Demand Analysis under Latent Choice Constraints

Consumer choices are constrained in many markets due to either supply-side rationing or information frictions. Examples include matching markets for schools and colleges; entry-level labor markets; limited brand awareness and inattention in consumer markets; and selective admissions to healthcare services. We analyze a general random utility model for consumer preferences that allows for endogenous characteristics and a reduced-form choice-set formation rule that can be derived from models of the examples described above. We show non-parametric identification of this model, propose an estimator, and apply these methods to study admissions in the market for kidney dialysis in California. Our identification results require two sets of instruments, one that only affects consumer preferences and the other that only affects choice sets. We show that both instruments are necessary for identification. These results also suggest tests of choice-set constraints, which we apply to the dialysis market. We find that dialysis facilities are less likely to admit new patients when they have a higher-than-normal caseload and that patients are more likely to travel further when nearby facilities have high caseloads. Finally, we estimate consumers’ preferences and facilities’ rationing rules using a Gibbs sampler.