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Robust Priors In Nonlinear Panel Data Models

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Author Info
Manuel Arellano ()
Stephane Bonhomme () (CEMFI, Centro de Estudios Monetarios y Financieros)

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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 in this category. We provide a characterization of the class of weights (or priors) that produce estimators that are firstorder unbiased. We show that such bias-reducing weights must depend on the data 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. Finally, we show that random effects estimators are not bias reducing in general and discuss important exceptions. Three examples and some Monte Carlo experiments illustrate the results.

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Paper provided by CEMFI in its series Working Papers with number wp2006_0614.

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Date of creation: Dec 2006
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Handle: RePEc:cmf:wpaper:wp2006_0614

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Related research
Keywords: Panel data; incidental parameters; bias reduction; integrated likelihood; priors.;

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Find related papers by JEL classification:
C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data

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  1. 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, Blackwell Publishing, vol. 58(2), pages 277-97, April. [Downloadable!] (restricted)
  2. Laura Hospido, 2007. "Modelling heterogeneity and dynamics in the volatility of individual wages," Banco de España Working Papers 0738, Banco de España. [Downloadable!]
    Other versions:
  3. Manuel Arellano & Jinyong Hahn, 2005. "Understanding Bias In Nonlinear Panel Models: Some Recent Developments," Working Papers wp2005_0507, CEMFI. [Downloadable!]
  4. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, 07. [Downloadable!] (restricted)
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  5. Javier Alvarez & Manuel Arellano, 2004. "Robust Likelihood Estimation Of Dynamic Panel Data Models," Working Papers wp2004_0421, CEMFI. [Downloadable!]
  6. Lancaster, Tony, 2002. "Orthogonal Parameters and Panel Data," Review of Economic Studies, Blackwell Publishing, vol. 69(3), pages 647-66, July.
  7. Tiemen Woutersen, 2002. "Robustness against Incidental Parameters," UWO Department of Economics Working Papers 20028, University of Western Ontario, Department of Economics. [Downloadable!]
  8. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August. [Downloadable!] (restricted)
  9. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-20, May. [Downloadable!] (restricted)
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  10. Hahn, Jinyong, 2004. "Does Jeffrey's prior alleviate the incidental parameter problem?," Economics Letters, Elsevier, vol. 82(1), pages 135-138, January. [Downloadable!] (restricted)
  11. Chamberlain, Gary, 1980. "Analysis of Covariance with Qualitative Data," Review of Economic Studies, Blackwell Publishing, vol. 47(1), pages 225-38, January. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
  13. Manuel Arellano, 2003. "Discrete choices with panel data," Investigaciones Economicas, Fundación SEPI, vol. 27(3), pages 423-458, September. [Downloadable!]
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  14. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
  16. Gary Chamberlain & Guido Imbens, 2004. "Random Effects Estimators with many Instrumental Variables," Econometrica, Econometric Society, vol. 72(1), pages 295-306, 01. [Downloadable!] (restricted)
  17. 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. [Downloadable!] (restricted)
  18. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April. [Downloadable!] (restricted)
  19. 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. [Downloadable!] (restricted)
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