Shrinkage priors for linear instrumental variable models with many instruments

Abstract: This paper addresses the weak instruments problem in linear instrumental variable models from a Bayesian perspective. The new approach has two components. First, a novel predictor-dependent shrinkage prior is developed for the many instruments setting. The prior is constructed based on a factor model decomposition of the matrix of observed instruments, allowing many instruments to be incorporated into the analysis in a robust way. Second, the new prior is implemented via an importance sampling scheme, which utilizes posterior Monte Carlo samples from a first-stage Bayesian regression analysis. This modular computation makes sensitivity analyses straightforward. Two simulation studies are provided to demonstrate the advantages of the new method. As an empirical illustration, the new method is used to estimate a key parameter in macro-economic models: the elasticity of inter-temporal substitution. The empirical analysis produces substantive conclusions in line with previous studies, but certain inconsistencies of earlier analyses are resolved.