Since the invention of instrumental variable regression in 1928, its analysis has been predominately frequentist. In this talk we will explore whether Bayes or empirical Bayes may be more appropriate for this purpose. We will start with Mendelian randomization—-the usage of genetic variation as the instrument variable, and demonstrate how an empirical partially Bayes approach proposed by Lindsay (1985) is incredibly useful when there are many weak instruments. Selective shrinkage of the instrument strength estimates is crucial to improve the statistical efficiency. In a real application to estimate the causal effect of HDL cholesterol on heart disease, we find that the classical model with a homogeneous causal effect is not realistic. I will demonstrate evidence of this mechanistic heterogeneity and propose a Bayesian model/shrinkage prior to capture the heterogeneity. To conclude the talk, several other advantages of using (empirical) Bayes in instrumental variable regression will be discussed.