Simultaneous equation estimation with first order auto correlated disturbances

Abstract

The estimation of the parameters of simultaneous equation problem is usually affected by the existence of mutual correlation between pairs of random deviates, which is a violation of the assumption of no autocorrelation between the error terms. In practice the form of correlation between the pairs of random deviates is not known. This study therefore examined a two-equation model in which the correlation between the random deviates is assumed to follow a first-order Autoregressive [AR (1)] process. Data was simulated using Monte Carlo approach with varying sample sizes each replicated 1000 times. The behaviour of OLS, 2SLS, LIML and 3SLS were evaluated using Variance, Root Mean Square Error (RMSE) and Absolute Bias (AB). The absolute bias estimates decrease in most cases as the sample size increases. The variances obtained by all the estimators reduced consistently as the sample size increases. There was no clear pattern in the behaviour of the RMSE across sample sizes. The results for = 0.3 were better than when = 0.0 with respect to each criterion but retained the same pattern. This work established that when was different from zero, the estimators performed better, hence the choice of should be carefully made as this may significantly affect the performances of the estimators