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An Adjusted profile likelihood for non-stationary panel data models with fixed effects

  • Geert Dhaene

    (KU Leuven)

  • Koen Jochmans

We calculate the bias of the profile score for the autoregressive parameters p and covariate slopes in the linear model for N x T panel data with p lags of the dependent variable, exogenous covariates, fixed effects, and unrestricted initial observations. The bias is a vector of multivariate polynomials in p with coefficients that depend only on T. We center the profile score and, on integration, obtain an adjusted profile likelihood. When p = 1, the adjusted profile likelihood coincides with Lancaster's (2002) marginal posterior. More generally, it is an integrated likelihood, in the sense of Arellano and Bonhomme (2009), with fixed effects integrated out using a new data-independent prior. It appears that p and B are identified as the unique point where the large N adjusted profile likelihood reaches a local maximum (or a at inection point, as a limiting case) inside or on an ellipsoid centered at the maximum likelihood estimator. We prove this when p = 1 and report numerical calculations that support it when p > 1. The global maximum of the adjusted profile likelihood lies at infinity for any N.

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Date of creation: 22 Mar 2011
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Handle: RePEc:spo:wpmain:info:hdl:2441/eu4vqp9ompqllr09ij4oge90i
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  1. Kruiniger, Hugo, 2008. "Maximum likelihood estimation and inference methods for the covariance stationary panel AR(1)/unit root model," Journal of Econometrics, Elsevier, vol. 144(2), pages 447-464, June.
  2. Nerlove, Marc, 1971. "Further Evidence on the Estimation of Dynamic Economic Relations from a Time Series of Cross Sections," Econometrica, Econometric Society, vol. 39(2), pages 359-82, March.
  3. Phillips, Peter C.B. & Sul, Donggyu, 2007. "Bias in dynamic panel estimation with fixed effects, incidental trends and cross section dependence," Journal of Econometrics, Elsevier, vol. 137(1), pages 162-188, March.
  4. Lancaster, Tony, 2002. "Orthogonal Parameters and Panel Data," Review of Economic Studies, Wiley Blackwell, vol. 69(3), pages 647-66, July.
  5. Ahn, Seung C. & Schmidt, Peter, 1995. "Efficient estimation of models for dynamic panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 5-27, July.
  6. Bun M.J.G. & Carree M.A., 2002. "Bias-corrected estimation in dynamic panel data models," Research Memorandum 025, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  7. Javier Alvarez & Manuel Arellano, 2004. "Robust Likelihood Estimation Of Dynamic Panel Data Models," Working Papers wp2004_0421, CEMFI.
  8. Manuel Arellano & Stephane Bonhomme, 2006. "Robust Priors In Nonlinear Panel Data Models," Working Papers wp2006_0614, CEMFI.
  9. Tony Lancaster, 2002. "Orthogonal Parameters and Panel Data," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 647-666.
  10. Gary Chamberlain & Marcelo J. Moreira, 2009. "Decision Theory Applied to a Linear Panel Data Model," Econometrica, Econometric Society, vol. 77(1), pages 107-133, 01.
  11. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-26, November.
  12. Kiviet, Jan F., 1995. "On bias, inconsistency, and efficiency of various estimators in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 68(1), pages 53-78, July.
  13. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-33, November.
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