# Econometrica

## Journal Of The Econometric Society

### An International Society for the Advancement of Economic Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 1977, Volume 45, Issue 2

# Asymptotic Expansions of the Distributions of Estimates in Simultaneous Equations for Alternative Parameter Sequences

T. W. Anderson

The distributions of the LIML and TSLS estimates of the coefficient of an endogenous variable in a single equation can be approximated by asymptotic expansions. This paper relates the expansions in terms of the noncentrality parameter and the sample size going to infinity, the noncentrality parameter going to infinity with the sample size held fixed, and the standard deviation of the disturbance going to zero ("small-$\sigma$'s").