All high level parameters are given prior distributions. The prior distributions for the regression coefficients are noninformative flat priors. The prior distributions for the other parameters are gamma priors that generally carry little information.
For both models, modeling choices, including assumptions of independence, the choice of variance forms, and the use of two variables - tax exemptions and non-filing rate - derived from tax data, have not been completely validated. Hence, we may have underestimated variances of the estimates.