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1、ACCOUNTING FRAMEWORK FOR SOCIETAL COST-OUTCOME ANALYSES OF MORBIDITY REDUCTIONTed Miller, Pacific Institute for Research and EvaluationJanusz Mrozek, Pacific Institute for Research and EvaluationCharles Calhoun, Calhoun ConsultingW. Brian Arthur, Santa Fe InstituteApril 24, 2006Key Words: accounting
2、 framework, willingness to pay, externality, cost-benefit, cost-utility, cost of illnessJEL Classification: J17: Value of Life; Foregone IncomeAbstract. Building on prior work in economic welfare theory, this paper derives the appropriate accounting framework and theoretical foundation for conductin
3、g societal cost-outcome analyses of morbidity and mortality risk reduction. This neoclassical approach models consumption and production over time, with intergenerational transfers. The resulting framework essentially states that the societal life-cycle welfare increase equals the utility of extra l
4、ife years and improved health status plus human capital net of consumption plus the positive or negative value of extra children to the society. Utility loss can be valued, as tastes and circumstances dictate, with quality-adjusted life years (QALYs), willingness to pay, willingness to accept, or ju
5、ry willingness to award. When the utility measure used is an individual measure like a QALY, the societal externalities added include intra-familial consumption transfers and often will exceed $750,000 per death prevented. Published cost-utility analyses, in particular, have been using a seriously f
6、lawed accounting framework that omits the impact on human capital, which should be treated as a societal externality. The framework also provides a theoretical foundation for treating human capital net of consumption, a traditional cost of illness measure, as a lower bound on societal willingness to
7、 pay.1. IntroductionThree approaches are commonly used to value morbidity or morbidity risk reduction. Individual willingness to pay (WTP) measures are popular in environmental and safety economics (Tolley et al. 1986, Miller et al. 1995). The venerable cost of illness (human capital) approach still
8、 has health policy champions. This method calculates the loss of production caused by a morbid condition, then adds associated medical and resource costs (Rice & Cooper 1967, Hodgson & Meiners 1982). It has declined in popularity largely because its failure to account for lost quality of life distor
9、ts the results. In response, some recent analyses supplemented human capital costs with quality of life loss estimates derived from jury willingness to award (Lopez et al. 1995, Miller et al. 1996, Lawrence et al. 2000). Finally, a non-monetized quality-adjusted life year (QALY) approach has been po
10、pularized by pharmaco-economists and health policy analysts (Gold et al. 1996). Although some of these approaches have stronger theoretical support than others, the current societal cost accounting frameworks used with them all are ad hoc.Building on prior work in economic welfare theory, this paper
11、 derives the appropriate accounting framework and theoretical foundation for conducting societal cost-outcome analysis using any of these methods. The derivation builds on the model for valuing changes in mortality risk constructed by Arthur (1981). This neoclassical approach models consumption and
12、production over time, with intergenerational transfers. Arthur (1981) creates a social welfare equivalent of life at any particular age and, for a more restrictive form of the utility function, a social consumption equivalent (SCE) of a life. The results show that the correct social value, essential
13、ly societal WTP (SWTP), is a combination of an individual utility loss measure and the social value of changes in consumption and production. We extend this model by incorporating health status as an argument of the utility function.2. Social Consumption Equivalent Value of LifeThe theoretical basis
14、 for our model is the Social Consumption Equivalent Value of Life (SCE) method developed in Arthur (1981). That method uses an age-specific, overlapping generation, economic model to assess the cost of loss of life or the value of lives saved as the result of a change in the pattern of mortality by
15、age. The SCE method has the following advantages: (1) is based on economic welfare theory, (2) gives values in dollar terms that are a function of the age of the victim, (3) gives values that can be expressed in terms of human capital and individual willingness to pay for fatal risk reduction, and (
16、4) is fully actuarial, in that it uses full age-specific accounting based on healthy life expectancy. Under SCE, fatal risk reduction can be evaluated for situations where the age distribution of loss of life is important, such as: (1) changes in age-specific survival risks (caused, say, by an impro
17、ved pollution scrubber), (2) “statistical” lives lost at a given age, and (3) specific causes (cancer, airline accidents) where loss of life occurs with a known age and gender distribution that differs from the distribution inherent in existing studies of the value of fatal risk reduction.SCE emphas
18、izes that valuation must account for the additional consumption of those whose lives are saved or lengthened. For example, when a 70 year-old life is “saved,” society gains that persons enjoyment or utility of additional years that are otherwise lost. But the extra consumption that supports utility
19、in these additional years must be paid for possibly by additional social security payments, by transfers from younger relatives, or by additional saving earlier in life.Building on preliminary work in Miller et al. (1989a), we modify Arthurs (1981) SCE model to include nonfatal risks by including a
20、term for health status in the welfare function and by adding appropriate components to the budget constraint. The social welfare function takes the following form: oW = * Uc(x),h(x),xp(x)dx.(1) 0where Uc,h,x is the utility of being alive at age x, given consumption rate c and the state of health h;
21、p(x) is the probability of surviving from birth to age x; and w is the maximum age of survivorship.Health status is also assumed to have a direct impact on health costs, consumption, fertility, mortality, and labor productivity. Changes in fertility, mortality, and labor productivity will induce cha
22、nges in the equilibrium stable population growth rate and the equilibrium capital-labor ratio. Suppose that some activity (e.g., a reduced ozone shield or improved auto emission controls) alters the health state by dh(x) over the age dimension. Suppose also that this change has associated with it di
23、rect health costs dcHdh, and alterations in consumption dcdh, labor effectiveness dldh, fertility dmdh, and especially mortality dpdh. The latter are all directly observed changes for a specific category of morbidity.Thus, the societal budget constraint is:o o o* e-gxp(x)c(x)dx + * e-gxp(x)cH(x)dx /
24、 (f(k)-gk) * e-gxp(x)l(x)dx (2)0 0 0where g is the constant rate of population growth; f(k)=F(K,L)/L is output per worker at capital-labor ratio K/L for an economy with constant returns to scale production function F; and l(x) is the age schedule of labor participation. Thus, the sum of aggregate so
25、cial consumption expenses and aggregate health costs equals aggregate production. By considering the total differentials of (1) and (2) with respect to an arbitrary pattern of changes in morbidity, one can show that the change in expected lifetime welfare caused by dh is given by: oodW = MU/Mc(0) *
26、e-gxdcdhp(x)dx + * MU/Mhdh(x)p(x)dx 00 o+ * Uc(x),h(x),xdpdhdx.(3) 0In words, this formula states the welfare change equals the sum of welfare changes due to adjustments in consumption, changed incidence of injuries and illnesses, and extra years of life. The change in h will also cause adjustments
27、across the societal budget constraint: o o0 = * e-gxc(x)dpdhdx + * e-gxdcdhp(x)dx 0 0 o o+ * e-gxcH(x)dpdhdx + * e-gxdcHdhp(x)dx 0 0 o o- (f(k)-gk) * e-gxl(x)dpdhdx + * e-gxp(x)dldhdx 0 0 o- dkdh(f-g) * e-gxl(x)p(x)dx - bdgdh.(4) 0where w is the wage rate and b is the life-cycle value of a marginal
28、increase in the population growth rate (Arthur & McNicoll, 1978). Equation (4) is identical to equation (16) in Arthur (1981) except for the addition of the terms related to changes in medical costs (dcHdh) and in labor productivity (dldh) related to changes in health status. Also, the change in the
29、 population growth rate now includes the combined effect of changes in fertility and mortality. Note that the next to last term equals zero, because f = g at equilibrium.Using equation (4) to substitute for the first term in equation (3) yields: o odW = * Uc(x),h(x),xdpdhdx + * MU/Mhdh(x)p(x)dx 0 0
30、o o + MU/Mc(0) w * e-gxl(x)dp(dh)dx + w * e-gxdldhp(x)dx 0 0 o o - * e-gxdcHdhp(x)dx - * e-gxcH(x)dp(dh)dx 0 0 o - * e-gxc(x)dp(dh)dx + bdgdh (5) 0This can be simplified to:dW= Udp + Udh + MU/Mc(0) wLdp + wLdh - cH,dh - cH,dp - cdp + (vdp + vdm)b/Am (6)where Ldp , cdp , and cH, dp are expected extra
31、 person-years of production, consumption, and health costs, respectively, resulting from variation in mortality arising from variation in morbidity; Ldh , cdh , and cH, dh are the expected life-cycle increases in productivity, consumption, and health costs directly associated with improved health st
32、atus; vdp and vdh are additional children per person due to variation in mortality and health, respectively; and Am is the average age of reproduction in the stable population.In words, equation (6) means the life-cycle welfare increase equals the sum of (i) the utility of extra life years, (ii) the
33、 utility of improved health status, (iii) the value of extra labor years, and (iv) the value of increased productivity, MINUS (v) the social cost of health status improvements, (vi) the social cost of health maintenance over extra years, and (vii) the social cost of consumption upkeep, PLUS (viii) t
34、he value of extra children. Thus, improving health status has benefits and costs above and beyond those associated with improved longevity. There is a quality-of-life aspect to living longer, now captured by the second term in equation (6), which was ignored in Arthurs original model. A healthier po
35、pulation will also be a more productive one, but at the additional social cost of maintaining good health. Finally, health status changes may affect fertility rates, which in turn affect social welfare either negatively or positively depending on the value of additional children to the society.In or
36、der to express the value of life in consumption units, we follow Arthur 1981 in assuming the utility function U does not vary with age and has constant elasticity of consumption: Uc(x),x = cp(7)where e=(dU/dc) (c/U(c) is the constant elasticity of consumption. The societal willingness to pay for mor
37、bidity variation dh (which Arthur calls a social consumption equivalent) is given by: SWTPdh = (1/e - 1)cdp + (1/e)cdh + wLdp - wLdh - cH,dp - cH,dh + (vdp + vdh)b/Am (8)Equation (8) makes explicit that fact that the enjoyment of better health and additional years of life is directly offset by its c
38、onsumption cost. Thus, this equation connects the social consumption equivalent method with human capital and individual WTP or QALY criteria for valuing variations in morbidity risks.In Landefeld & Seskins (1982) formulation, individual WTP for life and safety essentially equals the product of the
39、present value of the individuals future monetary and nonmonetary goods consumption times A, the reciprocal of the goods consumption elasticity of lifetime utility. The first component is given in equation (8) by cp, and the second by 1/e. QALYs value these components in non-monetary terms, WTP in do
40、llars. The human capital approach uses the present value of the change in expected lifetime earnings, which appears as the wLp term in equation (8). Human capital net of consumption, thus, equals the negative part of the first term in (8) plus the third term. Analogous terms exist for the equivalent
41、 morbidity concepts. Thus, the second term is another aspect of individual consumption, and the fourth is another aspect of human capital.This suggests that (8) be rearranged to yield the following definition of SWTP in terms of individual WTP or QALYs and human capital: SWTPdh = (1/e)cdp + (1/e)cdh
42、 Average individual WTP or QALY value for life and for health + wLdp - wLdh - cdp Human capital net of consumption- cH,dp - cH,dh Social cost of health changes, both improvement and extra years+ (vdp + vdh)b/Am Value of additional children(9)Equation (9) shows that SWTP for morbidity improvements ma
43、y be greater or less than individual willingness to pay or QALY value for the same change, because of the effects on society at large of changes in production and consumption and because of changes in future populations.3. ImplementationFrom equation (9) one can see that estimation of societal WTP r
44、equires calculation of both changes in utility and changes in various categories of other costs and benefits. The first two factors represent the utility loss measure. That measure could be an individual WTP measure or a QALY or more debatably a jury verdict willingness to award. If the value is sta
45、ted in QALYs, a popular practice has been to monetize them with a value per quality unit derived from WTP for a statistical life (e.g., Cutler & Richardson 1998; French et al. 1996; Miller 2000; Miller et al.1989b, 1995, 2000; Tolley et al. 1994). The advisability of that approach is debated elsewhe
46、re in this issue. Furthermore, a willingness to accept estimate fits naturally in the framework when it is the theoretically appropriate measure to use for valuing utility change.The third through seventh terms of the SWTP together constitute the change in human capital net of consumption that resul
47、ts from the health status change. The value of extra labor years and increased workforce and household productivity is measured by the gain in earnings and household production attributable to averting the illness or injury. The social costs related to health status changes essentially are medical costs borne by third-party payers, charity, or government. The impact of the health status change on consumption, including consumption funded by transfer payments, insurance payouts, and earnings is complex to measure, however.This complexity arises becaus
