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Robust Priors in Nonlinear Panel Data Models

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  • Manuel Arellano
  • Stéphane Bonhomme

Abstract

Many approaches to estimation of panel models are based on an average or integrated likelihood that assigns weights to different values of the individual effects. Fixed effects, random effects, and Bayesian approaches all fall into this category. We provide a characterization of the class of weights (or priors) that produce estimators that are first-order unbiased. We show that such bias-reducing weights will depend on the data in general unless an orthogonal reparameterization or an essentially equivalent condition is available. Two intuitively appealing weighting schemes are discussed. We argue that asymptotically valid confidence intervals can be read from the posterior distribution of the common parameters when N and T grow at the same rate. Next, we show that random effects estimators are not bias reducing in general and we discuss important exceptions. Moreover, the bias depends on the Kullback-Leibler distance between the population distribution of the effects and its best approximation in the random effects family. Finally, we show that, in general, standard random effects estimation of marginal effects is inconsistent for large T, whereas the posterior mean of the marginal effect is large-T consistent, and we provide conditions for bias reduction. Some examples and Monte Carlo experiments illustrate the results. Copyright 2009 The Econometric Society.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 77 (2009)
Issue (Month): 2 (03)
Pages: 489-536

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Handle: RePEc:ecm:emetrp:v:77:y:2009:i:2:p:489-536

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  1. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  2. Jinyong Hahn & Whitney Newey, 2003. "Jackknife and analytical bias reduction for nonlinear panel models," CeMMAP working papers CWP17/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Hahn, Jinyong & Kuersteiner, Guido & Cho, Myeong Hyeon, 2004. "Asymptotic distribution of misspecified random effects estimator for a dynamic panel model with fixed effects when both n and T are large," Economics Letters, Elsevier, vol. 84(1), pages 117-125, July.
  4. Laura Hospido, 2007. "Modelling Heterogeneity And Dynamics In The Volatility Of Individual Wages," Working Papers wp2007_0717, CEMFI.
  5. Chamberlain, Gary, 1984. "Panel data," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 22, pages 1247-1318 Elsevier.
  6. L. Wasserman, 2000. "Asymptotic inference for mixture models by using data-dependent priors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 159-180.
  7. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
  8. Chamberlain, Gary, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Wiley Blackwell, vol. 47(1), pages 225-38, January.
  9. Gary Chamberlain & Guido Imbens, 2004. "Random Effects Estimators with many Instrumental Variables," Econometrica, Econometric Society, vol. 72(1), pages 295-306, 01.
  10. Javier Alvarez & Manuel Arellano, 2004. "Robust Likelihood Estimation Of Dynamic Panel Data Models," Working Papers wp2004_0421, CEMFI.
  11. Arellano, M., 2001. "Discrete Choices with Panel Data," Papers 0101, Centro de Estudios Monetarios Y Financieros-.
  12. Manuel Arellano & Jinyong Hahn, 2005. "Understanding Bias In Nonlinear Panel Models: Some Recent Developments," Working Papers wp2005_0507, CEMFI.
  13. Hahn, Jinyong & Kuersteiner, Guido, 2011. "Bias Reduction For Dynamic Nonlinear Panel Models With Fixed Effects," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1152-1191, December.
  14. Carro, Jesus M., 2007. "Estimating dynamic panel data discrete choice models with fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 503-528, October.
  15. Bester, C. Alan & Hansen, Christian, 2009. "A Penalty Function Approach to Bias Reduction in Nonlinear Panel Models with Fixed Effects," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 131-148.
  16. Arellano, Manuel & Bond, Stephen, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," Review of Economic Studies, Wiley Blackwell, vol. 58(2), pages 277-97, April.
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Cited by:
  1. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09ij4oge90i is not listed on IDEAS
  2. Laura Hospido, 2007. "Modelling heterogeneity and dynamics in the volatility of individual wages," Banco de Espa�a Working Papers 0738, Banco de Espa�a.
  3. Geert Dhaene & Koen Jochmans, 2014. "Split-Panel Jackknife Estimation of Fixed-Effect Models," Sciences Po Economics Discussion Papers 2014-03, Sciences Po Departement of Economics.
  4. Yoonseok Lee & Peter C.B. Phillips, 2013. "Model Selection in the Presence of Incidental Parameters," Center for Policy Research Working Papers 159, Center for Policy Research, Maxwell School, Syracuse University.
  5. Iván Fernández-Val & Martin Weidner, 2013. "Individual and time effects in nonlinear panel models with large N,T," CeMMAP working papers CWP60/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Geert Dhaene & Koen Jochmans, 2011. "Profile-score Adjustements for Nonlinearfixed-effect Models," Sciences Po publications info:hdl:2441/eu4vqp9ompq, Sciences Po.
  7. Michael Creel, 2009. "A Data Mining Approach to Indirect Inference," UFAE and IAE Working Papers 788.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 25 Oct 2009.
  8. Creel, Michael & Kristensen, Dennis, 2011. "Indirect Likelihood Inference," Dynare Working Papers 8, CEPREMAP.
  9. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09j0031f620 is not listed on IDEAS
  10. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09ij4j0h0h1 is not listed on IDEAS
  11. Geert Dhaene & Koen Jochmans, 2013. "Likelihood inference in an Autoregression with fixed effects," Sciences Po Economics Discussion Papers 2013-07, Sciences Po Departement of Economics.
  12. Shiu, Ji-Liang & Hu, Yingyao, 2013. "Identification and estimation of nonlinear dynamic panel data models with unobserved covariates," Journal of Econometrics, Elsevier, vol. 175(2), pages 116-131.
  13. Geert Dhaene & Koen Jochmans, 2011. "An Adjusted profile likelihood for non-stationary panel data models with fixel effects," Sciences Po publications info:hdl:2441/eu4vqp9ompq, Sciences Po.
  14. Karyne B. Charbonneau, 2014. "Multiple Fixed Effects in Binary Response Panel Data Models," Working Papers 14-17, Bank of Canada.
  15. Stéphane Bonhomme & Elena Manresa, 2012. "Grouped Patterns Of Heterogeneity In Panel Data," Working Papers wp2012_1208, CEMFI.

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