Bayesian learning in the presence of misreporting and endogeneity

<h3>Abstract</h3> We examine the role of survey misreporting in a study of the impact of SNAP participation on diet quality. Our Bayesian econometric model allows for endogenous and possibly misreported program participation. The prior distribution incorporates information about misreporting rates and selection into treatment based on recent related work in this area. In our empirical analysis of NHANES data, we do not find clear evidence for an average causal effect of SNAP participation on diet quality. Changes in prior beliefs about the degree of misreporting, however, have a substantial impact on the precision of inference.