Suppose you obtained data from a car insurance company. For each customer, you observe detailed personal information such as demographics and drivers’ histories. You also observe the insurance plan they purchased: (i) a basic plan that covers only at-fault accidents with a high deductible, or (ii) a comprehensive plan that covers any accident, loss, or theft, with no deductible. Finally, the data also contains the insurance claims that these customers have filed.
a) Describe how you would test for the presence of private information in this market using a positive correlation test. Be precise.
b) Explain conceptually what would be the difference between adverse selection and moral hazard in this market (car insurance).
c) Does your positive correlation test allow you to distinguish between these two types of private information?