Bayesian Heteroskedasticity-Robust Standard Errors

Use of heteroskedasticity-robust standard errors has become common in frequentist regressions. I offer here a Bayesian analog. The Bayesian version is derived by first focusing on the likelihood function for the sample values of the identifying moment conditions of least squares and then formulating a convenient prior for the variances of the error terms. The first step introduces a sandwich estimator into the posterior calculations, while the second step allows the investigator to set the sandwich for either heteroskedastic or homoskedastic error variances. If desired, the Bayesian estimator can be made to look very similar to the usual heteroskedasticity-robust frequentist estimator. Bayesian estimation is easily accomplished by a standard MCMC procedure.