# Behavioral hazard in health insurance

Suppose your health insurance becomes more generous, decreasing the proportion of the cost of care for which you are responsible. At the same time, your premium goes up to cover the extra costs faced by your insurer. In standard theory you are better off because you face less financial uncertainty, but you will also tend to consume too much health care because the price you pay is lower than the cost of your treatment. Standard theory suggests that insurance should be designed to optimally trade-off these benefits and costs. But standard theory assumes rationality: suppose instead people systematically make errors when choosing how much health care to consume. Does it make a difference to how we think about health insurance?

In a recently released NBER working paper, “Behavioral hazard in health insurance,” Katherine Baicker, Sendhil Mullainathan, and Joshua Schwartzstein consider behavioral biases that lead people to (specifically, and with loss of generality) underutilize health care. How should we think about designing health insurance in the presence of such biases?

We have solid evidence that changing the copayment (the amount you pay) affects use of care, so the design of health insurance plans matters for both our finances and our health. For example, the graph shows results from the RAND health insurance experiment, in which people were randomly assigned various levels of health insurance. People assigned to pay high prices for care used less care. In Canada, patients face a copayment of zero for “necessary” care, which suggests we get way too much health care—lots of treatments for which costs exceed benefits. We’re over at the level of care associated with a coinsurance rate of zero in the graph, and the standard model tells us that even small out-of-pocket payments from patients would greatly reduce demand for treatments. Further, we should expect those treatments to have very little net benefit, so we might greatly reduce costs at little consequence to our health.

The standard model helps us to explain overuse of expensive care with low health benefits. However, it is difficult to reconcile with evidence that people often underutilize certain treatments: treatments with minimal side effects, low prices, and large health benefits. For example, Choudry et al (2011) show that eliminating a roughly $20 copayment heart attack patients made for statins, beta blockers, and other drugs substantially increased adherence. The standard model requires us to infer that patients who would take the drugs at a price of zero but not at$20 either receive less than $20 worth of health benefits from the drugs or experience severe side effects which greatly reduce net benefit. Neither of these hypotheses sits well with the clinical evidence on efficacy and side effects. Baicker et al consider behavioral models to help understand such outcomes. They start with a simple rational choice model as a point of departure. There is one illness with severity $$s$$ which varies across people. Everyone pays an insurance premium (or tax) $$P$$, and people who choose to receive treatment must also pay a copayment $$p$$. The treatment leads to an increase in health worth $$b(s)$$, with $$b'(s)>0$$. A person with income $$y$$ who receives treatment gets utility $$U( y – P – s + b(s) – p)$$ and a person who does not receive treatment gets $$U( y – P – s)$$. In this simple setup a person will choose to receive treatment if $$b(s)>p$$, that is, if the health benefits are worth more to them than the copayment they must make. Since people are rational and have full information in this model, anything that makes price deviate from marginal cost then causes inefficiency ex post. Optimal insurance contracts in this environment involve over-utilization when people are rational and risk-averse. The copayment that maximizes social welfare, $$p^*$$, satisfies $$\frac{c-p^*}{p^*} = \frac{I}{\eta}$$, where $$c$$ is the cost of providing treatment, $$I$$ is the benefit of reduced financial risk (which depends on the curvature of the utility function), and $$eta$$ is the elasticity of demand for care. More elastic demand implies more moral hazard, and more moral hazard means copayments should be higher. For example, if the price of a visit to an emergency room rises from$50 to $100 and almost no one is deterred from emergency care, then moral hazard is not a big issue and insurance mostly reduces risk, which means in turn that we should heavily insure emergency care. As the authors emphasize, policy makers in this world only need to know the elasticity of demand and the degree of risk aversion to design optimal insurance systems, they do not need to know how effective care is (the schedule $$b(s)$$) because rational fully-informed agents make their decisions on the basis of health benefits. The result that the elasticity of demand determines optimal insurance leads to some strange conclusions. For example, demand for beta blockers appears to be about as elastic as demand for cold remedies, even though beta blockers are “essential” and cold remedies are not (to put it mildly). A policy maker should then set similar copayments for cold remedies and beta blockers. But suppose people make systematic errors. They choose treatment if $$b(s) + \epsilon(s) > p$$, where $$\epsilon(s)$$ can represent a variety of “internalities,” that is, behavioral biases, including present bias, inattention, and false beliefs (systematic over or underestimation of efficacy). Here, $$(b(s)-p)$$ is the “experienced utility” of treatment whereas $$(b(s) + \epsilon(s) – p)$$ is the “decision utility” of treatment. Conventionally, these coincide: if you choose A over B, you are better off with A. Here, when you choose A over B, you might be better off with B. In effect, the paper considers what happens when we allow for the possibility that demand does not coincide with marginal benefits, and much of the analysis is similar to standard analysis of activities with positive externalities, for example, vaccines against communicable diseases. Subsidizing such a vaccine such that price falls below marginal cost can be sound policy; similarly, we may want insurance to decrease the price of some treatments below cost, even if everyone is risk neutral. The graph illustrates the outcome with behavioral underutilization: suppose first that price is set to equal marginal cost. The blue line is the demand curve, so the outcome is Q treatments. However, marginal benefits do not coincide with demand, marginal benefits are given by the green line. Setting the price to zero through full insurance increases treatments to Q’. In the standard model, we would conclude that moral hazard leads to a welfare loss equal to area shaded green. In the behavioral model, we instead conclude that setting the price to zero increases welfare by an amount equal to the area of the blue triangle. In the behavioral model, the optimal copayment satisfies $$\frac{c-p^*}{p^*} = \frac{I}{\eta} – \frac{\epsilon'(\tilde s)}{p^*}$$, where $$\epsilon'(\tilde s)$$ is approximately equal to $$\epsilon(\tilde s)$$ (see page 18 for details) and $$\tilde s$$ denotes illness severity for the patient who’s just indifferent to treatment. The standard model is the special case in which $$\epsilon’=0$$ and the second term on the right-hand side disappears. Optimal insurance now depends on more than just the elasticity of demand $$eta$$ and the value of financial risk reduction $$I$$. Treatments with larger behavioral distortions (more negative values of $$\epsilon’$$) should have lower copayments, holding $$\eta$$ and $$I$$ constant. Cold medication and beta blockers need not have the same copayment. Even if everyone were risk neutral so that $$I=0$$, it would be still optimal to provide insurance, because insurance can correct the behavioral issues leading to inefficiently low levels of care. If behavioral issues are severe enough, it may even be optimal to force people to pay more than marginal cost, or subsidize rather than charge for treatment. The authors present an empirical illustration of how dramatically these effects can change standard results. Again consider the heart attack patients studied by Choudry et al (2011). The standard model forces us to conclude that eliminating the copayment for heart attack drugs leads to extra costs of about$106 per patient and extra health benefits worth about $26 per patient. The incremental care provided when copayments are eliminated costs more than it’s worth; moral hazard reduces welfare by about$106 – $26 =$80 per patient. The standard model tells us to conclude that eliminating copayments is bad policy. The behavioral model, conversely, implies that the incremental care is worth roughly $3,000 per patient, not$26. According to the behavioral model, eliminating copayments is a very good policy.

What do these results imply for health care in Canada? One immediate implication is that frequently-proposed small copayments for necessary care may not be good policy. Usually, a large demand response to small copayments would be considered evidence that Canadians consume lots of care they don’t really need, that is, that moral hazard is prevalent. But we should also consider the possibility that people mistakenly forego high net benefit treatments due to behavioral bias. If we were to introduce copayments, we should do so selectively: charge people for only types of care with low health benefits or for which patients (or physicians) tend to overestimate health benefits.