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LIKELIHOOD INFERENCE IN AN AUTOREGRESSION WITH FIXED EFFECTS

Published online by Cambridge University Press:  11 May 2015

Geert Dhaene  and
Koen Jochmans
Geert Dhaene*
Affiliation:
University of Leuven
Koen Jochmans*
Affiliation:
Sciences Po
*
*Address correspondence to Geert Dhaene, University of Leuven, Department of Economics, Naamsestraat 69, B-3000 Leuven, Belgium; e-mail: [email protected]; and Koen Jochmans, Sciences Po, Department of Economics, 28 rue des Saints-Pères, 75007 Paris, France; e-mail: [email protected].
*Address correspondence to Geert Dhaene, University of Leuven, Department of Economics, Naamsestraat 69, B-3000 Leuven, Belgium; e-mail: [email protected]; and Koen Jochmans, Sciences Po, Department of Economics, 28 rue des Saints-Pères, 75007 Paris, France; e-mail: [email protected].
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Abstract

We calculate the bias of the profile score for the regression coefficients in a multistratum autoregressive model with stratum-specific intercepts. The bias is free of incidental parameters. Centering the profile score delivers an unbiased estimating equation and, upon integration, an adjusted profile likelihood. A variety of other approaches to constructing modified profile likelihoods are shown to yield equivalent results. However, the global maximizer of the adjusted likelihood lies at infinity for any sample size, and the adjusted profile score has multiple zeros. Consistent parameter estimates are obtained as local maximizers inside or on an ellipsoid centered at the maximum likelihood estimator.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 5 , October 2016 , pp. 1178 - 1215
Copyright
Copyright © Cambridge University Press 2015 

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References

REFERENCES

Ahn, S.C. & Schmidt, P. (1995) Efficient estimation of models for dynamic panel data. Journal of Econometrics 68, 5–27.Google Scholar
Ahn, S.C. & Thomas, G.M. (2006) Likelihood based inference for dynamic panel data models. Mimeo, Arizona State University, W.P. Carey School of Business.Google Scholar
Alvarez, J. & Arellano, M. (2003) The time series and cross-section asymptotics of dynamic panel data estimators. Econometrica 71, 1121–1159.Google Scholar
Alvarez, J. & Arellano, M. (2004) Robust likelihood estimation of dynamic panel data models. Working Paper #0421, CEMFI.Google Scholar
Arellano, M. (2003a) Discrete choices with panel data. Investigaciones Económicas 27, 423–458.Google Scholar
Arellano, M. (2003b) Panel Data Econometrics. Oxford University Press.Google Scholar
Arellano, M. & Bond, S. (1991) Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58, 277–297.Google Scholar
Arellano, M. & Bonhomme, S. (2009) Robust priors in nonlinear panel data models. Econometrica 77, 489–536.Google Scholar
Arellano, M. & Hahn, J. (2006) A likelihood-based approximate solution to the incidental parameter problem in dynamic nonlinear models with multiple effects. Working Paper #0613, CEMFI.Google Scholar
Bester, C.A. & Hansen, C. (2009) A penalty function approach to bias reduction in non-linear panel models with fixed effects. Journal of Business and Economic Statistics 27, 131–148.CrossRefGoogle Scholar
Blundell, R.W. & Bond, S. (1998) Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87, 115–143.CrossRefGoogle Scholar
Bun, M.J. & Carree, M.A. (2005) Bias-corrected estimation in dynamic panel data models. Journal of Business and Economic Statistics 23, 200–210.Google Scholar
Cox, D.R. & Reid, N. (1987) Parameter orthogonality and approximate conditional inference (with discussion). Journal of the Royal Statistical Society, Series B 49, 1–39.Google Scholar
Cruddas, A., Reid, N., & Cox, D. (1989) A time series illustration of approximate conditional likelihood. Biometrika 76, 231–237.Google Scholar
Dhaene, G. & Jochmans, K. (2007) An adjusted profile likelihood for non-stationary panel data models with incidental parameters. Mimeo, K.U. Leuven, Department of Economics.Google Scholar
Dhaene, G. & Jochmans, K. (2015) Split-panel jackknife estimation of fixed-effect models. Review of Economic Studies. doi:10.1093/restud/rdv007.Google Scholar
DiCiccio, T.J., Martin, M.A., Stern, S.E., & Young, A. (1996) Information bias and adjusted profile likelihoods. Journal of the Royal Statistical Society, Series B 58, 189–203.Google Scholar
Gagliardini, P. & Gouriéroux, C. (2014) Efficiency in large dynamic panel models with common factors. Econometric Theory 30, 961–1020.Google Scholar
Godambe, V.P. & Thompson, M.E. (1974) Estimating equations in the presence of a nuisance parameter. Annals of Statistics 2, 568–571.Google Scholar
Hahn, J. & Kuersteiner, G. (2002) Asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and T are large. Econometrica 70, 1639–1657.Google Scholar
Hahn, J. & Kuersteiner, G. (2011) Bias reduction for dynamic nonlinear panel models with fixed effects. Econometric Theory 27, 1152–1191.Google Scholar
Hahn, J. & Newey, W.K. (2004) Jackknife and analytical bias reduction for nonlinear panel models. Econometrica 72, 1295–1319.CrossRefGoogle Scholar
Juodis, A. (2012) On the relative merits of bias correction methods in panel var models. MPhil Thesis, Tinbergen Institute.Google Scholar
Kalbfleish, J.P. & Sprott, D.A. (1970) Application of likelihood methods to models involving large numbers of parameters (with discussion). Journal of the Royal Statistical Society, Series B 32, 175–208.Google Scholar
Kent, J.T. (1982) Robust properties of likelihood ratio tests. Biometrika 69, 19–27.Google Scholar
Kiviet, J.F. (1995) On bias, inconsistency, and efficiency of various estimators in dynamic panel data models. Journal of Econometrics 68, 53–78.Google Scholar
Kruiniger, H. (2014) A further look at modified ML estimation of the panel AR (1) model with fixed effects and arbitrary initial conditions. Available at SSRN: http://ssrn.com/abstract=2559784.Google Scholar
Lancaster, T. (2002) Orthogonal parameters and panel data. Review of Economic Studies 69, 647–666.CrossRefGoogle Scholar
Li, H., Lindsay, B., & Waterman, R. (2003) Efficiency of projected score methods in rectangular array asymptotics. Journal of the Royal Statistical Society, Series B 65, 191–208.Google Scholar
McCullagh, P. & Tibshirani, R. (1990) A simple method for the adjustment of profile likelihoods. Journal of the Royal Statistical Society, Series B 52, 325–344.Google Scholar
Neyman, J. & Scott, E.L. (1948) Consistent estimates based on partially consistent observations. Econometrica 16, 1–32.Google Scholar
Nickell, S. (1981) Biases in dynamic models with fixed effects. Econometrica 49, 1417–1426.CrossRefGoogle Scholar
Pace, L. & Salvan, A. (2006) Adjustments of profile likelihood from a new perspective. Journal of Statistical Planning and Inference 136, 3554–3564.Google Scholar
Rotnitzky, A., Cox, D.R., Bottai, M., & Robins, J. (2000) Likelihood-based inference with singular information matrix. Bernoulli 6, 243–284.Google Scholar
Sargan, J. (1983) Identification and lack of identification. Econometrica 51, 1605–1633.Google Scholar
Sartori, N. (2003) Modified profile likelihood in models with stratum nuisance parameters. Biometrika 90, 533–549.Google Scholar
Severini, T.A. (1998) An approximation to the modified profile likelihood function. Biometrika 85, 403–411.CrossRefGoogle Scholar
Severini, T.A. (2000) Likelihood Methods in Statistics. Oxford University Press.CrossRefGoogle Scholar
Sweeting, T.J. (1987) Discussion of the paper by Professors Cox and Reid. Journal of the Royal Statistical Society, Series B 49, 20–21.Google Scholar
Vuong, Q.H. (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57, 307–333.Google Scholar
White, H. (1982) Maximum-likelihood estimation of misspecified models. Econometrica 50, 1–25.Google Scholar
Woutersen, T. (2002) Robustness against incidental parameters. Working Paper 2002_8, University of Westerm Ontario, Department of Economics.Google Scholar
Woutersen, T. & Voia, M. (2004) Efficient estimation of the dynamic linear model with fixed effects and regressors. Working Paper 2002_10, University of Westerm Ontario, Department of Economics.Google Scholar
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