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Individual and time effects in nonlinear panel models with large N, T

  • Ivan Fernandez-Val

    (Institute for Fiscal Studies and University of Boston)

  • Martin Weidner

    ()

    (Institute for Fiscal Studies and cemmap and UCL)

Fixed effects estimators of nonlinear panel data models can be severely biased because of the well-known incidental parameter problem. We develop analytical and jackknife bias corrections for nonlinear models with both individual and time effects. Under asymptotic sequences where the time-dimension (T) grows with the cross-sectional dimension (N), the time effects introduce additional incidental parameter bias. As the existing bias corrections apply to models with only individual effects, we derive the appropriate corrections for the case when both effects are present. The basis for the corrections are general asymptotic expansions of fixed effects estimators with incidental parameters in multiple dimensions. We apply the expansions to M-estimators with concave objective functions in parameters for panel models with additive individual and time effects. These estimators cover fixed effects estimators of the most popular limited dependent variable models such as logit, probit, ordered probit, Tobit and Poisson models. Our analysis therefore extends the use of large-T bias adjustments to an important class of models. We also develop bias corrections for functions of the data, parameters and individual and time effects including average partial effects. In this case, the incidental parameter bias can be asymptotically of second order, but the corrections still improve finite-sample properties.

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File URL: http://www.cemmap.ac.uk/wps/cwp601313.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP60/13.

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Date of creation: 02 Dec 2013
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Handle: RePEc:ifs:cemmap:60/13
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  1. 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.
  2. Luojia Hu, 2002. "Estimation of a Censored Dynamic Panel Data Model," Econometrica, Econometric Society, vol. 70(6), pages 2499-2517, November.
  3. Victor Chernozhukov & Iván Fernández‐Val & Jinyong Hahn & Whitney Newey, 2013. "Average and Quantile Effects in Nonseparable Panel Models," Econometrica, Econometric Society, vol. 81(2), pages 535-580, 03.
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  7. Hyungsik Roger Moon & Martin Weidner, 2014. "Linear regression for panel with unknown number of factors as interactive fixed effects," CeMMAP working papers CWP35/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Javier Alvarez & Manuel Arellano, 2003. "The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators," Econometrica, Econometric Society, vol. 71(4), pages 1121-1159, 07.
  9. Jinyong Hahn & Hyungsik Roger Moon, 2005. "Reducing Bias of MLE in a Dynamic Panel Model," IEPR Working Papers 05.36, Institute of Economic Policy Research (IEPR).
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  12. Tony Lancaster, 2002. "Orthogonal Parameters and Panel Data," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 647-666.
  13. M. Hashem Pesaran, 2004. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," CESifo Working Paper Series 1331, CESifo Group Munich.
  14. Iván Fernández-Val & Joonhwan Lee, . "Panel Data Models with Nonadditive Unobserved Heterogeneity: Estimation and Inference," Boston University - Department of Economics - Working Papers Series wp2010-001, Boston University - Department of Economics.
  15. DHAENE, Geert & JOCHMANS, Koen, 2010. "Split-panel jackknife estimation of fixed-effect models," CORE Discussion Papers 2010003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  16. Ivan Fernandez-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.
  17. Antonio F. Galvao & Kengo Kato, 2014. "Estimation and Inference for Linear Panel Data Models Under Misspecification When Both n and T are Large," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 285-309, April.
  18. Dennis Kristensen & Bernard Salanie, 2013. "Higher-order properties of approximate estimators," CeMMAP working papers CWP45/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  19. Fernández-Val, Iván & Vella, Francis, 2007. "Bias Corrections for Two-Step Fixed Effects Panel Data Estimators," IZA Discussion Papers 2690, Institute for the Study of Labor (IZA).
  20. Karyne B. Charbonneau, 2014. "Multiple Fixed Effects in Binary Response Panel Data Models," Staff Working Papers 14-17, Bank of Canada.
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  24. Hyungsik Roger Moon & Martin Weidner, 2013. "Dynamic linear panel regression models with interactive fixed effects," CeMMAP working papers CWP63/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  25. Olsen, Randall J, 1978. "Note on the Uniqueness of the Maximum Likelihood Estimator for the Tobit Model," Econometrica, Econometric Society, vol. 46(5), pages 1211-15, September.
  26. 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.
  27. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
  28. Okui Ryo, 2014. "Asymptotically Unbiased Estimation of Autocovariances and Autocorrelations with Panel Data in the Presence of Individual and Time Effects," Journal of Time Series Econometrics, De Gruyter, vol. 6(2), pages 53, July.
  29. Manuel Arellano & Stéphane Bonhomme, 2009. "Robust Priors in Nonlinear Panel Data Models," Econometrica, Econometric Society, vol. 77(2), pages 489-536, 03.
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  32. 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.
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