Why insurance works better with some adverse selection

Adverse selection, a process whereby low-risk individuals drop out of the insurance pool, leaving only high-risk individuals, arises when the individuals purchasing insurance have better information regarding their risk status than does the insurer. […] In the limit, adverse selection can make insurance markets unsustainable. Even short of the market disappearing altogether… The market cannot offer a full set of insurance contracts, reducing allocative efficiency.

The story summarised above (by Jeremiah Hurley) is familiar to all health economists. Adverse selection is generally understood to be a universal problem for efficiency in health insurance (and indeed all insurance), which should always be avoided or minimised, or else traded off against other objectives of equity. In my book, Loss Coverage: Why Insurance Works Better with Some Adverse Selection, I put forward a contrary argument that a modest degree of adverse selection in insurance can increase efficiency.

My argument depends on two departures from canonical models of insurance, both realistic. First, I assume that not all individuals will buy insurance when it is risk-rated; this is justified by observation of extant markets (e.g. around 10% of the US population has no health insurance, and around 50% have no life insurance). Second, my criterion of efficiency is based not on Pareto optimality (unsatisfactory because it says so little) or utilities (unsatisfactory because always unobservable), but on ‘loss coverage.’

In its simplest form, loss coverage is the expected fraction of the population’s losses which is compensated by insurance.

Since the purpose of insurance is to compensate the population’s losses, I argue that higher loss coverage is more efficient than lower loss coverage. Under this criterion, insurance of one high risk will contribute more to efficiency than insurance of one low risk. This is intuitively reasonable: higher risks are those who most need insurance!

If this intuition is accepted, the orthodox arguments about adverse selection seem to overlook one point. True, adverse selection leads to a higher average price for insurance and a fall in numbers of individuals insured. But it also leads to a shift in coverage towards higher risks (those who need insurance most). If this shift in coverage is large enough, it can more than outweigh the fall in numbers insured, so that loss coverage is increased.

My argument can be illustrated by the following toy example. The numbers are simplified and exaggerated for clarity, but the underlying argument is quite general.

Consider a population of just ten risks (say lives), with three alternative scenarios for insurance risk classification: risk-differentiated premiums, pooled premiums (with some adverse selection), and pooled premiums (with severe adverse selection). Assume that all losses and insurance cover are for unit amounts (this simplifies the discussion, but it is not necessary).

The three scenarios are represented in the three panels of the illustration. Each ‘H’ represents one higher risk and each ‘L’ represents one lower risk. The population has the typical predominance of lower risks: a lower risk-group of eight risks each with probability of loss 0.01, and a higher risk-group of two risks each with probability of loss 0.04.

In Scenario 1, risk-differentiated premiums (actuarially fair premiums) are charged. The demand response of each risk-group to an actuarially fair price is the same: exactly half the members of each risk-group buy insurance. The shading shows that a total of five risks buy insurance.

Scenario 1

 

The weighted average of the premiums paid is (4 x 0.01 +1 x 0.04)/5 = 0.016. Since higher and lower risks are insured in the same proportions as they exist in the population, there is no adverse selection.

Exactly half the population’s expected losses are compensated by insurance. I describe this as ‘loss coverage’ of 50%. (The calculation is (4 x 0.01 + 1x 0.04) / (8 x 0.01 + 2 x 0.04) = 0.50.)

In Scenario 2, risk classification has been banned, and so insurers have to charge a common pooled premium to both higher and lower risks. Higher risks buy more insurance, and lower risks buy less (adverse selection). The pooled premium is set as the weighted average of the true risks, so that expected profits on low risks exactly offset expected losses on high risks. This weighted average premium is (1 x 0.01 +2 x 0.04)/3 = 0.03. The shading symbolises that that three risks (compared with five previously) buy insurance.

Scenario 2

 

Note that the weighted average premium is higher in Scenario 2, and the number of risks insured is lower. These are the essential features of adverse selection, which Scenario 2 accurately and completely represents. But there is a surprise: despite the adverse selection in Scenario 2, the expected losses compensated by insurance for the whole population are now higher. That is, 56% of the population’s expected losses are now compensated by insurance, compared with 50% before. (The calculation is (1 x 0.01 + 2 x 0.04) / (8x 0.01 + 2 x 0.04) = 0.56.)

I argue that Scenario 2, with a higher expected fraction of the population’s losses compensated by insurance – higher loss coverage – is more efficient than Scenario 1. The superiority of Scenario 2 arises not despite adverse selection, but because of adverse selection.

At this point an economist might typically retort that that the lower numbers insured in Scenario 2 compared with Scenario 1 is suggestive of lower efficiency. However, it seems surprising that an arrangement such as Scenario 2, under which more risk is voluntarily traded and more losses are compensated, is always disparaged as less efficient.

A ban on risk classification can also reduce loss coverage, if the adverse selection which the ban induces becomes too severe. This possibility is illustrated in Scenario 3. Adverse selection has progressed to the point where only one higher risk, and no lower risks, buys insurance. The expected losses compensated by insurance for the whole population are now lower. That is, 25% of the population’s expected losses are now compensated by insurance, compared with 50% in Scenario 1, and 56% in Scenario 2. (The calculation is (1 x 0.04) / (8x 0.01 + 2 x 0.04) = 0.25.)

Scenario 3

 

These scenarios suggest that banning risk classification can increase loss coverage if it induces the `right amount’ of adverse selection (Scenario 2), but reduce loss coverage if it generates `too much’ adverse selection (Scenario 3). Which of Scenario 2 or Scenario 3 actually prevails depends on the demand elasticities of higher and lower risks.

The argument illustrated by the toy example applies broadly. It does not depend on any unusual choice of numbers for the example. The key idea is that loss coverage – and hence, I argue, efficiency – is increased by a modest degree of adverse selection.

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Sam Watson’s journal round-up for 12th June 2017

Every Monday our authors provide a round-up of some of the most recently published peer reviewed articles from the field. We don’t cover everything, or even what’s most important – just a few papers that have interested the author. Visit our Resources page for links to more journals or follow the HealthEconBot. If you’d like to write one of our weekly journal round-ups, get in touch.

Machine learning: an applied econometric approach. Journal of Economic Perspectives [RePEcPublished Spring 2017

Machine learning tools have become ubiquitous in the software we use on a day to day basis. Facebook can identify faces in photos; Google can tell you the traffic for your journey; Netflix can recommend you movies based on what you’ve watched before. Machine learning algorithms provide a way to estimate an unknown function f that predicts an outcome Y given some data x: Y = f(x) + \epsilon. The potential application of these algorithms to many econometric problems is clear. This article outlines the principles of machine learning methods. It divides econometric problems into prediction, \hat{y}, and parameter estimation, \hat{\beta} and suggests machine learning is a useful tool for the former. However, this distinction is a false one, I believe. Parameters are typically estimated because they represent an average treatment effect, say E(y|x=1) - E(y|x=0). But, we can estimate these quantities in ‘\hat{y} problems’ since f(x) = E(y|x). Machine learning algorithms, therefore, represent a non-parametric (or very highly parametric) approach to the estimation of treatment effects. In cases where functional form is unknown, where there may be nonlinearities in the response function, and interactions between variables, this approach can be very useful. They do not represent a panacea to estimation problems of course, since interpretation rests on the assumptions. For example, as Jennifer Hill discusses, additive regression tree methods can be used to estimate conditional average treatment effects if we can assume the treatment is ignorable conditional on the covariates. This article, while providing a good summary of methods, doesn’t quite identify the right niche where these approaches might be useful in econometrics.

Incorporating equity in economic evaluations: a multi-attribute equity state approach. European Journal of Health Economics [PubMedPublished 1st June 2017

Efficiency is a key goal for the health service. Economic evaluation provides evidence to support investment decisions, whether displacing resources from one technology to another can produce greater health benefits. Equity is generally not formally considered except through the final investment decision-making process, which may lead to different decisions by different commissioning groups. One approach to incorporating equity considerations into economic evaluation is the weighting of benefits, such as QALYs, by group. For example, a number of studies have estimated that benefits of end-of-life treatments have a greater social valuation than other treatments. One way of incorporating this into economic evaluation is to raise the cost-effectiveness threshold by an appropriate amount for end-of-life treatments. However, multiple attributes may be relevant for equity considerations, negating a simplistic approach like this. This paper proposed a multi-attribute equity state approach to incorporating equity concerns formally in economic evaluation. The basic premise of this approach is to firstly define a set of morally relevant attributes, to secondly derive a weighting scheme for each set of characteristics (similarly to how QALY weights are derived from the EQ-5D questionnaire), and thirdly to apply these weights to economic evaluation. A key aspect of the last step is to weight both the QALYs gained by a population from a new technology and those displaced from another. Indeed, identifying where resources are displaced from is perhaps the biggest limitation to this approach. This displacement problem has also come up in other discussions revolving around the estimation of the cost-effectiveness threshold. This seems to be an important area for future research.

Financial incentives, hospital care, and health outcomes: evidence from fair pricing laws. American Economic Journal: Economic Policy [RePEcPublished May 2017

There is a not-insubstantial literature on the response of health care providers to financial incentives. Generally, providers behave as expected, which can often lead to adverse outcomes, such as overtreatment in cases where there is potential for revenue to be made. But empirical studies of this behaviour often rely upon the comparison of conditions with different incentive schedules; rarely is there the opportunity to study the effects of relative shifts in incentive within the same condition. This paper studies the effects of fair pricing laws in the US, which limited the amount uninsured patients would have to pay hospitals, thus providing the opportunity to study patients with the same conditions but who represent different levels of revenue for the hospital. The introduction of fair pricing laws was associated with a reduction in total billing costs and length of stay for uninsured patients but little association was seen with changes in quality. A similar effect was not seen in the insured suggesting the price ceiling introduced by the fair pricing laws led to an increase in efficiency.

Credits

Meeting round-up: 18th European Health Economics Workshop (EHEW)

I attended the European Health Economics Workshop (EHEW) in Oslo. The workshop has been running for almost 20 years and it shows. Most participants have attended many editions of EHEW, which has and continues to shape the field of health economics theory. This is “the theory workshop”. The atmosphere is one of great friendship and constructive feedback, based on long-term collaborations that set the tone of the workshop. I am definitely not a theorist but found a very welcoming group of people, interested in fostering collaboration between theory, experiments, and empirical work.

EHEW is also a perfect example of the law of small numbers. The smaller the workshop, the more useful the feedback. The smaller the workshop, the larger the potential for fruitful research co-authorship.

Over two days, we went through 15 papers, building up to a total of not more than 30 participants, all of whom had an active role. The author presents in 25 minutes, followed by 10 minutes from the discussant and floor debate, a format that has become the golden rule.

We started off the proper way, with a wine reception at our headquarters hotel in downtown Oslo. I have to say, the organizers – Tor Iversen, Oddvar Kaarboe and Jan Erik Askildsen – did a terrific job. We all know what people remember from a workshop or conference: food and venue. It will be hard to beat EHEW Oslo (although we are possibly headed to Paris next year). We spent Friday and Saturday in an old stable, transformed into a delightful meeting room (see below). The catering was also on point, but what really stood out were the dinners. I think we can all agree that the dinner on Friday night was the best conference meal of all time; a 4-course dinner with paired wine at Restaurant Eik (I leave this here in case you ever go to Oslo – trust me, you want to go there.)

What about scientific content, you might ask? Jonathan Kolstad set the tone with an opening keynote lecture on the role of IT in physician response to pay for performance. The lecture combined theory with empirics, and I was rapidly drawn into a data-envy generating process. Tremendous physician and patient level data from the largest provider in Hawaii. Can you imagine the hardships of field work?

As for the presentations, we covered a broad range of topics. Luigi Siciliani, Helmuth Cremer and Francesca Barigozzi teamed up for a session on long-term care. Their theoretical approaches ranged from a standard IO two-sided market approach to strategic bequests and informal caregiving within the family. We had sessions on the regulation of drugs and unhealthy food, hospital, pharmaceutical and insurance markets, and on GP and health behavior. The paper by Marcos Vera-Hernandez (Identifying complementarities across tasks using two-part contracts. An application to family doctors) was a fantastic example of how to combine theory and empirical analysis. Johannes Schunemann gave a thought-provoking talk on The marriage gap: optimal aging and death in partnerships. I don’t quite agree with the assumptions and conclusions of the study, but then again I think that’s why I’m not a theorist… The main problem, in this case, is that there is nothing about the model that is specific to the variables being studied. We also covered the hot topic of antibiotic prescribing, with a model for prescription under uncertainty about resistance that got us all guesstimating our risk aversion.

The discussions within the workshop highlighted the potential benefits from having cross-field feedback. Empirically-minded researchers provided very useful feedback for theory articles, and vice-versa (for the few exceptions to the theory rule). In retrospect, I am convinced this arises from getting less caught up in technicalities of the theoretical model or the econometric specification, and placing a stronger emphasis on the basic assumptions of the models and the corresponding story.

All in all, we had a terrific time in Oslo. I was impressed by the level of collegiality amongst long-term participants, as well as their welcoming attitude towards newbies like myself. We worked hard and partied hard – even brought back dancing to EHEW – and I look forward to meeting up with the theorists in the near future. Lise, it’s on you!