Chapters 3–6 argued that a degree of restriction on risk classification leading to adverse selection can be beneficial to the population as a whole, provided that the adverse selection does not go ‘too far’. This argument implicitly assumes that restrictions can easily induce sufficient adverse selection to go ‘far enough’. If adverse selection is in fact a weak and unreliable phenomenon, there might be even less reason to be worried about unintended consequences of restrictions on risk classification. The main problem of adverse selection might then often be that there is not enough of it (in the sense that more adverse selection would produce higher loss coverage).
It turns out that for most insurance markets and contexts, the empirical evidence for adverse selection is indeed weak and equivocal when compared with the strong predictions of insurance theory. Many econometric studies which were conceived in the expectation of demonstrating adverse selection have failed to do so. Unsurprisingly, there are exceptions: some studies do find evidence for a certain amount of adverse selection. But where adverse selection can be demonstrated, it often relates to minor contract features chosen by the insured, rather than the overall amount of cover chosen by the insured. There is almost no evidence for the more florid rhetorical representations, such as the ‘adverse selection spiral’ which insurance folklore predicts will quickly destroy any insurance market where risk classification is restricted. This chapter reviews some of the empirical evidence on adverse selection.
Interpretations of Adverse Selection: Informational, Competitive and Spiral
The question of whether adverse selection is evident in an insurance market can be interpreted in three ways: informational adverse selection, competitive adverse selection or the ‘adverse selection spiral’.
Economists tend to interpret the question as one about information asymmetry between insurers and their customers: do customers know more about their risks than insurers, after whatever risk classification methods the insurers choose to apply? Economists tend to assume axiomatically that any information advantage will be exploited, and therefore be capable of detection by observation of customers’ purchasing decisions. This is the main concept of adverse selection used in this book, and in other chapters I refer to it simply as ‘adverse selection’. But in this chapter, I shall call this interpretation informational adverse selection.
The second interpretation, which is often more salient to actuaries and others concerned with practical insurance pricing, is that adverse selection is about competition between insurers: are innovations in risk classification an important means by which one insurer can gain advantage over other insurers? In this chapter, I shall call this interpretation competitive adverse selection.
The third interpretation is that restrictions on adverse selection will lead to an adverse selection spiral in which the market eventually collapses. A succinct statement of this concept is given in the policy document Insurance & superannuation risk classification policy published by the Institute of Actuaries of Australia, which I quoted in Chapter 1 and repeat here:
In the absence of a system that allows for distinguishing by price between individuals with different risk profiles, insurers would provide an insurance or annuity product at a subsidy to some while overcharging others. In an open market, basic economics dictates that individuals with low risk relative to price would conclude that the product is overpriced and thus reduce or possibly forgo their insurance. Those individuals with a high level of risk relative to price would view the price as attractive and therefore retain or increase their insurance. As a result the average cost of the insurance would increase, thus pushing prices up. Then, individuals with lower loss potential would continue to leave the marketplace, contributing to a further price spiral. Eventually the majority of consumers, or the majority of providers of insurance, would withdraw from the marketplace and the remaining products would become financially unsound.Footnote 1
To clarify the distinction between the first two interpretations, note that when a new risk classification variable is introduced by one insurer, this can lead to competitive adverse selection, even when there is no asymmetry of information between customers and insurers, and hence no informational adverse selection. For example, in recent decades some insurers have introduced ‘postcode pricing’ (zip code pricing): lower prices for life insurance or higher prices for annuities for customers living in affluent areas. This may lead to competitive adverse selection against insurers who do not use postcodes in pricing. But customers have not suddenly acquired better information than insurers about their own addresses, which have been known to insurers for every policy ever written.Footnote 2
Another way of characterising the distinction between informational adverse selection and competitive adverse selection is to note that the first is about games customers play with insurers and the second is about games insurers play with each other.Footnote 3
Most empirical tests for adverse selection have been conducted by economists, and so focus on informational adverse selection. Competitive adverse selection seems to be much less formally studied, and so we have to rely mainly on anecdotal examples. For evidence on the ‘adverse selection spiral’, we again have to rely on anecdotal examples – or rather, the lack of credible examples.
Econometric Tests for Informational Adverse Selection
In testing for informational adverse selection, it is usually difficult to make comparisons between purchasers and non-purchasers of insurance, because insurers generally do not collect data on the losses of non-purchasers. Tests of informational adverse selection therefore generally focus on differences in realised losses and levels of cover between different purchasers of insurance across an insurer’s clientele, rather than differences between purchasers and non-purchasers across the whole population. Informational adverse selection implies that purchasers who experience higher losses will have purchased more cover, where ‘more’ may mean choosing a larger sum insured, or a smaller deductible, or other product features which give greater coverage.
Econometric tests for informational adverse selection are therefore typically based on testing for a positive covariance (or equivalently, correlation) between realised losses and quantity of insurance purchased. There are three main approaches: univariate, bivariate or non-parametric tests.
Univariate Regression Tests
A regression with a single dependent variable (i.e. ‘univariate’ regression) is carried out:
where
– Lossi is a variable representing the ex post realisation of the risk of policyholder i
– Coveri is a variable representing the quantity of insurance purchased by policyholder i
– Xi is a vector of all the characteristics of policyholder i observable by the insurer and potentially relevant to the risk.Footnote 4
Adverse selection is then said to be present in the market if the regression estimates β > 0 with significance.
Bivariate Regression Tests
The second approach is separate models for losses and amounts of cover (i.e. ‘bivariate’ regression), with the following two regressions carried out:
where Lossi, Coveri and Xi are defined as before.Footnote 5 Then the correlation between the residuals from the two regressions is examined. A significant positive correlation of ηi and ɛi indicates informational adverse selection.
Non-parametric Tests
The third approach avoids the restricted functional forms of the tests above by using non-parametric chi-squared tests for independence.Footnote 6 Suppose there are m explanatory variables used in risk classification, each of which can be represented as a dummy (0, 1) variable (e.g. in car insurance 0 for small engine, 1 for large engine). Then we can define 2 m ‘cells’, and allocate to each cell all individuals in the insurer’s clientele who have exactly the same set of values for all the explanatory variables. For example if we have three explanatory variables, we need 23 = 8 cells to cover all possible combinations of the three (0, 1) explanatory variables.
Then for each of the eight cells, a 2 × 2 table is created from counts of the numbers of individuals having each combination of loss and cover (high–low loss, high–low cover). Then we test the independence of loss and cover, conditional on being in a given cell. If the null hypothesis of independence holds good in every cell, then there is no informational adverse selection.
Relating These Tests to the Model in Chapters 4–6
The concept of informational adverse selection which is evaluated using tests such as those above can be related to the model used in Chapters 4–6, but it is not fully represented in that model.
In the tests above, informational adverse selection is defined as a positive covariance of realised losses and cover in the insurer’s clientele, after controlling for explanatory variables observable by the insurer (e.g. gender, age, etc.). In other words, informational adverse selection is standardised such that the ‘null’ corresponds to covariance which is fully explained by the explanatory variables. The rationale for this standardisation is that in most real-world markets, risk classification is largely unrestricted, so insurers can adjust (and economists tend to assume, will adjust) premiums to allow for any covariance explained by observable explanatory variables. Covariance which is so explained does not represent an informational advantage of the customer.
Previously in the model in Chapters 4–6, adverse selection was defined as simply a positive covariance of losses and cover in the whole population. There was no concept of controlling for explanatory variables observable by the insurer (there was only one explanatory variable, membership of risk-group 1 or 2, which was observable by all and fully explained the risk). Instead, adverse selection was standardised by the concept of adverse selection ratio, such that ‘null’ adverse selection was the value under risk-differentiated premiums.
A comparison of concepts between this chapter and Chapters 4–6 is summarised in Table 8.1.
| Concept | Variable or method in Chapter 8 | Closest equivalent in Chapters 4–6 |
|---|---|---|
| Quantum of cover | Coveri | Realisations of Q |
| Quantum of realised loss | Lossi | Realisations of L |
| Explanatory variables | Vector Xi (e.g. age, gender, etc.) | Risk-groups 1 and 2 |
| Adverse selection | Positive correlation of Coveri and Lossi in insurer’s clientele | Positive correlation of Q and L in whole population |
| Standardisation concept | Control for Xi (i.e. correlation explained by observables is the null) | Use adverse selection ratio (i.e. correlation with risk-differentiated premiums is the null) |
Limitations of These Tests
Three limitations apply equally to all three of the above approaches – univariate, bivariate and non-parametric – to testing for informational adverse selection.
First, a correlation between realised losses and cover may be a consequence of moral hazard (behaviour after buying insurance) rather than adverse selection (behaviour when buying insurance). Since the two phenomena are generally indistinguishable in the data, tests for informational adverse selection have to be based on an assumption that moral hazard is not a significant factor.
Second, the focus on decisions about amounts within the insurer’s clientele, a subset of the population, neglects decisions across the wider population to forgo insurance altogether. This is an understandable consequence of data limitations, but it possibly overlooks an important locus of informational adverse selection.
Third, if customers vary their purchase decisions according to expected losses, but stringent underwriting is fully effective in classifying this behaviour, all three approaches will characterise the situation as one of ‘no informational adverse selection’. Actuaries and underwriters might not agree with this characterisation: their perception might be that adverse selection is strong, but is being countered by vigilant underwriting. In other words, actuaries and underwriters sometimes regard informational adverse selection as a behavioural tendency which can be fully offset by underwriting, and so is not normally expected to be observable after underwriting. This expansive concept of adverse selection is not amenable to testing using data from insurance policies after underwriting, so I shall not consider it further.
Evidence on Informational Adverse Selection
Econometric tests of informational adverse selection as outlined in the previous section have typically produced null results.Footnote 7 Examples include life insurance,Footnote 8 car insurance,Footnote 9 health insuranceFootnote 10 and fire insurance.Footnote 11 Outside of insurance, even in the used vehicle market – the canonical example in the ‘lemons’ model of informational adverse selectionFootnote 12 – pickup trucks purchased in the second-hand market have been found to require no more maintenance than other trucks of similar age and mileage.Footnote 13 Some studies have even found a negative relationship between risk and insurance purchase – the opposite to that predicted by adverse selection. ‘Negative’ informational adverse selection (advantageous selection) is discussed later in this chapter.
There appears to be some evidence for informational adverse selection in annuity markets in the UK based on the insured’s shrewd choice of contract features rather than the amount of the annuity.Footnote 14 Specifically, annuitants who choose contracts with more ‘back-loading’ of payments – increases in line with the retail prices index, or no initial guaranteed payment period – tend to live longer. Also, annuitants who do not choose a spouse’s benefit payable after their own death tend to live longer. The better evidence for selection in annuities compared with insurances may be a reflection of the more likely nature of the contingent events under an annuity, which gives more scope for a large difference between probabilities as assessed by the customer and by the insurer (a large information edge). The idea of the customer’s information edge is discussed further in Chapter 11.
There is some evidence for informational adverse selection in crop insurance in agriculture in the USA.Footnote 15 Again, this may reflect the relatively likely nature of the events over which selection is exercised, which gives scope for a large difference between customer and insurer probability assessments, and hence a large information edge. Also, a farmer is a ‘repeat player’ who can learn from experience and smooth results over several years. This is a more promising context for the customer to exploit any superior information than the ‘one-shot gamble’ of a typical life insurance purchase.
Evidence on Competitive Adverse Selection
As noted earlier, there seem to be no econometric investigations of competitive adverse selection, and so we have to rely on anecdotal evidence.
(a) Postcode pricing for annuities. This has already been covered earlier in this chapter, in the section defining informational adverse selection and competitive adverse selection. To recap: the introduction of lower prices for life insurance or higher prices for annuities for customers living in affluent areas may lead to competitive adverse selection against insurers who do not use postcodes in pricing. In the UK, once one large insurer (Legal and General) adopted postcode pricing for annuities in 2007, other insurers quickly followed, possibly because of concerns about competitive adverse selection. Note that there was no question of insurers not knowing their customers’ addresses, and thus no possibility of informational adverse selection.
(b) Nonsmoker discounts for life insurance. Before the early 1980s, the UK life insurance market functioned well with no distinction by smoking status, despite the link with mortality having become increasingly apparent in the medical literature from the 1950s onwards.Footnote 16 But once a few large companies offered a nonsmoker discount, other companies quickly followed, and within a few years almost all companies differentiated life insurance prices by smoking status. It seems plausible that this was a response to competitive adverse selection (although we cannot disprove the alternative that it was merely fashion). Note that customers always had private knowledge of their smoking status, but nobody suggested that this led to adverse selection prior to the competitive innovation.
(c) Telematics for car insurance. A possible future example of competitive adverse selection is more widespread use of telematics in car insurance. At present, the installation and data transmission costs of ‘black box’ tracking mean that insurance priced from telematics data is a niche market; the costs are viable only for policies with high risk premiums (e.g. very young drivers). But if costs fall and a few companies successfully market telematics to the wider market, this may be particularly attractive to conscientious or low-mileage drivers, who anticipate receiving discounts for their lower risk. Higher-risk drivers might then become overrepresented in other companies’ clienteles. This competitive dynamic might then pressure all companies to offer a telematics option. As in the postcode and nonsmoker examples, the competitive adverse selection arises from the innovation; there is no change in customers’ information about their risk, and no informational adverse selection.
Evidence on ‘Adverse Selection Spirals’
The ‘adverse selection spiral’ concept is very influential in both academic and policy discussions. But it is rare to find well-documented reports of real examples. There are many examples of markets where regulators impose substantial restrictions on risk classification without causing a market collapse. Examples of partial restrictions include the prohibition on using gender, race or genetic test results in many insurance markets. More comprehensive (albeit not quite total) bans on risk classification are common in health insurance. Examples include voluntary health insurance schemes in Ireland and Australia; and in the USA, Obamacare (formally the Patient Protection and Affordable Care Act) allows rating only by age, geographical location and smoking status. The persistence of these schemes indicates that not all restrictions on risk classification lead inevitably to an ‘adverse selection spiral’.Footnote 17
One supposed example often cited by academic economists involves, rather parochially, health insurance for employees of Harvard University.Footnote 18 The employees were offered a choice between different plans with different benefits, originally with an employer contribution as a fixed percentage of the (different) premiums for different plans. The employer contribution was then changed to the same flat contribution irrespective of which plan the employee chose. This led to a rapid migration of younger (presumably healthier) employees from the more expensive plan with better benefits to the cheaper plan with lower benefits. The more expensive plan suffered reducing enrolments and progressively increasing per capita costs, leading to its withdrawal 3 years later.
But this example is essentially a case of selection against one insurer among many (competitive adverse selection) in a scenario where different health insurance plans offered differing benefit structures and premiums. It is not the same as the selection against the whole market (informational adverse selection) which it is said will lead to collapse of the market when risk classification is banned for all insurers. In the scenario of multiple health plans, the various choices are reasonably close substitutes, and so demand elasticity for any one plan may be high; but in the scenario where risk classification is banned for all insurers, remaining uninsured is often not a close substitute for being insured, and so demand elasticity for insurance from all providers will probably be low.
As well as not being supported by many real-world examples, florid metaphors such as ‘adverse selection spiral’ or ‘death spiral’ are not supported by models of insurance markets with restricted risk classification. In the models in Chapter 4–6, with plausible demand elasticities for low and high risks, an equilibrium is reached well before the point where only high risks remain insured. For the market to ‘spiral’ to the point where only a few very high risks remain insured requires an implausible divergence of demand elasticities for low and high risks.
Advantageous Selection
Sometimes the evidence from empirical tests for informational adverse selection is not merely null, but actually negative: a statistically significant coverage-loss correlation is found, but it has the wrong sign. In other words, people who incur lower losses tend to have bought more insurance (the opposite of the prediction of adverse selection). This was first described as propitious selection, but is now more often called advantageous selection.Footnote 19
Advantageous selection – ‘wrong sign’ correlation of cover and losses – can be explained by considering a third variable, financial risk aversion. Higher financial risk aversion means that an individual is prepared to pay more for insurance against a given quantum and probability of loss. In some contexts, it seems psychologically plausible that financial risk aversion might be negatively correlated with risk level. This is particularly plausible where risks are partly endogenous, in the sense of being determined by the character of the insured. In other words, ‘cautious’ individuals may be both more financially risk averse, and more inclined to take more preventive health and other precautions. When all risks are pooled at a single price, financial risk aversion negatively correlated with risk level implies lower insurance demand from higher risks. This can offset – or sometimes more than offset – higher demand from higher risks for whom the pooled price appears cheap (as in the usual adverse selection story).
Two papersFootnote 20 by David Hemenway which introduced the concept of propitious selection give evidence for several examples using US data, including:
– for car drivers, a positive correlation between purchase of noncompulsory liability insurance and a range of health-related risk avoidance activities
– also for car drivers, a positive correlation between purchase of noncompulsory liability insurance and not driving after drinking alcohol
– for motorcyclists, a positive correlation between wearing a helmet and holding medical insurance.
Similarly, it has been shown that those who are most cautious about their health (as measured by participation in preventive health checks) are the most likely to purchase long-term care insurance, and yet the least likely to enter nursing homes.Footnote 21 Other markets where a negative correlation between insurance coverage and losses has been documented in empirical studies include medigap insurance (drugs coverage in the USA), health insurance in Australia and commercial fire insurance.Footnote 22
Despite these examples, I suspect advantageous selection is probably not a typical aggregate outcome in insurance markets. Weak adverse selection is probably more common. But advantageous selection is, at the very least, common enough to falsify the traditional notion that all selection is always one way.
Empirical Estimates of Demand Elasticity
One reason why econometric studies may fail to detect informational adverse selection could be that customers do have some superior information, but are not very motivated to act upon it. Purchasing decisions may reasonably be more influenced by the customer’s perceived need for insurance, such as providing for family or ill health, and by life events such as house purchase, rather than by exploiting small bargains in insurance prices. A slightly lower price or slightly higher risk may not make much difference to buying decisions. In other words, the price and risk elasticities of demand for insurance may be low. Empirical estimates of price elasticity of demand for various classes of insurance are indeed low, typically very roughly around –0.5; some figures were summarised in Table 5.1.
Big Data and Adverse Selection
Most of the evidence in this chapter showing that informational adverse selection is generally a weaker phenomenon than insurance theory suggests is several years old. Informational adverse selection depends on insureds having some information advantage over the insurer in knowledge about their risks. The increasing availability to insurers of big data from new surveillance technologies as described in Chapter 13 may mean that any information advantages which insureds may have enjoyed in the past may become less prevalent in the future. Hence in the absence of new restrictions on risk classification, informational adverse selection may become even weaker in future than it is in the empirical studies reported in this chapter.Footnote 23
Summary
This chapter has reviewed evidence for three concepts of adverse selection: informational adverse selection (games customers play with insurers), competitive adverse selection (games insurers play with each other) and the ‘adverse selection spiral’.
The adverse selection spiral is the most rhetorically appealing but least well-evidenced of these three concepts. The idea of a progressive spiral whereby restrictions on risk classification always lead to market collapse is a major theme of insurance folklore. But it is not supported either by equilibrium models of insurance markets with realistic elasticity parameters, or by convincing real-world examples.
Informational adverse selection, which arises from an information advantage of customers which is reflected in their purchasing decisions, is a central concept of insurance theory. Evidence for this concept, while not entirely absent, is surprisingly weak and equivocal compared with the strong predictions of insurance theory. Empirical estimates of insurance demand elasticity are typically low. This suggests that even where customers do have some private information about risk, they may not be very motivated to act on it.
Competitive adverse selection, which arises from the efforts of insurers to gain an advantage over competitors by introducing new ways to differentiate risks, is probably more robust than the two concepts above. Adverse selection in practice is often more about games insurers play with each other, rather than games customers play with insurers.
