Finite sample bias corrected IV estimation for weak and many instruments

Abstract

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 outperforms Fuller (1977) estimators in terms of mean bias and MSE.JEL: C31, C13, C15

Unbiased Instrumental Variables Estimation Under Known First-Stage Sign

“…Angrist & Krueger (1995), Imbens et al (1999), Donald & Newey (2001), Ackerberg &Devereux (2009), andHarding et al (2015), but none of the resulting feasible estimators is unbiased either in finite samples or under weak instrument asymptotics. Indeed, Hirano & Porter (2015) show that mean, median, and quantile unbiased estimation are all impossible in the linear IV model with an unrestricted parameter space for the first stage.…”