisher information is zero," Biometrika, Biometrika Trust, vol. 90(1), pages 73-84, March.
    7. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
    8. Kruiniger, Hugo, 2008. "Maximum likelihood estimation and inference methods for the covariance stationary panel AR(1)/unit root model," Journal of Econometrics, Elsevier, vol. 144(2), pages 447-464, June.
    9. Manuel Arellano & Stéphane Bonhomme, 2009. "Robust Priors in Nonlinear Panel Data Models," Econometrica, Econometric Society, vol. 77(2), pages 489-536, March.
    10. Prosper Dovonon & Eric Renault, 2013. "Testing for Common Conditionally Heteroskedastic Factors," Econometrica, Econometric Society, vol. 81(6), pages 2561-2586, November.
    11. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    12. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, August.
    13. Kruiniger, Hugo, 2009. "Gmm Estimation And Inference In Dynamic Panel Data Models With Persistent Data," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1348-1391, October.
    14. Han, Chirok & Phillips, Peter C. B. & Sul, Donggyu, 2014. "X-Differencing And Dynamic Panel Model Estimation," Econometric Theory, Cambridge University Press, vol. 30(01), pages 201-251, February.
    15. Hsiao, Cheng & Hashem Pesaran, M. & Kamil Tahmiscioglu, A., 2002. "Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods," Journal of Econometrics, Elsevier, vol. 109(1), pages 107-150, July.
    16. repec:eee:econom:v:205:y:2018:i:1:p:76-111 is not listed on IDEAS
    17. Harris, Richard D. F. & Tzavalis, Elias, 1999. "Inference for unit roots in dynamic panels where the time dimension is fixed," Journal of Econometrics, Elsevier, vol. 91(2), pages 201-226, August.
    18. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-1426, November.
    19. Juodis, Artūras, 2013. "A note on bias-corrected estimation in dynamic panel data models," Economics Letters, Elsevier, vol. 118(3), pages 435-438.
    20. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," Review of Economic Studies, Oxford University Press, vol. 58(2), pages 277-297.
    21. Anderson, T. W. & Hsiao, Cheng, 1982. "Formulation and estimation of dynamic models using panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 47-82, January.
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    More about this item

    Keywords

    dynamic panel data; expected Hessian; fixed effects; Generalized Method of Moments (GMM); inflection point; Modified Maximum Likelihood; Quasi LM test; second-order identification; singular information matrix; weak moment conditions.;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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