This paper considers the finite-sample distribution of the 2SLS estimator and derives bounds on its exact bias in the presence of weak and/or many instruments. We then contrast the behavior of the exact bias expressions and the asymptotic expansions currently popular in the literature, including a consideration of the no-moment problem exhibited by many Nagar-type estimators. After deriving a finite-sample unbiased k-class estimator, we introduce a double-k-class estimator based on Nagar (1962) that dominates k-class estimators (including 2SLS), especially in the cases of weak and/or many instruments. We demonstrate these properties in Monte Carlo simulations showing that our preferred estimators outperform Fuller (1977) estimators in terms of mean bias and MSE.
We are grateful to Tim Armstrong for providing excellent research assistance. Thanks to Plamen Koev for sharing his code for the computation of hypergeometric functions.
Harding, M., Hausman, J. and Palmer, C.J. (2016), "Finite Sample BIAS Corrected IV Estimation for Weak and Many Instruments", Essays in Honor of Aman Ullah (Advances in Econometrics, Vol. 36), Emerald Group Publishing Limited, Leeds, pp. 245-273. https://doi.org/10.1108/S0731-905320160000036016
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