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A Likelihood-Based Approximate Solution to the Incidental Parameter Problem in Dynamic Nonlinear Models with Multiple Effects

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  • Manuel Arellano
  • Jinyong Hahn

Abstract

We discuss a modified objective function strategy to obtain estimators without bias to order 1/T in nonlinear dynamic panel models with multiple effects. Estimation proceeds from a bias corrected objective function relative to some target infeasible criterion. We consider a determinant based approach for likelihood settings, and a trace based approach, which is not restricted to the likelihood setup. Both approaches depend exclusively on the Hessian and the outer product of the scores of the fixed effects. They produce simple and transparent corrections even in models with multiple effects. We analyze the asymptotic properties of both types of estimators when n and T grow at the same rate, and show that they are asymptotically normal and centered at the truth. Our strategy is to develop a theory for general bias corrected estimating equations, so that we can obtain asymptotic results for a specific bias correction method using the first order conditions.

Suggested Citation

  • Manuel Arellano & Jinyong Hahn, 2006. "A Likelihood-Based Approximate Solution to the Incidental Parameter Problem in Dynamic Nonlinear Models with Multiple Effects," Working Papers wp2006_0613, CEMFI.
  • Handle: RePEc:cmf:wpaper:wp2006_0613
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    1. Hahn, Jinyong & Kuersteiner, Guido, 2011. "Bias Reduction For Dynamic Nonlinear Panel Models With Fixed Effects," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1152-1191, December.
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    Cited by:

    1. Lee, Yoonseok & Phillips, Peter C.B., 2015. "Model selection in the presence of incidental parameters," Journal of Econometrics, Elsevier, vol. 188(2), pages 474-489.
    2. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," Review of Economic Studies, Oxford University Press, vol. 82(3), pages 991-1030.
    3. L. Hospido, 2012. "Modelling heterogeneity and dynamics in the volatility of individual wages," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 386-414, April.
    4. Geert Dhaene & Koen Jochmans, 2011. "Profile-score Adjustements for Nonlinearfixed-effect Models," Working Papers hal-01073733, HAL.
    5. Mingyang Li & Linlin Niu & Andrew Pua, 2020. "Market Pricing of Fundamentals at the Shanghai Stock Exchange: Evidence from a Dividend Discount Model with Adaptive Expectations," Working Papers 2020-12-30, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    6. Dhaene, Geert & Jochmans, Koen, 2016. "Likelihood Inference In An Autoregression With Fixed Effects," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1178-1215, October.
    7. Dmitry Arkhangelsky & Guido Imbens, 2018. "The Role of the Propensity Score in Fixed Effect Models," Papers 1807.02099, arXiv.org, revised Apr 2019.
    8. Chappell, Henry W. & McGregor, Rob Roy, 2018. "Committee decision-making at Sweden's Riksbank," European Journal of Political Economy, Elsevier, vol. 53(C), pages 120-133.
    9. Gagliardini, Patrick & Gourieroux, Christian, 2014. "Efficiency In Large Dynamic Panel Models With Common Factors," Econometric Theory, Cambridge University Press, vol. 30(5), pages 961-1020, October.
    10. Javier Mejia, 2018. "Social Networks and Entrepreneurship. Evidence from a Historical Episode of Industrialization," Documentos CEDE 016380, Universidad de los Andes - CEDE.
    11. Joris Pinkse & Margaret E. Slade, 2010. "The Future Of Spatial Econometrics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 103-117, February.
    12. Lee, Yoonseok, 2012. "Bias in dynamic panel models under time series misspecification," Journal of Econometrics, Elsevier, vol. 169(1), pages 54-60.
    13. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09ij4j0h0h1 is not listed on IDEAS
    14. Pakel, Cavit, 2019. "Bias reduction in nonlinear and dynamic panels in the presence of cross-section dependence," Journal of Econometrics, Elsevier, vol. 213(2), pages 459-492.
    15. Vasilis Sarafidis & Tom Wansbeek, 2020. "Celebrating 40 Years of Panel Data Analysis: Past, Present and Future," Monash Econometrics and Business Statistics Working Papers 6/20, Monash University, Department of Econometrics and Business Statistics.
    16. Fernández-Val, Iván, 2009. "Fixed effects estimation of structural parameters and marginal effects in panel probit models," Journal of Econometrics, Elsevier, vol. 150(1), pages 71-85, May.
    17. Lai, Hung-pin & Kumbhakar, Subal C., 2019. "Technical and allocative efficiency in a panel stochastic production frontier system model," European Journal of Operational Research, Elsevier, vol. 278(1), pages 255-265.
    18. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09j0031f620 is not listed on IDEAS

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