Advanced Econometrics Takeshi Amemiya

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

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

d2S = (Z'1PZ1)-1Z'1Pyl,

where P = X(X'X)-1X.