Optimal Ins (Theory)

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A recent paper by Hai Zhong (2011) finds that health insurance that provides immediate reimbursement for health care services significantly increases the likelihood of patients seeking outpatient treatment in China compared to reimbursement beneficiaries with a delay. China isn’t the only country where insurance companies provide delayed reimbursement. In fact, in France patients pay the full cost of physician visits up front and only later are reimbursed 70 percent of the cost.

Why would the delayed reimbursement make a difference? I can think of three reasons.

  1. Liquidity Constraints.  Some individuals may not be able to afford the payment.  Poor individuals may literally not have the capital to pay for these services up front.  Getting loans from formal institutions (e.g., banks) or informal ones (e.g., friends and family) may be costly either in terms of interest of obligations to family and friends.  Even if an individual is rich, acquiring extra money may be costly (e.g., trip to ATM, ATM fees, interest on credit card).
  2. Probability of Non-Payment.  Although may policies are written where payment is assured, in practice reimbursement rates will not be 100 percent.  For instance, individuals could fail to submit the correct forms for reimbursement, they could move addresses, or the patient could die.  In addition, patients may have some uncertainty surrounding the benefits covered and thus they may not be 100% sure that they will receive reimbursement.  Beneficiaries may not trust their insurance plan; they may assume it is trying to cheat them and thus with some non-zero probability the beneficiary will not get paid.
  3. Reflection of value.  Even if a patient is rich and payment probabilities are 100%, the patient may still be less likely to use the service if they don’t need it if they realize the true cost.  Alternatively, patients who realize a service is valuable may also be more likely to use it.
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Many economists claim that insurance that gives  sick people cash to pay for their medical treatments is more efficient than insurance that provides in-kind medical services directly.  Although providing in-kind services is more likely to decrease the number of false claimants than insurance that provides cash, cash benefits allow beneficiaries to control how they spend their money.  These patients will generally be more frugal since any savings in medical spending goes directly into their pocket.

The Cash and Counselling demonstration is one effort to give beneficiaries cash when they become disabled.  A Health Affairs paper by Foster et al. describes the demonstration.

About 1.2 million Medicaid beneficiaries receive disability-related supportive services in their homes. Most receive them from government-regulated agencies, whose professional staff arrange services and monitor quality, but a growing number manage their services themselves.As one model of consumer-directed supportive services, Cash and Counseling gives consumers a flexible monthly allowance to purchase disability-related goods and services (including hiring relatives as workers), provides counseling and financial assistance to help them plan and manage their responsibilities, and allows them to designate representatives (such as family members) to make decisions on their behalf.

Did it work?

Our survey of 1,739 elderly and nonelderly adults showed that relative to agency-directed services, Cash and Counseling greatly improved satisfaction and reduced most unmet needs. Moreover, contrary to some concerns, it did not adversely affect participants’ health and safety.

Rather than spending this money on formal care services, almost all beneficiaries used their cash benefit  to hire family members or friends.  Other funds were directed to pay for assistive equipment, personal care supplies, and medications.  Could the Cash and Counselling model be a viable care alternative, especially for high cost patients?

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Many policy experts have been proponents of value-based cost sharing.  Under value-based cost sharing, medical care that is seen to provide a higher marginal benefit to the patient will have lower coinsurance rates than medical care with lower marginal benefits.  If value-based cost sharing would be implemented, preventive care should have low coinsurance rates because of the subsequent health benefit.

This seems like a very attractive way to design health insurance benefits, but a paper by Pauly and Blavin (JHE 2008) asks if value-based cost sharing is truly a novel concept.

First, under perfect information, there is no reason to have value-based cost sharing.  In this case, patients should internalize the marginal benefits–now and in the future.  ”When all agents have perfect knowledge of patient illness states and benefits of care, optimal coinsurance should be zero; insurance should take the form of a fixed dollar (indemnity) payment to cover the full cost of care when care is cost-effective, and should pay nothing in circumstances in which care has benefits that fall short of cost.”

Under asymmetric information, however, patients may make naive decisions.  For instance, patients may decide to forgo preventive care because the do not realize its long-term health benefits.  Coinsurance rates must still be designed to balance the twin goals of risk sharing and averting moral hazard.  Lower coninsurance rates will incentivize patients to get needed care.  However, designing coinsurance rates solely based on the marginal benefit of the procedure may not be optimal once we take into account that patient moral hazard may increase medical care above optimal levels.  

Pauly and Blavin also note that under asymmetric information, “it may now be the more price responsive service that should get the cost reduction, since lowering its cost sharing will have a larger effect in terms of moving it closer to the ideal level than would be the case for a less responsively demanded service.  That is, if patient ignorance resulting in underestimation of benefits from care in a given setting is severe enough, the direct relationship between price responsiveness and optimal cost sharing should be reversed.”

Yet just because value-based cost sharing can work does not mean that is the only solution.  Instead of spending money to reduce coinsurance rates, insurance companies or policymakers could spend money to inform consumers of the true benefits and costs of different types of medical care.  This is especially true of medical services that are not price responsive; where the only way to convince patients to undergo these potentially uncomfortable procedures is to increase information dissemination.  For instance, most people would prefer not to undergo a colonoscopy even at a price of 0.  The only way to convince patients that the procedure is needed is by information dissemination.

Value-based cost sharing is not a magic bullet, but may be a useful technique in the presence of asymmetric information.

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Can technological change make people worse off? Most economists think technical improvements are always good. Producing more of the output with fewer input is considered a more efficient use of resources. But is this the case in the medical field? John Goddeeris shows that this may not always be the case in his 1984 paper.

The Model

Let us assume that individuals maximize utility of the for developed by Arrow (1976):

  • V=Σi pi ui(xi, hi(mi))

Here, i indexes the state of illness, where the probability that each stat of illness occurs is pi. Individuals can spend their income on consumer goods, xi, or medical care, mi, where medical care is translated into health by the function hi(mi). A technological advancement is defined as hia(mi)≥hib(mi), for all mi, and strict inequality for some mi.

We can now introduce insurance into the model. Individuals who buy insurance pay a premium equal to π and a coinsurance rate z. The price of the medical premium must be equal to the expected value that the insurance company expects to pay out in medical benefits (less the copayments).

One would think that V*a>V*b, but this may not always be the case. For instance, let us assume that a person can either be healthy or sick (i.e., i=2). Further, assume the following utility functions:

  • V=(1-p)u1(x1) + p u2(x2,h2)
  • u1(x1) = -exp[-x1]
  • u2(x2,h2) = -exp[-(x2+h2)]

If individuals are endowed with income x0, then:

  • x1 = x0 – π,
  • x2 = x0 – π – zm2,
  • π = p(1-z)m2.

Assume p=.1, x0=10 and the original technology is:

  • h2(m2) = -10 if m2 < 5
  • h2(m2) = -4 if m2 > 5

This means that if medical spending is above 5, health will be partially restored. Goddeeris finds that the optimal coinsurance rate to maximize utility is no coinsurance (i.e., z=0). With no coinsurance, sick individuals choose m2=5. The utility level under the original technology (i.e., V*b) equals -.000476. What happens when there is a positive technological changes as follows:

  • h2(m2) = -10 if m2 < 5
  • h2(m2) = -4 if 5 ≤ m2 <15
  • h2(m2) = -3 if m2 > 15

Again, the author finds that no coinsurance (i.e., z=0) is optimal. With no coinsurance, individuals of course choose m2 = 15. However , tutility level under the new technology (i.e., V*a) equals -.000592. How can this technological improvement have decreased utility?

In this example, the true cost of the innovation is so large relative to its benefits are so large, people only choose to use it since coinsurance is 0. A higher coinsurance rate would have induced individuals to choose m2 = 5. According to Goddeeris, “the larger added expenditures in the ill state leads to an even greater reduction in expected utility. A ero co-insurance rate remains optimal after the innovation. Thus V*a < V*b, and the innovation –which clearly expands productive capabiities and is in fact adopted–is welfare reducing by our standard.”

The reason this occurs, is that individuals act ex post as if their expenditure decisions have no impact on insurance premiums. While no individual person’s actions will affect insurance rates, since all sick individuals act similarly, health insurance premiums increase much more after the technological innovation than before it.

Despite the finding that technology is welfare reducing in this particular case, technological improvement are of course welfare improving in other cases. One question that remains is how to operationally decide when a technology is welfare enhancing and when is it welfare reducing. In which category do MRI machines fall? What about CT scanners?

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Typically, economists when economists look at the health insurance market, they focus on the insurance side of it. By this I mean to define insurance as the purchase of a product which will reimburse the buyer in the case of an adverse event. However, one must also look at the concept of protection. Protection is defined as expending a costly effort to reduce the probability of an adverse event. This costly effort, however, will not effect the amount of the loss, only the probability that it occurs.

A seminal paper by Ehrlich and Becker (JPE 1972) finds the optimal levels of self-protection and how optimal self-protection change when insurance markets are introduced. Let us assume that the probability of a loss is p(e) where e is the effort expended and p’<0. An expected utility maximizer optimizes the following function:

  • maxe [1-p(e)]*U(I -e) + p(e)*U(I – L – e)

The first order condition is:

  • -p’*[U(I -e)-U(I - L - e)]=(1-p)*U’(I -e) + p*U’(I – L – e)

Ehrlich and Becker note that “[t]he term on the left is the marginal gain from the reduction in p; that on the right, the decline in utility due to the decline in both incomes, is the marginal cost.”

When we introduce an insurance market, the expected utility maximizer faces a new objective function.

  • maxe,s ,s [1-p(e)]*U(I-e-s*π(e)) + p(e)*U(I – L – e + s)

Here s is the insurance benefit and π(e) is price of the insurance; s*π(e) is the insurance premium. Let U(0)=U(I-L-e+s) and U(1)=U(I-e-s*π(e)). The first order conditions now become:

  • -(1-p)U’(1) + p*U’(0)=0
  • -p’*[U(1)-U(0)] – (1-p)*U’(1)*[1+s*π'] – p*U’(0)=1

How does self protection change when insurance markets are introduced? According to Ehrlich and Becker “On the one hand, self protection is discouraged because its marginal gain is reduced by the reduction of the difference between the incomes and thus the utilities in different states, on the other hand, it is encouraged if the price of market insurance is negatively related to the amount spent on protection through the effect of these expenditures on the probabilities.”

If insurance companies are actually able to measure self-protection and can price insurance accordingly, then individuals will have some incentive to increase prevention in order to lower their premiums. If insurance is priced in an actuarially fair manner (i.e., π=p(e)/[1-p(e)]) we can show that premiums will drop when self-protection increases:

  • ∂π/∂e=p’/(1-p)2<0

However, if insurance companies are not able to observe self-protection efforts, than it is likely that moral hazard will occur–self protection will decrease. In the words of the authors, “Self-protection would then usually be discouraged by market insurance–moral hazard would exist–because the main effect of introducing market insurance would be to narrow the differences between incomes in different states.”

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Despite much public rhetoric, why is preventative and chronic care so poor in the U.S.? The easy answer is that patients switch plans so frequently that insurance companies who invest in preventative care will incur the cost, but not reap the benefits. The harder question is why patients are switching health plans.

According to a working paper by Cebul, Herschman, Rebitzer, Taylor and Votruba featured on Slate, the answer may be “search frictions.” In the paper, turnover is generated from two sources: 1) from employees leaving the company for new jobs and 2) by having the employer switch to a new health plan. Data from the Community Track Study in 1996/7, 1998/9, 2001 and 2003 show that average annual insurance cancellations are about 21%. More than one third of the turnover is caused by employers switching health plans. Small employers were more likely to switch insurance plans than larger employers. Why don’t they just stay with one plan?

The search friction model is developed from a labor economics paper by Burdett and Mortensen (1998). The authors argue persuasively that extending the model to the case of health insurance makes perfect sense.

“The market for health insurance is a natural place to expect search frictions. Health insurance is a complex, multi-attribute product and this complexity makes it difficult for clients to meaningfully compare more than a handful of proposals. Informal discussions with insurers suggest that they offer customers hundreds if not thousands of different policies. This complexity also makes the marketing of insurance costly so that companies can make only a limited number of appeals to employer groups in a period.”

The authors explain how the price friction mechanism works. The price of the insurance policy is p, the marginal cost of the policy is c, and the firm’s reservation price for buying insurance is pR.

Suppose all firms made the same price offers p=c and so earned zero profit. Then one maverick firm could clearly increase profits by charging some discretely higher price (less than or equal to the reservation price pR). This high offer would be rejected more frequently than the going price because any potential client who fielded more than one offer in a period would obviously reject the high offer. But on occasion the contacted client would have no other offers, and a policy would be sold. This would produce positive profit for the firm. Similarly, in a candidate equilibrium in which all firms were charging the same price (a price such that c<p<pR ), a maverick firm could always increase profit by undercutting slightly the price charged by competitors, thereby increasing the number of clients while reducing by profit per client by only a trivial amount. In short, an equilibrium must entail a distribution of price offers.

Once market friction reach a sufficient level, in equilibrium we will observe a churning of employers going through different insurance policies each year. Introducing the issues that come along with adverse selection is likely to only increase market frictions because insurance companies now will want to screen employees.

Possible Solutions

The authors offer arguments made that may be solutions to the problem.

  • Patient-financed health investments. Health care investments (i.e.: preventative care) should be financed by the client. This way, the person reaping the rewards from preventative care will also incur the costs. If the patient switches insurance plans, this will not be a problem since they will be eligible for lower premiums because of their preventative care history. On the other hand, determining what type of care is an expense and what is an investment may be very difficult practically. Further, shifting more risk onto the patient is the antithesis of what insurance is supposed to do. Finally, when switching insurers, it will be very difficult to verify the actual amount of preventative care received without a nation-wide standard for electronic medical records.
  • Long term contracts. Another simple solution is just for employers to purchase long term contracts from insurance companies. This way, insurers will be able to reap more of their rewards from earlier years’ health investments. On the other hand, “given constantly-evolving medical technology and treatment protocols, as well as hard to predict changes in governmental regulation and mandates, it is difficult to see how long-term contracts might be implemented.”
  • Price Caps. Government set price caps are probably the worse option. As Slate states, “But where should the government set the ceiling? If it’s too low, the government could end up destroying insurance companies’ incentives to stay in business at all.”
  • Legislate a basic insurance package. The authors conclude the paper with the following: “It follows from this that much of the distortions resulting from frictions could be mitigated if there were a simple, easily understood and reasonably priced alternative insurance policy that would be available to all market participants. In the context of our search models, we believe we can prove that by making this alternative insurance available on a voluntary basis to all purchasers the inefficiencies resulting from search frictions could be greatly reduced.” Another option would be to offer everyone the choice of a nationalized health plan (a la Medicaid). People who did not want Medicaid, could choose to have vouchers (see Healthcare Vouchers) used to pay towards a private insurance plan of their choice. Many of the basic private insurance plans will likely mimic the nationalized Medicaid, but some plans will offer alternatives which will be more flexible and easier to adapt to new technology advances.

Should hospitals with long waiting times have higher or lower budget transfers? Offering hospitals who have low wait times more money will increase a hospital’s incentives to decrease wait times. On the other hand, thus policy may hurt the busier hospitals and may not alleviate the wait times of those who are waiting the longest. In the case of public school transfers, if the best schools are rewarded, this encourages achievement, but may punish the worst off kids (i.e.: those at poorer schools). Transfers to low-performing school may mute incentives to increase achievement.

The issue of hospital payment structure is analyzed by Luigi Siciliani in his article on optimal contracts B.E. Journal of Economic Analysis & Policy. As with any thesis which claims to give an optimum solution, this optimum is based on some assumptions. This paper uses four major assumptions.

  1. Demand for treatment can be controlled by dumping some patients. Doctors can tell patients who wish to have medical treatment that they either a) don’t really need it or b) that they will not provide it
  2. The purchaser (i.e.: NHS, an insurance company, Medicare, etc.) can not observe the number of people dumped.
  3. Dumping is costly for the specialist. By dumping patients, the specialist receives more complaints about their service level. Thus, either the physician’s reputation is tarnished (a cost) or the physician must spent more time (another cost) convincing the patient that they do not need treatment.
  4. Hospitals differ in potential demand for treatment, either due to the catchment area of the hospital or from having a better or worse reputation.

Another key assumption is that no co-payment charges can be issued. This assumption is plausible, because it basically represents the British NHS system. Thus, the optimal solution must be seen not as the ideal optimal, but as the optimal with a centralized payer and no co-payments.

The Model

Hospitals have parameter θ which describes the public hospital type. This parameter θ indicates potential demand in the absence of a rationing system.

For each treatment, patients differ in the value they would receive from treatment. For instance, healthy patients would not benefit from heart surgery, but individuals with coronary artery blockages likely would benefit from surgery. Thus the author assumes that individuals’ value from treatment is uniformly distributed between v0 and v1.

Patients have three options:

  1. They can be treated at a public sector hospital after a wait of time w, [up(v,p)]={∫T0 v dt} -p=vT-p]
  2. They can be treated in a private sector hospital with no wait, but pay a price of p, [uNHS(v,w)]={∫Tw v*g(w) dt} =vg(w)(T-w)]
  3. or they can receive no treatment[unone=0]

There are two costs to going to the public hospital. First, the individual has to wait w weeks longer, so they do not get to enjoy the benefit of the treatment for as extended a period of time. Secondly, since 0<g(w)<1, the treatment becomes less effective or less valued the longer the patient waits.

Thus, from the math above, we can see that a person will choose a public hospital if and only if:

  • v<V(w)=p/{T-g(w)*(T-w)

The comparative statics show that longer wait times decrease the probability of using a public hospital, higher prices, p, decrease the probability of using a private hospital, and higher valuations, v, increase the probability of using a private hospital.

Demand for public hospital services is written as:

  • D(θ,w,x)=θV(w)-x
  • x is the number of patients who are dumped (i.e.: not added to the waiting list)

The number of treatment supplied by hospital θ is y(θ) and since supply must equal demand, we have:

  • θV(w)-x=y(θ)

The authors claim that providers receive disutility from dumping patients. Also, hospitals receive more disutility when they dump patients who value the treatment more (i.e.: high v, this is more likely to be the sicker patients). Thus, we are lead to our first major conclusion.

  • Conclusion 1: The patients who are dumped are the ones with the lower benefits from treatment. This means that hospitals dump the patients who don’t really need the treatment.

After some more math, the Dr. Siciliani states a second conclusion:

  • Conclusion 2: A mix of explicit rationing (through dumping) and implicit rationing (through waiting) is therefore optimal. Siciliani explains that: “Rationing by waiting alone induces excessive disutility for patients. Rationing by dumping alone generates excessive disutility for the specialists.”

The author continues to conclude that a separating or pooling equilibrium may occur.

“Under symmetric information, the optimal contract is for the purchaser simply to over a transfer in exchange for the provision of the desired level of activity and waiting time, without leaving any rent to the provider…Under asymmetric information, we found that a separating equilibrium exists when it is optimal for the purchaser of health services to contract more activity and higher waiting times to hospitals with higher demand. In this case providers with low potential demand have an incentive to mimic hospitals with high potential demand. To induce hospitals to self-select, the purchaser needs to pay a rent to hospitals with lower potential demand. [But] if it is not optimal for the purchaser to contract more activity and higher waiting time to hospitals with higher demand, then a separating equilibrium may not exist.”

Problems

One main problem with the paper is that it assumes that patients with a high value, v, cost the same to treat as low value patients. If v is a proxy for sickness, this is likely not to be the case; sicker patients with a high v are more expensive to treat. If this were the case, then conclusion 1 would not hold. Public hospitals would instead treat patients with the lowest benefit and dump patients with intermediate benefits–the high benefit patients would still go to the private sector hospital.

Also, the paper does not take into account any strategic interaction between hospitals. “If hospitals with higher potential demand are contracted higher waiting times, then patients will switch from the hospitals with high potential demand to hospitals with low potential demand, increasing excessively the amount of dumping and consequent disutility for hospitals with low potential demand.”

What is the optimal way to pay physicians? If there were a singular variable ‘health’ that could be easily measured, patients could pay physicians for each unit of health they receive. Of course, this is not how the physician-patient relationship operates in the real world. Physicians are paid either a base rate per person per month or receive a fixed fee for each service provided. In physician contracts with health plans, the physician effort level to gather information (diagnosis) is non-contractible and pay based on the patient’s health condition (physicians’ private information) is also non-contractible. In a setting with so much uncertainty, what is the optimal physician contract?

This is the question which Izabela Jelovac attempts to answer in her 2004 paper in Health Economics. In her model, patients who visit the doctor can have two types of illnesses, one mild and one severe. The doctor chooses an effort level ε, in order to diagnose the illness. The more effort the doctor puts forth, the more likely they will diagnose the disease correctly. In the next stage of the game, the doctor chooses whether to treat the patient with an expensive treatment which will cure the severe disease and or the inexpensive treatment which will cure the serious disease. Prescribing the expensive treatment when the patient has the mild disease causes a health loss. If the patient recovers, then the game ends, but if the patient does not recover then the patient returns to the physician and receives the alternative treatment.

So what does the physician do? Typically, we would guess that the doctor will prescribe the adequate treatment strategy of providing the expensive treatment for the severe disease and the inexpensive treatment for the mild disease. However, “…if a single visit is less profitable to the physician than two visits, the physician is better off providing the most inadequate treatment than the most adequate one in order to increase the likelihood of a second visit.” This is like a car mechanic who damages people’s cars when they come in for an oil change in order to earn more money during the second visit from fixing the problem which they caused in the first.

The author also found that a strategy of always prescribing the inexpensive (or expensive) treatment during the first visit can be optimal as well. For instance, if diagnosing the serious illness is very costly (numerous expensive tests and many physician labor hours are incurred) and if the serious illness isn’t too severe, then giving all patients the inexpensive treatment during the first visit may be optimal.

The authors go through some dense math, but end up concluding that some supply-side cost sharing by the physician is optimal since it induces the physician to provide the most adequate treatment. With the cost sharing, having the patient return for a second visit is never profit maximizing.

This paper does have a few problems. A key assumption in this model is that “the need for a second treatment is necessarily the physician’s fault.” In reality, this need not be the case. Also, the authors do not take into account issues of the physician’s reputation. If 100% of a physician’s patients had 2 visits, patients may decide to leave this physician and sign up with a doctor who choses the “adequate treatment” strategy.

Hillman (Ann Intern Med 1990) writes that “whereas most physicians will act in the patient’s best interest when the medical decision is clear-cut, the effect of financial incentives may be most important in cases where the correct decision is not obvious.”

Health savings accounts (HSAs) have been a major point of contention for health care reformers. Supporters claim that HSAs can reduce health care costs by decreasing the moral hazard problem inherent when third parties—such as insurance companies or the government—pay for medical services. Opponents claims that HSAs will attract rich and healthy individuals, leaving only poor or sick individuals in the ‘regular’ insurance pool.

One interesting point made in Cardon and Showalter (JHE 2007) is the following:

“Both opponents and advocates of HSAs tend to argue that HSAs will lead to less reliance on insurance, either through higher coinsurance rates and deductibles, or through fewer purchases of policies. This line of reasoning ignores the fact that accumulated HSA balances are wealth, and health insurance protects this wealth. Even individuals with large HSA balances would typically value insurance to protect those balances for future use. HSAs will tend to reduce levels of insurance coverage, but the effect seems unlikely to be as large as some previous researchers suggest.”

The Cardon and Showalter article also gives a nice description of the five main types of tax-preferred health savings accounts.

  1. Archer medical savings accounts (MSAs): accounts in which an individual and/or an employer can contribute pre-tax dollars to pay for most health care services. The tax advantage is the same as for employer-provided health insurance premiums. Unused monies can accumulate over time. An experiment authorized under the Kassebaum-Kennedy bill (Health Insurance Portability and Accountability Act of 1996) allowed for restricted introduction of MSAs which included the requirement of purchasing a catastrophic, (high-deductible) health insurance policy (MSA/CHP).
  2. Flexible spending accounts (FSAs): like HSAs, but with no link to insurance coverage. Funds not used by the end of the year revert to the employer.
  3. Rollover FSAs: these would allow limited rollover of FSA monies without the restrictions on insurance choices that the current HSA rules require.
  4. Health reimbursement arrangements (HRAs): tax-exempt individual accounts used to pay for medical expenditures. Accounts are funded by employers; employee contributions are not allowed. Ownership of the accounts remains with the employer, unlike HSAs and FSAs.
  5. Medical IRAs. This proposal would allow consumers to make penalty-free early withdrawals from their retirement plans to pay for allowable medical expenditures.”

Most economists believe that increasing the price of an item will decrease demand for the item. Health care is no different from any other good. If you increase the copayment or coinsurance rate, people will consume fewer medical services. The famous RAND Health Insurance Experiment (HIE) demonstrated that higher coinsurance rates discourage medical care consumption. As I said, health care is no different from any other good…or is it?

Dana Goldman and Tomas Philipson argue in their 2007 NBER working paper (“Integrated insurance design in the presence of multiple medical technologies“) that the problem of moral hazard in the health insurance market is different from moral hazard under most other insurance markets. For most other types of insurance, only one good is insured (e.g.: a car, a house, etc.). Health insurance, however, covers a wide variety of different services. Thus the authors claim that increasing prescription drug copay costs can actually increase health care spending and make patients worse off. Let us assume that prescription drugs and medical services are substitutes. If the price of prescription drugs increases, it is likely that the individual will consume the more of the expensive medical services which are fully covered by insurance. They suggest that a zero or negative copay may be optimal for some prescription drugs.

The optimal copay is determined by the patients elasticity of demand and the degree to which other medical services are complements or substitutes to the original item in question. The authors give some empirical evidence from other studies to support their claim:

  • Soumerai, Ross-Degnan, Avorn, McLaughlin and Choodnovsky (NEJM 1991) compare Medicaid patients in New Hampshire “who had a three-drug limit per patient” and Medicaid patients in New Jersey without the limit. The authors found a 35% reduction in drug use, but a doubling in nursing home admission rates.
  • Soumerai, McLaughlin, Ross-Degnan, Casteris, and Bollini (NEJM 1994) look at individuals on psychotropic medications and find that a drug cap led to a 15%-49% reduction in the use of drugs but a 43%-57% increase in mental health visits and emergency mental health services.
  • Horn, Sharkey, Tracey, Horn, James and Goodwin (Am. J Man Care 1996) find that formulary limitations in 6 HMOs were associated with increased ER visits and hospitalizations for otitis media, atraumatic arthritis, ulcers, hypertension, and asthma.
  • Gaynor, Li, and Vogt (NBER 2005) find that higher drug co-payments in a given year lead to increased spending during the following year.
  • On the other hand, studies such as Johnson, Goodman, Hornbrook and Eldredge (Med Care 1997) and Tamblyn, Reid, Mayo, McLeod, and Churchill-Smith (J Clin Epidemio. 2000) found that increased co-pays did not increase outpatient visits, hospitalizations or ER visits.

The authors conclude that “the preponderance of evidence suggests strong negative cross-price elasticities between drugs and other medical spending, at least for patients with chronic disease.”

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