When an econometric structural equation includes two endogenous variables and
their coefficients are normalized so that their sum of squares is 1, it is natural to
express them as the sine and cosine of an angle. The Limited Information Maximum
Likelihood (LIML) estimator of this angle when the error covariance matrix is known
has constant variance. Of all estimators with constant variance the LIML estimator
minimizes the variance. Competing estimators, such as the Two-Stage Least Squares
estimator, has much larger variance for some values of the parameter. The effect of
weak instruments is studied.
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