Review of a theory of insurance and gambling: Replacing risk preferences with quid pro quo By JohnNyman

In 2003, John Nyman (2003) published The Theory of Demand for Health Insurance, a book that synthesized his research of the previous decade on the normative and policy implications of the various ways to organize health insurance (in the US). As told in that book, Nyman's interest and motivation to study the topic was piqued at the time of the discussions around the so-called Clinton health care reform (which was never implemented). What struck him was the discrepancy between the economists' fixation on “moral hazard” (the welfare cost of insured individuals consuming too much health care) and the many poignant, sometimes tragic, stories collected from US residents about issues of lack of access to health care that seemed fully warranted (e.g., to treat a pediatric cancer case). The discrepancy, he showed, was due to a view among economists that the demand for health insurance was motivated by a demand for certainty (an aversion for risk). According to such a view, insurance is a way to neutralize the uncertainty of having to spend money on medical treatment; however, because health insurance pays off through a reduction in the price of medical treatments, rather than a lump-sum payment, it provides an incentive to spend more on medical treatments than the amount that would be spent without insurance (the infamous moral hazard). Nyman contrasted such a view with the view of residents who were telling the Clinton administration that the reason for having health insurance was precisely to be able to spend more on medical treatments than without coverage. He called that view the quid pro quo motivation for the demand of health insurance, and he developed the normative and policy consequences of replacing risk preferences with quid pro quo: not all the supplementary health care consumption of the insured relative to the uninsured is “overconsumption,” and the share of that supplementary health care consumption derived from the quid pro quo motivation is actually welfare enhancing (consumers derive a surplus from that extra consumption). Rather than Americans suffering from too much coverage, as the standard approach was concluding, the quid pro quo approach showed that Americans were suffering from not enough health care coverage; in that sense, Nyman helped economists see the world as most of the rest of the population or health policy analysts. After the 2003 publication, many of us teaching health economics sensed we could not continue to teach the standard theory (risk aversion and moral hazard), and we should at least present risk preferences and quid pro quo as two approaches to the normative understanding of health insurance. In this new book, published 21 years later, Nyman expands the theory beyond health insurance to insurance in general and gambling, offers more theoretical mechanisms for the quid pro quo theory (notably, state-dependent utility), and provides empirical support for the quid pro quo and against the risk preferences approach. The case against risk preferences is made stronger and, I dare say, compelling. Moreover, Nyman suggests a convincing integration of his theory into the prospect theory framework of Kahneman and Tversky (1979), for insurance in Chapter 5, and for gambling in Chapter 7. After reading this book, many economists will think that the quid pro quo is not so much an alternative approach to the conventional, risk preferences-based one, but rather an approach that does not fall prey to most of the inconsistencies and empirical contradictions of the risk preferences approach. This does not mean that the quid pro quo is the only approach economists should consider or that it is robust to any empirical challenges, not so much on its realism, but rather on its measurement and operationalization (e.g., how to decompose income and price effects when insurance pays off through a reduction in price?) or to conceptual ones (e.g., if both gambling and insurance purchase are explained by state-dependent preferences, what is the psychological difference between the two behaviors?). As a health economist, I will continue to teach the conventional theory of demand for health insurance alongside the quid pro quo approach; but I will present students with empirical evidence, mostly from the field of psychology, on the lack of realism of the risk preferences approach. A Theory of Insurance and Gambling: Replacing Risk Preferences with Quid pro Quo, is organized as follows (Nyman 2024). The book starts with a short introduction providing an overview of the subject matter and some definitional choices (e.g., use of income rather than wealth or consumption as the argument of utility, exclusion of lotteries or informal betting and risky investment from the definition of gambling, as well as informal insurance from the definition of insurance). Two subsequent chapters introduce the quid pro quo interpretation of demands for insurance and gambling. On the insurance side, it is partly an update and extension to fields other than health insurance of the previous book, stating that what individuals desire is a transfer of income in case they are on the wrong side of a risky situation (e.g., they are sick, their car was stolen, their house burned down)—not because they want a stable income stream ex ante but because they know, at the time they purchase their insurance policy, that they will need extra income if they happen to be unlucky. The novel aspect is the introduction of state-dependent utility as a motivation for the income transfer (more on this below). On the gambling side, the framework is entirely novel, never published before, even though it builds on Nyman's previous work (Nyman et al., 2008) and revolves around the idea already present in that previous work of the willingness to gain income that is not earned through labor. As outlined below, what makes the book novel and original is the attempt at connecting the demands for insurance and for gambling through the conceptual framework of state-dependent preferences. Chapter 4 then summarizes what we know about the supply of insurance and gambling. This chapter on supply is not added for the sake of completeness only (after all, the book's title is A theory of Insurance and Gambling, not A Theory of Demand for Insurance and Gambling) but mainly because it highlights a crucial point of the book: risk preferences do not play a major role in the markets for insurance and gambling. In what Nyman calls the “conventional theory of insurance,” the role of insurers is left somewhat vague and does not pass a simple introspection test: the theory builds on the idea that consumers buy insurance because they are risk-averse, but why, then, would insurers sell insurance? The conventional answer is that, thanks to the law of large numbers, insurers manage to control risk and to run a business under certainty, but this does tell us why they are immune to uncertainty, not how they could make profit and choose to enter the business in the first place. Chapter 4 provides a different interpretation that actually answers that question: insurers see that risk is a potential source of profit because consumers demand not that risk be eliminated but that something (an income transfer in the quid pro quo theory) be done in situations that involve risk. In such a framework, insurers can be as risk-averse or risk-loving as anyone else; it simply does not enter in their decision to sell policies. Chapters 5 to 8 provide empirical evidence to support the theoretical assertion that risk preferences have not much to contribute to explaining the demand for insurance or gambling, at least compared to the willingness to transfer income across states of the world as made clear by the quid-pro-quo framework. Chapter 5 mostly summarizes empirical evidence from psychology that refutes the convenient specification of utility of income that Friedman and Savage (1948) devised to explain the insurance-purchaser gambler puzzle and then, as stated previously, reframe the quid-pro-quo into the language of prospect theory. Chapter 6 examines whether a specific tenet of prospect theory, namely loss aversion, could be added to the numerous motives for demand for insurance in the quid-pro-quo. Chapter 7 summarizes what we know about motivations of gamblers and, again, shows that love for risk is not a major one but that the possibility of getting “free” money is. Chapter 8 gathers all empirical evidence on the demand for health insurance: surveys about motivations (similar to Chapter 7 for gambling), a critical review of empirical decompositions of the income and price effects in insurance that pays off by reducing the price of the covered commodity (mostly health care) and, last, an empirical analysis of the welfare effects of the same kind of insurance (again, mostly health insurance). Chapter 9 lists and comments on the various theories that have been offered by economists to explain the insurance-purchasing gambler puzzle, among which are risk preferences and the quid-pro-quo plus three other theories (consumption indivisibilities, probability weighting, and entertainment from gambling). Finally, Chapter 10 summarizes the book, discusses the importance of the contribution, and, quite interestingly, speculates in an appendix (pages 230-237, the very last of the book) on the reasons why economists seem so fixated on risk aversion and oblivious of income transfers. I will organize my assessment of the contribution of the book, focusing on three aspects of the book that I found particularly interesting: what is the unifying theoretical element of the quid-pro-quo framework applied to insurance and gambling? What is the value of the empirical evidence against risk preferences when Friedman and Savage write that, epistemologically, their theory has nothing to do with realism? Last, why is it the case that the quid-pro-quo approach has not been embraced by the profession, despite all the pitfalls of the conventional approach it is meant to replace? Firstly, even though the book does not state it explicitly, it can be said that state-dependent utility is the theoretical link between the quid pro quo approaches of insurance and gambling. Of course, state-dependent utility is not necessary to interpret the demand for insurance as a quid pro quo, since income effects explain that, even under indemnity insurance, the insured spend more on the covered good than the non-insured in a way that is welfare-enhancing. However, Section 4 of Chapter 2 is an entirely new development that could lead to a dramatic re-assessment of the share of moral hazard that is welfare-enhancing, compared to what Nyman and colleagues have produced based on the income effect without any shift in utility. Moreover, the shift in utility across states is what gambling and insurance have in common in this new quid pro quo approach: The demand for insurance reflects the fact that individuals appreciate income more when unlucky than when lucky and, therefore, want to transfer income to the unlucky state of the world. The demand for gambling reflects the fact that individuals appreciate income more when it is not earned through labor or because it is money that will allow them a splurge in consumption that they would not access with their regular income even if not earned, for example, they are retired or rentiers (the lucky case) than when they have to work to earn it (the unlucky case). In both instances, it is the absolute and the marginal utility of income that is greater in the “other” state of the world (i.e., unlucky for insurance, lucky for gambling). If it could be shown that the utility of income shifts in those cases in the way predicted by the theory (more utility of income in the unlucky case for insurance and in the lucky case for gambling), and if the shift could be estimated, that would not only provide a unifying theoretical base for the quid pro quo framework but also open an entire new field of empirical inquiry into the welfare effects of insurance and gambling, with clear policy implications. As Nyman shows, state-dependent utility has not been tested much as an hypothesis (he cites six such empirical studies in the case of health) and it has not necessarily been tested in a manner that would be compatible with the quid pro quo framework (as he notes on page 223, it is usually utility of consumption excluding health care whereas his framework would require testing a shift in utility of income). There is more consensus among economists around the disutility of labor (and that it increases with the amount of work already produced), but Nyman could find only one study measuring it using data on self-rated happiness (page 61) and no empirical studies about the attractiveness of the splurge in consumption—even though empirical evidence on the stated motivations of gamblers is clear that the possibility of getting free income is the main attraction of gambling. Secondly, and this is perhaps the other unifying theme of the book, it is a convincing and compelling effort at undermining the credibility of risk preferences as a motivation for purchasing insurance or gambling. Nyman goes as far as stating that consumers of insurance and gambling use “uncertainty” to their benefit, as a “multiplier of the premium or wager to determine an often much larger income transfer for the consumer” (page 104) and suppliers use it to “reduce … the firm's expenditures.” (page 105). “Uncertainty” (Nyman's words), or the fact that the event state is concentrated on a few individuals only (small probabilities), is used to improve welfare: it is better to live in a world where some have their car stolen and are compensated by the others than in a world where everyone has their mirror broken. Here, I would beg to disagree with Nyman's assertion in his introduction that uncertainty and risk can be used indifferently: if we really want to make the case that randomness and small probabilities are a good thing for welfare, we need to distinguish good randomness (probabilities are known and can be insured or gambled) from bad randomness (unknown probabilities), as Knight suggested we should. In such a case, we could say that risk is welfare-enhancing, whereas uncertainty is bad for society and the economy. This seems intuitively correct: the world is uncertain when it depends on the whims of autocrats, and this is bad for the economy, but well-managed risk is what allows entrepreneurs to thrive. The reader can find a lot of survey, experimental, or quasi-experimental evidence in the book showing that gamblers are not so much motivated by the excitement of randomness as they are by the possibility of getting free income (pp 166–72); in particular, not that many people would pay to play with random numbers without any financial stakes. Chapter 8 provides survey evidence on the motivation for purchasing health insurance, and, again, avoiding financial risk is not a major motivation (access to care is). Such evidence can be dismissed on the grounds that it reflects stated rather than revealed preferences but the book also musters a lot of empirical evidence from experiments in psychology, mostly prospect theory, “against risk preferences as a source of motivation for the purchase of insurance” (p 109). Such evidence shows that the specification imagined by Friedman and Savage in their 1948 article is not realistic in the sense that it is rejected by the data. It is important, I think, to reflect on such a criticism of the Friedman-Savage model, because Friedman and Savage tried to make their theoretical model immune to the criticism of “unrealism.” To do so, we need to go back to what Friedman and Savage were trying to do: Their problem was to salvage expected utility as the criterion by which rational individuals make decisions in situations of uncertainty. There is a problem because, if we accept both expected utility and diminishing marginal utility of income, nobody should ever gamble. Since it can be observed that a lot of people are gambling on a regular but not pathological basis, economics has a problem. The solution adopted by many economists was to reject expected utility as a criterion in the case of gambling, arguing that the excitement of gambling or some distorted perceptions of probabilities would be enough to explain gambling when the marginal utility of income is decreasing. The reason these economists wanted to salvage diminishing marginal utility of income and were ready to sacrifice expected utility in the process was that the former seemed to make a lot of sense from an introspective, psychological perspective. Friedman and Savage decided to sacrifice the diminishing marginal utility of income, to which they granted no special value, in order to salvage expected utility. The reason they granted no special value to the diminishing marginal value of income was that they rejected any notion of cardinal utility of certain income: in their view of the by most economists see the utility of certain income does not have any or psychological have a cardinal for of simply as if they If that is the case, the utility we from their choices has no reasons to be This is the argument to the of their specification of the utility of income as then then whether or not it makes sense from a psychological does not all that is that it (which it to If such is the case, what could be the value of all the empirical evidence against the of the utility of income that they Here, is a but difference in the of the What Friedman and Savage in was the criticism that their was too to be used by any that criticism with the of the who does not know the the but as if he However, what Kahneman and Tversky was not to whether individuals were using a utility as their criterion to make but rather that a utility such as the one devised by Friedman and Savage predicted all actually predicted the of what individuals actually do when with or when Nyman that risk preferences do not lead to a realistic of he states that the theory of risk preferences does not for has no and is the very that Friedman to any good theory. Last, why is risk the theory of demand for insurance and gambling, despite all the empirical evidence against it or the fact that theoretical to it against empirical evidence, such as the one suggested by are and to Nyman offers an argument (pp based on some on the of To interpret risk aversion as the of the utility of income is and not a of that a lot of and the a of that some economists seem to He then suggests that the quid-pro-quo approach is rejected mostly because of as its main transfer in would and even open the to a on the role of the state when markets to reason he suggests is more based on the of any to accept a He also that the empirical of measuring income effects due to price effects to from the explain the of many to the new theory. I with these but would to to accept the quid-pro-quo approach is to accept that a cardinal utility of income that has some psychological that individuals actually value income, and the value they to different is an with a However, such a is as of the of the analysis of welfare, and as against and Of course, quite a few economists a of those who do applied use some of cardinal utility of income, or wealth when they run welfare A good is the of the standard this is a used by and to a cardinal value to the utility of income in situations uncertainty, they stated that no such cardinal value was when was no uncertainty, and, therefore, it should not be However, the standard is used to to health states in situations of certainty, as if individuals a value to health it is one thing to use a of cardinal utility in applied work and quite to an entire theory and welfare analysis on such a work on state-dependent utility, which stated happiness as a of cardinal utility under various prey to the same criticism from which explain why it is not more as an to make the quid pro quo approach more by the be to present it using the framework, what and in their on the demand for insurance, and In that the insurance-purchaser gambler is without any need for a utility of income and a quid-pro-quo compatible diminishing marginal utility of As and about risk be made of a to be a under one of and potential and a under (p In even though and about risk aversion in their the is not in their model of income across states of the and it the quid-pro-quo approach could be that framework, income and state-dependent utility simply by the of the across the first welfare analysis would need to and a cardinal utility of income and would be subject to the to about income and income effects among but it would be in that to as these three this is an and book by numerous that I the will This book should do a lot for the and of the quid-pro-quo as a alternative to a theory of demand for insurance and gambling that (as the book many empirical The book will be to anyone teaching in the economics of risk and insurance, as well as health I never the of diminishing marginal utility of income the and I know perhaps more it many fields of research in these to answer empirical of policy importance and with theoretical implications. In particular, I of empirical to decompose income and price effects in insurance, the value of income to the and to state-dependent utility based on The and and for very comments on a first of this