Details

Autor(en) / Beteiligte

• Chamberlain, Gary
• Moreira, Marcelo J.

Titel

Decision Theory Applied to a Linear Panel Data Model

Ist Teil von

• Econometrica, 2009-01, Vol.77 (1), p.107-133

Ort / Verlag

Oxford, UK: Blackwell Publishing Ltd

Erscheinungsjahr

2009

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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 γ and a nuisance parameter τ, a N x 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 τ to (δ, ρ, ω), where δ is a J x K matrix of coefficients from the least-squares projection of τ on a N x J matrix x of strictly exogenous variables, ρ is a K x K symmetric, positive semidefinite matrix obtained from the residual sums of squares and cross-products in the projection of τ on x, and to 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 ω. There is a unique invariant distribution for ω. 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 ω by integration with respect to the invariant prior distribution or by working with the marginal likelihood function. The two approaches coincide. Decision rules based on the invariant distribution for ω have a minimax property. Given a loss function that does not depend upon ω and given a prior distribution for (γ, δ, ρ), we show how to minimize the average--with respect to the prior distribution for (γ, δ, ρ)--of the maximum risk, where the maximum is with respect to ω. There is a family of prior distributions for (δ, ρ) that leads to a simple closed form for the integrated likelihood function. This integrated likelihood function coincides with the likelihood function for a normal, correlated random-effects model. Under random sampling, the corresponding quasi maximum likelihood estimator is consistent for γ as N → ∞, with a standard limiting distribution. The limit results do not require normality or homoskedasticity (conditional on x) assumptions.