Alternative Approximations to the Distributions of Instrumental Variable Estimators

Paul A Bekker

Econometrica, 1994, vol. 62, issue 3, 657-81

Abstract: This paper considers the instrument variable and method-of-moments estimators, as generalizations of two-stage least squares and limited information maximum likelihood, of the coefficients of a single equation. Motivated by a simple principle, asymptotic distributions are derived based on a parameter sequence where both the number of instruments and the sample size increase. The approximations to the distributions provided by this sequence are more accurate than traditional ones. The instrument variable estimator appears to be inconsistent. The asymptotic covariance matrix of the method-of-moments estimator can be consistently estimated under the alternative parameter sequence. The resulting approximate confidence regions have exact levels very close to their nominal levels. Copyright 1994 by The Econometric Society.

Date: 1994
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