Abstract
Recently LIML and 2SLS estimators have been derived under constraints on the reduced-form covariance matrix. However, the LIML estimator has not been derived under linear constraints on the structural coefficients. In this paper the LIML estimator is derived under general linear constraints and the efficiency of the derived estimator is compared with existing estimators. Likelihood ratio, Lagrange multiplier, Wald and Hausman test statistics are derived for testing the adequacy of the linear constraints. 2SLS versions of estimation and testing follow naturally and the same 2SLS test statistics are derived using the auxiliary regression approach. A similar technique is applied to full information estimation and testing.
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