Attenuation bias vs selection bias: a multi-outcome three-stage model

We propose a Bayesian inferential framework for a multi-outcome endogenous three-stage model that accounts for incidental truncation in outcomes (intensive margin), selection into participation (extensive margin), and access restrictions. Simulation exercises assessing finite-sample properties under various misspecification settings suggest that incorporating access restrictions and unobserved correlations is crucial. In particular, access restrictions play a critical role, as failing to account for them may introduce measurement error when correcting for selection bias. This suggests a potential tension between attenuation and selection biases. We apply our framework to two novel datasets on credit and utility demand. We extend our parametric specification to a semi-parametric one in the latter application, modeling stochastic errors using a Dirichlet process mixture. The credit demand application suggests that better socioeconomic conditions increase the probability of using credit cards but decrease the likelihood of taking bank loans. In addition, women are more likely to use credit than men, but men tend to borrow larger amounts. The utility application highlights the importance of urban areas in increasing the probability of access to piped utilities, water and gas are inelastic goods, whereas electricity is elastic.