False Diagnoses: Pitfalls of Testing for Asymmetric Information In Insurance Markets

Abstract

The widely applied ‘positive correlation test’ concludes that there is symmetric information in an insurance market if observationally identical buyers of high and low cover contracts have the same loss rate. As standard assumptions imply that only full‐cover contracts are bought when information is symmetric, a contradiction arises. The existence of a variety of contracts can be reconciled with symmetric information by claim‐processing costs but existing tests are then shown to fail. Ignoring the nature of loading factors may also cause recent studies to mismeasure the welfare costs of asymmetric information but these errors can be rectified.

Multidimensional private information, market structure, and insurance markets

“…Because the marginal cost curve is typically nonmonotonic in price, a property Einav, Finkelstein, and Cullen () do not emphasize, but Einav and Finkelstein () do acknowledge, the two notions may reach different conclusions under multiple consumer heterogeneity, as explicitly shown in our Claim above. This is a point that was already made by de Meza and Webb () in their two‐type (bad and good risks) example, where they also argue that the local sign of the slope of the average cost with respect to quantity , which may not be monotonic, can be a useful measure of selection as well.…”

“…Clarifying the distinction between local selection (adverse or advantageous) and the equilibrium positive/negative correlation is important. As noted by de Meza and Webb (), this distinction is sometimes not clearly made. Einav, Finkelstein, and Levin () state that, “contract j is adversely selected if the expected cost of insuring j 's enrollees under contract j is greater than the expected cost of insuring the population I under contract j ” and is advantageously selected otherwise.…”

“…To the extent that our article investigates on whether the positive correlation property is robust to environments with multidimensional consumer heterogeneity, it is most related to CJSS () and de Meza and Webb (). CJSS argue that, as long as consumers are rational and the per‐contract expected profit does not increase with the coverage of the contract (which they refer to as “nonincreasing profit” [NIP] condition), then the positive correlation property is robust to multidimensional private information.…”

“…We will provide more details of the comparison when we discuss Proposition . Also related, de Meza and Webb () provide an insightful discussion that the positive correlation test is not a valid test to distinguish asymmetric information from symmetric information environment. The reason is that under symmetric information, the only insurance purchased by consumers will be the one with full coverage, unless the claim processing costs (or other loading factors) are formally modelled.…”

Multidimensional Private Information, Market Structure and Insurance Markets

“…Note that the upper bound on the loading factor specified by (11) depends on the ratio of the WTP for the consumer with average risk and lower-bound risk preference relative to its expected claim. Proposition 2 shows that if the loading factor is bounded by (11), then competitive insurance market will always exhibit positive correlation property in equilibrium even in the presence of loading factors. The intuition is again quite simple.…”