Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-09T05:18:19.686Z Has data issue: false hasContentIssue false
  • English
  • Français

BOOTSTRAP AND k-STEP BOOTSTRAP BIAS CORRECTIONS FOR THE FIXED EFFECTS ESTIMATOR IN NONLINEAR PANEL DATA MODELS

Published online by Cambridge University Press:  15 February 2016

Min Seong Kim  and
Yixiao Sun
Min Seong Kim
Affiliation:
Ryerson University
Yixiao Sun*
Affiliation:
UC San Diego
*
*Address correspondence to Yixiao Sun, Department of Economics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0508; e-mail: yisun@ucsd.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

Because of the incidental parameters problem, the fixed effects maximum likelihood estimator in a nonlinear panel data model is in general inconsistent when the time series length T is short and fixed. Even if T approaches infinity but at a rate not faster than the cross sectional sample size n, the fixed effects estimator is still asymptotically biased. This paper proposes using the standard bootstrap and k-step bootstrap to correct the bias. We establish the asymptotic validity of the bootstrap bias corrections for both model parameters and average marginal effects. Our results apply to static models as well as some dynamic Markov models. Monte Carlo simulations show that our procedures are effective in reducing the bias of the fixed effects estimator and improving the coverage accuracy of the associated confidence interval.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 6 , December 2016 , pp. 1523 - 1568
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andersen, E. (1970) Asymptotic properties of conditional maximum likelihood estimators. Journal of the Royal Statistical Society, Series B 32(2), 283–301.Google Scholar
Andrews, D.W.K. (2002) Higher-order improvements of a computationally attractive k-step bootstrap for extremum estimators. Econometrica 70(1), 119–162.Google Scholar
Andrews, D. (2005) Higher-order improvements of the parametric bootstrap for Markov Processes. In Andrews, D.W.K. & Stock, J.H. (eds.), Identification and Inference for Econometric Models: A Festschrift in Honor of Thomas J. Rothenberg, pp. 171–215. Cambridge University Press.Google Scholar
Amemiya, T. (1985) Advanced Econometrics, Harvard University Press.Google Scholar
Arellano, M. & Hahn, J. (2006) Understanding bias in nonlinear panel models: Some recent developments. Advances in Economics and Econometrics. Ninth World Congress, Cambridge University Press.Google Scholar
Bester, A. & Hansen, C. (2009) A penalty function approach to bias reduction in nonlinear panel models with fixed effects. Journal of Business and Economic Statistics 27(2), 131–148.CrossRefGoogle Scholar
Davidson, R. & MacKinnon, J. (1999) Bootstrap testing in nonlinear models. International Economic Review 40(2), 487–508.CrossRefGoogle Scholar
Davidson, R. & MacKinnon, J. (2002) Fast double bootstrap tests of nonnested linear regression models. Econometric Review 21(4), 419–429.CrossRefGoogle Scholar
Davidson, R. & MacKinnon, J. (2007) Improving the reliability of bootstrap tests with the fast double bootstrap. Computational Statistics and Data Analysis 51(7), 3259–3281.Google Scholar
Dhaene, G. & Jochmans, K. (2015) Split-panel jackknife estimation of fixed-effect models. Review of Economic Studies 82, 991–1030.Google Scholar
Doukhan, P. (1995) Mixing: Properties and Examples. Springer-Verlag.Google Scholar
Ferández-Val, I. (2009) Fixed effects estimation of structural parameters and marginal effects in panel probit models. Journal of Econometrics 150(1), 71–85.CrossRefGoogle Scholar
Giacomini, R., Politis, D., & White, H. (2013) A warp-speed method for conducting Monte Carlo experiments involving bootstrap estimators. Econometric Theory 29(3), 567–589.CrossRefGoogle Scholar
Greene, W. (2004) The behavior of the fixed effects estimator in nonlinear models. The Econometrics Journal 7(1), 98–119.CrossRefGoogle Scholar
Hahn, J. & Kuersteiner, G. (2002) Asymptotically unbiased inference for a dynamic panel model with fixed effects. Econometrica 70, 1639–1657.CrossRefGoogle Scholar
Hahn, J. & Kuersteiner, G. (2011) Bias reduction for dynamic nonlinear panel models with fixed effects. Econometric Theory 27(6), 1152–1191.Google Scholar
Hahn, J., Kuersteiner, G., & Newey, W. (2004) Higher order efficiency of bias corrections. Unpublished Manuscript, MIT.Google Scholar
Hahn, J. & Newey, W. (2004) Jackknife and analytical bias reduction for nonlinear panel models. Econometrica 72(4), 1295–1319.Google Scholar
Hall, P. (1992) The Bootstrap and Edgeworth Expansion. Springer-Verlag.Google Scholar
Heckman, J. (1981) The incidental parameters problem and the problem of initial conditions in estimating a discrete time-discrete data stochastic process. In Manski, C.F. & McFadden, D.L. (eds.), Structural Analysis of Discrete Data With Economic Applications. MIT Press.Google Scholar
Honoré, B. & Kyriazidou, E. (2000) Panel data discrete choice models with lagged dependent variables. Econometrica 68(4), 839–874.CrossRefGoogle Scholar
Lancaster, T. (2000) The incidental parameter problem since 1948. Journal of Econometrics 95(2), 391–413.CrossRefGoogle Scholar
Neyman, J. & Scott, E. (1948) Consistent estimates based on partially consistent observations. Econometrica 16(1), 1–32.CrossRefGoogle Scholar
Pace, L. & Salvan, A. (2006) Adjustments of the profile likelihood from a new perspective. Journal of Statistical Planning and Inference 136(10), 3554–3564.CrossRefGoogle Scholar
Yokoyama, R. (1980) Moment bounds for stationary and mixing sequences. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 52, 45–57.CrossRefGoogle Scholar