Health Capital

Chapter 5

Kenneth Arrow, Partha Dasgupta, and Kevin Mumford

Key Messages

Health is an essential characteristic of Most health capital services influence human well-being. human well-being directly rather than through the production of goods and services that are Health capital is an important part of inclu- counted in GDP. sive wealth. In the absence of better estimates of the The economic model of health capital pre- direct and productivity effects, gains in life sented in this chapter allows health to affect expectancy should be used as the primary mea- human well-being through three distinct sure of health capital. channels: direct well-being, productivity, and longevity. Annual gains in health capital in the U.S. are worth approximately US$10,000 per person.

CHAPTER 5: Health capital 123 1. Introduction 2. Health as a capital asset

Attempting to measure human well-being with- Health is a multidimensional concept. There is out considering health would be a great over- no single standard way to measure the health sight. Health is central to our happiness. Health of an individual or a population group. A physi- affects our enjoyment of life, our productivity in cian may examine a patient and measure health employment, and our risk of death. Our desire along several dimensions including mental for good health influences our decisions regard- health, severity of illnesses, nutrition, body ing eating, sleeping, exercising, and our demand mass index (BMI), risk of disease, and level of for medical services. As shown in Table 1, total pain or discomfort. An individual may track spending on medical care from both public exercise and eating behavior or rate his or her and private source makes up an important and own subjective health along a scale of overall fit- generally increasing share of national income ness. For a population group, a researcher may in many countries. use life expectancy, infant mortality rate, avail- The improvement in life expectancy at birth ability of healthcare services, or prevalence of has been quite dramatic in most countries over preventable diseases as indicators of the health the past 60 years (see Figure 1). Several stud- of the group. Our term, health capital, refers ies, including Nordhaus (2005), Becker et al. to a satisfactory measure of the overall health (2005), Murphy and Topel (2006), and Jones and of an individual or a population. It may be a Klenow (2011), have shown that recent gains single all-encompassing measure or perhaps a in life expectancy have been at least as impor- weighted combination of the health measures tant to human welfare as gains in income. The described above. Inclusive Wealth Report 2012 treated health The question of whether it is appropriate to as a form of wealth by estimating the value treat health as a capital asset it important. Doubts of the improvement in life expectancy over a about treating health as a form of capital arise nineteen-year period. However, health capi- when one compares health to other forms of capital was treated separately from other forms of tal and notes the obvious differences. Economists capital because it was found that even modest generally describe capital as an input into a pro- gains in life expectancy outweighed other gains. duction function. We think of manufactured Though understandable, this is not a theoret- capital assets such as machines, equipment, ically-sound reason to exclude health capital buildings, roads, and ports that are used in the from an inclusive measure of national wealth. production of goods and services. Manufactured capital assets have value that is equivalent to their future marginal productivity. The produc- Table 1 tive services can be rented or the capital asset Total health expenditure (percentage of GDP) itself can be sold to another individual without destroying its value. Unlike inputs that are consumed as part of the production process, manu- Country 1995 2000 2005 2010 factured capital can be employed in the pro- Brazil 6.7 7.2 8.2 9.0 duction process multiple times. Manufactured capital may depreciate over time, but it is not China 3.5 4.6 4.7 5.0 consumed in the production of goods and ser- Germany 10.1 10.4 10.8 11.5 vices. To summarize, economists generally think India 4.0 4.3 4.2 3.7 of a manufactured capital asset as (1) a durable object that could be sold to someone else, (2) an United States 13.6 13.6 15.8 17.7 input in the production of goods and services, Source: The World Bank (2013), World Development Indicators and (3) a store of value to achieve consumption.

124 Inclusive Wealth Report 85

65 Figure 1 Life expectancy at birth 60 Source: UN Department of Economic and Social Affairs (2012) “World Population Prospects” 55 Life expectancy at birth 50 Key

Brazil 45 China Germany 40 India United States 35 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Like manufactured capital, health is dura- Health is not commonly thought of as an ble. A person’s health is relatively constant input in the production of final goods and over time. Health depreciates, but it is not services. The evidence suggests that improve- consumed as it provides current well-being. ments in health do lead to productivity gains, At times, health may depreciate rapidly due particularly in low-income countries (Bhargava to some illness, similar to the risk of some et al. 2001). The estimates suggest that large catastrophe reducing the value of a manu- increases in health cause only small increases factured capital asset. Unlike a manufactured in GDP growth rates and there is little evidence capital asset, health capital cannot be directly for productivity gains from health in devel- purchased from a health-rich person. One oped countries. However, health does provide cannot rent the well-being services that flow health services – greater enjoyment of current from health nor can one sell health to another consumption and longer life – directly to the individual. However, the ability to transfer a individual. That these health services are not capital asset to another individual does not part of measured gross domestic product does seem to be an essential characteristic of capi- not mean that they have no value. To the con- tal. The knowledge, skills, and abilities that trary, health is of great value to humans and is make up what is commonly called “human an essential characteristic of well-being. Our capital” cannot be directly transferred from view is that health capital is similar to consumer one person to another and this does not cause durables (e.g., houses, consumer electronics, fur- economists to question if human capital can niture, home appliances, and sports equipment) be considered a capital asset. that provide well-being to consumers, but are

CHAPTER 5: Health capital 125 Figure 2 Use of capital in production Human well-being

Direct provision of human Indirect provision of well-being through services human well-being through not counted in GDP production and consumption

Consumption

Final goods and services (gross domestic product)

Capital is an input in the production of goods and services Services not counted in G D P Services not

Production process

Manufactured Health capital Natural capital Human capital capital

not generally direct inputs in the production services which increase human well-being, and of a final good or service that is counted as part (3) a store of value to achieve the consumption of gross domestic product. of health services. Services from capital assets, Figure 2 illustrates the point that capital which are not counted as part of GDP, including assets can both directly and indirectly (through health services, have value. Therefore, the value the production process) affect human well-being. of the capital asset itself is equal to the present Machines and business equipment primarily discounted value of the future services. From the increase human well-being through the produc- point of view of an economist, health is a form of tion process. Forests have both a direct influence capital. This chapter seeks to measure the stock on human well-being through ecological and of health capital, estimate its value, and measure recreational services as well as an indirect influ- the value of the change in health capital for sev- ence through the consumption of final goods for eral countries over a period of five years. which timber is an input. Similarly, health capital has a direct influence on human well-being as well as an indirect affect through increased 3. The value of health capital productivity. That health increases human well- being primarily through a direct channel rather We begin with a stylized model to illustrate the than through the indirect production/consump- role of health capital in providing human well- tion channel does not raise any concerns about being. We propose a rather simple two-period its treatment as a capital asset. model as it is sufficient for providing general To summarize, health is (1) durable and non- intuition about how to measure and value transferable, (2) both an input in the production health capital. The model is an expanded ver- of goods and services and the source of a flow of sion of the Arrow et al. (2013) model. We assume

126 Inclusive Wealth Report that the economic agent is alive in period 1 with The agent’s lifetime budget constraint is certainty, but there is uncertainty about being given by Expected Lifetime Utility = U H,c + ! H U H,c alive in period 2. The agent’s expected lifetime Equation 2 ( 1) ( ) ( 2 ) utility is given by c12++ pc h≤ W() H Equation 1 whereExpect ewealthd Lifet icanme Ubetil ispentty = U on(H either(h),c) +consump! (H(h))-U (H(h),c) + ! Expected Lifetime Utility = U (H,c1) (H) U (H,c2 ) tion in period 1, consumption in period 2, or Expected Lifetime Utility = U H,c + ! H U H,c investing in health. In our notation, an invest- c12++( pc1) h≤( W)() H ( 2 ) ment in! UhealthH,c is!H given by!U h(H and,c) !weW !assumeH !! !H !U (H,c) 1+ ! ( ) + + U (H,c) = c++ pc h≤ W() H Ewherexpect eHd Lisif ehealthtime U ticapital,lity = U (cH is(h )consumption,c) + ! (H(h)) U (Hthat((h) ,healthc) ! Hcapital,!h H, is increasing!c !H in! hh. We !H !h !c 12 1 !### "###$ !###"###$ !##"##$ in period 1, c is consumption in period 2, and haveDi rnormalizedect Wellbein gthe price ofPr oconsumptionductivity in Longevity Expected Lifetime Utility = U (H(h),c) + !2 (H(h))U (H(h),c) π(H) is the probability of survival to the second period 1 to one. Survival to period 2 is uncertain, period. !WeU ( Hassume,c) !H that the!U (probabilityH,c) !W !H of sur- so the!! agent!H can !purchaseU (H,c) a contract granting (1+ ! ) + + U ( H,c) = vival!# depends##"!H# #on# !$theh amount!#! c#of# "health#!H#!# $hcapital !#consumption#"!#H#!$h in period!c 2 at price p which is less !U (H,c) !H !U (H,c) !W !H !! !H !U (H,c) ∂UH( ,c) ∂H (1+ ! ) + whereDire cmoret Wel lbhealtheing+ Uincreases(H,c)Pro dtheuct ivprobabilityit=y L(than1o+ngπe )one.vity If the probability of survival is very !H !h !c !H !h !H !h !c ∂∂Hh !###"###$ !of# being##"# alive##$ in period!# #2," though##$ diminish- low, the contingent price for consumption in Direct Wellbeing Productivity Longevity ing returns imply that each additional unit of period 2 would also be low. We will assume that health capital has less of a positive effect on the∂UH (agent ,c) ∂∂can W purchase H period 2 consumption at ∂UH( ,c) ∂H (the1+ πprobability) of survival. The current utility the ∂actuarially-fairc ∂∂ Hh price of p = π. ∂∂Hh ∂UH( ,c) ∂H (felicity) depends both on the level of health We should consider the difference between (1+π ) ∂∂Hh capital and the amount of consumption. There an investment!! !H in health, h, and consumption, c. ∂UH( ,c) ∂∂ W H U (H,c) are diminishing marginal returns to both Purchasing!H !ah pain reliever, like Aspirin, should ∂c ∂∂ Hh ∂UH( ,c) ∂∂ W H health capital and consumption. The utility be treatedt as consumption. A short-term pain ∂c ∂∂ Hh function is the same in both periods and for relieverF(t) = provides∑ f (a )a health service, but it has no simplicity!! we!H assume that the agent does not effect ona= 0health capital, H, because the effect U (H,c) !1 discount!H the!h future, though this could easily isf (temporary.t | t ! a) = The[1! resultingF(a)] freduction(t) in pain !! !H t U (H,c) be relaxed. increases 100current well-being, but the effect !H !h F(Thet) = agentf is(a endowed) with financial wealth does not carry over into other periods. In this t ∑ H(a) = f (t | t ≥ a)V (a,t) a=0 ∑ given by W(H). We assume that an increase model, thet= aprimary characteristic of an invest- F(t) = f (a) !1 ∑ t−a a=0 inf ( thealth| t ! a )causes= [1! anF( aincrease)] f ( t)in the agent’s ment in health is that it increases the stock V (a,t) = 1−δ u !wealth.1 The100 mechanism we have in mind is of health capital.∑( Therefore,) many healthcare f (t | t ! a) = [1! F(a)] f (t) u=0 thatH(a a) healthier= f ( tagent| t ≥ ais) moreV (a, productivet) and services and medicines would be categorized 100 ∑ 100 earns highert=a wages. Alternatively, we could as consumption rather than health investment. H(a) = f (t | t ≥ a)V (a,t) t−a H = !H(a)P(a) ∑ assume that a healthieru agent is able to work A true investment in health would increase t=a V (a,t) = (1−δ ) a=0 t−a more hours ∑ and thus has a higher income. future health services. u=0 u However, to keep the model focused on health, The agent wants to maximize expected util- V (a,t) = ∑(1−δ ) 100 u=0 weH =abstractH( afrom)P(a the) labor-leisure decision ity given by Equation (1) subject to the budget 100 ! and simplya=0 assume that the agent is directly constraint given by Equation (2). With no dis- H = !H(a)P(a) endowed with wealth. Making wealth a func- counting, the agent will choose to perfectly a=0 tion of health capital embeds the productive smooth consumption by selecting c1 = c2. Thus Expected Lifetime Utility = U H,c + ! H U H,c impacts of health in a straight-forward way. By we can rewrite Equation (1) as( 1) ( ) ( 2 ) assumption, there are diminishingExpected Lif ereturnstime Ut iltoity = UEquatH i,ocn 3+ ! H U H,c c(++ pc1) h≤( W)() H ( 2 ) additional health capital. The increase in the 12 c++ pc h≤ W() H Expected Lifetime Utility = U H(h),c + ! H(h) U H(h),c agent’s wealth caused by12 an additional unit of ( ) ( ) ( ) health capital is much Esmallerxpected Lforife taim healthye Utility = U (H(h),c) + ! (H(h))U (H(h),c) agent than for a malnourished one. !U H,c !H !U (H,c) !W !H !! !H !U (H,c) 1+ ! ( ) + + U (H,c) = ( ) !H !h !c !H !h !H !h !c !U H,c !H !U!(H#,#c)#!"W#!H##$ !#!!##!"H###$!U (H,!c)##"##$ 1+ ! ( ) + + U (H,c) = CHAPTER 5: Health capital ( ) Direct Wellbeing Productivity Longevity 127 !###"!H###!$h !#!c##"#!H#!#$h !##"!#H#!$h !c Direct Wellbeing Productivity Longevity

∂UH( ,c) ∂H (1+π ) ∂∂Hh ∂UH( ,c) ∂H (1+π ) ∂∂Hh ∂UH( ,c) ∂∂ W H ∂c ∂∂ Hh ∂UH( ,c) ∂∂ W H ∂c ∂∂ Hh !! !H U (H,c) !H !h !! !H U (H,c) t !H !h F(t) = f (a) t ∑ F(t) = f (a) a=0 ∑ !1 a=0 f (t | t ! a) = [1! F(a)] f (t) !1 f (t | t ! a) = [1! F(a)] f (t) 100 H a = f t | t ≥ a V (a,t) 100 ( ) ∑ ( ) t=a H(a) = ∑ f (t | t ≥ a)V (a,t) t−a t=a V (a,t) = 1−δ u t−a ∑( ) V (a,t) = 1−δ u u=0 ∑( ) 100 u=0 H = H(a)P(a) 100 ! a=0 H = !H(a)P(a) a=0 Expected Lifetime Utility = U H,c + ! H U H,c ( 1) ( ) ( 2 ) c++ pc h≤ W() H 12 Expected Lifetime Utility = U (H(h),c) + ! (H(h))U (H(h),c) where consumption, c = c = c , is the same in increases health capital. Given our assumption 1 2 + ! Expected Lifetime Utility = U (H,c1) (H) U (H,c2 ) both periods and health capital, H(h), is written that the surgery has no impact on the agent’s cas++ a pc function h≤ W ()of H health investment h. The first productivity!U H or,c longevity,!H ! Uthe(H entire,c) !W marginal!H !! !H !U (H,c) 12 1+ ! ( ) + + U (H,c) = order condition with respect to health invest- benefit( ) of !thisH investment!h in! chealth! His captured!h !H !h !c Expected Lifetime Utility = U (H(h),c) + ! (H(h))U (H(!h),#c)##"###$ !###"###$ !##"##$ Expected Lifetime Utility = U H,c + ! H U Hment,c is given by: by Dtheire cdirectt Wel limprovementbeing inPr owell-beingductivity given Longevity ( 1) ( ) ( 2 ) Equation 4 by the first term of Equation (4): c12++ pc h≤ W() H Equation 5 !U (H,c) !H !U (H,c) !W !H !! !H !U (H,c) Expected Lifetime Utility = U H(h),c + ! H(h) U1+H!(h),c + + U (H ,c) = ( ) ( ) ( ( ) !)H !h !c !H !h !H∂!UHh( ,c) ∂H!c !###"# ##$ !###"###$ !#(#1"+π#) #$ Direct Wellbeing Productivity Longevity ∂∂Hh The term (1 + π) above represents the last- !U (H,c) !H !U (H,c) !W !H !! !H !U (H,c) (1+ ! ) + + U (H,c) = ing∂UH (impact ,c) ∂∂W of the H investment in health as the !###"!H###!$h !#!c##"#!H#!#$h !##"!#H#!$h !c ∂UH( ,c) ∂H increase∂c in ∂∂ Hhutility occurs in both period 1 and Direct Wellbeing Productivity (1+πLo)ngevity ∂∂Hh period 2. Surviving to period 2 is uncertain, so Equation (4) illustrates the trade-off between the increase in expected utility reflects that !! !H using wealth for consumption or health. The Uthe(H agent,c) will only be alive for period 2 with ∂UH( ,c) ∂∂ W H !H !h ∂UH( ,c) ∂H additional utility from an increase in consump- probabilityt π. The rest of this expression is the (1+π ) ∂c ∂∂ Hh ∂∂Hh tion is given by the right-hand side of Equation additionalF(t) = ∑ utilityf (a )or current well-being that the (4). The expected-utility-maximizing agent agent enjoysa=0 because the level of health capital !! !H !1 ∂UH( ,c) ∂∂ W H Uinvests(H,c) in additional health up to the point isf (higher.t | t ! aIt) is= of[1 particular! F(a)] interestf (t) to note that ∂c ∂∂ Hh where,! Hat !theh margin, the value of additional the demand for health investment, h, will be t 100 health is equal to the marginal value of con- largerH(a) if= the probabilityf (t | t ≥ aof) Vsurvival(a,t) to period 2, π, Fsumption.(t) = ∑ Thef (a )value of additional health has is larger. The∑ intuitive explanation is that long- !! !H a=0 t=a U (H,c) three components: well-being, productivity, lasting medicalt−a intervention that improves !H !h !1 u fand(t | tlongevity! a) = [ 1as! givenF(a) ]by thef (t )three terms on Vwell-being(a,t) = is more(1− valuableδ ) to those who expect t ∑ F(t) = f (a) the left-hand100 side of Equation (4). We will to live longer.u=0 Holding other things constant, as ∑ 100 a=0 Hexamine(a) = ∑ eachf ( tof| tthese≥ a) Vthree(a, tcomponents) in mortality rates decline, the demand for medical t=a H = H(a)P(a) !1 greater detail. services! that offers only short-term improve- f (t | t ! a) = [1! F(a)] f (t) t−a a=0 u ments in well-being will also decline as indi- 100 V (a,t) = (1−δ ) ∑ viduals substitute towards medical services that H(a) = f (t | t ≥ a)V (a,t) u=0 ∑ 3.1 Direct well-being offer long-term improvements. t=a 100 t−a H = H(a)P(a) We are not familiar with any empirical esti- u ! V (a,t) = ∑(1−δ ) The firsta=0 term on the left-hand side of Equation mates of the consumption equivalent value of u=0 (4) is the direct utility from additional health this direct increase in well-being. One approach 100 capital. Consider a health investment that would be to estimate the willingness to pay H = !H(a)P(a) offers no increase in productivity and no for a medical service similar to the hypotheti- a=0 increase in longevity. For example, a surgical cal surgery discussed above. The key would be procedure that offers long-lasting pain reduc- to identify treatments that have no effect on tion, but does not improve the agent’s ability either productivity or longevity. Calculating the to work nor does it offer any reduction in the willingness to pay for any health intervention risk of mortality. This hypothetical surgery’s which also affects these other two components only effect is to permanently reduce the would produce upwardly biased estimates. agent’s chronic pain. The reduction in pain directly makes the agent better off and may also increase the agent’s enjoyment of consumption. Because the pain reduction is long- lasting, the surgery is an investment which

128 Inclusive Wealth Report Expected Lifetime Utility = U H,c + ! H U H,c ( 1) ( ) ( 2 ) c++ pc h≤ W() H 12 Expected Lifetime Utility = U (H(h),c) + ! (H(h))U (H(h),c)

!U (H,c) !H !U (H,c) !W !H !! !H !U (H,c) (1+ ! ) + + U (H,c) = !###"!H###!$h !#!c##"#!H#!#$h !##"!#H#!$h !c 3.2D Productivityirect Wellbeing Productivity Lintake,ongevi tcausesy an increase in future labor market income (Behrman and Rosenzweig 2004). The second term on the left-hand side of The evidence shows only productivity gains for Equation∂UH (4)( is,c the) ∂H productivity gains from addi- low calorie intake. Thomas and Strauss (1997) (1+π ) tional health∂∂Hh capital: find evidence only for a positive impact of addi- Equation 6 tional calories below 2,000 calories per day. Evidence for a causal effect of health on ∂UH( ,c) ∂∂ W H productivity in developed countries is weaker. ∂c ∂∂ Hh Several papers have shown that increases in The health investment increases the stock average life expectancy in a country lead to !! !H Uof( Hhealth,c) capital which increases the agent’s increases in GDP growth (see Bloom, Canning, wealth. !TheH ! agenth values the additional wealth and Sevilla 2004). However, we are not aware because itt can be spent on additional consump- of convincing micro evidence in developed = tion,F(t) c, the∑ marginalf (a) value of which is given countries that worker productivity is increasing a=0 by the first term in the above!1 expression. The in health. The evidence that workplace well- assumptionf (t | t ! a) =that[1! wealthF(a)] increasesf (t) as health ness programs increase productivity is mixed. capital increases,100 with diminishing returns, is a While these programs generally increase worker simpleH(a) =way∑ tof represent(t | t ≥ a the)V (increasea,t) in produc- health as measured by increased physical activ- tivity fromt= health.a ity, reduction in tobacco use, and decreased t−a V (aThere,t) = is a(1 −strongδ )u correlation between body mass index, there is little evidence of pro- income and∑ health (see Fogel 1994). We gen- ductivity gains (Osilla et al. 2012). The stron- u=0 erally 10assume0 that the causal relationship is gest evidence seems to be that an exogenous thatH = !additionalH(a)P income(a) allows an individual increase in worker health reduces absenteeism to makea=0 health investments which increase (Baicker et al. 2010). health. However, there is strong evidence for a causal relationship running the other direction. An increase in health causes higher labor pro- 3.3 Longevity ductivity through fewer lost workdays, greater physical energy at work, and greater mental The defining characteristic of this simple focus and ability.1 model is that life expectancy is not fixed. We Leibenstein (1957) first proposed that work- assume that an investment in health increases ers with low levels of calorie intake would have the probability of survival to the second period. lower productivity. There is strong evidence that It is clear from Equation (1) that an exog- improvements in nutrition lead to productivity enous increase in the probability of survival, gains in agriculture for those with low levels of π, increases the expected lifetime utility. How calorie intake (Strauss 1986). Similarly, there is much does the agent value an increase in the strong evidence that an increase in birthweight, probability of survival to the second period? reflecting an increase in intrauterine nutrient Note that the rate of increase in the expected lifetime utility when π is increased margin- ally is U(H,c). This means that the value of the 1 Jayachandran and Lleras-Muney (2013) point out increase in the probability of survival depends that health indirectly affects productivity through education. As longevity increases, so does the return on on the living standard of the agent. An agent investments in education. This encourages additional with better health and more consumption will education which makes workers more productive. We place a higher value on an increase in the prob- do not consider this indirect relationship because ability of survival. improvements in education (even if motivated by increased longevity) are already included in inclusive The same point is clear from the third term wealth via the measurement of human capital. on the left-hand side of Equation (4):

CHAPTER 5: Health capital 129 Table 2 Estimated value of the average annual increase in life expectancy in theEx pUec.Ste.d Lifetime Utility = U H,c + ! H U H,c ( 1) ( ) ( 2 ) c++ pc h≤ W() H 12 EStudyxpected Lifetime Utility = U (H(h),c) + ! (H(hT))imeU ( periodH(h),c) Value of increase Nordhaus (2005) 1975 – 2000 US$52,000 Becker, !Philipson,U (H,c) and!H Soares! (2005)U (H,c) !W !H 1960 – 2000!! !H !U (HUS,c$2,000) (1+ ! ) + + U (H,c) = Murphy!## #and"! HTopel### (2006)!$h !#!c##"#!H#!#$h 1970! –# 2000#"!#H#!$h !cUS$40,000 Direct Wellbeing Productivity Longevity Jones and Klenow (2011) 1980 – 2000 US$60,000

Arrow et al. (2012) 2000 – 2005 US$11,400 ∂UH( ,c) ∂H (1Inclusive+π ) Wealth Report (2012) 1990 – 2008 US$7,000 ∂∂Hh

∂UH( ,c) ∂∂ W H ∂c ∂∂ Hh Equation 7 US$12,000 multiplied by GDP per capita raised to the 0.6 power. This implies a 2014 VSL of !! !H U (H,c) US$8.3 million in the United States, US$2.5 mil- !H !h lion in China, and US$315,000 in Malawi. t F(Thet) = ∑marginalf (a) value of an increase in π The large VSL estimates imply that invest- depends aon=0 the utility the agent would realize ments in health that result in even a small in the second period. To express!1 U(H,c) in dollar reduction in mortality risk have great value. f (t | t ! a) = [1! F(a)] f (t) terms, economists divide by the marginal utility Many studies have estimated the value of the 100 of consumption and call the resulting object the increase in life expectancy in the U.S. including H a = f t | t ≥ a V (a,t) value( )of a∑ statistical( life )or VSL (Ashenfelter Nordhaus (2005), Becker et al. (2005), Murphy t=a 2006). It is timportant−a to note that economists and Topel (2006), Jones and Klenow (2011), Vdo( nota,t )claim= ∑ that(1 −VSLδ ) isu the value of life. Instead, Arrow et al. (2012), and the Inclusive Wealth one shouldu think=0 of VSL as the amount people Report 2012. Table 2 reports the estimated value would1 0be0 willing to collectively spend in order of the increase in life expectancy from each toH reduce= !H the(a number)P(a) of expected deaths by 1. study. The time frame for each study is differ- Thea= 0value of a statistical life can be inferred ent, so we report the total estimated increase from individual choices. For example, work- in value divided by the number of years. This ers who wash the windows of skyscrapers face results in an average increase in value per year. a higher risk of death and are paid more than Differences across studies therefore are due workers who wash the windows of single-story both to differences in methods but also in the businesses. The additional compensation from time period studied. assuming the additional risk of death reflects the The estimate of the value of the average workers’ willingness to pay to reduce mortality annual increase in life expectancy by Becker et risk. There are many similar opportunities for al. (2005) is far lower than the other estimates. economists to observe a group’s willingness to The time period they considered did not have pay for a reduction in mortality risk. In a survey smaller gains in life expectancy, so the differ- of country-level VSL estimates, Viscusi and Aldy ence comes from their methods. Their model (2003) found that VSL is approximately equal to implies a value of a statistical life from the

130 Inclusive Wealth Report other parameters of the model. Rather than claims that this must be due to double count- going to the literature for a VSL estimate, they ing. He correctly points out that VSL reflects calibrate the other parameters of the model and the value of all good things that come with the resulting VSL is fairly small. The Nordhaus living, not only good health. He then argues (2005), Murphy and Topel (2006), and Jones that if we have already measured the value of and Klenow (2011) studies use similar methods natural, manufactured, and human capital, and find large estimates. The Inclusive Wealth wouldn’t it be double counting to then add Report 2012 follows the Arrow et al. (2012) the value of health capital as the VSL depends methods. Both consider a more recent time on the living standards which are themselves period and find similar results. a function of the other forms of capital? This The Arrow et al. (2012) approach is to cal- concern is understandable but incorrect. Living culate the expected discounted years of life is complementary with consumption. Even if remaining for each age- and gender-specific health offered no direct increase in well-being group in the population in each year. The pop- or an increase in productivity, health would ulation-weighted average of the group-specific still have value simply because it extends life changes in the expected discounted year of life and allows a person to enjoy living longer. The remaining over the period is then multiplied model presented here illustrates the important by the value of a statistical life year (VSLY) for point that the value of health capital does and that country. The VSLY is the VSL divided by should depend on the level of well-being and the expected discounted years of life remaining thus by extension on the levels of the other and thus represents a per-year valuation of the forms of capital and on the state of technol- reduction in risk of mortality.2 Note that popu- ogy. Note that the term U(H,c) appears in the lation aging mechanically decreases the average expression for the value of increased longevity expected discounted years of life remaining, from an increase in health. That utility term but that the increase in longevity for the old represents the value of all good things that have outpaced this mechanical decrease (see come with living. Appendix 1 for the details of this method). The Arrow et al. (2012) approach is straight-forward requiring only life expectancy data combined 3.4 Combined value of health capital with an estimate of the VSL for the country. It makes no attempt to adjust the VSL for age or The value of an increase in the stock of health cohort effects as in Aldy and Viscusi (2008). In capital is the summation of all three compo- the model presented here, an agent with higher nents: direct well-being, productivity, and lon- wealth should have a higher VSL. This is con- gevity. Accepted empirical estimates of the first sistent with the cross-country VSL estimates. two components are lacking, so economists However, this also suggests that where the life have relied on the third alone to estimate the expectancy increases occur within the wealth value of health capital. This is fine, but it should distribution within a country should matter be recognized that the resulting estimates are in calculating the value of the improvement in biased downward. The large value of health health. Our method does not account for this. capital reported in this chapter is probably too Hamilton (2012) suggests that the Arrow et small rather than too large. al. (2012) estimates are implausibly large and An additional issue is how to measure health capital itself. Recall that there are various measures of health and not clear theoretical justi- 2 There are alternative methods for calculating fication for selecting any particular measure. the value of a statistical life year (VSLY). Our method implies a constant VSLY for all individuals within a Restricting the value of health capital to the country but allows for differences across countries. longevity component makes it easy to justify

CHAPTER 5: Health capital 131 using expected discounted remaining years It is likely the most important form of capital of life expectancy as the measure of the stock in producing human well-being. Health ser- of health capital. However, assume that we vices primarily affect human well-being directly wish to add the productivity component to rather than passing through the production the value of health capital. Also assume that process to generate goods and services. we have a convincing estimate of the effect of some measure of health, say BMI, on productivity. With this estimated effect we can value the productivity gains or losses from a change in BMI. However, it would be incorrect to refer to this as the value of the change in BMI as this would only be the productivity component. It would also be incorrect to calculate the effect of a change in BMI on longevity and then use this to supplement our longevity valuation. That would be double counting. The Inclusive Wealth Report 2012 and Arrow et al. (2012) decision to include total factor productivity (TFP) as a measure of technological progress introduces an issue here. TFP growth is included as growth in an additional form of technological capital or time capital. Suppose that a change in BMI causes an increase in productivity. This would be picked up in the TFP growth measure as coming from technological change, when in reality it was the result of an improvement in health. This suggests that it may be appropriate to exclude the productivity component from our valuation of health capital if TFP growth is included in the measure of inclusive wealth. The health effect on productivity should already be captured by the change in TFP.

4. Conclusion

Measuring health capital using only data on life expectancy seems appropriate given the measurement challenges and lack of empirical estimates for the direct welfare and productivity components of the value of health capital. That the value of the change in health capital is large is not surprising given the large willingness to pay for reductions in mortality rates. Health capital should no longer be relegated to the appendix when measuring inclusive wealth.

132 Inclusive Wealth Report References Leibenstein, H. (1957). Economic Backward- ness and Economic Growth: Studies in the Theory of Economic Development. New York: Wiley & Sons.

Aldy, J.E. & Viscusi, W.K. (2008). Adjusting Murphy, K.M. & Topel, R.H. (2006). The Value the Value of a Statistical Life for Age and of Health and Longevity. Journal of Political Cohort Effects. The Review of Economics and Economy, 114(5), 871-904. Statistics, 90(3), 573-581. Nordhaus, W.D. (2005). Irving Fisher and the Arrow, K.J., Dasgupta, P., Goulder, L.H., Contribution of Improved Longevity to Liv- Mumford, K.J. & Oleson, K. (2012). Sustain- ing Standards. American Journal of Economics ability and the Measurement of Wealth. and Sociology, 64(1), 367-392. Environment and Development Economics, 17(3), 317-353. Osilla, K.C., Van Busum, K., Schnyer, C., Larkin, J.W., Eibner, C. & Mattke, S. (2012). Arrow, K.J., Dasgupta, P., Goulder, L.H., Systematic Review of the Impact of Worksite Mumford, K.J. & Oleson, K. (2013). Sustain- Wellness Programs. The American Journal of ability and the Measurement of Wealth: Managed Care, 18(2), 68-81. Further Reflections. Environment and Devel- opment Economics, 18(4), 504-516. Strauss, J. (1986). Does Better Nutrition Raise Farm Productivity. Journal of Political Ashenfelter, O. (2006). Measuring the Value Economy, 94(2), 297-320. of a Statistical Life: Problems and Prospects. The Economic Journal, 116(510), C10-C23. Thomas, D. & Strauss, J. (1997). Health and Wages: Evidence on Men and Women in Baicker, K., Cutler, D. & Song, Z. (2010). Urban Brazil. Journal of Econometrics, 77(1), Workplace Wellness Programs Can Generate 159-86. Savings. Health Affairs, 29(2), 1-8. United Nations, Department of Economic Becker, G.S., Philipson, T.J. & Soares, R.R. and Social Affairs, Population Division (2005). The Quantity and Quality of Life and (2014). World Population Prospects: The the Evolution of World Inequality. American 2012 Revision, Methodology of the United Economic Review, 95(1), 277-291. Nations Population Estimates and Projec- Behrman, J.R. & Rosenzweig, M.R. (2004). tions, Working Paper No. ESA/P/WP.235. Returns to Birthweight. Review of Economics Viscusi, W.K. & Aldy, J.E. (2003). The Value and Statistics, 86(2), 586-601. of a Statistical Life: A Critical Review Bhargava, A., Jamison, D.T., Lau, L.J. & of Market Estimates Throughout the Murray, C.J.L. (2001). Modeling the Effects World. Journal of Risk and Uncertainty, of Health on Economic Growth. Journal of 27(1), 5-76. Health Economics, 20(3), 423-440. World Bank. 2013. World Development Indi- Bloom, D.E., Canning, D. & Sevilla, J. (2004). cators 2013. Washington, DC: World Bank. The Effect of Health on Economic Growth: doi: 10.1596/978-0-8213-9824-1. A Production Funciton Aproach. World Development, 32(1), 1-13.

Fogel, R. (1994). Economic Growth, Popula- tion theory and Physiology: the Bearing of Long-Term Process on the Making of Economic Policy. American Economic Review, 84(3), 369-395.

Hamilton, K. (2012). Comments on Arrow et al., ‘Sustainability and the measurement of wealth’. Environment and Development Economics, 17(3), 356-361.

Jones, C.I. & Klenow, P.J. (2011). Beyond GDP? Welfare across Countries and Time. (NBER Working Paper no. 16352).

CHAPTER 5: Health capital 133 Expected Lifetime Utility = U H,c + ! H U H,c ( 1) ( ) ( 2 ) c++ pc h≤ W() H 12 Expected Lifetime Utility = U (H(h),c) + ! (H(h))U (H(h),c)

!U (H,c) !H !U (H,c) !W !H !! !H !U (H,c) (1+ ! ) + + U (H,c) = !###"!H###!$h !#!c##"#!H#!#$h !##"!#H#!$h !c Direct Wellbeing Productivity Longevity

∂UH( ,c) ∂H (1+π ) ∂∂Hh

∂UH( ,c) ∂∂ W H ∂c ∂∂ Hh

!! !H U (H,c) !H !h t F(t) = ∑ f (a) a=0 !1 f (t | t ! a) = [1! F(a)] f (t) 100 Appendix 1: H(a)H(a by) = the∑ numberf (t | t ≥ofa people)V (a ,oft) age a in that t=a country, P(a). Thus, the total health capital (mea- t−a EMethodologyxpected Lifetime Ufortili tvaluingy = U H, cthe+ ! H U H,c sured in discounted life-years)u of a country is: ( 1) ( ) ( 2V) (a,t) = ∑(1−δ ) Equation 5 u=0 clongevity++ pc h≤ component W() H of health 12 100 Expected Lifetime Utility = U (H(h),c) + ! (H(h))U (HH(h=),c!) H(a)P(a) + ! a=0 Expected Lifetime Utility = U (H,c1) (H) U (H,c2 ) This appendix provides a description of the The value of a unit of health capital is the c++ pc h≤ W() H methodology12!U H ,employedc !H in! ArrowU (H,c et) ! al.W (2012)!H as value! of! a! Hstatistical!U life-year(H,c) or VSLY. Thus, the 1+ ! ( ) + + U (H,c) = well( as) the Inclusive Wealth Report 2012. value of the total stock of health capital is sim- E!xp#ec#ted# L"!ifH#eti#me#! $Uhtility =! U#(!Hc##(h"),#c!)H+#!!#$h(H(h))U!(#H#(h"),!c#H) #!$h !c DLetire cf(t)t W ebellb theeing density ofP rageodu cofti vdeath,ity F(t) Lplyon gHe vmultipliedit y by the VSLY. the cumulative distribution of age of death, and f(t|t ≥ a) the conditional density of age of death Expecte!dU Li(fHet,imc)e! UHtility = !UU (HH,,cc) !+W! !HH U H,c !! !H !U (H,c) 1+ ! + ( 1) ( ) +( U (2H) ,c) = given( survival) !H to !ageh a. We obtain!c !anH estimate!h !H !h !c !##∂#UH"#,c##$ !###"###$ !##"##$ of the number( )of∂H people who survive to age t (c112+++Dπ pcir)ect W h≤el Wlbe()i Hng Productivity Longevity ∂∂Hh Eoutxp eofct ead starting Lifetim ecohort Ut ility of= U100,000H,c +(column! H U l(x)H ,c Expected Lifetime Utility = U (H(h1)),c) +(! ()H(h())U (2H) (h),c) of life tables) for each year and each country. c++ pc h≤ W() H From∂12UH( this, ,c) ∂∂ Wwe calculate H the unconditional num- ∂UH( ,c) ∂H Eberx+p ∂πeofcct edeathsd L ∂∂i Hhfet ibyme ageUtil iandty = divideU H( hby),c 100,000+ ! H( hto) U H(h),c (1 ) !U H,c ! H !U((H,c) !W) !H( ) ( !!) !H !U (H,c) give1+ f(t),! the∂∂(Hh density) of+ age of death. From f(t)+ = U (H,c) = ( ) !H !h !c !H !h !H !h !c f(t|t!# ≥ #0)# we" #calculate##$ F(t): !###"###$ !##"##$ !! !H U (DHi,rce)ct Wellbeing Productivity Longevity ∂EquatUH(io ,c)n! 1UH ∂∂ W!Hh,c H!H !U (H,c) !W !H !! !H !U (H,c) 1+ ! ( ) + + U (H,c) = ( ∂c) ∂∂t Hh !###"!H###! $h !#!c##"#!H#!#$h !##"!#H#!$h !c F(t) = f (a) Direct ∑Wellbeing Productivity Longevity ∂UHa=(0 ,c) ∂H (1+π ) !! !H ! U (H,c) ∂∂Hh 1 f (t | t !!Ha)!=h [1! F (a)] f (t) The conditional density of age of death is 100t obtained∂UH from( ,c f(t)) ∂H and F(t): (∂HF1UH+(((tπa))= ,c)= ∂∂ Wff( H(at)| t ≥ a)V (a,t) ∑∑∂∂Hh Equat∂cion 2at ∂∂==0 Hha t−a !1 f (t | t ! a) = [1! F(ua)] f (t) V (a,t) = (1−δ ) ∂UH( ,c) 100 ∂∂ W∑ H !! u!=H0 U (HFuture∂c,c) ∂∂ Hhyears are discounted at a constant H(a)10=0!H∑!hf (t | t ≥ a)V (a,t) rate d, assumingt=a that the value of an additional H = Ht (a)P(a) year is! independentt−a of age. The health capital of F(t)a==0!! !Hf (a) u UVan(( Hindividuala,ct)) ∑= of(1 age−δ a is) the discounted expected !Ha=0∑!h year of life remaining:u=0 t !1 f (t | t10!0 a) = [1! F(a)] f (t) EFquat(t)io=n 3 f (a) H = ∑H100(a)P(a) !a=0 = H(a)a =0 f (t | t ≥ a)V!1(a,t) ! ∑= ! f (t | t at=)a [1 F(a)] f (t) 100t−a u VwhereH((aa,)t V(a,t))== ∑ isf (given(1t−| tδ ≥by:) a)V (a,t) Equation 4 ∑ t=ua=0 100 t−a u VH(a=,!t) =H∑(a)(1P−(aδ)) a=0 u=0 The10 0total health capital of all individuals of = ageH a !in aH country(a)P(a is) calculated by multiplying a=0

134 Inclusive Wealth Report