An Asymptotic Expansion of the Distribution of the Limited Information Maximum Likelihood Estimate of a Coefficient in a Simultaneous Equation System
- 1 June 1974
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 69 (346) , 565
- https://doi.org/10.2307/2285698
Abstract
An asymptotic expansion is made of the distribution of the limited information maximum likelihood estimate of the coefficient of one endogenous variable in an equation with two endogenous variables when the coefficient of the other endogenous variable is prescribed to be unity. The equation is one of a system of simultaneous equations, and all the predetermined variables in the system are assumed to be exogenous. The expansion in terms of the noncentrality parameter, which increases with the sample size, is carried out to the order of the negative power of the noncentrality parameter (i.e., four terms). Comparison is made with the expansion of the distribution of the two-stage least squares estimate.Keywords
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