European Central Bank working paper proposes concentration-parameter priors to make Bayesian IV inference robust to weak instruments

The European Central Bank published Working Paper No 3189 by Domenico Giannone, Michele Lenza and Giorgio E. Primiceri on Bayesian inference in instrumental variables (IV) regressions when instruments are weak. The paper argues that standard frequentist inference and Bayesian approaches using diffuse priors can both produce misleadingly precise results, and proposes specifying an uninformative prior directly on the concentration parameter (which captures instrument relevance) to restore robust inference. The authors show that flat priors on first-stage coefficients can unintentionally overweight strong-instrument regions of the parameter space, distorting posteriors and narrowing credible intervals even when identification is weak. They derive a prior on the first-stage coefficients that induces a flat prior on the concentration parameter (implemented via a hierarchical shrinkage specification), and report theory, simulations and an application indicating that resulting Bayesian credible intervals are conservative when instruments are irrelevant and achieve correct coverage when instruments are weak or strong, aligning closely with conditioning-based frequentist procedures such as Moreira’s Conditional Likelihood Ratio approach. In a reanalysis of Angrist and Krueger’s returns-to-schooling IV specification using 177 instruments (first-stage F-statistic 2.43), Two-Stage Least Squares and naive Bayesian estimates remain statistically significant even with artificial (random) instruments, while the proposed approach produces wider credible intervals and largely avoids false significance in the artificial-instrument exercises.