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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: Dec 2013
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Handle: RePEc:ifs:cemmap:60/13
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  1. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Cowles Foundation Discussion Papers 1222, Cowles Foundation for Research in Economics, Yale University.
  2. M. Hashem Pesaran, 2004. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," CESifo Working Paper Series 1331, CESifo Group Munich.
  3. Manuel Arellano & Stéphane Bonhomme, 2009. "Robust Priors in Nonlinear Panel Data Models," Econometrica, Econometric Society, vol. 77(2), pages 489-536, 03.
  4. Geert Dhaene & Koen Jochmans, 2010. "Split-panel jackknife estimation of fixed-effect models," Sciences Po publications info:hdl:2441/eu4vqp9ompq, Sciences Po.
  5. 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.
  6. Howitt, Peter & Griffith, Rachel & Aghion, Philippe & Blundell, Richard & Bloom, Nick, 2005. "Competition and Innovation: An Inverted-U Relationship," Scholarly Articles 4481507, Harvard University Department of Economics.
  7. 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.
  8. Luojia Hu, 2002. "Estimation of a Censored Dynamic Panel Data Model," Econometrica, Econometric Society, vol. 70(6), pages 2499-2517, November.
  9. Ivan Fernandez-Val & Frank Vella, 2007. "Bias corrections for two-step fixed effects panel data estimators," CeMMAP working papers CWP04/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. 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.
  11. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09ij4j0h0h1 is not listed on IDEAS
  12. 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.
  13. Hahn, Jinyong & Moon, Hyungsik Roger, 2006. "Reducing Bias Of Mle In A Dynamic Panel Model," Econometric Theory, Cambridge University Press, vol. 22(03), pages 499-512, June.
  14. 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.
  15. Ivan Fernandez-Val & Martin Weidner, 2014. "Individual and time effects in nonlinear panel models with large N, T," CeMMAP working papers CWP32/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  16. Tiemen Woutersen, 2002. "Robustness against Incidental Parameters," UWO Department of Economics Working Papers 20028, University of Western Ontario, Department of Economics.
  17. Tony Lancaster, 2002. "Orthogonal Parameters and Panel Data," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 647-666.
  18. Kato, Kengo & F. Galvao, Antonio & Montes-Rojas, Gabriel V., 2012. "Asymptotics for panel quantile regression models with individual effects," Journal of Econometrics, Elsevier, vol. 170(1), pages 76-91.
  19. 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.
  20. 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.
  21. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, 07.
  22. 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.
  23. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-26, November.
  24. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
  25. Alvarez, J. & Arellano, M., 1998. "The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators," Papers 9808, Centro de Estudios Monetarios Y Financieros-.
  26. Tony Lancaster, 2002. "Orthogonal Parameters and Panel Data," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 647-666.
  27. 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.
  28. 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.
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