Foundations of Insurance Economics

Although the prevalence of risk in economic activity has always been recognized (Green, 1984), deterministic models dominated economic explanations of observed phenomena for many years. As a result, the economics of insurance has a relatively short history. In early work that formally introduced risk and uncertainty in economic analysis (von Neumann and Morgenstern, 1947; Friedman and Savage, 1948; Allais, 1953; Arrow, 1953; Debreu, 1953), insurance was viewed either as a contingent good or was discussed in relation to gambling. Before 1960, economic literature was largely void of analyses of the nature of insurance markets or of the economic behavior of individual agents in these markets.1

Ffifteen years ago, the theory of choice under uncertainty could be considered one of the “success stories” of economic analysis: it rested on solid axiomatic foundations, it had seen important breakthroughs in the analytics of risk, risk aversion and their applications to economic issues, and it stood ready to provide the theoretical underpinnings for the newly emerging “information revolution” in economics.1 Today choice under uncertainty is a field in flux: the standard theory is being challenged on several grounds from both within and outside economics. The nature of these challenges, and of our profession’s responses to them, is the topic of this paper.

This paper concerns utility functions for money. A measure of risk aversion in the small, the risk premium or insurance premium for an arbitrary risk, and a natural concept of decreasing risk aversion are discussed and related to one another. Risks are also considered as a proportion of total assets.

This paper attempts to answer the question: When is a random variable Y “more variable” than another random variable X?

Problems concerned with purchasing of insurance coverage appear to be a fascinating and potentially fruitful field for application and testing of theories of riskbearing. In this note we shall analyze a series of such problems from the point of view of an individual facing certain risks. Given his risk situation and his economic background (as measured by his initial wealth), his problem is to decide whether he should provide for in­surance coverage and, if so, how much.

An area of much recent theoretical attention is the modeling of insurance decisions when markets are incomplete. Such incompleteness is said to exist when insurance contracts do not exist for all risks facing an individual or a firm. In such a market, insurance decisions cannot be made myopically and must recognize the presence of uninsurable background risk. This paper presents a nontechnical overview of the incomplete-market theory. The way in which market incompleteness may invalidate some long-standing theoretical results — and may indeed even cause seemingly perverse results — is examined. Possible causes of incomplete markets as well as some implications of the theory for reinsurance and for corporate purchases of insurance are also discussed.

We analyze the individual’s demand for insurance as a special case of general portfolio hedging activity. The demand for insurance contracts is determined simultaneously with the demands for other assets in the portfolio. We demonstrate that when the payoffs of the policy are correlated with the payoffs to the individual’s other assets, the demand for insurance contracts is generally not a separable portfolio decision. We argue that this separability condition is not generally met because of significant interdependence of claims across different insurance policies. Furthermore, our generalizations can reverse the standard prediction that wealthier individuals will demand less insurance.

The article develops a theory of demand for insurance that emphasizes the interaction between market insurance, “self-insurance,” and “self-protection.” The effects of changes in “prices,” income, and other variables on the demand for these alternative forms of insurance are alalyzed using the “state preference” approach to behavior under uncertainty. Market insurance and self-insurance are shown to be substitutes, but market insurance and self-protection can be complements. The analysis challenges the notion that “moral hazard” is an inevitable consequence of market insurance, by showing that under certain conditions the latter may lead to a reduction in the probabilities of hazardous events.

Insurance contracts are regularly purchased by corporations. The Insurance Information Institute reports that “business insurance accounted for approximately 54.2 percent of the $79, 032,923,000 in direct property and liability insurance premiums written in the United States in 1978” (1979, p. 9). Yet even though annual premiums exceeded $42.8 billion,1 the importance of these contracts has been largely ignored by the finance profession. For example, the topic of insurance is completely absent from the index of virtually all corporate finance textbooks.

Insurance and protection against various kinds of losses are both valuable activities provided to a large and perhaps increasing extent by the public sector.

Insurance is an item of considerable importance in the economies of advanced nations, yet it is fair to say that economic theorists have had little to say about it, and insurance theory has developed with virtually no reference to the basic economic concepts of utility and productivity. Insurance is not a material good; although it is usually classified as a service, its value to the buyer is clearly different in kind from the satisfaction of consumers’ desires for medical treatment or transportation. Indeed, unlike goods and services, transactions involving insurance are an exchange of money for money, not money for something which directly meets needs. The closest analog in ordinary economic theory to an insurance policy is a bond or note, an exchange of money now for money later. But an insurance is a more subtle kind of contract; it is an exchange of money now for money payable contingent on the occurrence of certain events.

This paper investigates the possibility of generalizing the classical theory of commodity markets to include uncertainty. It is shown that if uncertainty is considered as a commodity, it is possible to define a meaningful price concept, and to determine a price which makes supply equal to demand. However, if each participant seeks to maximize his utility, taking this price as given, the market will not in general reach a Pareto optimal state. If the market shall reach a Pareto optimal state, there must be negotiations between the participants, and it seems that the problem can best be analysed as an n-person cooperative game.

Almost every phase of economic behavior is affected by uncertainty. The economic system has adapted to uncertainty by developing methods that facilitate the reallocation of risk among individuals and firms. The most apparent and familiar form for shifting risks is the ordinary insurance policy. Previous insurance decision analyses can be divided into those in which the insurance policy was exogenously specified (see John Gould, Jan Mossin, and Vernon Smith), and those in which it was not (see Karl Borch, 1960, and Kenneth Arrow, 1971, 1973). In this paper, the pioneering work of Borch and Arrow—the derivation of the optimal insurance contract form from the model—is synthesized and extended.

A game-theoretic model is used to study the effect of risk aversion on the outcome of bargaining over the terms of an insurance contract. When the insurer is risk netural, it prefers to bargain with the more risk averse of any two potential clients, since that client will agree to spend more, for less insurance, than will a less risk averse client. Bargaining over insurance contracts leads to results that differ from those obtained in a competitive insurance market. In a competitive market, clients seeking to insure against the same loss choose the same insurance contract, regardless of their risk posture.

Moral hazard refers here to the tendency of insurance protection to alter an individual’s motive to prevent loss. This affects expenses for the insurer and therefore, ultimately, the cost of coverage for individuals. Beginning with Arrow [1963] and Pauly [1968], economists have discussed two partial solutions to the problem of moral hazard: (i) incomplete coverage against loss and (ii) “observation” by the insurer of the care taken to prevent loss. Incomplete coverage gives an individual a motive to prevent loss by exposing him to some financial risk; and observation of care also gives an individual a motive to prevent loss, as it allows the insurer to link to the perceived level of care either the insurance premium or the amount of coverage paid in the event of a claim.

Most analyses of the principal-agent problem assume that the principal chooses an incentive scheme to maximize expected utility subject to the agent’s utility being at a stationary point. An important paper of Mirrlees has shown that this approach is generally invalid. We present an alternative procedure. If the agent’s preferences over income lotteries are independent of action, we show that the optimal way of implementing an action by the agent can be found by solving a convex programming problem. We use this to characterize the optimal incentive scheme and to analyze the determinants of the seriousness of an incentive problem.

Parties who cause harm to others may sometimes turn out to be ‘judgment proof,’ that is, unable to pay fully the amount for which they have been found legally liable.1 This possibility is an important and realistic one. Certainly individuals may readily be imagined to cause personal injury or property damage resulting in judgments that exceed their assets plus any liability insurance coverage; and the same is true of firms.2

Economic theorists traditionally banish discussions of information to footnotes. Serious consideration of costs of communication, imperfect knowledge, and the like would, it is believed, complicate without informing. This paper, which analyzes competitive markets in which the characteristics of the commodities exchanged are not fully known to at least one of the parties to the transaction, suggests that this comforting myth is false. Some of the most important conclusions of economic theory are not robust to considerations of imperfect information.

Statistical discrimination occurs when a characteristic, such as sex, is used as an indicator of the risk group of an individual. The theory of adverse selection is used to explain the occurrence of statistical discrimination. A model of the market for collision insurance, which is based on the theory of adverse selection, is estimated on Canadian data. The results suggest that adverse selection occurs in this market. Simulations of the effect of prohibiting sexual discrimination in the 21–24 age group indicate that the premiums for single females would increase substantially and that a significant proportion would no longer purchase collision insurance.

This paper examines the form of insurance contracts in the presence of asymmetric information about consumers’ accident probabilities. Our goal is to understand the adjustment in contract terms as a function of accident histories in a finite horizon model. We also compare these adjustments between alternative market structures. Our principal findings indicate that history dependent insurance contracts serve a useful sorting role. Individuals who declare themselves ‘low risks’ to insurance companies face adverse contracturai terms if they subsequently have many accidents. These adjustments are strongest in the case of a single insurance seller but are present in the competitive model as well.

Adverse selection in insurance markets is defined as a problem of misallocation of resources explained by a situation of asymetrical information between the insured and the insurer. The insured has no incentive to reveal his true risk and it is costly for the insurer to observe the individual risk. In order to reduce this problem of resource allocation, insurers have developed imperfect mechanisms such as 1) the use of risk classes, 2) partial insurance coverage and 3) experience rating to establish the appropriate premium.

The effect of asymmetric information between buyers and sellers on product quality was first explored by Akerlof (1970) in his pathbreaking paper on the market for ‘lemons’. He showed that if all purchasers have imperfect information on quality, then a market for the product may not exist, or if it does function it may not be efficient. These results have led to a number of papers concerning insurance and labor markets under different assumptions regarding how agents discriminate between ‘products’ of varying quality [see Pauly (1974), Rothschild and Stiglitz (1976), Wilson (1977), Miyasaki (1977), and Spence (1978)].

Recent public policy debate has focused concern on the equity dimensions of categorical discrimination based on sex, age, or race in insurance and similar markets. We consider the efficiency effects of such discrimination and establish that costless imperfect categorization always enhances efficiency. When categorization entails a nonnegligible resource cost, however, no unambiguous efficiency ranking of informational regimes is possible. When categorization is costless, we demonstrate that government, having no better information than market participants, can effect redistribution without assuming dictatorial control of the market, implying that a market equilibrium with costless categorization is potentially Pareto superior to one without it. When categorization is costly, however, the market may categorize when Pareto improvements are not possible.

This paper provides a detailed study of the structure, behavior, and performance of the property and liability insurance industry in the United States. The property insurance industry is shown to possess all of the structural characteristics normally associated with competitive markets. Despite a competitive market structure, however, the property-liability insurance industry has traditionally set prices through cartel-like rating bureaus and has been subjected to pervasive state rate regulation. The study concludes that the combination of state regulation, cartel pricing, and other legal peculiarities has resulted in the use of an inefficient sales technique, supply shortages, and overcapitalization. Free entry, however, tends to drive profits toward the cost of capital. Based on recent experience in states where the competitive market is used to determine insurance rates, the study suggests a movement away from rate regulation and cartel pricing to open competition, as a means of eliminating prevailing performance problems.

Property-liability insurance is distributed through two major marketing channels—the independent and the exclusive agency systems. Independent agents place business with several companies, while exclusive agents write insurance for only one company. We find that the independent agency system is less efficient than the exclusive agency system. The efficiency differential did not change significantly during the period 1968 through 1976. When we used the total rather than the underwriting costs to measure expenses, we found that the relative but not the absolute expense differential was reduced. This suggests that the inefficiencies of the independent agency companies stem from marketing and administrative rather than loss adjustment procedures. The findings imply that regulators should play a more active role in the dissemination of information on property-liability insurance prices.

The range of ownership structures within the insurance industry is perhaps the broadest of any major industry. Included are Lloyds associations, where insurance contracts are offered by individual underwriters, stock companies that employ the standard corporate form, and mutuals and reciprocals that are more like cooperatives where customer and ownership functions are merged.

This paper examines insurance pricing and its regulation in the context of efficient capital markets. Starting with an aggregated model and generalizing results reported recently in the literature about “proper” underwriting profit, the paper turns to disaggregation of the model with m insurance lines. The main result is that no unique set of rates exists that regulators may impose to avoid disturbing market equilibrium. Preliminary empirical evidence presented shows that the “systematic risk” of underwriting profits approaches zero in most lines. Thus an intuitive solution for underwriting profit rates in these lines equal to minus the riskless interest rate, is reasonable.

A discrete-time option-pricing model is used to derive the “fair” rate of return for the property-liability insurance firm. The rationale for the use of this model is that the financial claims of shareholders, policyholders, and tax authorities can be modeled as European options written on the income generated by the insurer’s asset portfolio. This portfolio consists mostly of traded financial assets and is therefore relatively easy to value. By setting the value of the shareholders’ option equal to the initial surplus, an implicit solution for the fair insurance price may be derived. Unlike previous insurance regulatory models, this approach addresses the ruin probability of the insurer, as well as nonlinear tax effects.

Insurance guaranty funds have been adopted in all states to compensate policyholders for losses resulting from insurance company insolvencies. The guaranty funds charge flat premium rates, usually a percentage of premiums. Flat premiums can induce insurers to adopt high-risk strategies, a problem that can be avoided through the use of risk-based premiums. This article develops risk-based premium formulas for three cases: a) an ongoing insurer with stochastic assets and liabilities, b) an ongoing insurer also subject to jumps in liabilities (catastrophes), and c) a policy cohort, where claims eventually run off to zero. Premium estimates are provided and compared with actual guaranty fund assessment rates.

Most prior analyses of underwriting cycles have explained cycles as a supply-side phenomenon involving irrational behavior on the part of insurers. This paper proposes instead that insurance prices are set according to rational expectations. Although rational expectations per se would be inconsistent with an underwriting cycle, the authors hypothesize that cycles are “created” in an otherwise rational market through the intervention of institutional, regulatory, and accounting factors. Empirical evidence is presented indicating that underwriting profits in several industrialized nations are consistent with the hypothesis.

Commercial liability insurance premiums increased dramatically in 1985 and 1986. The growth for general liability insurance was especially pronounced: net premiums written increased from $6.5 billion in 1984 to $20 billion in 1986. During this time, limits of coverage were shrinking for many of those insured, and cancellations and denials of renewal were widespread for some types of business in some states. Premium growth had moderated substantially by the end of 1986, but the large increases in the previous two years undoubtedly imposed high costs on many businesses and professionals. Insurers reported large accounting losses on operations in 1984 and 1985. The causes of the premium increases—whether rapidly escalating and unpredictable claim costs, severe underpricing of business written before 1985 because of cyclical influences in the industry, or both—have been vigorously debated, as has the extent to which industry operations actually were unprofitable. While widespread deregulation of commercial insurance rates occurred during the 1970s, a few states have enacted new forms of rate regulation in response to recent experience.

Virtually all western countries regulate the reserves of insurance firms, even when they do not directly regulate the premiums charged. The justification for such reserve requirements is usually based on consumer ignorance; it is alleged to be costly if not impossible for a typical consumer of insurance to determine the level of reserves held by insurance firms from which he buys; consequently, consumers would often be unprepared for insurer default.1 But even if one accepts the premise of consumer ignorance, the premise only implies that reserves regulation may be useful. To show that regulation will be needed to improve things, two additional propositions must hold: (1) If not regulated, firms will hold levels of reserves that deviate from (usually below) the social optimum. (2) Regulators can determine and enforce a level of reserves that is at least closer to the social optimum than the unregulated level. Crucial to the empirical or theoretical establishment of either of these propositions is a positive model which predicts the level of reserves the unregulated firm will choose in different circumstances.

This article reports empirical evidence concerning the effects of solvency regulation on the number of companies and frequency of insolvencies. Minimum capital requirements appear to reduce insolvencies by reducing the number of small, domestic firms. This supports the view of capital requirements as a differentially higher tax on small, new firms. Other forms of regulation have ambiguous effects or none. A comparison of the characteristics of insolvent and solvent firms supports the model of insolvency as the (unlucky) outcome of value-maximizing risk-taking.

The impact of rate regulation on auto insurance loss ratios during 1976–81 is estimated using cross-state data to determine whether regulation significantly affected rates. The methodology allows for random variation in the impact of rate regulation and no-fault laws on loss ratios. The model controls for the influence of the average expected loss per insured vehicle in a state, and growth rates for the average loss per insured vehicle are analyzed to determine whether unanticipated growth in losses is likely to have affected the estimated mean impact of regulation. The results suggest that regulation reduced rates during the period studied.