Academic journal article Journal of Risk and Insurance

On the Role of Patience in an Insurance Market with Asymmetric Information

Academic journal article Journal of Risk and Insurance

On the Role of Patience in an Insurance Market with Asymmetric Information

Article excerpt

ABSTRACT

We analyze a two-period competitive insurance market that is characterized by the simultaneous presence of moral hazard and adverse selection with regard to consumer time preferences. It is shown that there exists an equilibrium in which patient consumers use high effort and buy an insurance contract with high coverage, whereas impatient consumers use low effort and buy a contract with low coverage or even remain uninsured. This finding may help to explain why the opposite of adverse selection with regard to risk types can sometimes be observed empirically.

INTRODUCTION

Empirically, personal discount rates vary to a significant degree among people. For example, Warner and Pleeter (2001) use data from the U.S. military downsizing program of the early 1990s to estimate the discount rates of separatees who could choose between an annuity and a lump-sum payment. Their estimates of discount rates range from 0 percent to over 30 percent. Frederick, Loewenstein, and O'Donoghue (2002) survey articles that try to estimate the annual discount rate of individuals. Across and within the various studies, there is a tremendous variance in results, which take values from zero to infinity, with some results even being negative. These findings seem to underline the relevance of accounting for different time preferences among consumers. However, this issue, to our knowledge, has not received attention so far in the context of insurance markets.

Since the typical insurance contract requires insurees to pay the premium up front for several periods (e.g., months), there exists a role for time preference in the consumers' ex ante valuation of the contract. The aim of this article is to analyze the effects of the differences in the personal discount rate of individuals in a competitive insurance market. For this purpose, we employ a two-period model with both moral hazard and adverse selection in the spirit of de Meza and Webb (2001). However, it is assumed that the informational asymmetry is not with regard to risk aversion but with regard to the individuals' personal discount rate, which can either be high (impatient) or low (patient). This corresponds to a low (impatient) or high (patient) discount factor. The discount factor will be used for modeling purposes throughout this article.

We show that there exists a separating equilibrium in which patient consumers use high effort and buy an insurance contract with an unfair premium. In contrast, impatient consumers use low effort and buy a contract with lower cover than the patient consumers or even prefer to remain uninsured. In this sense, accounting for the differences in the personal discount rate helps to explain the opposite of adverse selection ("advantageous" selection, as it is called by de Meza and Webb).

This finding contrasts with traditional models of adverse selection in insurance, for example, as represented by Rothschild and Stiglitz (1976), which predict that it is the high risks who are more keen on buying insurance.

However, there is some evidence that does not seem to fit these predictions. Dionne, Gourieroux, and Vanasse (2001) criticize an empirical study by Puelz and Snow (1994) that finds that adverse selection is a relevant problem for automobile insurance. They show that under refined estimation methods, the result cannot be confirmed. Cawley and Philipson (1999) analyze whether data from life insurance are consistent with the adverse selection hypothesis. They report that in several regards the data exhibit the opposite of the expected pattern. For example, there is a negative covariance between risk and quantity. This suggests that it is actually the low risks who are inclined to buy more insurance.

This article draws on de Meza and Webb (2001) who develop a model that can explain the opposite of adverse selection in a competitive insurance market. This follows from adverse selection on risk aversion in the simultaneous presence of moral hazard. …

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.