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Decision Theory Applied to a Linear Panel Data Model

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  • Gary Chamberlain
  • Marcelo J. Moreira

Abstract

This paper applies some general concepts in decision theory to a linear panel data model. A simple version of the model is an autoregression with a separate intercept for each unit in the cross section, with errors that are independent and identically distributed with a normal distribution. There is a parameter of interest Gamma and a nuisance parameter τ, a N×K matrix, where N is the cross-section sample size. The focus is on dealing with the incidental parameters problem created by a potentially high-dimension nuisance parameter. We adopt a "fixed-effects" approach that seeks to protect against any sequence of incidental parameters. We transform tau to (delta, rho, omega), where delta is a J x K matrix of coefficients from the least-squares projection of tau on a N x J matrix x of strictly exogenous variables, rho is a K x K symmetric, positive semidefinite matrix obtained from the residual sums of squares and cross-products in the projection of tau on x, and omega is a (N - J) x K matrix whose columns are orthogonal and have unit length. The model is invariant under the actions of a group on the sample space and the parameter space, and we find a maximal invariant statistic. The distribution of the maximal invariant statistic does not depend upon omega. There is a unique invariant distribution for omega. We use this invariant distribution as a prior distribution to obtain an integrated likelihood function. It depends upon the observation only through the maximal invariant statistic. We use the maximal invariant statistic to construct a marginal likelihood function, so we can eliminate omega by integration with respect to the invariant prior distribution or by working with the marginal likelihood function. The two approaches coincide. Copyright 2009 The Econometric Society.

Suggested Citation

  • Gary Chamberlain & Marcelo J. Moreira, 2009. "Decision Theory Applied to a Linear Panel Data Model," Econometrica, Econometric Society, vol. 77(1), pages 107-133, January.
  • Handle: RePEc:ecm:emetrp:v:77:y:2009:i:1:p:107-133
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    File URL: http://hdl.handle.net/10.3982/ECTA6869
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    Cited by:

    1. Bai, Jushan, 2013. "Likelihood approach to dynamic panel models with interactive effects," MPRA Paper 50267, University Library of Munich, Germany.
    2. Geert Dhaene & Koen Jochmans, 2011. "An Adjusted profile likelihood for non-stationary panel data models with fixed effects," Sciences Po publications info:hdl:2441/eu4vqp9ompq, Sciences Po.
    3. Jann Spiess, 2017. "Unbiased Shrinkage Estimation," Papers 1708.06436, arXiv.org, revised Oct 2017.
    4. Marc Hallin & Marcelo Moreira J. & Alexei Onatski, 2013. "Group Invariance, Likelihood Ratio Tests, and the Incidental Parameter Problem in a High-Dimensional Linear Model," Working Papers ECARES ECARES 2013-04, ULB -- Universite Libre de Bruxelles.
    5. repec:eee:econom:v:204:y:2018:i:1:p:86-100 is not listed on IDEAS
    6. Marcelo Moreira, 2008. "A Maximum Likelihood Method for the Incidental Parameter Problem," NBER Working Papers 13787, National Bureau of Economic Research, Inc.
    7. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09ij4oge90i is not listed on IDEAS
    8. Kociecki, Andrzej, 2012. "Orbital Priors for Time-Series Models," MPRA Paper 42804, University Library of Munich, Germany.

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