Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jul, 1984, Volume 52, Issue 4

Approximate Normality of Generalized Least Squares Estimates<811:ANOGLS>2.0.CO;2-C
p. 811-825

Thomas J. Rothenberg

When the error covariance matrix in a linear model depends on a few unknown parameters, the regression coefficients can be estimated by a two-step procedure. Consistent estimates of the covariance parameters are first obtained and then used in a generalized least squares regression. Under the assumption that the errors are normal and the covariance parameter estimates are well behaved, an asymptotic expansion is developed for the distribution function of the two-step GLS estimate. the error in treating the estimate as normal is found to be of order n^-^2 as the sample size n tends to infinity.

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