Prosper Dovonon

This paper introduces a semiparametric Bayesian method for high-dimensional linear instrumental variables (IV) models. More specifically, we develop a quasi-Bayesian framework for variable selection in high-dimensional settings with endogenous regressors, where instrumental variables are available to address endogeneity. We study the properties of the quasi-posterior distribution as the number of regressors increases and provide a set of conditions under which the quasi-posterior concentrates asymptotically around the true parameter value. We also propose an efficient and easy-to-implement Markov chain Monte Carlo (MCMC) algorithm for sampling from the quasi-posterior distribution. The finite-sample performance of the proposed method is evaluated through Monte Carlo experiments.