An Asymptotic Expansion of the Distribution of the Limited Information Maximum Likelihood Estimate of a Coefficient in a Simultaneous Equation System

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.

[1]  R. Mariano,et al.  The Exact Finite-Sample Distribution of the Limited-Information Maximum Likelihood Estimator in the Case of Two Included Endogenous Variables , 1972 .

[2]  Takamitsu Sawa,et al.  DISTRIBUTIONS OF ESTIMATES OF COEFFICIENTS OF A SINGLE EQUATION IN A SIMULTANEOUS SYSTEM AND THEIR , 1973 .

[3]  J. Kadane.  Comparison of k-Class Estimators When the Disturbances Are Small , 1971 .

[4]  T. W. Anderson,et al.  An Introduction to Multivariate Statistical Analysis , 1959 .

[5]  A. L. Nagar.  The Bias and Moment Matrix of the General k-Class Estimators of the Parameters in Simultaneous Equations , 1959 .

[6]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis , 1959 .

[7]  Roberto S. Mariano,et al.  Approximations to the Distribution Functions of the Ordinary Least-Squares and Two-Stage Least-Squares Estimators in the Case of Two Included Endogenous Variables , 1973 .

[8]  J. Sargan,et al.  A General Approximation to the Distribution of Instrumental Variables Estimates , 1971 .

[9]  R. L. Basmann.  A GENERALIZED CLASSICAL METHOD OF LINEAR ESTIMATION OF COEFFICIENTS IN A STRUCTURAL EQUATION , 1957 .

[10]  H. Theil,et al.  Economic Forecasts and Policy. , 1959 .

[11]  H. Chernoff.  A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[12]  T. W. Anderson,et al.  Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations , 1949 .

[13]  T. W. Anderson,et al.  The Asymptotic Properties of Estimates of the Parameters of a Single Equation in a Complete System of Stochastic Equations , 1950 .

[14]  Takamitsu Sawa,et al.  The Exact Sampling Distribution of Ordinary Least Squares and Two-Stage Least Squares Estimators , 1969 .

[15]  D. H. Richardson,et al.  The Exact Distribution of a Structural Coefficient Estimator , 1968 .