Econometrica: Mar, 1978, Volume 46, Issue 2

Constrained Indirect Least Squares Estimators

https://doi.org/0012-9682(197803)46:2<435:CILSE>2.0.CO;2-N
p. 435-449

Leon L. Wegge

An over-identified model could be defined as an exactly identified model that issubject to over-identifying restrictions. One could therefore define a constrained indirect least squares estimator for systems of equations similar togeneralized least squares estimators under constraints for single equations. The estimator differs from three stage least squares in using the indirect leastsquares estimated covariance instead of the two stage least squares estimated covariance. With linear constraints, the estimator is linear. Under the overall null hypothesis with all constraints obtaining, the constrained indirect least squares estimator has the same asymptotic properties as the full information maximum likelihood estimator. The main advantage of the estimator lies in its easy adaptability to the multiple comparisonist's preferred testing procedure given the exactly identified model as maintained hypothesis. In this paper we stay with the likelihood principle and the corresponding preliminary Wald-type multiple xg^2 tests.