Week 6 - Finkelstein and Poterba (2004) Adverse Selection in Insurance Markets: Policyholder Evidence from the UK Annuity Market

What is the summary of this paper?

Aim: This paper asks whether there is adverse selection in the annuity market. A life annuity provides a predetermined amount to the owner until she dies, in exchange for a one-time premium paid up front. The fact that insurers do not know who are the riskier (longer-lived) buyers may lead to adverse selection in the market. This paper shows that although there appears to be no adverse selection in the size of annuity payments, selection does exist along other dimensions of the contract: the degree of back-loading in the contract and whether the annuity makes payments to the annuitant’s estate.

Empirical strategy: The authors use 17 years of data on all insurance contracts from an insurance company in the U.K., including all information that the company observed about the annuitant as well as the contract features. The authors also calculate the price of each annuity and regress it on contract features to see whether companies price “adversely selected” products higher.

Main Findings: They find that, controlling for sources of heterogeneity that the insurance company use in their price setting (age and gender), longer-lived individuals self-select into contracts that are more valuable to them. They find that the insurance company charges relatively higher prices for back-loaded annuities but lower prices for annuities with payments to the estate.

In your own words, explain the idea behind the positive correlation test for adverse selection, why it is often unclear what we learned from previous implementations of that test, and why the setting of this paper may be better suited to apply such a test.

The positive correlation test states that under adverse selection there should be a positive correlation between the quantity of insurance and the ex-post occurrence of the adverse event. This test reflects the notion that when adverse selection exists, riskier individuals purchase more insurance so that those with a higher quantity of insurance are also more likely to experience the adverse event they are insuring against. Note that in the context of this paper, the “adverse event” is living a longer life.
One problem with this test is that the positive correlation could be due to a combination of adverse selection and moral hazard, and so the results can be difficult to interpret. Moral hazard would also induce a positive correlation between the quantity of insurance purchased and the probability of the adverse event occurring. This is because insurance coverage might encourage people, e.g., to take unnecessary risks which increase the probability of the adverse event occurring (e.g. car insurance leads to more accidents).
However, the setting in this paper may be better for applying the positive correlation test since moral hazard plays a smaller role in annuity markets. That is, holding an annuity is unlikely to encourage the buyer to take additional measures to prolong their life. Another advantage to applying this test to annuities is that the test can be applied to several dimensions of the insurance contract, not just the quantity of insurance purchased.

In your own words, explain the four features of annuities that the authors consider (index-linked, escalating, guaranteed, capital-protected) and what the sign of the coefficients on these four features in Table 2 tells us about the presence of adverse selection in the UK annuity market.

The authors consider the following annuity types:

1. index-linked: payments are linked to inflation;

2. escalating: nominal payments increase over time;

3. guaranteed: the insurer is guaranteed payments for a period of time, so that payments would continue to go to his/her estate even after death; and

4. capital-protected: if at the time of death the sum of annuities paid is less than the up-front premium, the difference is given to the buyer’s estate.

Features (1) and (2) are measures of back-loading, so theory predicts that the coefficients for these should be negative (purchasers are less likely to die) under adverse selection. In contrast, features (3) and (4) are measures of estate payments so theory predicts that the coefficients for these should be positive (purchasers are more likely to die) under adverse selection. In Table 2 we see significant negative coefficients for (1) and (2), as well as positive, although not always significant, coefficients for (3) and (4). This is evidence of adverse selection in the U.K. annuity market for contracts that offer back-loading and payments to an estate.

Explain why the results in the first two columns of Table 4 suggest that insurance companies are taking into account adverse selection in their pricing policies.

Table 4 contains results estimated from regressions of the “effective price” on contract features, controlling for annuitant characteristics used in the price setting (age and gender). The results in the first two columns suggest that insurance companies are taking into account adverse selection in their pricing policies within the compulsory market because the annuities favoured by riskier customers are priced higher, while those favoured by less risky customers are priced lower. That is, the coefficients for the index-linked and escalating contracts are positive and significant, while the coefficient for guaranteed contracts is negative and significant.

What is the main takeaway of this paper?

The idea of the positive correlation test is that “when observationally identical individuals are offered a choice from the same menu of insurance contracts, higher-risk individuals will buy more insurance. (...) Of course, this prediction, and any empirical test based on it, applies conditional on the characteristics of the individual observed by the insurance company and used in setting insurance prices.”

What is the main limitation of this paper?

The observationally identical individuals for the purpose of the positive correlation test in this paper are only those with the same age and gender. So the adverse selection taking place here might not come from some hard-to-observe differences across individuals, but from easy-to-observe differences such as health, socio-economic status, etc. As a result, the degree of adverse selection may be partly due to the firm’s own choice to not use more information in setting different prices for different buyers, which may limit the external validity of these results.