Asymptotic expansions of the distributions of the structural variance estimators in a simultaneous equations system

Asymptotic expansions of three alternative classes of structural variance estimators associated with the k-class estimators of structural coefficients are derived for two parameter sequences: a sequence in which the non-centrality parameter increases while the sample size stays fixed (called large-μ or small-disturbance sequence), and that in which the number of observations increases. The accuracy of approximations to small-sample distributions are numerically examined with help of Monte Carlo studies. Properties of the sum of squared residuals of an estimated structural equation are also found from our study.