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• W2336937020 abstract "This paper contains the derivation of the exact finite sample distribution function of the LIML identifiability test statistic associated with an overidentified nondynamic structural equation which contains two endogenous variables. Some of the properties of the moments of this statistic are also investigated. FREQUENTLY IN THE construction of econometric models overidentifying restrictions are imposed on the parameters of the model. Identifiability test statistics have been constructed to test these hypothetical restrictions when they take the form of excluding particular exogenous variables from the structural equation under consideration.2 The asymptotic distribution functions of these statistics have been derived and are reported in Anderson and Rubin [5], Basmann [8 and 9], and Hood and Koopmans [13]. In light of Basmann's [9] experimental investigation, the accuracy of predictive statements for finite samples, based on asymptotic results, seems to be questionable in some instances. Basmann [11] has derived the exact finite sample distribution function of the generalized classical linear (two-stage least squares) identifiability test statistic for the case in which the structural equation includes two endogenous variables (Ga = 2) and exactly one overidentifying restriction. In the case where GQ = 2, Richardson [21] has derived the exact distribution function of this test statistic for any number of overidentifying restrictions. This paper contains the derivation of the limited information maximum likelihood (LIML) identifiability test statistic corresponding to a structural equation which includes two endogenous variables and hypothetically excludes two or more exogenous variables that appear in at least one of the other structural equations in the model. This derivation is found in Section 2. The derivation of expressions for the moments of the LIML identifiability test statistic is contained in Section 3. It has demonstrated that the LIML identifiability test statistic has no fewer defined integer moments than does the corresponding 2SLS identifiability test statistic, but as the concentration parameter grows indefinitely large the defined moments of these two statistics approach the same limit-the moments of a central F statistic." @default.
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• W2336937020 date "1972-01-01" @default.
• W2336937020 modified "2023-09-27" @default.
• W2336937020 title "THE EXACT FINITE SAMPLE DISTRIBUTION FUNCTION OF THE LIMITED INFORMATION MAXIMUM LIKELIHOOD" @default.
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