《卫生经济学》课程参考文献：7.Richard Dusansk_Implications of the Interaction between Insurance Choice and Medical Care Demand 2010

The Journal of Risk and Insurance O The Journal of risk and Insurance, 2010, Vol 77, No 1, 129-144 DO:10.11/1539-6975200901335X IMPLICATIONS OF THE NTERACTION BETWEEN INSURANCE CHOICE AND MEDICAL CARE DEMAND Richard dusansky Ko ABSTRACT The gross price elasticity of demand for medical care is decomposed into wo separate observable components: the medical care gross price elasticity of insurance choice and the cost-sharing elasticity of medical care. When con- sumers alter their choice of health-care plans, the price elasticity of medical care is no longer equivalent to the cost-sharing elasticity; using the latter as a proxy for the former may produce misleading results. We present condi tions under which the medical care price elasticity is positive, the case of a quasi-Giffen good, and provide a theoretical foundation for extant empirical findings of a positive medical care price elasticity of insurance demand INTRODUCTION Among the developed, higher-income countries, medical care expenditures have been rising at a pace that is distinctly above overall growth rates. In the United States, for example, total medical cost outlays have increased at an average rate of 8.9 percent since 1980, which is about 2.6 percentage points above the average for the aggregate economy, as measured by gross domestic product(GDP). Similar patterns prevail when one examines medical expenditures in both per capita and budget share terms As a share of the U.S. economy, medical care has nearly doubled over the 25-year period 1980 to 2005, rising from 9 percent of GDP in 1980 to 16 percent in 2005.2 Medical care spending per ca has also increased dramatically during this period, expenditure leader, similar trends exist in most developed countries, ?T the medical increasing to $6,697 from $1, 102. Although the United States is by These observations prompt interest in the forces underlying medical care demand and in how individuals respond to its rising costs. In this article, we analyze con sumer medical care demand response to a change in the gross price of medical care, paying special attention to the interaction between the consumer's demand for Richard dusansky is with the Department of Economics, University of Texas at Austin. Cagatay Koc is with the Department of Economics, University of Texas at Arlington. Dusansky can be contacted via e-mail: dusansky @eco. utexas. edu 1 Centers for Medicare and Medicaid Services 2 Centers for Medicare and Medicaid Services 3 Centers for Medicare and Medicaid Services 4 Kaiser Family Foundation 129

C The Journal of Risk and Insurance, 2010, Vol. 77, No. 1, 129-144 DOI: 10.1111/j.1539-6975.2009.01335.x IMPLICATIONS OF THE INTERACTION BETWEEN INSURANCE CHOICE AND MEDICAL CARE DEMAND Richard Dusansky C¸ agatay Koc ˘ ¸ ABSTRACT The gross price elasticity of demand for medical care is decomposed into two separate observable components: the medical care gross price elasticity of insurance choice and the cost-sharing elasticity of medical care. When con￾sumers alter their choice of health-care plans, the price elasticity of medical care is no longer equivalent to the cost-sharing elasticity; using the latter as a proxy for the former may produce misleading results. We present condi￾tions under which the medical care price elasticity is positive, the case of a quasi-Giffen good, and provide a theoretical foundation for extant empirical findings of a positive medical care price elasticity of insurance demand. INTRODUCTION Among the developed, higher-income countries, medical care expenditures have been rising at a pace that is distinctly above overall growth rates. In the United States, for example, total medical cost outlays have increased at an average rate of 8.9 percent since 1980, which is about 2.6 percentage points above the average for the aggregate economy, as measured by gross domestic product (GDP).1 Similar patterns prevail when one examines medical expenditures in both per capita and budget share terms. As a share of the U.S. economy, medical care has nearly doubled over the 25-year period 1980 to 2005, rising from 9 percent of GDP in 1980 to 16 percent in 2005.2 Medical care spending per capita has also increased dramatically during this period, increasing to $6,697 from $1,102.3 Although the United States is by far the medical expenditure leader, similar trends exist in most developed countries.4 These observations prompt interest in the forces underlying medical care demand and in how individuals respond to its rising costs. In this article, we analyze con￾sumer medical care demand response to a change in the gross price of medical care, paying special attention to the interaction between the consumer’s demand for Richard Dusansky is with the Department of Economics, University of Texas at Austin. C¸ agatay ˘ Koc¸ is with the Department of Economics, University of Texas at Arlington. Dusansky can be contacted via e-mail: dusansky@eco.utexas.edu 1 Centers for Medicare and Medicaid Services. 2 Centers for Medicare and Medicaid Services. 3 Centers for Medicare and Medicaid Services. 4 Kaiser Family Foundation. 129

30 THE JOURNAL OF RISK AND INSURANCE medical care and his demand for health insurance, and the ensuing implications for the measurement of demand elasticities Private health insurance contracts provide for a price discount at the time the insured purchases medical care; therefore, the more generous an individual's insurance cov erage is, the higher might be his demand for medical care. This effect of insurance on medical care demand is known as the moral hazard effect(Arrow, 1963; Pauly, 1968) It refers to the effect of insurance on the net price of medical care (i.e, percentage of cost sharing times the gross price)and to the consequent incentive effects on medical 6are consumption In medical care, moral hazard combines with the interdependence tween utilization and the insurance contract decision. The choice of type of insur ance is influenced by expected utilization of medical care services, whereas utilization itself is affected by the consumer's insurance contract. This interaction complicates the analysis of the consumer s response to changes in medical care prices. We present a principal-agent model of individual consumer medical care demand that highlights this interaction, so that the consumer is allowed to change both his demand for med ical care and his selection of insurance contract in response to changes in medical oare prices. A change in the gross price of medical care has two effects on demand: a rect effect, for fixed cost sharing, and an indirect effect through a moral hazard re- sponse that results from cost-sharing changes associated with price-induced changes in the choice of insurance plan. Much of the extant literature studies the demand for medical care by examining responses to changes in cost sharing, with the gross price held constant and the choice of health insurance contract remaining fixed. However, if one wants to compare medical care demand with the demand for other goods or categories of goods-or if one simply recognizes the fact that most insured consumers choose from among several insurance plans and can alter their intended choice-then the response to a change in gross price is important. Our analysis reveals that the indirect demand effect through the moral hazard effect of insurance can have a major role in determining the consumers medical care demand response to a price change. Indeed it is possible for the own-demand curve for medical care to be upward sloping, even though medical care is a noninferior good For this possibility to occur, it turns out, the demand for health insurance must be increasing in the price of medical care. Although there is empirical support for this it lacks a theoretical foundation. We provide one by developing a formal analytical condition, which embodies a dominant expenditure risk effect under which it holds There has been some work done on the possibility that in response to an increase in the premium rate, consumers may choose to increase their insurance coverage, i.e This article concerns the case where individuals have some choice about the extent or generos- ity of their insurance coverage. It does not apply to systems where coverage is set exogenously as in some national health insurance systems. However, even in the presence of national health insurance participation such as Medicare, what follows applies if the individual can privately upplement the mandated coverage 6 This interaction in the medical care industry has received recent attention. For example, Mougeot and Naegelen(2009)analyze the optimal outlier payment policy in a prospective yment system for hospitals under both adverse selection and moral hazard Housing is another example of a noninferior good whose own demand can be upward sloping See Dusansky and Kos (2007)

130 THE JOURNAL OF RISK AND INSURANCE medical care and his demand for health insurance, and the ensuing implications for the measurement of demand elasticities.5 Private health insurance contracts provide for a price discount at the time the insured purchases medical care; therefore, the more generous an individual’s insurance cov￾erage is, the higher might be his demand for medical care. This effect of insurance on medical care demand is known as the moral hazard effect (Arrow, 1963; Pauly, 1968). It refers to the effect of insurance on the net price of medical care (i.e., percentage of cost sharing times the gross price) and to the consequent incentive effects on medical care consumption. In medical care, moral hazard combines with the interdependence between utilization and the insurance contract decision. The choice of type of insur￾ance is influenced by expected utilization of medical care services, whereas utilization itself is affected by the consumer’s insurance contract. This interaction complicates the analysis of the consumer’s response to changes in medical care prices.6 We present a principal–agent model of individual consumer medical care demand that highlights this interaction, so that the consumer is allowed to change both his demand for med￾ical care and his selection of insurance contract in response to changes in medical care prices. A change in the gross price of medical care has two effects on demand: a direct effect, for fixed cost sharing, and an indirect effect through a moral hazard re￾sponse that results from cost-sharing changes associated with price-induced changes in the choice of insurance plan. Much of the extant literature studies the demand for medical care by examining responses to changes in cost sharing, with the gross price held constant and the choice of health insurance contract remaining fixed. However, if one wants to compare medical care demand with the demand for other goods or categories of goods—or if one simply recognizes the fact that most insured consumers choose from among several insurance plans and can alter their intended choice—then the response to a change in gross price is important. Our analysis reveals that the indirect demand effect through the moral hazard effect of insurance can have a major role in determining the consumer’s medical care demand response to a price change. Indeed, it is possible for the own-demand curve for medical care to be upward sloping, even though medical care is a noninferior good.7 For this possibility to occur, it turns out, the demand for health insurance must be increasing in the price of medical care. Although there is empirical support for this, it lacks a theoretical foundation. We provide one by developing a formal analytical condition, which embodies a dominant expenditure risk effect under which it holds. There has been some work done on the possibility that in response to an increase in the premium rate, consumers may choose to increase their insurance coverage, i.e., 5 This article concerns the case where individuals have some choice about the extent or generos￾ity of their insurance coverage. It does not apply to systems where coverage is set exogenously, as in some national health insurance systems. However, even in the presence of national health insurance participation such as Medicare, what follows applies if the individual can privately supplement the mandated coverage. 6 This interaction in the medical care industry has received recent attention. For example, Mougeot and Naegelen (2009) analyze the optimal outlier payment policy in a prospective payment system for hospitals under both adverse selection and moral hazard. 7 Housing is another example of a noninferior good whose own demand can be upward sloping. See Dusansky and Koc¸ (2007)

INTERACTION BETWEEN INSURANCE CHOICE AND MEDICAL CARE DEMAND 131 the demand for insurance may be upward sloping(Hoy and Robson, 1981; Briys, Dionne, and Eeckhoudt, 1989: Hau, 2008). Our analysis complements this literature nd suggests that health insurance, via its moral hazard effect, can make the demand for medical care upward sloping We also examine medical care's price elasticity of demand and demonstrate that the gross price elasticity can be decomposed into two separate and observable compo- lents, the medical care gross price elasticity of insurance choice and the cost-sharing mine a measure of the gross price elasticity. When one allows for the contract choice response, the gross price elasticity of demand for medical care and the cost-sharing demand elasticity diverge. Consequently, using cost-sharing elasticities as a proxy for gross price elasticities would be unwise, if not misleading THE MODEL We employ a principal-agent model in which the agent(consumer)first choose an insurance plan, when there is uncertainty about his future health status, and then makes optimal choices of medical care and the standard consumer goods, after the health status uncertainty is resolved. The insurance contracts among which the consumer chooses can vary considerably across the basic health characteristics. For example, there can be differences in the annual deductible per person and /or per family, in the physician co-pays per physician type, in the percentage cost shares for hospital stays, for in-network versus out-of-network services, etc. We follow Feldstein (1971)in assuming that the characteristics of any insurance policy can be represented y asingle metric We designate this by o, the percentage of cost sharing. An increase in the deductible or co-pay, for example, increases a. For simplicity, we assume that our consumer faces a continuum of policies, arrayed by percentages of cost sharing, and for a given gross price of medical care chooses a policy with a particular percentage of cost sharing, say a =a*. Here we acknowledge the reality that the majority nsured consumers choose from among several insurance policies. In 1995, 62 percent of insured U.S. workers were offered two or more health plans For firms with 200 or more workers, this figure was 84 percent The consumers ex post budget constraint can be represented by Y一R=C+pm s Hoy and Robson( 1981)show that for the class of constant relative risk-aversion utility func- tions, the coefficient of relative risk aversion must be greater than 1 for insurance to be a Giffen good. Briys, Dionne, and Eeckhoudt(1989)demonstrate that insurance is not a Giffen good if and only if the variation of risk aversion is lower than a minimal bound, which is satisfied with increasing and constant absolute risk-aversion utility functions. Assuming that there are two states of the world (loss and no loss), they confirm Hoy and robsons result by reversing their necessary and sufficient condition. Hau(2008)shows that the necessary condition for insurance to be a giffen good can be made less restrictive than that proposed by the above studies by extending their result to the case with a continuum of states of the world and without the class of constant relative risk-aversion utility functions See Jensen et al. (1997)

INTERACTION BETWEEN INSURANCE CHOICE AND MEDICAL CARE DEMAND 131 the demand for insurance may be upward sloping (Hoy and Robson, 1981; Briys, Dionne, and Eeckhoudt, 1989; Hau, 2008).8 Our analysis complements this literature and suggests that health insurance, via its moral hazard effect, can make the demand for medical care upward sloping. We also examine medical care’s price elasticity of demand and demonstrate that the gross price elasticity can be decomposed into two separate and observable compo￾nents, the medical care gross price elasticity of insurance choice and the cost-sharing elasticity of medical care. We show how the two can be combined in order to deter￾mine a measure of the gross price elasticity. When one allows for the contract choice response, the gross price elasticity of demand for medical care and the cost-sharing demand elasticity diverge. Consequently, using cost-sharing elasticities as a proxy for gross price elasticities would be unwise, if not misleading. THE MODEL We employ a principal–agent model in which the agent (consumer) first chooses an insurance plan, when there is uncertainty about his future health status, and then makes optimal choices of medical care and the standard consumer goods, after the health status uncertainty is resolved. The insurance contracts among which the consumer chooses can vary considerably across the basic health characteristics. For example, there can be differences in the annual deductible per person and/or per family, in the physician co-pays per physician type, in the percentage cost shares for hospital stays, for in-network versus out-of-network services, etc. We follow Feldstein (1971) in assuming that the characteristics of any insurance policy can be represented by a single metric. We designate this by σ, the percentage of cost sharing. An increase in the deductible or co-pay, for example, increases σ. For simplicity, we assume that our consumer faces a continuum of policies, arrayed by percentages of cost sharing, and for a given gross price of medical care chooses a policy with a particular percentage of cost sharing, say σ = σ∗. Here we acknowledge the reality that the majority of insured consumers choose from among several insurance policies. In 1995, 62 percent of insured U.S. workers were offered two or more health plans. For firms with 200 or more workers, this figure was 84 percent.9 The consumer’s ex post budget constraint can be represented by Y − R = c + σ pm, (1) 8 Hoy and Robson (1981) show that for the class of constant relative risk-aversion utility func￾tions, the coefficient of relative risk aversion must be greater than 1 for insurance to be a Giffen good. Briys, Dionne, and Eeckhoudt (1989) demonstrate that insurance is not a Giffen good if and only if the variation of risk aversion is lower than a minimal bound, which is satisfied with increasing and constant absolute risk-aversion utility functions. Assuming that there are two states of the world (loss and no loss), they confirm Hoy and Robson’s result by reversing their necessary and sufficient condition. Hau (2008) shows that the necessary condition for insurance to be a Giffen good can be made less restrictive than that proposed by the above studies by extending their result to the case with a continuum of states of the world and without the class of constant relative risk-aversion utility functions. 9 See Jensen et al. (1997)

32 THE JOURNAL OF RISK AND INSURANCE where Y is income, R is the cost to the consumer for participating in the health insurance plan(i.e, health insurance premium), c is a composite consumption good whose price is normalized to one without any loss of generality, and m is composite medical care services with gross price p. Since a is the fraction of p that the consumer must pay out of pocket, o p is the net price for a unit of medical care service to the The consumer's utility function, which is assumed to be continuous and bounded, 0 is represented by u=u(, H(m, s)), where u1=au>0,U= ≤0,andU22 <0. We assume y does nah 20; i.e., the consumer's marginal utility of consumption rises(tech- at lh ot fall)as health improves. This ensures that the second-order condition with respect to the ex post decision problem about purchases of medical care and other goods conditional on the ex ante choice of insurance plan is satisfied. H(,)is the health production function with H1 五= as in Dardanoni and Wagstaff (1990). It determines the amount of health produced measured as income equivalent with input m in state s The model is solved by backward induction. First, the consumer solves for the opti mizing values of m and c conditional upon the choice of insurance policy o for each possible realization of the unknown health state s. Second, the consumer formulates a prior probability measure F of the future health states denoted by F(s). Next, substi tuting these optimal values of m and c into the utility function and integrating over s gives the indirect conditional expected utility associated with insurance policy o. This indirect conditional expected utility function forms the basis of choice of insurance policy o. Assuming a perfectly competitive health insurance market, the consumer maximizes this function over the set of zero-profit insurance policies, yielding the For any arbitrary health status, given a choice of insurance policy, our consumer chooses the level of medical care that maximizes u(r-R-opm, H(m, s)), where we have used the budget constraint to rewrite the first argument of u. The first-order condition uap+u2H1=0 Rearranging the first-order condition gives the optimality condition for this second stage problem 10 If the consumers utility functionis continuous and bounded, the expected utility ofinsurance is well defined This assumption appears elsewhere in the literature. See, for example, Wagstaff (1986), Blomqvist(1997), and Jack(2002)

132 THE JOURNAL OF RISK AND INSURANCE where Y is income, R is the cost to the consumer for participating in the health insurance plan (i.e., health insurance premium), c is a composite consumption good whose price is normalized to one without any loss of generality, and m is composite medical care services with gross price p. Since σ is the fraction of p that the consumer must pay out of pocket, σ p is the net price for a unit of medical care service to the consumer. The consumer’s utility function, which is assumed to be continuous and bounded,10 is represented by U = U(c, H(m,s)), (2) where U1 = ∂U ∂c > 0,U2 = ∂U ∂ H > 0, U11 = ∂2U ∂c2 ≤ 0, and U22 = ∂2U ∂ H2 ≤ 0. We assume that U12 = ∂2U ∂c∂ H ≥ 0; i.e., the consumer’s marginal utility of consumption rises (tech￾nically does not fall) as health improves. This ensures that the second-order condition with respect to the ex post decision problem about purchases of medical care and other goods conditional on the ex ante choice of insurance plan is satisfied.11 H(., .) is the health production function with H1 = ∂ H ∂m > 0 , H11 = ∂2H ∂m2 ≤ 0, and H2 = ∂ H ∂s > 0, as in Dardanoni and Wagstaff (1990). It determines the amount of health produced measured as income equivalent with input m in state s. The model is solved by backward induction. First, the consumer solves for the opti￾mizing values of m and c conditional upon the choice of insurance policy σ for each possible realization of the unknown health state s. Second, the consumer formulates a prior probability measure F of the future health states denoted by F (s). Next, substi￾tuting these optimal values of m and c into the utility function and integrating over s gives the indirect conditional expected utility associated with insurance policy σ. This indirect conditional expected utility function forms the basis of choice of insurance policy σ. Assuming a perfectly competitive health insurance market, the consumer maximizes this function over the set of zero-profit insurance policies, yielding the optimal insurance plan choice. For any arbitrary health status, given a choice of insurance policy, our consumer chooses the level of medical care that maximizes U(Y − R − σ pm, H(m,s)), (3) where we have used the budget constraint to rewrite the first argument of U. The first-order condition is −U1σ p + U2H1 = 0. (4) Rearranging the first-order condition gives the optimality condition for this second￾stage problem: 10 If the consumer’s utility function is continuous and bounded, the expected utility of insurance is well defined. 11 This assumption appears elsewhere in the literature. See, for example, Wagstaff (1986), Blomqvist (1997), and Jack (2002)

INTERACTION BETWEEN INSURANCE CHOICE AND MEDICAL CARE DEMAND 133 u2 where I=#, the shadow price of health, is the insurance adjusted(net)cost to the consumer of producing an extra unit of health. Since the price of the composite consumption good is normalized to one, the consumers marginal rate of substitution between health and the composite consumption good, at the optimum, equals the The presence of uncertainty complicates planning. Although all prices and the current health state are known when the consumer chooses his insurance policy, the future health state s is unknown. Hence, the consequences of the ex ante action o depend crucially on s, which is revealed in the second stage. When making his choice, the consumer must therefore forecast his ex post consumption stream according to the future health state s, given that he makes some insurance choice a. The consumer is assumed to have a prior subjective probability distribution of the future health states denoted by F(s) In choosing a health insurance plan, the consumer is assumed to confront a per fectly competitive health insurance market. Given the utility-maximizing me care schedule m(o, s)characterized by (4), the consumers expected utility function for a particular insurance plan as represented by its cost sharing o and premium r is V(o, R)=U(Y-R-opm(o, s), H(m(o, s), s)dF(s) The competitive equilibrium health insurance policy maximizes(6)subject to the zero-profit insurance policy constraint R=/(1-0)pm(o, s)dF(s) Our model is similar to those presented in Zeckhauser (1970), Spence and Zeckhauser (1971), Feldstein and Friedman (1977), Baumgardner (1991),and Blomqvist(1997). It is a principal-agent model where the agent(insured consumer observes his future health status(s)and decides on the level of composite medical care services(i. e, his effort). Given a level of medical care chosen by the insured according to(4)and assuming a perfectly competitive health insurance market, the principal (the insurer) maximizes the expected utility of the insured subject to the zero-profit insurance policy constraint, which also incorporates the utility-maximizing medical care schedule. Since health insurance policies provide for a price discount at the time 12 Zeckhauser( 1970), Feldstein and Friedman( 1977), and Baumgardner(1991)consider linear insurance schedules, i.e. a constant coinsurance parameter where health insurance pays the same fraction of the cost of the consumers medical care services, regardless of the tota amount spent. Spence and Zeckhauser (1971)and Blomqvist (1997)analyze the properties of nonlinear health insurance policies that depend on the amount of medical expenditures pent

INTERACTION BETWEEN INSURANCE CHOICE AND MEDICAL CARE DEMAND 133 U2 U1 = σ p H1 = π, (5) where π = σ p H1 , the shadow price of health, is the insurance adjusted (net) cost to the consumer of producing an extra unit of health. Since the price of the composite consumption good is normalized to one, the consumer’s marginal rate of substitution between health and the composite consumption good, at the optimum, equals the shadow price. The presence of uncertainty complicates planning. Although all prices and the current health state are known when the consumer chooses his insurance policy, the future health state s is unknown. Hence, the consequences of the ex ante action σ depend crucially on s, which is revealed in the second stage. When making his choice, the consumer must therefore forecast his ex post consumption stream according to the future health state s, given that he makes some insurance choice σ. The consumer is assumed to have a prior subjective probability distribution of the future health states denoted by F (s). In choosing a health insurance plan, the consumer is assumed to confront a per￾fectly competitive health insurance market. Given the utility-maximizing medical care schedule m(σ,s) characterized by (4), the consumer’s expected utility function for a particular insurance plan as represented by its cost sharing σ and premium R is V(σ, R) = S U(Y − R − σ pm(σ,s), H(m(σ,s),s)) dF (s). (6) The competitive equilibrium health insurance policy maximizes (6) subject to the zero-profit insurance policy constraint R = S (1 − σ)pm(σ,s)dF (s). (7) Our model is similar to those presented in Zeckhauser (1970), Spence and Zeckhauser (1971), Feldstein and Friedman (1977), Baumgardner (1991), and Blomqvist (1997).12 It is a principal–agent model where the agent (insured consumer) observes his future health status (s) and decides on the level of composite medical care services (i.e., his effort). Given a level of medical care chosen by the insured according to (4) and assuming a perfectly competitive health insurance market, the principal (the insurer) maximizes the expected utility of the insured subject to the zero-profit insurance policy constraint, which also incorporates the utility-maximizing medical care schedule. Since health insurance policies provide for a price discount at the time 12 Zeckhauser (1970), Feldstein and Friedman (1977), and Baumgardner (1991) consider linear insurance schedules, i.e., a constant coinsurance parameter where health insurance pays the same fraction of the cost of the consumer’s medical care services, regardless of the total amount spent. Spence and Zeckhauser (1971) and Blomqvist (1997) analyze the properties of nonlinear health insurance policies that depend on the amount of medical expenditures spent.