Alternative Approximations to the Distributions of Instrumental Variable Estimators

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    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.

    Originele taal-2English
    Pagina's (van-tot)657-681
    Aantal pagina's25
    Nummer van het tijdschrift3
    StatusPublished - mei-1994

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