Asymptotic Expansions of the Distributions of Estimators in a Linear Functional Relationship and Simultaneous Equations

Abstract

We derive asymptotic expansions of the distributions of the maximum likelihood (ML) estimator and the ordinary least squares (OLS) estimator in a linear functional relationship model as the sample size increases infinitely. These expansions are equivalent to the asymptotic expansions of the distributions of the limited information maximum likelihood (LIML) estimator when the covariance is known to within a proportionality constant and the two-stage least squares (TSLS) estimator as the number of excluded exogenous variables increases in a simultaneous equations system.

Key Words:

• Linear functional relationship
• Maximum likelihood
• Least squares
• Asymptotic expansion
• Simultaneous equations
• Large econometric model