Payday loans are small short-term loans that a borrower must repay or renew on his/her next payday. In states where payday lending is legal, many terms of these loans are regulated, ostensibly to protect the consumer from excessively burdensome lending practices.

We consider the problem of causal effect heterogeneity from a Bayesian point of view. This is accomplished by introducing a three-equation system, similar in spirit to the work of Heckman and Vytlacil (1998), describing the joint determination of a scalar outcome, an endogenous "treatment"...