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Model Selection in the Presence of Incidental Parameters

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Abstract

This paper considers model selection in nonlinear panel data models where incidental parameters or large-dimensional nuisance parameters are present. Primary interest typically centres on selecting a model that best approximates the underlying structure involving parameters that are common within the panel after concentrating out the incidental parameters. It is well known that conventional model selection procedures are often inconsistent in panel models and this can be so even without nuisance parameters (Han et al, 2012). Modifications are then needed to achieve consistency. New model selection information criteria are developed here that use either the Kullback-Leibler information criterion based on the profile likelihood or the Bayes factor based on the integrated likelihood with the robust prior of Arellano and Bonhomme (2009). These model selection criteria impose heavier penalties than those associated with standard information criteria such as AIC and BIC. The additional penalty, which is data-dependent, properly reflects the model complexity arising from the presence of incidental parameters. A particular example is studied in detail involving lag order selection in dynamic panel models with fixed individual effects. The new criteria are shown to control for over/under-selection probabilities in these models and lead to consistent order selection criteria.

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File URL: http://cowles.econ.yale.edu/P/cd/d19a/d1919.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1919.

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Length: 38 pages
Date of creation: Oct 2013
Date of revision:
Handle: RePEc:cwl:cwldpp:1919

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: (Adaptive) model selection; incidental parameters; profile likelihood; Kullback-Leibler information; Bayes factor; integrated likelihood; robust prior; model complexity; fixed effects; lag order;

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References

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  1. Manuel Arellano & Stéphane Bonhomme, 2007. "Robust priors in nonlinear panel data models," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP07/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Newey, W.K., 1991. "The Asymptotic Variance of Semiparametric Estimators," Working papers 583, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. N. Sartori, 2003. "Modified profile likelihoods in models with stratum nuisance parameters," Biometrika, Biometrika Trust, Biometrika Trust, vol. 90(3), pages 533-549, September.
  4. Lancaster, Tony, 2002. "Orthogonal Parameters and Panel Data," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 69(3), pages 647-66, July.
  5. Lee, Yoonseok, 2012. "Bias in dynamic panel models under time series misspecification," Journal of Econometrics, Elsevier, vol. 169(1), pages 54-60.
  6. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, Econometric Society, vol. 62(1), pages 43-72, January.
  7. 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, American Statistical Association, vol. 27(2), pages 131-148.
  8. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, Econometric Society, vol. 52(2), pages 271-320, March.
  9. Jinyong Hahn & Whitney Newey, 2003. "Jackknife and analytical bias reduction for nonlinear panel models," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP17/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. Maddala, G S, 1971. "The Use of Variance Components Models in Pooling Cross Section and Time Series Data," Econometrica, Econometric Society, Econometric Society, vol. 39(2), pages 341-58, March.
  11. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, Econometric Society, vol. 50(1), pages 1-25, January.
  12. Tony Lancaster, 2002. "Orthogonal Parameters and Panel Data," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 647-666.
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Cited by:
  1. Haruo Iwakura & Ryo Okui, 2014. "Asymptotic Efficiency in Factor Models and Dynamic Panel Data Models," KIER Working Papers 887, Kyoto University, Institute of Economic Research.

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