Alternative Approximations to the Distributions of Instrumental Variable Estimators

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    Abstract

    The paper considers the OLS, the IV, and two method-of-moments estimators, MM and MMK, of the coefficients of a single equation, where the explanatory variables are correlated with the disturbance term. The MM and MMK estimators are generalizations of the LIML and LIMLK estimators, respectively.

    Multivariate first-order approximations to the distributions are derived under normality, using a parameter sequence where the number of instruments increases as the number of observations increases. Numerical results show these approximations are more accurate, compared to large-sample approximations, even if the number of instruments is small.

    The moments of the multivariate limit distributions of the MM and MMK estimators can be consistently estimated under a variety of parameter sequences, including the large-sample sequence. The new approximate confidence regions perform well in terms of exact levels, compared to traditional ones.

    The IV estimator of the coefficient of a single explanatory endogenous variable is interpreted as a shrinkage estimator, which is dominated, in practical cases, by the MM and MMK estimators in terms of nearness to the true value in the sense of Pitman.

    Original languageEnglish
    Pages (from-to)657-681
    Number of pages25
    JournalEconometrica
    Volume62
    Issue number3
    DOIs
    Publication statusPublished - May-1994

    Keywords

    • INSTRUMENTAL VARIABLES
    • METHOD OF MOMENTS
    • LIMITED INFORMATION MAXIMUM LIKELIHOOD
    • ASYMPTOTIC DISTRIBUTIONS
    • PARAMETER SEQUENCE
    • SHRINKAGE ESTIMATOR
    • PITMAN NEARNESS
    • MONTE-CARLO EXPERIMENTS
    • SIMULTANEOUS EQUATION SYSTEM
    • ASYMPTOTIC EXPANSIONS
    • ECONOMETRICS
    • LIML

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