Limited Information Maximum Likelihood Estimator

The LIML estimator is obtained by maximizing the joint density of y! and Y! under the normality assumption with respect to а, П, and X without any constraint. Anderson and Rubin (1949) proposed this estimator (without the particular normalization on Г we have adopted here) and obtained an explicit formula for the LIML estimator:4

Подпись: where A is the smallest characteristic root of W,W l, W =

and m, = і – x, (x; x, r1 x;.

7.3.2 Two-Stage Least Squares Estimator

The two-stage least squares (2SLS) estimator of a, proposed by Theil (1953),5 is defined by

Подпись: (7.3.4)d2S = (Z’1PZ1)-1Z’1Pyl,

where P = X(X’X)-1X.

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