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

“…While the 2SLS estimator performs better in the just-identified case according to some measures of central tendency, in this case it has no first moment. 1 A number of papers have proposed alternative estimators to reduce particular measures of bias, for example, Angrist and Krueger (1995), Imbens, Angrist, and Krueger (1999), Donald and Newey (2001), Ackerberg and Devereux (2009), and Harding, Hausman, and Palmer (2015), but none of the resulting feasible estimators is unbiased either in finite samples or under weak instrument asymptotics. Indeed, Hirano and 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.…”

A Note on the Topology of the First Stage of 2SLS with Many Instruments

“…Indeed, in the its application of this asymptotic framework to the case of many weak instruments or sparse set of instrumental variables. This may explain the poor behavior of the many IVs asymptotic approaches noted by Harding, Hausman, and Palmer (2016).…”

“…In addition, the compactness assumption does not hold for orthonormal IVs. In conclusion, the drawbacks associated with these two asymptotic constructions suggests that finite sample distributional investigation may be better for many IVs, consistent with Harding, Hausman, and Palmer (2016) and Bun and Windmeijer (2011).…”

“…Therefore, it is Likely that these asymptotic estimators may not 3 Q is the limit in probability of a quantity, and the probability used in that limit calculation is different from that induced by the random variables used in the calculation of π ′ K. M K π K. . be very good approximation of finite sample behavior of the 2SLS estimator, as pointed out by Harding, Hausman, and Palmer (2016), who use a finite sample approximation as a solution to the many IVs problem. However, alternative asymptotic estimators could be helpful for inference in large samples.…”

Unbiased Instrumental Variables Estimation under Known First-Stage Sign

“…1 A number of papers have proposed alternative estimators to reduce particular measures of bias, e.g. Angrist & Krueger (1995), Imbens et al (1999), Donald & Newey (2001), Ackerberg & Devereux (2009), and Harding 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.…”