Academic journal article Journal of Risk and Insurance

Insurer Contract Nonperformance in a Market with Adverse Selection

Academic journal article Journal of Risk and Insurance

Insurer Contract Nonperformance in a Market with Adverse Selection

Article excerpt

ABSTRACT

In this study we examine the impact of insurer contract nonperformance upon Wilson's adverse selection equilibrium where consumers exhibit constant absolute risk aversion. When the market equilibrium retains its original form (i.e., pool or separation), premiums and coverage levels generally fall, although the change in coverage level for good risks is ambiguous when the equilibrium is separating. When the market equilibrium changes form, the change in premium and coverage levels is generally ambiguous, although one can determine that good risk premiums go down when the equilibrium shifts from pooling to separating and that bad risk premiums and coverage levels go down when the equilibrium shifts from separating to pooling. Interestingly, we find that although the introduction of insurer default risk makes good risks worse off, this is not necessarily true for bad risks. Bad risks can be better off because the decrease in the price differential between types can make pooling relatively more attractive to good risks in the presence of default risk.

INTRODUCTION

In a world with complete insurance markets, a risk adverse individual, facing fair prices, will fully insure her wealth across all states of the world. When insurance markets are incomplete, this result need not hold, and an individual's behavior will depend, among other things, upon the correlation of insurable and non-insurable risks (Doherty and Schlesinger, 1983a, 1983b; Mayers and Smith, 1983). The breakdown in the "standard" analysis is perhaps most severe when the uninsurable risk is itself created by the purchase of insurance, that is when there is a risk of contract nonperformance by the insurer.' Doherty and Schlesinger (1990) show that a risk averter will not purchase full coverage at fair prices, that coverage purchased is not, in general, a monotonic function of the risk of insurer default, coverage purchased is not necessarily negatively related to the level of loading, individuals who are "more risk averse" (in the sense of Ross,1981) need not purchase more insurance, and (when default is partial) there is no monotonic relationship between the level of coverage and the extent of recovery. The consequences of contract nonperformance upon "standard" insurance results are thus quite severe.

It is also well recognized in the literature that the operation of insurance markets is significantly affected by adverse selection (e.g., Rothschild and Stiglitz, 1976, Wilson, 1977, and Spence, 1978). Wilson's (1977) model of adverse selection suggests that the equilibrium will either involve a pooling contract or a pair of separating contracts. If a pool results, it provides the coverage level optimal to the good risks at the pool price. Separation occurs when the better risks prefer a limited coverage contract (with the better risk coverage level sufficiently limited that higher risks prefer a full coverage contract at a price fair to the higher risks) at a price fair to the better risks to any contract at a price fair to the overall pool. Adverse selection insurance markets may be significantly impacted when background risk (Agarwal, 1995) or severity risk (Doherty and Schlesinger, 1995; Ligon and Thistle, 1996) are present. The primary difference between these studies and ours is the correlation between insurable losses and the additional risk introduced; we explore the impact of contract nonperformance upon a market with adverse selection.

We analyze the impact of the introduction of a third (default) state of the world upon the nature of the Wilson equilibrium (pooling or separating), including its impact on the level of coverage, the premium paid, and societal welfare. We find, as did Doherty and Schlesinger (1990), that contract nonperformance often generates indeterminate results compared to "standard" models, even with strong restrictions on preferences. However, these ambiguities imply that nonperformance may have a surprising impact on insurance markets, including the possibility that some consumers may be better off in the presence of default risk. …

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