Comparative performance of the limited information techniques in a two equation structural model

Abstract

The samples with which we deal in practice are rather small. seldom exceeding 80 observations and frequently much smaller. 'Thus, it is of great interest to inquire into the properties of estimators for the typical sample sizes encountered in practice. The performances of three simultaneous estimation method using a model consisting of a mixture of an identified and over identified equations with correlated error terms and compared. The result of the Monte Carlo study revealed that the Two Stage least Squares (2SLS) and the Limited Information Maximum Likelihood (LIML) estimates are similar and in most cases identical in respect of the just-identified equation. The Total Absolute Biases (TAB) of 2SLS and LIML revealed asymptotic behavior under (upper triangular matrix) P1 while those of Ordinary Least Squares (OLS) exhibited no such behavior. For both upper and lower triangular matrices (P, and P2), 2SI.S estimates showed asymptotic behavior in the middle interval. The OI.S is the only stable estimator with a stable behavior of Root Mean Square Error (RM3F.) as its estimates increase (decrease) consistently for equation 1(equation 2) for P, (for P2).