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A welfare measure of “offset effects” in health insurance
Journal of Public Economics 96 (2012) 520–523
Contents lists available at SciVerse ScienceDirect
Journal of Public Economics journal homepage: www.elsevier.com/locate/jpube
A welfare measure of “offset effects” in health insurance Jacob Glazer a, b, Thomas G. McGuire c,⁎ a b c
Tel Aviv University, Israel Boston University, United States Department of Health Care Policy, Harvard Medical School, United States
a r t i c l e
i n f o
Article history: Received 20 October 2010 Received in revised form 8 February 2012 Accepted 20 February 2012 Available online 26 February 2012 Keywords: Health insurance design Offset effects
a b s t r a c t Changing health insurance coverage for one service may affect use of other insured services. When improving coverage for one service reduces use of another, the savings are referred to as “offset effects.” For example, costs of better coverage for prescription drugs may be partly “offset” by reductions in hospital costs. Offset effects have welfare implications but it has not been clear how to value these impacts in design of health insurance. We show that plan-paid – rather than total – spending is the right welfare measure of the offset effect, and go on to develop a “sufficient statistic” for evaluating the welfare effects of change in coverage in the presence of multiple goods. We derive a simple rule for when a coverage improvement increases welfare due to offset effects. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Health insurance coverage for one good or service can affect the quantity demanded of other goods or services in a health plan. Following an improvement in coverage for one good, a reduction in the quantity demanded of other services or goods is referred to as an offset effect. A large empirical literature in health economics and health services research, focusing on coverage for drugs, finds offset effects, and measures these effects by the change in total spending on the other covered goods. For example, Shang and Goldman (2007) use Medicare Current Beneficiary Survey (MCBS) data from 1992 to 2000 to show that the extra spending on drugs induced by medigap coverage is more than offset by reductions in total health care spending on other services. Hsu et al. (2006) compare medical spending for Medicare beneficiaries with a cap on drug coverage to spending by those without a cap at Kaiser Permanente of Northern California prior to Medicare Part D. Drug spending was 28% less in the capped group but other categories of expenditures were higher and total spending for all care was not significantly different between the groups, implying a near dollar-for-dollar offset in total costs. Gaynor et al. (2007) study the effect of increases in copayments charged for drugs among private employees on total (plan plus consumer) spending. Increases in non-drug spending, largely in outpatient care, offset
⁎ Corresponding author. Tel.: + 1 617 432 3536; fax: + 1 617 432 2905. E-mail address: [email protected] (T.G. McGuire). 0047-2727/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jpubeco.2012.02.007
$.35 of each dollar saved in drug costs. 1 Chandra et al. (2010) found that the savings in costs due to higher copayments for drugs were partly offset by higher spending on hospital services among retired state employees in California. They tracked offsets by payer since a primary (Medicare) and secondary (employer-provided supplemental) shared in offsets unequally. The implicit logic in offset papers is that if total medical costs fall due to an increase in coverage, then the change in coverage is welfare improving (i.e. “pays for itself”). This paper argues that change in total medical spending, meaning the sum of plan and patient outof-pocket spending, is not the right measure of the economic value (or cost) of a change in insurance coverage due to offset effects. Rather, health plan costs alone measure the economic value of savings due to reductions in the use of other services. Applying methods reviewed by Chetty (2009), we show that a “sufficient statistic” for evaluating the welfare effect of change in coverage for one good is
1 Other papers use total costs as the measure of offsets. Gibson et al. (2006) measured the effects of lower copayments for statins (drugs treating high cholesterol) on total medical expenditures, payments from any source, and evidence of an offset. Zhang et al. (2009) found an offset effect in added drug coverage for Medicare Part D. In their group with no prior drug coverage, drug spending went up $41 per person per month with Part D but other medical expenses fell by $33 per month. They computed the offset effect of Medicare Part D on other medical expenditures using total expenditures (plan plus copayments). Lichtenberg (2007) has conducted a series of studies of the health and medical care cost impacts of newer prescription drugs and found evidence for an offset effect on total health care costs. For a recent paper, see Lichtenberg (2007). Zhang and Soumerai (2007) question the conclusions of some of Lichtenberg's earlier offset findings. Offset effects of drugs have become so widely accepted that “null effect” papers are published. See Duggan (2005) who pursued the Lichtenberg line of inquiry for a specific area of treatment and found that newer antipsychotic drugs did not reduce total costs in comparison to older drugs. See also Zhang (2008).
J. Glazer, T.G. McGuire / Journal of Public Economics 96 (2012) 520–523
2. A model of offsets in health insurance Suppose a health plan covers services 1 and 2. Quantity of each received by a representative individual in the plan is x1 and x2 measured in dollars. Benefits to the individual are B(x1,x2), where Bi ≥ 0, Bii b 0, i = 1,2, with subscripts indicating partial derivatives. Letting ci denote the copayment charged for each unit of service i, then the individual demands service i to satisfy: Bi ðx1 ; x2 Þ ¼ ci
i ¼ 1; 2
ð1Þ
Let R denote the plan premium paid by the enrollee. Assuming the plan makes zero profit, the premium is: Rðc1 ; c2 Þ ¼ ð1−c1 Þx1 þ ð1−c2 Þx2 ;
ð2Þ
where (x1,x2) are given by Eq. (1). The individual's total utility from the plan is thus: U ðc1 ; c2 Þ ¼ Bðx1 ; x2 Þ–c1 x1 –c2 x2 –Rðc1 ; c2 Þ;
∂U ðc1 ; c2 Þ ∂x ∂x ¼ ðB1 −1Þ 1 þ ðB2 −1Þ 2 ∂c2 ∂c2 ∂c2 ∂x1 ∂x2 ¼ ðc1 −1Þ þ ðc2 −1Þ ∂c2 ∂c2
ð4Þ
The second equality follows from Eq. (1). Suppose copayment for ∂x1 > 0, there is an offset effect and consumpservice 2 is reduced. If ∂c2 tion of x1 falls with this change. What happens to welfare? Eq. (4) tells us how to value the offset. Reversing the sign of Eq. (4) to get an expression in terms of plan shares, when copayment for service 2 goes up (down), utility of the individual goes up (down) if and only if Eq. (5) holds: ð1−c1 Þ
∂x1 ∂c2
Offset effect
þ
ð1−c2 Þ
∂x2 ∂c2
b0 ð5Þ
½
Own‐price effect
The intuition for this result is the following: the second term on the left-hand side of the inequality captures the inefficiency in consumption induced by the reduction in copayment for service 2. With health insurance, the marginal benefit of health care is less than the marginal cost (B2 = c2 b 1), and the extra consumption of x2 due to the reduction in copay creates additional welfare loss. 3 The first term on the left-hand side in Eq. (5) is the offset effect due to the change in consumption (in this case reduction) of x1. Just as with the own-price effect, benefits and costs both matter in valuing ∂x1 welfare of any offset effect. The 1 part is the reduction in total ∂c2 ∂x1 part is the cost from the change in x1 and, since B1 = c1, the −c1 ∂c2 loss in benefits. Thus, the net welfare measure of offset effects is ∂x1 plan savings: ð1−c1 Þ : ∂c2 We can relate the analysis to changes in plan's costs. From Eq. (2) we know that when copayment for service 2 changes, the change in the plan's costs is given by: ∂Rðc1 ; c2 Þ ∂x ∂x ¼ ð1−c1 Þ 1 þ ð1−c2 Þ 2 −x2 ∂c2 ∂c2 ∂c2
ð6Þ
Expression Eq. (4) for welfare and Eq. (6) for plan costs are the same except for the presence of x2, the cost shifting effect of a change in c2, a transfer ultimately paid by the consumer in any case. Using Eqs. (4) and (6) we can state a rule for welfare in terms of planpaid costs. 2.1. Rule for welfare effects
ð3Þ
where (x1,x2) are from Eq. (1) and R is from Eq. (2). Substituting for R to recognize that the individual pays for services by a combination of the cost sharing and the premium: U ðc1 ; c2 Þ ¼ Bðx1 ; x2 Þ–x1 –x2 :
Consider now what happens to utility (welfare) (Eq. (3′)) if the plan were to change the copayment for service 2:
½
the change in total plan-paid costs less the change in costs transferred to/from consumers. 2 We go on to derive an elasticity rule for when the offset effects of an improvement in coverage increase welfare. A simple argument shows why total costs are not the right welfare measure of an offset effect. Suppose the plan covers just one service, “health care,” and an increase in coverage of health care increases a consumer's total expenditures on health care. The consumer budget constraint implies that spending on some other non-covered services has to fall. This “offset” says nothing about efficiency since coverage expansions are always exactly “offset” in this trivial sense. What if the affected other spending were on another form of health care that was minimally covered in the plan, say for one percent of costs with consumers paying ninety nine percent? Logically, token coverage cannot imply that we should count the full spending change as an offset. To see the intuition for our result about the role of plan-paid costs consider the following example. Suppose that there are two services and both are (partially) covered by insurance, namely the individual has to pay some copayment lower than the marginal cost of providing the services. What is the effect of a change in the level of copayment of one of the two services on welfare? Since the level of services the individual chooses to use is at the point where his marginal benefit equals the copayment, and since the copayment is less than marginal cost, there is a welfare loss associated with the consumption of the two services. The change in welfare loss is just the sum of the changes in consumption times the difference between marginal cost and marginal benefit for each of the two services. Note that the difference between marginal benefit and marginal cost is equal to the plan's share of costs. Our focus on plan-paid cost is due to this: plan paid costs are a measure of the welfare loss per unit, and total welfare effect of a change in the offset good's consumption is the change in quantity multiplied by the plan paid share of costs.
521
ð3′Þ
2 Chetty (2009) uses the term as follows. A statistic, e.g., the decline in plan-paid costs, is “sufficient” for welfare analysis in the sense that conditional on this information, no other statistics from the data are informative about welfare. An exact measure of welfare is obviously a sufficient statistic.
The welfare effect of a change in coverage is equal to minus the change in plan costs net of the cost-shifting effect of the coverage change. Proof. From Eqs. (4) and (6) we get: ∂U ðc1 ; c2 Þ ∂Rðc1 ; c2 Þ ¼− −x2 ∂c2 ∂c2
ð7Þ
3 In the conventional analysis of optimal health insurance, this welfare loss is weighted against the risk spreading gain to find the optimal copayment, c2 (Zeckhauser 1970). We return to the issue of risk below.
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J. Glazer, T.G. McGuire / Journal of Public Economics 96 (2012) 520–523
Our rule for welfare effects constitutes, in Chetty's (2009) term, a “sufficient statistic” for welfare evaluation of health insurance changes. 4 Our measure, change in plan costs less cost shifting, is equal to the welfare change, and thus yields an if and only if rule: welfare goes up if and only if plan costs less transfers go down. We can use our rule to interpret the existing logic of the offset literature which focuses on total costs, plan paid plus patient paid, and concludes that an improvement in coverage for good 2 is worthwhile if it “pays for itself” in savings on good 1. Consider a reduction in c2 that decreases use of covered good x1 (an offset effect). Suppose the improvement in coverage for x2 “pays for itself” in the sense that the reduction in the total cost of x1 exceeds the increase in plan costs for x2. Our rule tells us that this condition is neither necessary nor sufficient for an increase in welfare. It is not necessary because the cost-shifting effect of the change in c2 is disregarded for welfare. It is not sufficient because it is not total costs that measure the value of the offset, but plan-paid costs. Instead of looking for a coverage improvement to “pay for itself,” we propose the following simple rule expressed in terms of demand elasticities for when an improvement in coverage improves welfare via an offset effect. 5
3. Final comments
2.2. A simple elasticity rule for when offsets increase welfare Welfare goes up with a decrease in c2 (improvement in coverage) when the partial derivative in Eq. (4) is negative, or alternatively: ð1−c1 Þ
∂x1 ∂x > −ð1−c2 Þ 2 ∂c2 ∂c2
ð8Þ
Putting this in elasticity form and dividing through by −ε22 (a positive number), the criterion for a welfare improvement with a decrease in c2 becomes: −
ε12 ð1−c2 Þx2 > ε22 ð1−c1 Þx1
perceived value of the copayment increase.6 However, taking the plan rather than total cost perspective we would say that since drugs are covered at roughly 50% and hospital cost at 100%, the offset ratio doubles, to about two-to-three. Gaynor et al. (2007) in another drug offset paper conclude that offsets savings are about 35% of added drug costs. They report spending and estimated elasticities allowing us to apply the offset rule from above. Assuming drug coverage averages 50% and outpatient coverage is 90% (typical for US employer-based health insurance), plan spending is $312 per year on drugs and $1,453 for outpatient care, so the ratio of plan-paid shares (the RHS of Eq. (9)) is .21. The authors present a range of elasticities, but picking one pair from their Table 8 to illustrate our point, the own-price elasticity is −.40 and the cross-price is .17. The LHS of Eq. (9) is thus +.425, easily meeting the criterion for the offset effect to be welfare increasing. 7 While this and the previous example are only intended to be illustrative, the switch to regarding plan-paid rather than total cost changes in valuing offset effects will magnify these effects because the planpaid share for drugs is currently low.
ð9Þ
In Eq. (9), ε12 is the cross and ε22 is the own-price elasticity with respect to c2. The RHS of Eq. (9) is positive and equal to the ratio of plan paid costs for service 2 to service 1. Rule: for a decrease in c2 to improve welfare, the goods must be substitutes (ε12 > 0); and, the ratio of the absolute values of the cross to the own-price elasticity must exceed the ratio of the plan paid costs for the two services. The offset rule for welfare is simple to apply. Suppose we know that the own-price elasticity of drugs is −1.0 and the cross-price elasticity for hospital services is +.2. If the plan paid drug costs are less than 20% of the plan-paid hospital costs, an improvement in coverage for drugs improves welfare. Attention to plan rather than total cost can change the tenor of the policy implications of offset effects, particularly for drug coverage where plan shares are relatively small. Turning to some results in significant recent offset papers illustrates the quantitative importance of the plan-cost perspective. Comparing the change in total costs for drugs and hospitals, Chandra et al. (2010, p. 208) found that a decrease in coverage for drugs reduced total drug costs by $23.06 per member per month, but increased total hospital costs by only $7.23—the offset amounted to only a one-to-three ratio of hospital cost increases to drug cost savings, and in the authors' judgment was “unlikely to be enough” to reverse the 4 Chetty's primary analysis was directed to the welfare effects of tax changes, making use of consumer utility maximization and firm profit-maximization conditions. The analysis is very similar to the way we use Eq. (1) where the consumer equates marginal benefit to marginal cost to simplify the expression for a welfare change. 5 Any change in administrative costs associated with insurance should also be included in the welfare effects. Insurance premiums are often expressed as actual payouts and a “loading factor” above the payouts. Any part of the loading factor that represents incremental costs (but not profits) should be included in the welfare evaluation.
In applied policy research, offset effects played an important role in the discussion about the design of optimal health insurance for mental health treatment, 8 and more recently the do so in the case of coverage for drugs. 9 Most public and private plans cover drugs, but the coverage is partial in the sense that a drug formulary typically excludes many drugs, and for those drugs that are covered, the percent paid by the plan is much less than for other health care services. Interestingly, the copayment for generic drugs is often so high that it exceeds the acquisition cost to the health plan. 10 Our ideas about valuing offset effects have the most current direct application to the question of coverage for drugs, where a considerable amount of research, noted above, has studied how more drug coverage affects other service use. An important feature of the market for branded drugs under patent protection is that the price health plans pay is much higher than the social marginal cost of production. Lakdawalla and Sood (2009) point out that by lowering the out-of-pocket price to patients, insurance coverage for branded drugs can move price towards rather than away from social marginal cost and improve the social efficiency of consumption. This is distinct from our analysis of the welfare effects of offsets where we benchmark welfare against the plan's acquisition cost. 6 The California change studied in Chandra et al. (2010) also involved increases to outpatient copays, which we are ignoring in this illustrative example. These increases also saved money, making the offset ratio one to five. By ignoring this other benefit change in our discussion, we are in effect assuming it is the drug coverage change that causes the offset. 7 We choose the fixed-effect OLS dynamic model with lags. This is the most favorable to offsets from the table, though other estimates presented in the table also satisfy the criterion. 8 Jones and Vischi (1979) in their review concluded there were medical offset effects of psychotherapy visits. The research literature consisted mostly of pre-post naturalistic studies. The Rand Health Insurance Experiment included plans with differential cost sharing for mental health and physical health care in order to investigate offsets of mental health treatment. No evidence for such offsets was found in the HIE (Newhouse, 1993). 9 The clinical rationale for offset effects of coverage for mental health care is the connection between mental and physical health. Mental health problems can manifest themselves as physical symptoms and if the underlying mental health problem is treated successfully, physical health improves. In the case of drug treatment, the clinical rationale is that patient compliance with drug treatment for many chronic illnesses improves health and lessens the need for other costly treatment. See, for example, discussion in Goldman et al. (2006). 10 See Kaiser Family Foundation (2009) for description of coverage in drug formularies for private employers. Glazer et al. (forthcoming) apply ideas from price index theory to design of a drug formulary by characterizing the maximum premium a consumer would pay for a formulary with a certain set of copayments. Offset effects on other covered services figure into the expression in the form of savings on plan paid costs.
J. Glazer, T.G. McGuire / Journal of Public Economics 96 (2012) 520–523
We note that the literature on optimal health insurance with multiple services is consistent with our interpretation offset effects. Goldman and Philipson (2007) regard offset effects as a cross-price elasticity and characterize efficient (second-best) demand-side cost sharing in health insurance. Added hospital costs offset savings from reducing coverage of drugs in their example. Characterizing their results, they conclude, “When hospital care is substitutable and excessive – i.e. provided below cost – there is an additional marginal cost of raising drug copays.” (p.430). This echoes our point: if hospital care were not partly plan-paid, resulting in it being “provided below cost,” and “excessive,” there would be no offset effect to count. The measure of inefficiency of excessive use is the divergence between marginal benefit and marginal cost—the marginal plan contribution. 11 A natural question is to ask whether markets could succeed in setting coverage for various health care services to take account of cross-price effects. In a perfectly competitive market, a health plan would be forced to maximize welfare of the representative consumer, implying the efficiency issues discussed here would be taken care of in competitive equilibrium. Health insurance markets are fraught with market failure, however, making it worthwhile to have an explicit expression for the welfare effects of offsets. Health plan market power in pricing is probably not the main issue here. A monopolist would seek to provide a certain utility to enrollees at minimum cost, implying offsets would be taken into account within a benefit plan offered by a monopolist. More serious is adverse selection which leads to distorted plans in market equilibrium. And probably most important in the context of offset effects is the presence of multiple insurance plans. For example, most consumers with Medicare in the U.S. have coverage from multiple insurers, each with no reason to consider spillover effects on another plan. Finally, much of health insurance in the US and elsewhere is public insurance where plan design is not subject to a market test. In sum, there can be little assurance that market forces alone will lead to optimal coverage, leaving a role for explicit expressions for the value of offset effects in health insurance. The major limitation of our rule for offsets and model setup generally stems from the assumption that quantity is determined by the equality of marginal benefit to the consumer/patient and patient copayment. While the standard demand model is widely applied in theoretical and empirical health care research, it is also seriously questioned as a basis for describing the outcome of patient-provider interactions (Chandra et al., 2012). Effective physician agency on behalf of the patient would be consistent with our approach, but we acknowledge that the marginal benefit-marginal cost equality is still a strong assumption. Relatedly, health economists doubt whether consumer demand should be interpreted as marginal benefit when assessing the efficiency of changing coverage. Perspectives from “valuebased insurance design” and behavioral economics both question the conventional welfare framework for assessing the efficiency cost of added coverage for a service. 12 As Pauly and Blavin (2009) show,
11 Their Eq. (1) contains two pieces, like our Eq. (4). Their “offset effect” piece is the product of the marginal utility of hospital care times the derivative of hospital care with respect to drug coverage. Their expression for marginal utility includes recognition of full cost because their derivatives with respect to cost sharing implicitly include the effect on the premium. Their marginal utility is thus equivalent to our (B1 − 1) in Eq. (4). In another paper, Ellis and Manning (2007) find optimal cost sharing for a preventive service that reduces use of other health care. In their solution, terms involving other health care drop out of the expression for optimal insurance for prevention when demand side cost sharing for the other health care is equal to one (and there are no plan-paid costs). See their Eq. (15), page 1139. It is prevention of covered health care services that play into the optimal insurance for preventive health care. For integration of the cross-elasticity effect into the question of optimal insurance, see McGuire (2012). 12 Health insurance coverage corrects for consumer misevaluation of services in the value-based insurance design framework. See Chernew et al. (2007) for the proposal for the value-based approach, and Pauly and Blavin (2009) for an integration of the Pigouvian subsidy perspective into the conventional moral hazard framework. In a related point connected to behavioral economics, Newhouse (2006) illustrates how time-inconsistent preferences could lead to inefficient non-compliance with treatment that prevents (offsets) later illness.
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however, consumer over or undervaluation can be integrated with traditional considerations of optimal health insurance. One element of optimal design of health insurance is financial risk, absent from our welfare expressions above. Our purpose is to derive expressions for the welfare impacts of offset effects, so we have not directly considered gains/losses in terms of the associated risk spreading. Within a context where offset effects are of principal concern, since increases in costs of one service are counterbalanced by decreases in costs elsewhere, the overall effects on risk bearing are likely to be small. Acknowledgements This research was supported by the National Institute of Aging (P01 AG032952) and the National Institute of Mental Health (R01 MH094290). We are grateful to Sebastian Bauhoff, Mike Chernew, Randy Ellis, Haiden Huskamp, Joseph Newhouse, Aaron Schwartz, Tisa Sherry, Anna Sinaiko and Zirui Song for comments on an earlier draft. We also thank Editor Hanming Fang and a referee for very helpful guidance. References Chandra, A., Gruber, J., McKnight, R., 2010. Patient cost-sharing, hospitalization offsets in the elderly. American Economic Review 100 (1), 193–213. Chandra, A., Cutler, D., Song, Z., 2012. Who ordered that? The economics of treatment choices in medical care. In: Pauly, M.V., McGuire, T.G., Barros, P.P. (Eds.), Handbook of Health Economics, Vol. 2. Elsevier. Chernew, M.E., Rosen, A.B., Fendrick, A.M., 2007. Value-based insurance design. Health Affairs 26 (2), w195–w203. Chetty, R., 2009. Sufficient statistics for welfare analysis: a bridge between structural and reduced-form methods. Annual Review of Economics 1, 451–487. Duggan, M., 2005. Do new prescriptions pay for themselves? The case of secondgeneration antipsychotics. Journal of Health Economics 24 (1), 1–31. Ellis, R.P., Manning, W.G., 2007. Optimal health insurance for prevention and treatment. Journal of Health Economics 26 (6), 1128–1150. Gaynor, M., Li, J., Vogt, W.B., 2007. Substitution, spending offsets, and prescription drug benefit design. Forum for Health Economics and Policy 10 (2), 1–31. Gibson, T.B., Mark, T.L., Axelsen, K., Baser, O., Rublee, D.A., McGuigan, K.A., 2006. Impact of statin copayments on adherence and medical care utilization and expenditures. American Journal of Managed Care 12, SP11–SP19. Glazer, J., Huskamp, H.A., McGuire, T.G., forthcoming. A Prescription for Drug Formulary Design and Evaluation. Forum for Health Economics & Policy. Goldman, D., Philipson, T.J., 2007. Integrated insurance design in the presence of multiple medical technologies. The American Economic Review 97 (2), 427–432. Goldman, D.P., Joyce, G.F., Karaca-Mandic, P., 2006. Varying pharmacy benefits with clinical status: the case of cholesterol-lowering therapy. American Journal of Managed Care 12 (1), 21–28. Hsu, J., Price, M., Huang, J., Brand, R., Fung, V., Hui, R., Fireman, B., Newhouse, J.P., Selby, J.V., 2006. Unintended consequences of caps on Medicare drug benefits. New England Journal of Medicine 354 (22), 2349–2359. Jones, K., Vischi, T., 1979. Impact of alcohol, drug abuse, and mental health treatment on medical care utilization. Medical Care 17 (12), 1–82. Kaiser Family Foundation, 2009. Employer Health Benefits: 2009 Annual Survey. Publication # 7936. Available at:http://ehbs.kff.org/pdf/2009/7936.pdf. Lakdawalla, D., Sood, N., 2009. Innovation and the welfare effects of public drug insurance. Journal of Public Economics 93, 541–548. Lichtenberg, F.R., 2007. The impact of new drugs on U.S. longevity and medical expenditure, 1990–2003: evidence from longitudinal, disease-level data. American Economic Review 97 (2), 438–443. McGuire, T.G., 2012. Demand for health insurance. In: Pauly, M.V., McGuire, T.G., Barros, P.P. (Eds.), Handbook of Health Economics, Vol. 2. Elsevier. Newhouse, J.P., 1993. Free-For-All: Health Insurance, Medical Costs, and Health Outcomes: The Results of the Health Insurance Experiment. Harvard University Press, Cambridge, MA. Newhouse, J.P., 2006. Reconsidering the moral hazard-risk avoidance tradeoff. Journal of Health Economics 25 (5), 1005–1014. Pauly, M., Blavin, F., 2009. Moral hazard in insurance, value-based cost sharing, and the benefits of blissful ignorance. Journal of Health Economics 27 (6), 1407–1417. Shang, B., Goldman, D.P., 2007. Prescription Drug Coverage and Elderly Medicare Spending. NBER working paper 13358. Available at: http://www.nber.org/papers/w13358. Zeckhauser, R.J., 1970. Medical insurance: a case study of the tradeoff between risk spreading and appropriate incentives. Journal of Economic Theory 2 (1), 10–26. Zhang, Y., 2008. Cost saving effects of olanzapine as long-term treatment for bipolar disorder. Journal of Mental Health Policy and Economics 11 (3), 135–146. Zhang, Y., Soumerai, S.B., 2007. Do newer prescription drugs pay for themselves? A reassessment of the evidence. Health Affairs 26 (3), 880–886. Zhang, Y., Donohue, J.M., Lave, J.R., O'Donnell, G., Newhouse, J.P., 2009. The effect of Medicare Part D on drug and medical spending. New England Journal of Medicine 361 (1), 52–61.
Contents lists available at SciVerse ScienceDirect
Journal of Public Economics journal homepage: www.elsevier.com/locate/jpube
A welfare measure of “offset effects” in health insurance Jacob Glazer a, b, Thomas G. McGuire c,⁎ a b c
Tel Aviv University, Israel Boston University, United States Department of Health Care Policy, Harvard Medical School, United States
a r t i c l e
i n f o
Article history: Received 20 October 2010 Received in revised form 8 February 2012 Accepted 20 February 2012 Available online 26 February 2012 Keywords: Health insurance design Offset effects
a b s t r a c t Changing health insurance coverage for one service may affect use of other insured services. When improving coverage for one service reduces use of another, the savings are referred to as “offset effects.” For example, costs of better coverage for prescription drugs may be partly “offset” by reductions in hospital costs. Offset effects have welfare implications but it has not been clear how to value these impacts in design of health insurance. We show that plan-paid – rather than total – spending is the right welfare measure of the offset effect, and go on to develop a “sufficient statistic” for evaluating the welfare effects of change in coverage in the presence of multiple goods. We derive a simple rule for when a coverage improvement increases welfare due to offset effects. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Health insurance coverage for one good or service can affect the quantity demanded of other goods or services in a health plan. Following an improvement in coverage for one good, a reduction in the quantity demanded of other services or goods is referred to as an offset effect. A large empirical literature in health economics and health services research, focusing on coverage for drugs, finds offset effects, and measures these effects by the change in total spending on the other covered goods. For example, Shang and Goldman (2007) use Medicare Current Beneficiary Survey (MCBS) data from 1992 to 2000 to show that the extra spending on drugs induced by medigap coverage is more than offset by reductions in total health care spending on other services. Hsu et al. (2006) compare medical spending for Medicare beneficiaries with a cap on drug coverage to spending by those without a cap at Kaiser Permanente of Northern California prior to Medicare Part D. Drug spending was 28% less in the capped group but other categories of expenditures were higher and total spending for all care was not significantly different between the groups, implying a near dollar-for-dollar offset in total costs. Gaynor et al. (2007) study the effect of increases in copayments charged for drugs among private employees on total (plan plus consumer) spending. Increases in non-drug spending, largely in outpatient care, offset
⁎ Corresponding author. Tel.: + 1 617 432 3536; fax: + 1 617 432 2905. E-mail address: [email protected] (T.G. McGuire). 0047-2727/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jpubeco.2012.02.007
$.35 of each dollar saved in drug costs. 1 Chandra et al. (2010) found that the savings in costs due to higher copayments for drugs were partly offset by higher spending on hospital services among retired state employees in California. They tracked offsets by payer since a primary (Medicare) and secondary (employer-provided supplemental) shared in offsets unequally. The implicit logic in offset papers is that if total medical costs fall due to an increase in coverage, then the change in coverage is welfare improving (i.e. “pays for itself”). This paper argues that change in total medical spending, meaning the sum of plan and patient outof-pocket spending, is not the right measure of the economic value (or cost) of a change in insurance coverage due to offset effects. Rather, health plan costs alone measure the economic value of savings due to reductions in the use of other services. Applying methods reviewed by Chetty (2009), we show that a “sufficient statistic” for evaluating the welfare effect of change in coverage for one good is
1 Other papers use total costs as the measure of offsets. Gibson et al. (2006) measured the effects of lower copayments for statins (drugs treating high cholesterol) on total medical expenditures, payments from any source, and evidence of an offset. Zhang et al. (2009) found an offset effect in added drug coverage for Medicare Part D. In their group with no prior drug coverage, drug spending went up $41 per person per month with Part D but other medical expenses fell by $33 per month. They computed the offset effect of Medicare Part D on other medical expenditures using total expenditures (plan plus copayments). Lichtenberg (2007) has conducted a series of studies of the health and medical care cost impacts of newer prescription drugs and found evidence for an offset effect on total health care costs. For a recent paper, see Lichtenberg (2007). Zhang and Soumerai (2007) question the conclusions of some of Lichtenberg's earlier offset findings. Offset effects of drugs have become so widely accepted that “null effect” papers are published. See Duggan (2005) who pursued the Lichtenberg line of inquiry for a specific area of treatment and found that newer antipsychotic drugs did not reduce total costs in comparison to older drugs. See also Zhang (2008).
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2. A model of offsets in health insurance Suppose a health plan covers services 1 and 2. Quantity of each received by a representative individual in the plan is x1 and x2 measured in dollars. Benefits to the individual are B(x1,x2), where Bi ≥ 0, Bii b 0, i = 1,2, with subscripts indicating partial derivatives. Letting ci denote the copayment charged for each unit of service i, then the individual demands service i to satisfy: Bi ðx1 ; x2 Þ ¼ ci
i ¼ 1; 2
ð1Þ
Let R denote the plan premium paid by the enrollee. Assuming the plan makes zero profit, the premium is: Rðc1 ; c2 Þ ¼ ð1−c1 Þx1 þ ð1−c2 Þx2 ;
ð2Þ
where (x1,x2) are given by Eq. (1). The individual's total utility from the plan is thus: U ðc1 ; c2 Þ ¼ Bðx1 ; x2 Þ–c1 x1 –c2 x2 –Rðc1 ; c2 Þ;
∂U ðc1 ; c2 Þ ∂x ∂x ¼ ðB1 −1Þ 1 þ ðB2 −1Þ 2 ∂c2 ∂c2 ∂c2 ∂x1 ∂x2 ¼ ðc1 −1Þ þ ðc2 −1Þ ∂c2 ∂c2
ð4Þ
The second equality follows from Eq. (1). Suppose copayment for ∂x1 > 0, there is an offset effect and consumpservice 2 is reduced. If ∂c2 tion of x1 falls with this change. What happens to welfare? Eq. (4) tells us how to value the offset. Reversing the sign of Eq. (4) to get an expression in terms of plan shares, when copayment for service 2 goes up (down), utility of the individual goes up (down) if and only if Eq. (5) holds: ð1−c1 Þ
∂x1 ∂c2
Offset effect
þ
ð1−c2 Þ
∂x2 ∂c2
b0 ð5Þ
½
Own‐price effect
The intuition for this result is the following: the second term on the left-hand side of the inequality captures the inefficiency in consumption induced by the reduction in copayment for service 2. With health insurance, the marginal benefit of health care is less than the marginal cost (B2 = c2 b 1), and the extra consumption of x2 due to the reduction in copay creates additional welfare loss. 3 The first term on the left-hand side in Eq. (5) is the offset effect due to the change in consumption (in this case reduction) of x1. Just as with the own-price effect, benefits and costs both matter in valuing ∂x1 welfare of any offset effect. The 1 part is the reduction in total ∂c2 ∂x1 part is the cost from the change in x1 and, since B1 = c1, the −c1 ∂c2 loss in benefits. Thus, the net welfare measure of offset effects is ∂x1 plan savings: ð1−c1 Þ : ∂c2 We can relate the analysis to changes in plan's costs. From Eq. (2) we know that when copayment for service 2 changes, the change in the plan's costs is given by: ∂Rðc1 ; c2 Þ ∂x ∂x ¼ ð1−c1 Þ 1 þ ð1−c2 Þ 2 −x2 ∂c2 ∂c2 ∂c2
ð6Þ
Expression Eq. (4) for welfare and Eq. (6) for plan costs are the same except for the presence of x2, the cost shifting effect of a change in c2, a transfer ultimately paid by the consumer in any case. Using Eqs. (4) and (6) we can state a rule for welfare in terms of planpaid costs. 2.1. Rule for welfare effects
ð3Þ
where (x1,x2) are from Eq. (1) and R is from Eq. (2). Substituting for R to recognize that the individual pays for services by a combination of the cost sharing and the premium: U ðc1 ; c2 Þ ¼ Bðx1 ; x2 Þ–x1 –x2 :
Consider now what happens to utility (welfare) (Eq. (3′)) if the plan were to change the copayment for service 2:
½
the change in total plan-paid costs less the change in costs transferred to/from consumers. 2 We go on to derive an elasticity rule for when the offset effects of an improvement in coverage increase welfare. A simple argument shows why total costs are not the right welfare measure of an offset effect. Suppose the plan covers just one service, “health care,” and an increase in coverage of health care increases a consumer's total expenditures on health care. The consumer budget constraint implies that spending on some other non-covered services has to fall. This “offset” says nothing about efficiency since coverage expansions are always exactly “offset” in this trivial sense. What if the affected other spending were on another form of health care that was minimally covered in the plan, say for one percent of costs with consumers paying ninety nine percent? Logically, token coverage cannot imply that we should count the full spending change as an offset. To see the intuition for our result about the role of plan-paid costs consider the following example. Suppose that there are two services and both are (partially) covered by insurance, namely the individual has to pay some copayment lower than the marginal cost of providing the services. What is the effect of a change in the level of copayment of one of the two services on welfare? Since the level of services the individual chooses to use is at the point where his marginal benefit equals the copayment, and since the copayment is less than marginal cost, there is a welfare loss associated with the consumption of the two services. The change in welfare loss is just the sum of the changes in consumption times the difference between marginal cost and marginal benefit for each of the two services. Note that the difference between marginal benefit and marginal cost is equal to the plan's share of costs. Our focus on plan-paid cost is due to this: plan paid costs are a measure of the welfare loss per unit, and total welfare effect of a change in the offset good's consumption is the change in quantity multiplied by the plan paid share of costs.
521
ð3′Þ
2 Chetty (2009) uses the term as follows. A statistic, e.g., the decline in plan-paid costs, is “sufficient” for welfare analysis in the sense that conditional on this information, no other statistics from the data are informative about welfare. An exact measure of welfare is obviously a sufficient statistic.
The welfare effect of a change in coverage is equal to minus the change in plan costs net of the cost-shifting effect of the coverage change. Proof. From Eqs. (4) and (6) we get: ∂U ðc1 ; c2 Þ ∂Rðc1 ; c2 Þ ¼− −x2 ∂c2 ∂c2
ð7Þ
3 In the conventional analysis of optimal health insurance, this welfare loss is weighted against the risk spreading gain to find the optimal copayment, c2 (Zeckhauser 1970). We return to the issue of risk below.
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Our rule for welfare effects constitutes, in Chetty's (2009) term, a “sufficient statistic” for welfare evaluation of health insurance changes. 4 Our measure, change in plan costs less cost shifting, is equal to the welfare change, and thus yields an if and only if rule: welfare goes up if and only if plan costs less transfers go down. We can use our rule to interpret the existing logic of the offset literature which focuses on total costs, plan paid plus patient paid, and concludes that an improvement in coverage for good 2 is worthwhile if it “pays for itself” in savings on good 1. Consider a reduction in c2 that decreases use of covered good x1 (an offset effect). Suppose the improvement in coverage for x2 “pays for itself” in the sense that the reduction in the total cost of x1 exceeds the increase in plan costs for x2. Our rule tells us that this condition is neither necessary nor sufficient for an increase in welfare. It is not necessary because the cost-shifting effect of the change in c2 is disregarded for welfare. It is not sufficient because it is not total costs that measure the value of the offset, but plan-paid costs. Instead of looking for a coverage improvement to “pay for itself,” we propose the following simple rule expressed in terms of demand elasticities for when an improvement in coverage improves welfare via an offset effect. 5
3. Final comments
2.2. A simple elasticity rule for when offsets increase welfare Welfare goes up with a decrease in c2 (improvement in coverage) when the partial derivative in Eq. (4) is negative, or alternatively: ð1−c1 Þ
∂x1 ∂x > −ð1−c2 Þ 2 ∂c2 ∂c2
ð8Þ
Putting this in elasticity form and dividing through by −ε22 (a positive number), the criterion for a welfare improvement with a decrease in c2 becomes: −
ε12 ð1−c2 Þx2 > ε22 ð1−c1 Þx1
perceived value of the copayment increase.6 However, taking the plan rather than total cost perspective we would say that since drugs are covered at roughly 50% and hospital cost at 100%, the offset ratio doubles, to about two-to-three. Gaynor et al. (2007) in another drug offset paper conclude that offsets savings are about 35% of added drug costs. They report spending and estimated elasticities allowing us to apply the offset rule from above. Assuming drug coverage averages 50% and outpatient coverage is 90% (typical for US employer-based health insurance), plan spending is $312 per year on drugs and $1,453 for outpatient care, so the ratio of plan-paid shares (the RHS of Eq. (9)) is .21. The authors present a range of elasticities, but picking one pair from their Table 8 to illustrate our point, the own-price elasticity is −.40 and the cross-price is .17. The LHS of Eq. (9) is thus +.425, easily meeting the criterion for the offset effect to be welfare increasing. 7 While this and the previous example are only intended to be illustrative, the switch to regarding plan-paid rather than total cost changes in valuing offset effects will magnify these effects because the planpaid share for drugs is currently low.
ð9Þ
In Eq. (9), ε12 is the cross and ε22 is the own-price elasticity with respect to c2. The RHS of Eq. (9) is positive and equal to the ratio of plan paid costs for service 2 to service 1. Rule: for a decrease in c2 to improve welfare, the goods must be substitutes (ε12 > 0); and, the ratio of the absolute values of the cross to the own-price elasticity must exceed the ratio of the plan paid costs for the two services. The offset rule for welfare is simple to apply. Suppose we know that the own-price elasticity of drugs is −1.0 and the cross-price elasticity for hospital services is +.2. If the plan paid drug costs are less than 20% of the plan-paid hospital costs, an improvement in coverage for drugs improves welfare. Attention to plan rather than total cost can change the tenor of the policy implications of offset effects, particularly for drug coverage where plan shares are relatively small. Turning to some results in significant recent offset papers illustrates the quantitative importance of the plan-cost perspective. Comparing the change in total costs for drugs and hospitals, Chandra et al. (2010, p. 208) found that a decrease in coverage for drugs reduced total drug costs by $23.06 per member per month, but increased total hospital costs by only $7.23—the offset amounted to only a one-to-three ratio of hospital cost increases to drug cost savings, and in the authors' judgment was “unlikely to be enough” to reverse the 4 Chetty's primary analysis was directed to the welfare effects of tax changes, making use of consumer utility maximization and firm profit-maximization conditions. The analysis is very similar to the way we use Eq. (1) where the consumer equates marginal benefit to marginal cost to simplify the expression for a welfare change. 5 Any change in administrative costs associated with insurance should also be included in the welfare effects. Insurance premiums are often expressed as actual payouts and a “loading factor” above the payouts. Any part of the loading factor that represents incremental costs (but not profits) should be included in the welfare evaluation.
In applied policy research, offset effects played an important role in the discussion about the design of optimal health insurance for mental health treatment, 8 and more recently the do so in the case of coverage for drugs. 9 Most public and private plans cover drugs, but the coverage is partial in the sense that a drug formulary typically excludes many drugs, and for those drugs that are covered, the percent paid by the plan is much less than for other health care services. Interestingly, the copayment for generic drugs is often so high that it exceeds the acquisition cost to the health plan. 10 Our ideas about valuing offset effects have the most current direct application to the question of coverage for drugs, where a considerable amount of research, noted above, has studied how more drug coverage affects other service use. An important feature of the market for branded drugs under patent protection is that the price health plans pay is much higher than the social marginal cost of production. Lakdawalla and Sood (2009) point out that by lowering the out-of-pocket price to patients, insurance coverage for branded drugs can move price towards rather than away from social marginal cost and improve the social efficiency of consumption. This is distinct from our analysis of the welfare effects of offsets where we benchmark welfare against the plan's acquisition cost. 6 The California change studied in Chandra et al. (2010) also involved increases to outpatient copays, which we are ignoring in this illustrative example. These increases also saved money, making the offset ratio one to five. By ignoring this other benefit change in our discussion, we are in effect assuming it is the drug coverage change that causes the offset. 7 We choose the fixed-effect OLS dynamic model with lags. This is the most favorable to offsets from the table, though other estimates presented in the table also satisfy the criterion. 8 Jones and Vischi (1979) in their review concluded there were medical offset effects of psychotherapy visits. The research literature consisted mostly of pre-post naturalistic studies. The Rand Health Insurance Experiment included plans with differential cost sharing for mental health and physical health care in order to investigate offsets of mental health treatment. No evidence for such offsets was found in the HIE (Newhouse, 1993). 9 The clinical rationale for offset effects of coverage for mental health care is the connection between mental and physical health. Mental health problems can manifest themselves as physical symptoms and if the underlying mental health problem is treated successfully, physical health improves. In the case of drug treatment, the clinical rationale is that patient compliance with drug treatment for many chronic illnesses improves health and lessens the need for other costly treatment. See, for example, discussion in Goldman et al. (2006). 10 See Kaiser Family Foundation (2009) for description of coverage in drug formularies for private employers. Glazer et al. (forthcoming) apply ideas from price index theory to design of a drug formulary by characterizing the maximum premium a consumer would pay for a formulary with a certain set of copayments. Offset effects on other covered services figure into the expression in the form of savings on plan paid costs.
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We note that the literature on optimal health insurance with multiple services is consistent with our interpretation offset effects. Goldman and Philipson (2007) regard offset effects as a cross-price elasticity and characterize efficient (second-best) demand-side cost sharing in health insurance. Added hospital costs offset savings from reducing coverage of drugs in their example. Characterizing their results, they conclude, “When hospital care is substitutable and excessive – i.e. provided below cost – there is an additional marginal cost of raising drug copays.” (p.430). This echoes our point: if hospital care were not partly plan-paid, resulting in it being “provided below cost,” and “excessive,” there would be no offset effect to count. The measure of inefficiency of excessive use is the divergence between marginal benefit and marginal cost—the marginal plan contribution. 11 A natural question is to ask whether markets could succeed in setting coverage for various health care services to take account of cross-price effects. In a perfectly competitive market, a health plan would be forced to maximize welfare of the representative consumer, implying the efficiency issues discussed here would be taken care of in competitive equilibrium. Health insurance markets are fraught with market failure, however, making it worthwhile to have an explicit expression for the welfare effects of offsets. Health plan market power in pricing is probably not the main issue here. A monopolist would seek to provide a certain utility to enrollees at minimum cost, implying offsets would be taken into account within a benefit plan offered by a monopolist. More serious is adverse selection which leads to distorted plans in market equilibrium. And probably most important in the context of offset effects is the presence of multiple insurance plans. For example, most consumers with Medicare in the U.S. have coverage from multiple insurers, each with no reason to consider spillover effects on another plan. Finally, much of health insurance in the US and elsewhere is public insurance where plan design is not subject to a market test. In sum, there can be little assurance that market forces alone will lead to optimal coverage, leaving a role for explicit expressions for the value of offset effects in health insurance. The major limitation of our rule for offsets and model setup generally stems from the assumption that quantity is determined by the equality of marginal benefit to the consumer/patient and patient copayment. While the standard demand model is widely applied in theoretical and empirical health care research, it is also seriously questioned as a basis for describing the outcome of patient-provider interactions (Chandra et al., 2012). Effective physician agency on behalf of the patient would be consistent with our approach, but we acknowledge that the marginal benefit-marginal cost equality is still a strong assumption. Relatedly, health economists doubt whether consumer demand should be interpreted as marginal benefit when assessing the efficiency of changing coverage. Perspectives from “valuebased insurance design” and behavioral economics both question the conventional welfare framework for assessing the efficiency cost of added coverage for a service. 12 As Pauly and Blavin (2009) show,
11 Their Eq. (1) contains two pieces, like our Eq. (4). Their “offset effect” piece is the product of the marginal utility of hospital care times the derivative of hospital care with respect to drug coverage. Their expression for marginal utility includes recognition of full cost because their derivatives with respect to cost sharing implicitly include the effect on the premium. Their marginal utility is thus equivalent to our (B1 − 1) in Eq. (4). In another paper, Ellis and Manning (2007) find optimal cost sharing for a preventive service that reduces use of other health care. In their solution, terms involving other health care drop out of the expression for optimal insurance for prevention when demand side cost sharing for the other health care is equal to one (and there are no plan-paid costs). See their Eq. (15), page 1139. It is prevention of covered health care services that play into the optimal insurance for preventive health care. For integration of the cross-elasticity effect into the question of optimal insurance, see McGuire (2012). 12 Health insurance coverage corrects for consumer misevaluation of services in the value-based insurance design framework. See Chernew et al. (2007) for the proposal for the value-based approach, and Pauly and Blavin (2009) for an integration of the Pigouvian subsidy perspective into the conventional moral hazard framework. In a related point connected to behavioral economics, Newhouse (2006) illustrates how time-inconsistent preferences could lead to inefficient non-compliance with treatment that prevents (offsets) later illness.
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however, consumer over or undervaluation can be integrated with traditional considerations of optimal health insurance. One element of optimal design of health insurance is financial risk, absent from our welfare expressions above. Our purpose is to derive expressions for the welfare impacts of offset effects, so we have not directly considered gains/losses in terms of the associated risk spreading. Within a context where offset effects are of principal concern, since increases in costs of one service are counterbalanced by decreases in costs elsewhere, the overall effects on risk bearing are likely to be small. Acknowledgements This research was supported by the National Institute of Aging (P01 AG032952) and the National Institute of Mental Health (R01 MH094290). We are grateful to Sebastian Bauhoff, Mike Chernew, Randy Ellis, Haiden Huskamp, Joseph Newhouse, Aaron Schwartz, Tisa Sherry, Anna Sinaiko and Zirui Song for comments on an earlier draft. 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