## Exact Distributions of the Limited Information Maximum Likelihood Estimator and the Two-Stage Least Squares Estimator

The exact finite sample distributions of the two estimators differ. We shall discuss briefly the main results about these distributions as well as their approximations. The discussion is very brief because there are several excellent survey articles on this topic by Mariano (1982), Anderson (1982), Taylor (1982), and Phillips (1983).

In the early years (say, until the 1960s) most of the results were obtained by Monte Carlo studies; a summary of these results has been given by Johnston (1972). The conclusions of these Monte Carlo studies concerning the choice between LIML and 2SLS were inconclusive, although they gave a slight edge to 2SLS in terms of the mean squared error or similar moment criteria...

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