Performances Of The Full Information Estimators In A Two-Equation Structural Model With Correlated Disturbances

Aa Adepoju

doi:10.4314/gjpas.v15i1.44903

Abstract

The performances of two full information techniques, Three Stage Least Squares (3SLS) and Full Information Maximum Likelihood (FIML) of simultaneous equation models with correlated disturbance terms are compared with the Ordinary Least Squares (OLS) method in small samples. Comparative performance evaluation of the estimators was done using Average of Estimates, Total Absolute Bias (TAB) of Estimates, Root Mean Squared Error (RMSE) and Sum of Squared Residuals (RSS) of parameter estimates. The results of the Monte Carlo experiment showed that OLS is best with large negative or positive correlation, while 3SLS is best with feebly correlated error terms in the case of replication-based averages. The total absolute biases increase consistently as the sample size increases for OLSwhile FIML estimates reveal no distinct pattern. The magnitudes of the estimates yielded by two estimators, OLS and 3SLS, exhibited fairly consistent reaction to changes in magnitudes and direction of correlations of error terms.

Highlights

The single equation estimation methods lead to estimates that are consistent but, in general, not asymptotically efficient
While asymptotic properties of estimators obtained by using various econometric methods are deductive in character, an approach which is often described as analytical, small sample properties of such estimators have always been studied from simulated data referred to as the Monte Carlo studies which is inductive in nature Nwabueze[6] (2005)
2.0 CONCLUSION The magnitudes of the estimates yielded by two estimators, Ordinary Least Squares (OLS) and 3SLS exhibited fairly consistent reaction to changes in magnitudes and direction of correlations of error terms

Summary

INTRODUCTION

The single equation estimation methods lead to estimates that are consistent but, in general, not asymptotically efficient. Where there exists no prior information on the variancecovariance matrix of the structural disturbances, Σ (for example, no covariance restrictions of the formσ ij = 0 ), the 3SLS and FIML estimators, though numerically distinct in small samples, have the same asymptotic distribution (Schmidt[8] (1976)). It follows that 3SLS, is asymptotically efficient in the presence of normally distributed errors.

Using the upper triangular matrix

3SLS FIML