We develop the panel limited information maximum likelihood (PLIML)
approach for estimating dynamic panel structural equation models. When
there are dynamic effects and endogenous variables with individual effects
at the same time, the PLIML estimation method for the filtered data does
give not only a consistent estimator, but also it has the asymptotic normality
and often attains the asymptotic bound when the number of orthogonal
conditions is large. Our formulation includes Alvarez and Arellano (2003),
Blundell and Bond (2000) and other linear dynamic panel models as special
cases. We also compare the PLIML and dynamic GMM (generalized
method of moments) estimation methods and suggest an asymptotically
optimal modification of LIML under heteroscedastic disturbances among
individuals.
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