T. W. Anderson, Takamitsu Sawa, Distributions of Estimates of Coefficients of a Single Equation in a Simultaneous System and Their Asymptotic Expansions, Econometrica, Vol. 44, No. 6 (Nov., 1976), p. 1329

[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.]

Journal Article Two Trials to Determine Expectation Models Applicable to Agriculture Get access T. W. Schultz, T. W. Schultz Iowa State College Search for other works by this author on: Oxford Academic Google Scholar O. H. Brownlee O. H. Brownlee Iowa State College Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 56, Issue 3, May 1942, Pages 487–496, https://doi.org/10.2307/1882212 Published: 01 May 1942