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date: 18 January 2020

# Health Insurance and the Demand for Healthcare

## Summary and Keywords

Health insurance increases the demand for healthcare. Since the RAND Health Insurance Experiment in the 1970s this has been demonstrated in many contexts and many countries. From an economic point of view this fact raises the concern that individuals demand too much healthcare if insured, which generates a welfare loss to society. This so-called moral hazard effect arises because individuals demand healthcare that has less value to them than it costs to provide it. For that reason, modern health insurance plans include demand side cost-sharing instruments like deductibles and copayments. There is a large and growing literature analyzing the effects of these cost-sharing instruments on healthcare demand.

Three issues have recently received increasing attention. First, cost-sharing instruments such as yearly deductibles combined with stop losses create nonlinear price schedules and dynamic incentives. This generates the question of whether patients understand the incentives and what price individuals use to determine their healthcare demand. Second, it appears implausible that patients know the benefits of healthcare (which is crucial for the moral hazard argument). If patients systematically underestimated these benefits they would demand too little healthcare without health insurance. Providing health insurance and increasing healthcare demand in this case may increase social welfare. Finally, what is the role of healthcare providers? They have been completely absent in the majority of the literature analyzing the demand for healthcare, but there is striking evidence that the physicians often determine large parts of healthcare spending.

# Introduction

In his seminal article “Uncertainty and the Welfare Economics of Medical Care,” which may be seen as founding the field of health economics, Arrow stated that “the welfare case for insurance of all sorts is overwhelming. It follows that the government should undertake insurance where the market, for whatever reason, has failed to emerge” (Arrow, 1963, p. 961). He argues that the benefits of insurance (financial risk reduction) clearly outweigh the potential costs, such as moral hazard. In his comment on Arrow, Pauly (1968, p. 532) remarked that “for the welfare proposition given above to be valid, the costs of medical care must be random variables.” His argument is that “even if the incidence of illness is a random event, whether the presence of insurance will alter the randomness of medical expenses depends on the elasticity of demand for medical care.” In his view the case for health insurance becomes weaker when we allow for behavioral responses to the insurance-induced lower price of healthcare. Patients may demand more healthcare if they are insured. This is the well-known moral hazard effect of insurance. Arrow in turn replied by giving three possible ways an insurance company might ration “the amount of medical services it will support” (Arrow, 1968, p. 538): (a) close monitoring of all medical bills, only allowing those that are normal (where “normal” is defined as what would have been bought without insurance), (b) reliance on the professional ethics of physicians “not to prescribe frivolously expensive cost of treatment,” and (c) the reliance on “the willingness of the individual to behave in accordance with some commonly accepted norm.” Thus, Arrow imposed high ethical responsibility on both the supply and the demand sides of medical care. It is astonishing how much of the health economics debate in the 40 years that followed can be traced back to this exchange.

Arrow (1963) also provided results for the optimal design of health insurance. He showed that if insurance is not actuarially fair (which it never truly is) and if utility is not state dependent, the optimal health insurance contract was full insurance above a deductible. Later, Arrow (1974) showed that with health state dependent utility the optimal deductible fluctuates depending on how marginal utility varies with health status. Today, many health insurance plans are characterized by different levels of deductibles.

The aim of this article is not a review of the vast literature of estimating the price sensitivity of healthcare demand that has emerged since the debate between Arrow and Pauly. Such reviews have been provided by, among others, Cutler and Zeckhauser (2000), Finkelstein (2014), Swartz (2014), and Bundorf (2016). Rather, the aim is to highlight important insights and questions that have emerged in recent years. These include dynamic incentives created by health insurance plans with high deductibles, models that allow for behavioral mistakes (both in the choice of insurance plans and the demand for healthcare), and the role of healthcare providers.

Arrow attributed an important role to the supply side. However, this role was more or less ignored in the subsequent literature, in part because both Pauly (1968) and Zeckhauser (1970) framed their analysis of health insurance in terms of healthcare demand. As a consequence, the observed quantity of healthcare is determined solely by demand, with the supply side providing whatever the patients demand (the supply curve is horizontal with constant marginal cost). Almost detached from this literature, a separate strand analyzed the supply side with a focus on the effects of payment systems on the quantity of healthcare that is provided. This literature assumed that patients are more or less passive and accept any treatment offered by physicians.1 McGuire (2000) provides a survey of this literature on physician agency. Chandra, Cutler, and Song (2012) provide a rare attempt to combine the demand and supply sides to analyze treatment choices.

In the section “Theory,” I lay out a simple theoretical framework for healthcare demand and the choice of health insurance plan. The section “Empirical Evidence” provides a selective review of empirical studies with a focus on the effects of deductibles on healthcare demand. Because health insurance plans with deductibles create nonlinear price schedules, the section “Dynamic Incentives” provides a discussion of this issue. In the section “Behavioral Hazard,” I discuss the insights from models that allow behavioral mistakes such as assigning the wrong benefit to medical treatments. Finally, the supply side, which has been neglected in the discussion so far, is introduced in the section “The Role of the Supply Side.” The section “Concluding Remarks” provides some concluding remarks.

# Theory

In this section I first discuss a simple theoretical model of individual behavior that highlights the central issues with respect to healthcare demand and health insurance. Second, I briefly lay out the analysis of health insurance plan choice.

## Demand for Healthcare

Individual $i$ is assumed to have preferences over health $H$ and consumption $C$, represented by the utility function $Ui=u(Hi,Ci)$ satisfying the usual assumptions. Health is produced according to a concave production function given by $Hi=h(mi;θi)$, where $m$ denotes the input of medical services and $θ$ is an underlying random state variable affecting health, such as medical conditions or health shocks. This implies that utility is conditional on the realized value of $θ$. Consumption is defined as $C=Y−πj−γj(m)$, where $Y$ is income, $πj$ is the health insurance premium of plan $j$ (equal to zero if the individual is not insured), and $γj(m)$ are the out-of-pocket payments for the used healthcare services $m$ under plan $j$. Through the budget constraint, the optimal choice of healthcare is also conditional on the chosen health insurance plan.

To simplify the analysis, the resource costs of medical care are normalized to unity. This implies that $m$ corresponds to the social cost of providing $m$ units of healthcare. Without insurance, $m$ is equal to the out-of-pocket payments of the individual. In this setting, the price of healthcare an individual is facing is defined as the share of social cost of healthcare paid out-of-pocket by the individual. Denote this price by $p$. Without insurance, $p$ is equal to 1. One reason for defining the price this way is that in empirical applications we usually observe healthcare expenditures and the fraction that is paid out-of-pocket (i.e., $p$), not individual units of healthcare and their actual prices.

Assume for simplicity that the utility function is quasilinear in $C$, so the marginal utility of consumption is unity. Then, in equilibrium the following condition must hold

$Display mathematics$

where the right-hand side is the marginal benefit of healthcare, denoted by $b(m)$, and the left-hand side is the marginal cost of healthcare. This equilibrium constraint implicitly defines the demand for healthcare as a function of the price $p$ (and the underlying health status $θ$). The corresponding indirect utility is a function of income and the previously chosen health insurance characteristics, which determine the price of healthcare.

Without insurance ($p=1$), the private marginal utility of healthcare is equal to the marginal social cost of providing it. With insurance, we have $p<1$, so to maintain the identity the right-hand side must become smaller as well. Due to the concavity assumptions, this is achieved by increasing $m$. Now, the marginal private utility of healthcare is below the social cost of providing it (which is still 1). This is the mechanism creating moral hazard: individuals demand healthcare with marginal benefits that are below the marginal cost of providing it.

This simple model ignores (at least) three important aspects. First, cost-sharing instruments such as yearly deductibles combined with stop losses create nonlinear price schedules and dynamic incentives. This generates the question of what price individuals use to determine their healthcare demand. If they are forward-looking they anticipate their end-of-year price, which is close to zero if they expect to exceed the deductible. In that case the deductible should not influence their utilization decisions. If individuals are myopic, however, they make decisions based on the price of the next unit of healthcare. So there are at least two prices that patients may consider in determining their demand for healthcare. This problem has received a lot of attention recently (e.g., Aron-Dine, Einav, Finkelstein, & Cullen, 2015; Einav, Finkelstein, & Schrimpf, 2015) and is addressed in the section “Dynamic Incentives.”

Second, the assumption that patients know the health benefits of healthcare (i.e., ∂H/∂m) is crucial for deriving optimal healthcare demand. However, if patients were to systematically underestimate these benefits they would demand too little healthcare for any given price, so reducing the price through insurance may indeed increase the efficient use of healthcare. This phenomenon has been called behavioral hazard by Baicker, Mullainathan, and Schwartzstein (2015) and is discussed in the section “Behavioral Hazard.”

Third, as discussed in the introduction, the model assumes that all demanded healthcare is provided by more or less passive physicians. However, under fee-for-service payment systems physicians have incentives to provide more healthcare than patients are demanding, so observed spending may be driven by supply and not by demand.

## Insurance Choice

Insurance choice is a choice under uncertainty. Individuals do not know which health state $θ$ will realize in the next period. They only know the probability distribution of the possible health states, $F(θ)$. Assume that there are $J$ health plans to choose from, characterized by their premium $πj$, deductible $δj$, and stop loss $lj$. No insurance is also an option. The deductible and the stop loss determine $γj(m)$, the function of out-of-pocket payments under plan $j$. The individual chooses the health plan that maximizes her expected utility, where the expectation for health plan $j$ is computed by integrating all conditional utilities (on $θ$) over $F(θ)$.

In many real-world examples, some health plans among the choice set are dominated, that is, there is no level of healthcare costs at which this particular plan minimizes out-of-pocket payments. Still, many individuals choose these dominated plans (see, e.g., Abaluck & Gruber, 2011; Handel, 2013; or Heiss et al., 2016). As with the behavioral hazard mentioned previously, these findings suggest that individuals are prone to make mistakes in their evaluation of healthcare plans. We discuss potential explanations for these mistakes in the section “Behavioral Hazard.”

# Empirical Evidence

Several important studies empirically analyze the price responsiveness of healthcare demand. Given that cost sharing in modern health insurance typically takes the form of deductibles combined with a stop loss, this section focuses on studies that analyze the response of healthcare demand to the introduction of deductibles or changes in the deductible levels. The RAND Health Insurance Experiment, despite being somewhat dated, still serves as the benchmark for all empirical studies in this field, and a recent article by Brot-Goldberg, Chandra, Handel, and Kolstad (2017) exploits an informative natural experiment and an unusually rich data set, which allow the authors to gain important insights.

## The RAND Health Insurance Experiment

Between 1974 and 1981, the RAND Health Insurance Experiment (HIE) provided health insurance to more than 5,800 individuals from about 2,000 households in six different locations across the United States, a sample designed to be representative of families with adults under the age of 62. The experiment randomly assigned the families to health insurance plans with different levels of cost sharing, ranging from full coverage to plans that provided almost no coverage until a maximum of out-of-pocket payments (maximum dollar expenditure, mde) was reached. The mde was also randomly assigned, ranging from 5% to 15% of family income with a cap at $750 or$1,000. The main findings are summarized in Newhouse (1993), the most cited papers being Manning et al. (1987) and Keeler and Rolph (1988). Aron-Dine, Einav, and Finkelstein (2013) provide a reanalysis of the RAND data in the modern causal analysis framework. The main results of the original analysis hold when using the modern framework (e.g., the famous elasticity of –0.2).

This article focuses on only one comparison: the full insurance plan and the 95% copayment plan with a stop loss at the mde. The second plan is almost a high-deductible plan with a stop loss, comparable to many high-deductible plans that are in use at the moment in the United States and Europe. This links the RAND evidence to modern analyses of the effects of high deductibles. Aron-Dine et al. (2013) estimate an arc elasticity of –0.23 when comparing full insurance to a high-deductible plan.2 More impressive than the elasticity is the associated drop in medical spending by 38%.3 The effect is more pronounced for outpatient care (46%) than for inpatient care (25%). The probability of having positive spending falls by 17 percentage points, where almost all of this effect is driven by the reduced probability of positive outpatient spending (also 17 percentage points). This suggests that the reduced use of healthcare resulted primarily from participants deciding not to initiate care (the extensive margin), which is confirmed by the finding that the average cost per treatment episode does not vary significantly by plan assignment (Keeler & Rolph, 1988). This is a not really surprising but still important result; it points to the role of providers who seem to prescribe the same treatments independent of their patients insurance plans. This suggests that spending once in system is supply driven.

Further important findings of the RAND HIE include the result that cost sharing reduces the demand for both necessary and unnecessary care and that cost sharing has no immediate impact on health. Lohr et al. (1986) find that cost sharing reduces the use of less effective care by 26% and the use of effective care by 21%. Examples for the latter are reductions of 40% in the use of beta blockers and 44% in the use of insulin.4 Regarding the effects on health the results summarized in Newhouse (1993) suggest that cost sharing is associated with a slightly higher blood pressure, but many other health measures like cholesterol or hemoglobin levels are not significantly different across health plans.

The large empirical literature on the demand for healthcare following the RAND experiment is summarized by Cutler and Zeckhauser (2000) and Swartz (2014), among others. The main findings of the RAND study hold up very well for the most part. Some studies find substantially larger elasticities (e.g., Kowalski, 2016, who reports an elasticity of −1.5). Some recent studies suggest that the use of prescription drugs is very price sensitive (e.g., Hsu et al., 2006). Several studies confirm that cost sharing reduces the use of both effective and less effective care. For example, Chandra, Gruber, and McKnight (2010) analyze the effect of increasing the copay for drugs and estimate an elasticity of $−.15$ both for chronic care drugs and lifestyle drugs (cold remedies and acne medication).5 Overall, these findings suggest that there is more at play than only rational demand reactions; rational agents should cut down on low-value care, but not on high-value care if copayments are increased.

Finally, the Oregon health insurance experiment in 2008 also showed that the presence of full insurance increases healthcare spending across the board, including hospital admissions, emergency department visits, primary care, preventive care, and prescription drugs. This experiment, described in detail in Finkelstein et al. (2012) and Baicker and Schwartzstein (2013), is based on a lottery in the state of Oregon, which was used to allocate limited Medicaid slots to eligible adults. Also in this case, there is an increase in both high-value and in low-value care. Overall, the estimated increase of annual healthcare spending in the first year is 25% (Finkelstein et al., 2012, Table V). On the other hand, as in the RAND case, the beneficial effects on health are found to be limited. However, it is important to keep in mind that this experiment compares no insurance to full insurance, so not all of this spending increase should be considered as wasteful moral hazard.

## High-Deductible Plans

Brot-Goldberg et al. (2017) analyzed a natural experiment at a large self-insured firm that required all employees to switch from an insurance plan that provided free healthcare to a nonlinear, high-deductible plan. This change did not affect the set of providers and covered services, so only financial incentives changed. The authors distinguished three channels through which employees might react to the new insurance: (1) price shopping for cheaper providers, (2) quantity reductions, and (3) quantity substitutions to lower-cost procedures. They had access to administrative data over six consecutive years. The data included the universe of healthcare claims incurred by all employees and their dependents, including the total payment made both by the insurer and the employee as well as detailed codes indicating the diagnosis and procedures. In addition, age and gender, but also detailed job characteristics, income, and insurance plan characteristics were observed. Given the rich data at hand, Brot-Goldberg et al. (2017) were able to perform analyzes that are not possible with other data sets.

They found that the switch to the high-deductible plan caused an immediate spending reduction of between 11% and 15%, depending on how possible anticipatory spending was dealt with. Taking anticipatory spending into account is important because there is a visible increase in healthcare expenditures in the months prior to the reform (the reform was announced three years before it took place).6 The observed raw effect (a reduction by 18%) was biased because some individuals shifted the purchase of necessary medical care such as prescription drugs to the period prior to the reform.

Decomposing the overall spending reduction into the mentioned three channels revealed that quantity reductions were the only relevant channel through which healthcare spending was reduced. This was even true for the sickest quartile of the consumers, whose reaction appeared to be even stronger than the overall reaction. This is an important and somewhat surprising result given that the population under investigation was in general financially well off and faced reasonably low yearly out-of-pocket maximums. A recent paper using Swiss data (Boes & Gerfin, 2016) also found that the introduction of deductibles in HMO plans reduced the demand for healthcare almost exclusively on the extensive margin.

Next Brot-Goldberg et al. (2017) performed the decomposition analysis for a series of treatments that were considered to be of high value (e.g., preventive care, diabetes drugs) and low value (e.g., CT scans of sinus with acute sinusitis, antibiotics for respiratory infections). They found that the quantity of preventive care with prior diagnosis was reduced by 12% (despite the fact that preventive care remained free after the reform), the quantity of physical therapy was reduced by 30%, and the quantity of diabetes drugs was reduced by 48%. These are strong and undesired reactions to the introduction of the deductible. For low-value care there were large reductions across all of the considered low-value services in the range of 26% (CT scans for sinuses with acute sinusitis) to 44% (antibiotics for acute respiratory infections). The results so far clearly show who reduced spending (virtually everyone, including the sick) and how they did it (stop demanding treatments), but it does do not explain why they behaved like this.

The literature explicitly analyzing high-deductible plans (or consumer directed health plans) prior to Brot-Goldberg et al. (2017) was summarized by Bundorf (2016). By and large, most findings were consistent with the results described here: there was an overall reduction in healthcare spending by 5% to 14%, and both high-value and low-value care was reduced (although here the evidence is somewhat mixed, with some studies indicating that the reduction of low-value care is more pronounced).

There is a strong consensus in the empirical work starting with the RAND HIE that the extensive margin is the major channel through which consumers react to cost sharing, especially to deductibles. The bad news is that not only the demand for low-value care goes down but also the demand for high-value care, which may have negative impacts on health in the longer run.

# Dynamic Incentives

Deductibles with stop losses generate dynamic incentives by creating nonlinear price schedules, that is, the marginal price of healthcare falls with healthcare spending, so patients are able to influence the future price by the quantity they demand early on. If they are fully rational and forward-looking, they anticipate their end-of-year price and base demand in all periods on this price. If they are myopic, however, they make decisions based on the current marginal price (the “spot” price). The immediate consequence of this is that there is no unique price for healthcare, so the concept of a unique price elasticity cannot be maintained.

The RAND researchers were aware of this problem. Keeler, Newhouse, and Phelps (1977) developed a theoretical model for healthcare demand in the presence of deductibles and uncertain health shocks and showed that the theoretically correct price for consumers to use when making health consumption decisions is the marginal effective price.7 Using the realized end-of-year price as a proxy introduces a systematic measurement error, because it is always larger than the marginal effective price. For this reason, elasticity estimates will be biased if insurance policies in the sample contain deductibles, if the dependent variable is annual medical spending, and if the price is measured by the actual end-of-year price. Keeler et al. (1977) concluded that demand analysis by episode of illness was the appropriate framework in such circumstances, because for a specific episode the marginal price (i.e., the spot price) is the correct price measure to use. This of course requires that the data at hand contain information on illness episodes and their timing.

In their seminal article on estimating the elasticity of healthcare demand (the original source of the famous $−0.2$ estimate), Keeler and Rolph (1988) took account of these results and carefully made sure that they only included individuals who faced a constant price for their next medical episode by only including individuals and episodes that were sufficiently far away from the stop loss. An episode was defined as a perfectly known bundle of individual claims, depending on the diagnosis (for further details on the definition of episodes, see Keeler & Rolph, 1988; Aron-Dine et al., 2013). Their elasticity estimates are valid within their identification strategy (in which only spot prices are relevant) but should not be extrapolated to other settings. However, it appears that this has been done on a regular basis.8 Aron-Dine et al. (2013) demonstrated the problems that arise if you summarize a plan with a nonlinear price schedule by one price in order to obtain out-of-sample predictions. Using three different methods of mapping a nonlinear contract to a single price and applying the –0.2 elasticity leads to out-of-sample spending predictions that vary by a factor of 2.9 Hence it can be very misleading to summarize modern health insurance plans with one price. In this sense, it is somewhat unfortunate that the RAND elasticity is so prominent such that researchers are sometimes forced to convert their estimates into a single price elasticity in order to make it comparable to the RAND result, even if the comparison is not meaningful in the particular context.

Aron-Dine et al. (2015) used a different approach to test whether individuals respond to spot prices or expected end-of-year prices. Health insurance for the working population in the United States is usually provided by the employers. Workers who join the company later in the year have less time to hit the deductible, because independent of joining, date deductibles reset at the turn of the year. Hence, the expected end-of-year price is higher for late joiners. However, the spot price of the first unit of healthcare is the same for early and late joiners. Because the joining month is arguably independent of health status, this setup allows testing of the null hypothesis of myopia: under the null, early and late joiners have the same probability of initiating healthcare demand and the same spending amount for the initial claim (where initial refers to the first three months after joining). Aron-Dine et al. (2015) rejected the null, suggesting that individuals are not completely myopic. In a next step, they estimated the effect of the future price on initial spending. The future price is constructed as 1 minus the probability of hitting the deductible, conditional on joining month and plan type. Because this future price variable is likely to be endogenous, they instrumented it with a simulated future price (p. 734). The authors obtained an elasticity of having an initial claim with respect to the future price of about –0.16. They confirmed these findings using data from Medicare Part D, which provides prescription drug coverage for the elderly and disabled.

Einav, Finkelsteun, and Schrimpf (2015) also analyzed the Medicare Part D prescription drug benefit, which is characterized by a highly nonlinear price schedule.10 In 2008, the government-defined standard benefit design had an initial deductible of $275, which was followed by a 25% copayment rate on subsequent drug expenditures until total drug spending reaches$2,510. At this point, the copayment rate switched back to 100% until total drug expenditures reach $5,726, when catastrophic coverage sets in and the marginal out-of-pocket price of additional spending drops substantially. The range between$2,510 and $5,726 is often referred to as the “donut hole.”11 The authors showed significant bunching of annual spending levels around the kink created by the donut hole, as predicted by economic theory. Using detailed data on the timing of claims, they found a sharp decline in the claiming probability toward the end of the year for individuals who were close to the kink. In order to add more structure, the authors developed and estimated a dynamic model of a rational agent’s spending decisions within a year in the presence of a nonlinear contract design. Based on the estimated model, the counterfactual policy of eliminating the donut hole was evaluated. The result of this exercise was an increase of total annual drug spending by 8% per recipient and of Medicare drug spending by 25%. However, extending the model to allow for intertemporal substitution across the year suggests that the majority of the annual spending increase from filling the gap may be explained by patients who no longer shift claims to the subsequent year in order to avoid the coverage gap and not by an overall increase in spending. This is clear evidence for intertemporal substitution and suggests that it is important to analyze spending effects over horizons longer than one year.12 Lin and Sacks (2016) used the RAND data to analyze the importance of intertemporal substitution in the presence of nonlinear price schedules. They found that reaching the stop loss, which switches the effective price to zero, had a bigger effect on monthly healthcare spending and utilization in the remaining months compared to being in the free care plan. The intuition for this finding was that the former group would face high prices again, once the deductible reset at the end of the year. The estimated sensitivity to temporary price changes was substantially larger than the sensitivity to permanent changes. Patients appeared to stock up on healthcare when it went on “sale.”13 A similar result for Switzerland was shown in Gerfin, Kaiser, and Schmid (2015), who analyzed spending behavior after hitting the deductible and how this behavior changed when the deductible was reset. After hitting the deductible, individuals in high-deductible plans maintained the same level of spending until the end of the year, at which point spending was reduced immediately by 27%. The discussion of Brot-Goldberg et al. (2017) in the section “Empirical Evidence” ended with the question of why individuals behaved as described. To answer this question the authors carefully constructed measures of the spot price, the expected marginal end-of-year price (shadow price), and the prior year-end marginal price. They provided descriptive evidence showing that essentially all the observed spending reductions came from patients in periods in which they were still below the deductible. Given that the reduction in spending was also observed for less healthy individuals, this suggests that these individuals reacted to the spot price, because they expected to go beyond the deductible during the calendar year. These descriptive findings were confirmed by regression analyses, which showed that compared to shadow prices and prior end-of-year marginal prices, spot prices were the primary driver of the spending reductions. About 30% of all spending reductions come from patients with a very low expected shadow price in months in which they were still under the deductible. Furthermore, at least in the two-year period after the reform covered by the data, there was little evidence for learning to respond to the shadow price. These results are surprising because the employees in the company under analysis were mostly highly skilled and had high incomes. Hence liquidity constraints can be ruled out as an explaining factor for the spot price responses. Some possible explanations for the observed behavior are discussed in the next section. # Behavioral Hazard As mentioned in the section “Theory,” the standard model of healthcare demand is based on the assumption that individuals know the marginal benefits of healthcare. However, there is ample evidence that patients both under- and overestimate the benefits of some treatments. Examples for underestimation of high-value care include statins for heart attack patients, diabetes drugs, hypertension drugs, and preventive care. Examples for overestimation of low-value care are MRIs for low back pain, antibiotics for acute respiratory or ear infections, and Prostate-Specific Antigen (PSA) testing (see Schwartz et al., 2014; Baicker et al., 2015; Brot-Goldberg et al., 2017, for more examples and definitions of high-value and low-value care). Baicker, Mullainathan, and Schwartstein (2015) developed a model that explicitly allowed for behavioral mistakes (the model by Pauly & Blavin, 2008, is a special case of their model). Several psychologies may be the reason for the mistakes: individuals give more weight to salient symptoms like back pain or give too little weight to nonsalient symptoms like high blood pressure. They may be inattentive and forget to take their medications or refill their prescriptions. They may have false beliefs about the efficacy of care. They may be present biased such that they focus on the immediate costs of care (e.g., the out-of-pocket cost of a prescription drug) or are less concerned with the future benefits of treatment (e.g., avoiding complications caused by high blood pressure). Baicker et al. (2015) term these kind of mistakes “behavioral hazard” as opposed to moral hazard. Behavioral hazard is introduced by defining the marginal benefit individuals base their decisions on as $b˜(m)=b(m)+ε$, where $ε$ denotes the mistake individuals make and $b(m)$ is the true marginal benefit.14 If $ε>0$, individuals overestimate the true marginal benefit of treatment, whereas $ε<0$ means underestimation. So when deciding how much healthcare to demand, individuals set $b˜(m)$ equal to $p$, their out-of-pocket price. If $ε<0$, the true marginal benefit of $m$ is larger than $p$, so individuals forego treatment that has a larger private marginal benefit than private marginal cost, that is, the individual suffers a welfare loss. Reducing $p$ by decreasing cost sharing will increase the demand for healthcare as in the standard model, but now this increase not only may generate a social welfare loss (moral hazard) but also a private welfare gain (reduced behavioral hazard), so an overall reduction of cost sharing may enhance welfare.15 On the other hand, if $ε>0$, copayments must be increased in order to reduce the demand for healthcare that is overvalued by the consumers. This increase may be up to a 100% copayment and even beyond (penalizing the use of the overvalued treatment if the treatment is actually harmful). The main results of Baicker et al.’s (2015) research can be summarized as follows: with behavioral hazard, (1) a patient may not necessarily value treatment at the marginal cost; (2) demand responses may not measure the extent of moral hazard; and (3) measuring health responses may help to identify marginal benefits. The second result implies that the estimated change in quantity is no sufficient statistic for welfare calculations because observed demands may not correspond to true marginal benefits. The implications of these results were illustrated using the findings in Choudhry et al. (2011), who randomly assigned patients discharged after a heart attack to a control group with usual coverage (a copayment rate of 25% on average) and a treatment group with no copayments for drugs of known efficacy (e.g., statins) and tracked adherence rates and clinical outcomes over the next year. The treatment group increased the demand for these cardiovascular-specific prescription drugs by approximately$100 on average. Applying the standard moral hazard analysis to these findings decomposes the increase of $100 into a moral hazard effect of$75 and a health value effect of $25 (see Baicker et al., 2015, p. 1645, for details for this computation). Using the data on clinical outcomes allows estimatation of the health value in a different, more direct manner. Choudhry et al. (2011) found that the mortality rate in the treatment group was smaller by 0.3 percentage points. Applying the commonly used estimate of the value of a statistical life of$1 million to the reduction in mortality implies that the elimination of copayments has a health value of \$3,000, which is substantially larger than the health value obtained from the standard analysis. This is admittedly a very crude estimate of the health value, but it still suggests that the standard model implies that people place an unrealistically low value on their life and health. The example highlights the problem that interpreting observed demand changes as reflecting changes in marginal health benefits may be severely misleading for welfare analysis.

Baicker et al. (2015) also analyzed the consequences of behavioral hazard on the optimal design of health insurance. A main result of this analysis was that the presence of behavioral hazard health insurance can both provide financial protection and improve healthcare efficiency. Further, they showed that the optimal cost sharing depends both on demand responses and the health value of the treatment. For a given demand response, cost sharing should be lower when reducing demand has larger adverse effects on health (as illustrated in the heart attack victim experiment described earlier). These results can be connected to the idea of value-based insurance design, which postulates that, c.p., cost sharing should be lower for higher value care (Chernew, Rosen, & Fendrick, 2007). In other words, the average value of care may serve as a good signal for the optimal cost sharing. However, such differential cost sharing is still uncommon in practice, mostly because it renders the health insurance contract very complicated, both in terms of writing it down and of understanding it. Nevertheless, the Choosing Wisely initiative in the United States and the National Institute for Health and Care Excellence (NICE) in the United Kingdom demonstrate that it is possible to specify low- and high-value care in order to guide both physicians and patients.16

There is some evidence of the effectiveness of value-based insurance. The majority of studies have examined programs that reduce cost sharing for high-value services. These studies show that reduced cost sharing for high-value services can increase use of these services, but the response has been rather modest. Choudhry et al. (2011) is an example, and Look (2015) provides an overview. Gruber et al. (2016) was one of the first to address higher cost sharing for a range of low-value services by analyzing a value-based insurance program in the state of Oregon. Patient cost sharing for services considered to be of low value or overused by patients was increased by 46–156%. Gruber et al. found that the use of the targeted services fell by 12%, which was a much larger effect compared to results found for high-value care. This asymmetry may be explained by loss aversion (the copayment reduction is considered to be a financial gain, the increase a financial loss) and by the fact that patients not buying high-value medication do not learn that the price has decreased, whereas the price increases are salient because they are directed at people already using the services.

Dalton, Gowrisankaran, and Town (2017) attempted to identify whether there is evidence for behavioral hazard in Medicaid Plan D. They analyzed drug purchase decisions within a calendar year, which are dynamic because each drug purchase moves the consumer closer to the coverage gap. Their behavioral models allowed for (1) quasihyperbolic discounting of future periods or (2) limited price salience. The standard neoclassical model is a limiting case of both behavioral models. They first tested for deviations from the standard model and then estimated the structural parameters of both behavioral models. The estimated parameters were used to assess the importance of behavioral hazard and the impact of policies such as eliminating the coverage gap.

The sample was restricted to individuals who were close to the coverage gap early in the year. These individuals would enter the coverage gap almost with certainty, so a rational agent would not react to entering the gap. Hence, under the neoclassical model drug purchases should be smooth around the point of entry to the coverage gap. The behavioral models, however, implied that there would be a discontinuity in drug purchases at the entry point. This was the basis for the test of the neoclassical model. The results provided strong evidence against the neoclassical model. Individuals significantly reduced their prescription drug purchases upon reaching the coverage gap: mean drug spending fell by 28% and the number of filled prescriptions fell by 21%.

The estimation results of the structural behavioral models indicate that the price salience model fits the data better, because the quasihyperbolic discounting model cannot explain the sharpness of the drop in drug spending at the start of the coverage gap. This suggests that future coverage gap prices are not fully salient when individuals are still in the initial coverage region.17 However, once they get close, they realize the impact of the coverage gap. The counterfactual analysis of filling the donut hole predicts an increase in drug spending by 10%. A limitation of the models estimated by Dalton et al. (2017) is that they do not allow for intertemporal substitution, a feature that has been shown to be important by Einav and Schrimpf (2015).

There may also be a behavioral explanation for the observed mistakes in health insurance plan choice, which put many individuals in dominated plans. This article focuses on the literature analyzing plan choice in Medicare Part D.18 Early articles in this literature, such as Abaluck and Gruber (2011), find that for a substantial fraction of enrollees initial plan choices are dominated in the sense that plans exist that generate lower total costs than those in the chosen plan. Abaluck and Gruber (2016) later found that forgone savings from choosing suboptimal plans increased during the first four years of Medicare Part D, implying that there was little learning over time. Standard models of consumer choice attribute inertia to switching costs, but several studies found that switching costs must be unrealistically high to explain the observed inertia (e.g., Ho, Hogan, & Morton, 2015). In order to account for this, Heiss et al. (2016) used data from Medicaid Part D and estimated a two-stage panel data model of plan choice, where the two stages corresponded to two separate causes of inertia: inattention and switching costs. They found that the model with a separate attention stage fit the data better and provided more realistic estimates of switching costs. Patients were more likely to pay attention to plan choice if overspending in the previous year was salient and if the cost of their old plan increased. Their results provided evidence for an important interaction between inattention and salience of expected out-of-pocket payments. The literature in this field has made a lot of progress in recent years in the identification of behavioral causes for the observed inertia.

# The Role of the Supply Side

All of the evidence presented so far is implicitly based on equating healthcare spending to healthcare demand, assigning a passive role to providers. But in reality, providers play an important role in determining healthcare spending. One clear indication for this is the finding from the RAND HIE (and other studies) that patients decide on initiating healthcare episodes, but once they are in the system their utilization decision possibilities are limited. This implies that it is the physicians who determine most of the spending once a patient has initiated a contact. Furthermore, a large part of healthcare spending is generated by a relatively few high-cost patients whose spending is far above the range where deductibles and copayments play a role.19 This suggests that incentives for providers of healthcare for this patient class may be more important to control overall healthcare spending than demand side incentives for all classes of patients.

The literature on physician agency provides clear predictions on how physicians behave under different reimbursement systems. The classic model by Ellis and McGuire (1986) predicts that under a fee-for-service system physicians have an incentive to provide more healthcare than the (insured) patient would demand, even if they are perfect agents of the patient. Under a prospective system physicians have an incentive to provide less healthcare than the patient would demand, unless they are perfect agents of the patient. Agency is measured by the weight the physicians give to patient benefits relative to profits in their utility function. McGuire (2000) provides an overview of the empirical evidence on physician agency and physician-induced demand until the year 2000. Chandra et al. (2012) provides one of the first attempts to consider both demand side and supply side factors in modeling treatment choice. However, their focus was mostly on explaining small-area variations in practice styles.

In recent years some studies have been published estimating the effects of reimbursement reforms on the quantity of healthcare services. While these studies attribute the quantity effects to provider behavior, they allow provider behavior to be influenced by patients’ benefits, which enables them to explain the observed large effect heterogeneity by healthcare service. This feature was not present in the earlier empirical studies on provider reactions to price changes summarized in McGuire (2000).

Clemens and Gottlieb (2014) exploited the 1997 consolidation of geographic payment regions in Medicare, which reduced the number of payment regions nationally from 210 to 89 and led to area-specific price shocks that were plausibly exogenous. They used these price changes to estimate the effect of prices on care provision and patient health. The authors developed a theoretical model in which supply decisions drove the quantity of healthcare because patients were both insured and uninformed. Still, welfare in this model was tightly linked to patient health benefits because of the weight physicians attributed to patient benefits in their objective function (a perfect agent has a weight of 1, an imperfect agent of less than 1). The model predicted that supply responses were small when the marginal benefit curve was steep. This feature applies to emergency care, which has high benefits for a small fraction of the population and no benefit for the remainder. On the other hand, elective procedures like joint replacements offer moderate benefits for many patients, implying rather flat marginal benefit curves. The empirical analysis revealed that healthcare supply had a relatively large elasticity of around 1.5 with respect to reimbursement rates, indicating that healthcare supply was much more price sensitive than demand. As predicted by the model, physicians’ responses were strongest among relatively elective services. The authors concluded that when patients are well insured, physician discretion over what services to prescribe is an important driver of total healthcare spending. In their model, the quantity of health services would be socially optimal when the reimbursement rate was equal to the marginal benefit of treatment. This suggests that value-based reimbursement rates hold the promise of containing costs without losses in quality. This is an important analogy to the idea of value-based insurance, and the knowledge on low-value and high-value care can inform both insurance and reimbursement design. Physicians get low utility from prescribing low-value care when reimbursements are close to marginal cost because both patient benefits and profits are small. High-value care with a significant wedge between reimbursement and marginal cost, on the other hand, generates high utility. Hence, in such a system, incentives for physicians are clearly meant to provide efficient high-value care.

Chen and Lakdawalla (2016) exploited the same Medicare reform as Clemens and Gottlieb (2014) to analyze whether there is heterogeneity in price elasticities across medical procedures. They found substantial heterogeneity in price elasticities with both positive and negative elasticities. They denoted markets with positive elasticities as physician-driven and markets with negative elasticities as patient-driven. In order to generate explanations for the empirical findings, they extended the classic Ellis and McGuire (1986) model to allow physicians to care about patient benefit as well as patient spending. The optimality conditions of this model are weighted averages of the conditions for physician profit-maximization and patient utility-maximization. From a welfare perspective, for patient-driven services, classic moral hazard is more important to address (increasing patient cost sharing reduces physician utility), while physician reimbursement is more important for physician-driven services (as mentioned previously, the lever is making physicians’ profit a function of the value of care). Overall, their analysis suggested that policies aimed at reducing healthcare spending cannot be uniform reductions in reimbursement rates or uniform increases in patient cost sharing, but a mixture of both, depending on the sign of the price elasticity of the service.

Long-term care is a healthcare sector that is characterized by above-average spending growth. At the same time, it is a costly sector, so demand incentives are not likely to have an impact on quantity if patients are well insured. Hence the payment system for providers of long-term care is crucial for controlling costs. Eliason, Grieco, McDevitt, and Roberts (2016) and Einav, Finkelstein, and Mahoney (2017) analyzed a feature in the Medicaid reimbursement system in which providers were reimbursed a daily amount up to a threshold length of stay, at which point there is a large increase in payments for keeping a patient one additional day beyond the threshold, but no payments for any days beyond it. This sudden increase amounts to more than 50% of the cumulated reimbursements at the threshold. This schedule introduces a strong financial incentive to keep patients one day beyond the threshold in order to benefit from the “bonus” payment, but marginal health benefits around the threshold stay constant (or may even fall, as Eliason et al., 2016, argued). Both papers found significant bunching of the length of stay at the threshold, as predicted by economic theory. Both papers estimated structural models of long-term care hospital discharge decisions and applied them to evaluate counterfactual payment systems. Both found that there were payment systems that would provide substantial savings for Medicare (approximately 5%) without adversely affecting patients, sometimes even with increasing provider profits. This example illustrates that there is scope to significantly reduce healthcare spending by eliminating unfortunate provider incentives.20

# Concluding Remarks

Since Arrow (1963), a huge literature has emerged demonstrating that healthcare spending is increasing with the generosity of health insurance. While the earlier literature attributed this increase to moral hazard, that is, inefficient overuse, recent findings suggest that at least part of this increase may actually be efficient, because insurance encourages uninformed patients to buy treatments with objective health benefits greater than the subjective benefits, on which the patients base their demand decisions. Such behavioral hazards, such as insufficient adherence to hypertension drugs after a heart attack, have been identified repeatedly in the literature. These insights may prove to be of utmost importance for the optimal design of health insurance, which should allow health insurance to take on two roles: financial security and efficient provision of healthcare. Another takeaway from recent research is that insurance design should take into account that (dynamic) incentives may lead to undesired behavior. Examples include intertemporal substitution or discontinuation of high-value care.

Arrow attributed an important role to healthcare providers with respect to healthcare spending. This role has been more or less ignored in the research following Arrow, but several recent articles attempt to integrate both the demand side and the supply side in their analyses. In this sense, the research on health insurance and healthcare spending is beginning to come full circle. As mentioned in the final section, a system in which both patient cost sharing and provider reimbursement are functions of the value of healthcare holds the promise of aligning patient and provider preferences and improve the efficiency of medical care.

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## Notes:

(1.) Jonathan Gruber in Finkelstein (2014) also mentions this divide. In his view, the supply side perspective dominates the political discourse about containing healthcare costs.

(2.) Arc elasticities are used because in the full insurance plan, the price of healthcare is zero. Starting with a price of zero, a percent change is not well defined, so arc elasticities are easier to work with.

(3.) In Finkelstein (2014) Joseph Newhouse, one of the original RAND researchers, states that he believes it is more informative to report the percentage effects than the elasticities because the elasticities tend to dwarf the size of behavioral effect. In addition, reporting the percentage effect circumvents the problem of defining the price for which the elasticity in computed (see the section “Dynamic Incentives” for further discussions of this point).

(4.) These numbers are taken from Table 2 in Baicker and Schwartzstein (2015).

(5.) Also from Table 2 in Baicker and Schwartzstein (2015), which also provides further examples.

(6.) See Fig. 1 in Brot-Goldberg et al. (2017).

(7.) The marginal effective price at time $t$ is a function of demand prior to $t$ and of the time remaining in the year. If demand is linear, the correct price to use is the average of all marginal effective prices over the year.

(8.) For example, the US Congressional Budget Office regularly uses this elasticity estimate (Finkelstein, 2014, p. 33). I once had a discussion with a Swiss Office for Public Health representative who wanted to apply this elasticity to quantify the spending effects of changing deductible levels.

(9.) The three ways are a dollar-weighted average price, a person-weighted average price, and a person-weighted average end-of-year price.

(11.) Individuals may buy plans that have more coverage than the standard plan, so that the exact contract design varies across individuals. However, the described general features exist in all plans.

(12.) Another paper allowing for a period longer than one year is Cabral (2016).

(13.) This may explain the relatively large elasticity estimates reported in some studies. These studies instrument the realized end-of-year price by random events such as accidents, which unexpectedly put healthcare on “sale” for the rest of the year (e.g., Kowalski, 2016).

(14.) $b˜$ is the decision benefit and $b$ is the experienced benefit in the terms of Kahneman, Wakker, and Sarin (1997).

(15.) This is the case analyzed by Pauly and Blavin (2008).

(16.) For more information on Choosing Wisely, see http://www.choosingwisely.org. NICE publishes guidelines that determine the National Health Service’s coverage of healthcare technologies for specific diseases and conditions. Volpp, Lowenstein, and Asch (2012) discuss the merits and problems of Choosing Wisely.

(17.) Abaluck, Gruber, and Swanson (2015) also find evidence for limited price salience in Medicare Part D.

(18.) Studies analyzing the choice behavior of employees in private firms are, for example, Handel (2013) and Handel and Kolstad (2015).

(19.) An analysis of the claims data of a large Swiss health insurance company reveals that the top 10% spenders account for almost 60% of total healthcare spending.

(20.) Eliason et al. (2016) cite a Wall Street Journal article which describes meeting during which hospital staffers would discuss treatment plans, “armed with printouts from a computer tracking system that included, for each patient, the date at which reimbursement would shift to a higher, lump-sum payout.”