Asymmetric Information With Multiple Risks: The Case of the Chilean Private Health Insurance Market

We extend the Rothshild and Stiglitz (1976) model to two sources of risk -inpatient and outpatient risk- to better proxy real-world health insurance markets. We uncover an interesting theoretical possibility: Take individuals A and B, who are low risks in, say, the inpatient dimension but A is riskier in the outpatient dimension. Then, A may enjoy less coverage than B in the inpatient dimension (coverage reversal). This phenomenon indicates that when testing for adverse selection in a given dimension, one has to treat individuals who differ in the other dimension separately. With this insight in mind, we adapt the Chiappori and Salanié (2000) positive correlation test to this multi-dimensionality and use it to test for adverse selection using individual-level claims data for the privately insured in Chile. This empirical analysis indicates that overlooking the aforementioned need of separating samples can potentially lead to biased conclusions.