Econometrica Vol. 41 No. 4 1973
Distributions of Estimates of Coefficients of a Single Equation in a Simultaneous System and Their Asymptotic Expansions
Abstract
[The limited information maximum likelihood and two-stage least squares estimates have the same asymptotic normal distribution; the ordinary least squares estimate has another asymptotic normal distribution. This paper considers more accurate approximations to the distributions of the so-called "k-class" estimates. An asymptotic expansion of the distribution of such an estimate is given in terms of an Edgeworth or Gram-Charlier series (of which the leading term is the normal distribution). The development also permits expression of the exact distribution in several forms. The distributions of the two-stage least squares and ordinary least squares estimates are transformed to doubly-noncentral F distributions. Numerical comparisons are made between the approximate distributions and exact distributions calculated by the second author.]
- DOI
- 10.2307/1914090
- Volume
- 41
- Issue
- 4
- Pages
- 683
- Sources
- bibtex:phds-export.bib openalex crossref