Unbiased Instrumental Variables Estimation Under Known First-Stage Sign

TL;DR

This paper develops mean-unbiased estimators for instrumental variables models with known first-stage sign, improving estimation accuracy especially with a single instrument, and provides finite-sample and asymptotic results.

Contribution

It introduces a class of unbiased estimators for IV models with known first-stage sign, including a unique unbiased estimator for single instrument cases and an efficient class for multiple instruments.

Findings

Unbiased estimator is less dispersed than 2SLS in single instrument models.

A unique non-randomized unbiased estimator exists for single instrument models.

Proposed estimators are efficient with strong instruments.

Abstract

We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, there is a unique non-randomized unbiased estimator based on the reduced-form and first-stage regression estimates. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the 2SLS estimator. Our finite-sample results apply to normal models with known variance for the reduced-form errors, and imply analogous results under weak instrument asymptotics with an unknown error distribution.