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.

Sharing the burden of healthcare: providing care to our sickest patients

One of the major challenges to affordable, universal health insurance is the high cost of providing care to the sickest patients. According to Roy Vaughn, senior vice president at BlueCross BlueShield of Tennessee, “just 5 percent of the company’s marketplace customers had accounted for nearly 75 percent of its claims costs.” What is the cost of healthcare for the typical person in the United States?Distribution of per capita US health expenditures 2012

Data from 2012, the last year for which a full analysis is available, presents a complex and confusing picture. The graph above shows per capita expenditures by percentile starting with the highest per capita expenditure. 10% face expenditures of at least $10,250. The median per capita expenditure was $854. The mean average per capita expenditure was $4309 – five times the median – and “the top 1 percent ranked by their healthcare expenses accounted for 22.7 percent of total healthcare expenditures with an annual mean expenditure of $97,956″. In brief, there is no typical person: since the bottom 50% accounted for 2.7% of total expenditures, the average per capita expenditure of the top 1% was 420 times that of the bottom 50%. There really is no typical person in terms of healthcare expenditures.

Pareto/ power law distribution of healthcare costs

This extreme distribution of healthcare costs (approximately an “80/20”, Pareto/ power law distribution) poses a major challenge to providing universal healthcare through traditional insurance models based upon risk pooling. Prior to the Affordable Care Act (ACA), the US health insurance industry addressed these challenges with risk selection – adjusting premiums or denying insurance to patients with high predicted risks, such as those with pre-existing conditions, and imposing caps on annual and/or lifetime benefits, much like the way the auto insurance industry sets premiums and limits benefits to address extreme differences in projected driver risks. Come back tomorrow for another blog post with more technical details about the Pareto distribution and healthcare costs.

Risk selection is illegal but prevalent

The ACA makes both caps on benefits and risk selection based upon pre-existing conditions illegal. In particular, US insurance carriers are required to provide coverage to all, at rates independent of pre-existing conditions, a requirement which President-Elect Donald Trump would like to keep.

However, the extreme distribution of healthcare costs means that “Targeting the highest spenders represents the greatest opportunity to have a significant impact on overall spending”; an opportunity for insurance carriers as well as for public policy. Moreover, there are good predictors for high spending: age and end of life, chronic conditions, and high spending in a previous year. For example 44.8% of the top decile in 2008 healthcare expenditures “retained this top decile ranking with respect to their 2009 healthcare expenditures”; a fact cited in an extensive Forbes report. Swiss and Dutch experience found risk selection prevalent and persistent. However, with every adult paying the same premium – within a given fund for the same type of contract – but expected healthcare expenditure (HCE) varying widely, strong incentives for risk selection are created in the absence of an adequate risk adjustment scheme. Although risk selection is illegal, it is prevalent. Swiss conglomerates of insurance carriers have been reported to achieve risk selection by assigning applicants to “specific carriers based on their risk profiles.”

Removing the economic incentives for risk selection

There is one clear way to avoid built-in economic incentives for risk selection (incentives which seem to drive insurance company behavior); that is, a single payer system, universally or as excess coverage for significant, predictable expenses. The United States now has several parallel single payer systems, namely Medicare for the elderly, Medicaid for the very poor and CHIP for children; thus, in effect, a public/private partnership in healthcare. These pre-existing single-payer systems might serve as models for a more inclusive US single payer system. Alternatively, the United States might act as an insurer of last resort, providing umbrella insurance covering individual expenses above some relatively high limit, or for costly but treatable conditions using the End Stage Renal Disease (ESRD) Program, passed in 1972 as a model. This approach would also remove extreme costs from the health insurance risk pool, as both Medicare and the ESRD Program do now, by providing near-universal coverage for our sickest patients outside the private insurance system (elderly US citizens and those with severe chronic kidney disease, respectively).

Tomorrow I will return to the Pareto-like distribution of healthcare expenditures and its consequences for any competitive insurance program. But for now, a few conclusions. Medicare and the ESRD program provide models for a smooth transition from health insurance pre-ACA with its caps and limitations to a more universal system. Medicare can be expanded to a broader public alternative. Universal coverage for additional treatable but high-risk conditions can be modeled on the ESRD program. These steps should provide the basis for further evolution of the present public/private partnership into a more universal, more cost-effective system.

In my opinion, the extreme distribution of healthcare expenditures and the ability to perform risk selection, even though illegal, present a strong, essentially irrefutable argument for a single payer system; either overall, or for chronic conditions and expenditures predictable through risk selection. In the US, Medicare and the ESRD program provide illustrative, successful and useful models.