# Thesis Thursday: Mathilde Péron

On the third Thursday of every month, we speak to a recent graduate about their thesis and their studies. This month’s guest is Dr Mathilde Péron who graduated with a PhD from Université Paris Dauphine. If you would like to suggest a candidate for an upcoming Thesis Thursday, get in touch.

Title
Three essays on supplementary health insurance
Supervisors
Brigitte Dormont
https://basepub.dauphine.fr/handle/123456789/16695

How important is supplementary health insurance in France, compared with other countries?

In France in 2016, Supplementary Health Insurance (SHI) financed 13.3% of total health care expenditure. SHI supplements a partial mandatory coverage by covering co-payments as well as medical goods and services outside the public benefit package, such as dental and optical care or balance billing. SHI is not a French singularity. Canada, Austria, Switzerland, the US (with Medicare / Medigap) or the UK do offer voluntary SHI contracts. A remarkable fact, however, is that 95% of the French population is covered by a SHI contract. In comparison, although the extent of public coverage is very similar in France and in the UK, the percentage of British patients enrolled in a private medical insurance is below 15%.

The large SHI enrolment and the subsequent limited out-of-pocket payments – €230 per year on average, the lowest among EU countries – should not hide important inequalities in the extent of coverage and premiums paid. SHI coverage is now mandatory for employees of the private sector. They benefit from subsidized contracts and uniform premiums. Individuals with an annual income below €8,700 benefit from free basic SHI coverage which covers copayments, essentially. However, the rest of the population (students, temporary workers, unemployed, retirees, independent, and civil servants) buy SHI in a competitive market where premiums generally increase with age.

Can supplementary health insurance markets lead to an adverse selection death spiral?

Competitive health insurance markets are subject to asymmetric information that prevent the existence of pooling contracts (Rothschild and Stiglitz, 1976Cutler and Zeckhauser, 1998). The US market is a good example; in the 1950s not-for-profit insurance companies (Blue Cross, Blue Shields) – which offered pooled contracts – almost all disappeared (Thomasson, 2002). And, despite a notably higher public coverage that could limit adverse selection effects, the French SHI market is not an exception.

Historically, SHI coverage was provided by not-for-profit insurers, the Mutuelles, who relied on solidarity principles. But as the competition becomes more intense, the Mutuelles experience the adverse selection death spiral; they lose their low-risk clients attracted by lower premiums. To survive, they have to give up on uniform premiums and standardized coverage. Today 90% of SHI contracts in the individual market have premiums that increase with age. It is worth noting that in France insurers have strong fiscal incentives to avoid medical underwriting, so age remains the only predictor for individual risk. Still, premiums can vary with a ratio of 1 to 3, which raises legitimate concerns about the affordability of insurance and access to health care for patients with increasing medical needs.

How does supplementary health insurance influence prices in health care, and how did you measure this in your research?

A real policy concern is that SHI might have an inflationary effect by allowing patients to consume more at higher prices. Access to specialists who balance bill (i.e. charge more than the regulated fee) – a signal for higher quality and reduced waiting times – is a good example (Dormont and Peron, 2016).

To measure the causal impact of SHI on balance billing consumption we use original individual-level data, collected from the administrative claims of a French insurer. We observe balance billing consumption and both mandatory and SHI reimbursements for 43,111 individuals from 2010 to 2012. In 2010, the whole sample was covered by the same SHI contract, which does not cover balance billing. We observe the sample again in 2012 after that 3,819 among them decided to switch to other supplementary insurers, which we assume covers balance billing. We deal with the endogeneity of the decision to switch by introducing individual effects into the specifications and by using instrumental variables for the estimation.

We find that individuals respond to better coverage by increasing their proportion of visits to a specialist who balance bills by 9%, resulting in a 32% increase in the amount of balance billing per visit. This substitution to more expensive care is likely to encourage the rise in medical prices.

Does the effect of supplementary insurance on health care consumption differ according to people’s characteristics?

An important result is that the magnitude of the impact of SHI on balance billing strongly depends on the availability of specialists. We find no evidence of moral hazard in areas where specialists who do not charge balance billing are readily accessible. On the contrary, in areas where they are scarce, better coverage is associated with a 47% increase in the average amount of balance billing per consultation. This result suggests that the most appropriate policy to contain medical prices is not necessarily to limit SHI coverage but to monitor the supply of care in order to guarantee patients a genuine choice of their physicians.

We further investigate the heterogeneous impact of SHI in a model where we specify individual heterogeneity in moral hazard and consider its possible correlation with coverage choices (Peron and Dormont, 2017 [PDF]). We find evidence of selection on moral hazard: individuals with unobserved characteristics that make them more likely to ask for comprehensive SHI show a larger increase in balance billing per visit. This selection effect is likely to worsen the inflationary impact of SHI. On the other hand, we also find that the impact of a better coverage is larger for low-income people, suggesting that SHI plays a role in access to care.

As an economist, it’s interesting to reflect on your own decisions, isn’t it? Well, I master cost-benefit analysis, I have a good understanding of expected utility and definitely more information than the average consumer in the health insurance market. Still, my choice of SHI might appear quite irrational. I’m (reasonably) young and healthy, I could have easily switched to a contract with lower premiums and higher benefits, but I did not. I stayed with a contract where premiums mainly depend on income and benefits are standardized, an increasingly rare feature in the market. I guess that stresses out the importance of other factors in my decision to buy SHI, my inertia as a consumer, probably, but also my willingness to pay for solidarity.

# 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.

# “Doing the math” on the distribution of healthcare expenditures: a Pareto-like distribution is inevitable

Yesterday I explored one of the major challenges to affordable, universal health insurance, namely the high cost of providing care to the sickest patients. 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  to reduce costs by risk selection, as well as for public policy. Here is a deeper look into the math behind the distribution of healthcare expenditures, using 2012 US data as a model.

One can fit a Pareto (power law, 80/20) distribution with scale coefficient $\alpha$ – that is, $prob(expenditure)\sim 1/expenditure^{\alpha+1}$ – to the data in several ways. For a Pareto distribution with scale coefficient $\alpha$, the per-capita expenditure at a given percentile from the top scales as $1/\%ile^{1/\alpha}$. The first two of these approaches yield a scale coefficient $1/\%ile^{0.893}$, with expenditures scaling as :

1. Use the 80/20 rule modified to fit the data: the top 25% ranked by healthcare expenditures account for 86.7% of costs; thus $\alpha=1.115$.
2. Use the ratio of mean to median expenditure, 5.05:1; thus $\alpha=1.119$.
However, a graphical analysis finds that the data does not follow such a Pareto distribution, shown as a black dashed line in the following figure (representing a Pareto distribution with $\alpha=1.117$ and median expenditure $854, the actual median expenditure). 3. Use data for the most expensive patients (10% through 30% percentiles from the top), for these patients, per-capita expenditure scales as $1/\%ile^{1.24}, (R^{2}=0.994)$, shown as a dashed red line in the figure above; thus $\alpha=0.806$. 4. Use the fraction of total expenses paid by the most expensive patients. A comparison of the fraction of expenses paid by the most expensive 1%, 5% and 10% finds that this scales as $x^{0.4228}, (R^{2}=0.987)$, shown as a dashed black line in the figure below. This scaling exponent is $1-1/\alpha$; thus $\alpha=1.733$. (Scaling added to figure modified from Cohen, 2014) Thus, there really is no typical patient. For discussion and implications, see Feyman, who called the empirical distribution of healthcare costs “worse than Pareto”. The Pareto-like (hyper-Pareto?) empirical distribution of expenditures presents a severe challenge to risk pooling through insurance without limiting the highest expenditures through risk selection (illegal!). Pareto distributions differ sharply from normal distributions, with important consequences for payment models. For a Pareto-like distribution with $\alpha\leq2$ at large expenditures, the variance is not defined, and sample variance approaches infinity with increasing sample size. Therefore, unlike the case of distributions with finite variance, variability in the mean of a sample of size N does not decrease with N. This violates a standard requirement for insurance; that risk pooling over a large sample reduces variability in the mean expenditure, and thus, standard insurance models cannot effectively price health insurance when the highest per capita expenditures follow Pareto distributions. Moreover, a Pareto-like distribution may be a natural consequence of advances in healthcare: our growing ability to manage multiple simultaneous chronic conditions, with consequent exponential growth in costs, while extending life expectancy, so that the probability of dying is not only not reduced, but may actually increase. In a mathematically limiting case, with no bound on healthcare costs, these dynamics yield a Pareto distribution. In fact, if one extrapolates the power law for a broad range of the sickest patients (the 10th through 30th percentiles of expenditures from the top), obtaining a Pareto distribution with $\alpha\leq1$, even the mean is not defined and the sample mean approaches infinity with increasing sample size. The actual distribution of healthcare cost for the very sickest patients clearly falls below the empirical Pareto distribution with $\alpha=0.806$, such a distribution predicts a cost at the 1st percentile of$178,194, well above the average for the top 1% of \$97,956. Deviations from this distribution for the very sickest patients may reflect current limits on healthcare and thus healthcare expenses. These limits may be relaxed with advances in healthcare, causing further growth in costs.

A Pareto-like distribution of healthcare costs is here to stay, and must be reflected in how we share the burden of healthcare and provide care to our sickest patients.

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