New Bayesian method improves IV regressions with weak instruments

Standard statistical methods often fail in instrumental variable (IV) regressions with weak instruments, producing misleading results. This paper introduces a novel Bayesian inference approach that ensures robust and accurate causal effect estimation by re-evaluating the treatment of instrument strength uncertainty.

The concentration parameter's role

Standard frequentist and traditional Bayesian inference methods break down in instrumental variable (IV) regressions when instruments are weak.

The core issue, from a Bayesian perspective, is that diffuse priors on first-stage coefficients inadvertently overstate instrument strength.

This leads to overly confident and systematically distorted inference, even when data provide little information about the causal effect.

The authors propose a novel approach: specifying an uninformative prior directly on the concentration parameter, which is the key nuisance parameter capturing instrument relevance.

This new prior avoids favoring strong instruments by default, effectively shrinking unreliable first-stage relationships towards zero and preventing overfitting.

The resulting Bayesian credible intervals are robust to weak instruments and asymptotically equivalent to leading frequentist confidence intervals based on conditioning approaches.

A historical challenge revisited

The challenge of weak instruments in IV regressions has been well-documented since early simulation evidence by Nelson and Startz (1990) and Bound et al. (1995), which highlighted biased estimators and invalid inference.

Staiger and Stock (1997) formally defined weak instruments and introduced the first-stage F-statistic as a diagnostic, setting a standard for assessing instrument strength.

While much research has focused on developing tests for weak instruments, this paper contributes to the line of studies proposing inference procedures that remain valid under weak identification.

It builds upon and offers a robust Bayesian alternative to frequentist methods like the Conditional Likelihood Ratio test of Moreira (2003), which also aims to provide valid inference regardless of instrument strength.

Restoring Bayesian-classical alignment

This study offers a significant methodological advancement for a pervasive econometric problem.

By aligning Bayesian and frequentist robustness, it provides empirical researchers with a more reliable tool for causal inference.

Its practical implications are substantial, particularly for fields where instrument validity is often tenuous.