Flat-of-the-curve medicine: a new perspective on the production of health

Industrial countries have been spending a rising share of their economic resources on health care. From 1960 to 2004 health care expenditure (HCE) of OECD countries increased from 3.8 percent of GDP to 8.9 percent on average. Over the same period, health outcomes measured by average life expectancy at birth improved from 68.4 to 78.5 years. However, this increase has slowed recently. In the United States e.g., it has been 0.19 percent p.a. between 1980 and 2004, down from 0.3 between 1960 and 1980. Since HCE continued to grow at a rate of 7.7 percent p.a. between 1980 and 2004, this has often been interpreted as evidence of decreasing marginal returns ("flat-of-the-curve medicine"; [1, 2]), raising the question of why citizens and governments failed to reallocate resources away from medicine.

However, calling for such reallocation may be premature on at least two accounts. First, several studies based on individual health care expenditure data find that marginal returns to HCE still outweigh its marginal cost (see e.g. [3‐5]; for an overview see [6]). This would explain why, in countries where individual willingness to pay for medical services tends to prevail over political considerations of cost control (such as the United States, the Netherlands, and Switzerland), the share of HCE in the GDP keeps increasing. Second, the implicit assumption that individuals only value changes in the expected value of health status is open to criticism. If people are risk-averse with regard to their health, they value a reduction in the variance of health status even if its expected value does not change. Thus, judging the benefits of HCE by its marginal product in terms of expected health (as traditionally done in studies of the production of health) possibly neglects the willingness to pay of risk-averse individuals for reduced uncertainty surrounding their health status.

Following up on this second aspect, this study seeks to determine whether the marginal cost in terms of HCE matches its marginal benefit if the reduction in uncertainty surrounding life expectancy is accounted for. In order to do this, we will proceed as follows. First, a conventional production function with life expectancy as the dependent variable is reestimated to verify that the countries of our sample are characterized by flat-of-the-curve medicine. Second, we examine whether a reduction of uncertainty surrounding life expectancy indeed occurred over the past 46 years. Third, based on the econometric estimation of an appropriately modified health production function we determine the relative contribution of medical and non-medical factors to reduced uncertainty. Finally, we compare the marginal cost of HCE with its marginal benefit in terms of willingness to pay for reduced uncertainty.

We find HCE as well as GDP to be significant determinants of the variance of health status. A 10 percent increase of HCE is estimated to lead to a 0.42 percent reduction of the standard deviation of life years. Furthermore, according to our calculations willingness to pay both in the United States and Switzerland for such a reduction exceeds the extra HCE, implying that additional HCE may be worth its cost as "real insurance", bringing back health status to normal when illness strikes. Hence, flat-of-the-curve medicine need not be wasteful.

Our study is closely related to the empirical literature on the production of health which uses aggregated health care expenditure data (e.g. [7‐10], and [11]). Aggregated data have the advantage of providing panel measurements with variation between countries. However, rather than assessing the contribution of inputs exclusively to the expected value of health status, this study estimates their impact on the variability of health status as well. Furthermore, this work complements studies conducted on the individual level deriving willingness-to-pay values for health risk reductions either from experiments (see e.g. [12]) or from utility-theoretic models (see e.g. [13]).

The basic hypothesis underlying this work is that individuals have preferences with regard to health profiles that are reflected in survival curves and their development over time. As a convenient starting point, consider the two hypothetical health profiles of Figure 1. Health profile A presumably represents the ideal of western lifestyle, living in perfect health followed by sudden death, indicated by a health status of zero ([14]). In contrast, health profile B represents an alternative where health status deteriorates with age but remains positive up to a higher age, indicating survival. The two profiles can also be interpreted as reflecting the probability of being in perfect health, which starts at 100 percent and stays there (profile A) or decreases with age (profile B). Thus, they represent cumulative distribution functions (cdfs), defined over the absence of death rather than (say) wealth. Even if profile B should have higher expected value, they can still be ranked in terms of second-order stochastic dominance (see e.g [15], ch. 2.5). In the present case, the triangle-like area above profile B (indicating the cumulative difference between the two cdfs) exceeds the extra area below profile B. In this event, an individual who is risk-averse with regard to health status prefers profile A. He or she has a positive willingness-to-pay (WTP) for living in a country with a health profile A rather than B.

Health profiles of this type are not available at this time. However, if individuals are successful in moving from profile B to the more rectangular profile A, they should in the aggregate exhibit an increasingly rectangular survival curve because survival constitutes the necessary (but not sufficient) condition for being in perfect health. Therefore, variability of age at death will be used as an indicator of uncertainty surrounding health status.

Various indicators of variability of age at death (VAD) are used in the literature such as the interquartile range ([16]), the Gini coefficient ([17] and [18]), and the standard deviation ([19]). Regardless of choice of indicator, these studies document a secular decline in VAD for industrial countries, albeit at a somewhat reduced rate during the most recent decades. This development is tantamount to a rectangularization of the survival curve (see Figure 2 showing the case of Sweden). In keeping with the argument above, it is interpreted as evidence of individual's improved control over their health status. Note also that this improvement increasingly is reflected in the neighborhood of the nearly vertical segment of the nearly rectangular survival curve, calling for a special focus on the VAD of the elderly.

What this evidence is silent about is how individuals might have achieved this added control. In analogy with the production of health literature, it would be interesting to know whether the major contribution came from medical or non-medical inputs. To the authors' knowledge, there is only one study that relates a measure of VAD to medical and non-medical inputs ([20]). Due to data limitations, [20] performs but a cross-sectional regression for 1982 including 17 OECD countries. He relates public HCE, total HCE, GDP per capita, and a measure of income inequality (the share of the bottom quintile in national income) to the Gini coefficient of mortality. Public HCE has the expected negative impact on VAD but remains insignificant. Surprisingly, total HCE has a positive impact, whereas a higher GDP per capita and less income inequality are associated with lower VAD. However, the Gini coefficient is not translation independent (i.e. it changes if mean age at death differs between two periods or countries although the absolute differences between individuals' ages at death are the same). As to the interquartile range, it violates the transfer principle (it ignores a change in the distribution of deaths within a given age class if the number of deaths in that class does not change). For this reason, the standard deviation will be used as an indicator of VAD in the analysis below.

The present study extends previous work in three ways. First, it uses panel data tracing 24 OECD countries^a over the past 46 years, permitting to test the robustness of the results found by [20]. Second, since the relative contribution of medical and non-medical inputs may well change with age, VAD among the elderly (where rectangularization of the survival curve has been especially marked, see Figure 2) is examined in particular. Third, using evidence on the willingness to pay (WTP) for health risk reduction, WTP values are calculated for the two countries with the highest HCE per capita, the United States and Switzerland. These values are compared with the extra HCE to determine whether flat-of-the-curve medicine may be still worthwhile thanks to its effect on VAD. However, to address these research questions we first have to determine whether the countries of our sample indeed operate (on average) on the flat-of-the-curve. In sum, this leads to the following four research questions:

Q1: Are the countries of our sample characterized by flat-of-the-curve medicine?

Q2: Do medical or non-medical inputs contribute more to reducing variability of age at death (VAD)?

Q3: Are these effects different for VAD among the elderly?

Q4: Is flat-of-the-curve medicine wasteful?

One way to assess the contribution of a set of inputs to remaining life expectancy at age 60 (LE ₆₀) and variability of age at death (VAD) is by eliminating certain causes of death from the data (see [17, 16], but also [21], and [22]). However, comparing different countries over time entails the problem that this contribution may be conditioned by country-specific characteristics (e.g. the type of health care system). In contrast, econometric techniques designed for panel data permit to control for heterogeneity between countries either through fixed or random effects. In the fixed effects (FE) approach, the country-specific effects, c _i , are included in the set of independent variables as a set of country-specific dummies. Alternatively, the c _i can be netted out by measuring all variables as differences from their country-specific means. The random effects (RE) approach assumes the c _i to be stochastic, which means they must be uncorrelated with the independent variables for unbiased parameter estimation. Both the RE and FE estimation were found to suffer from heteroskedasticity, reflecting cross-sectional correlation of error terms in Eqs. (4) and (5) below. Correcting for heteroskedasticity with a first-order autoregressive error term [AR(1) process] and applying the Hausman test we find that RE is preferred over FE throughout at the 5 percent significance level or better.

However, three additional issues need to be clarified. First, medical and non-medical inputs were found to influence remaining life expectancy with a lag by [11]. The same may be true for our sample. Alcohol consumption, for instance, likely does not undermine control over one's health immediately but rather over the course of years. Likewise, earlier HCE may also contribute to higher remaining life expectancy and lower VAD, respectively. As to GDP, it is interpreted as a budget constraint and an indicator of individual productivity. In principle, it could influence VAD with a lag as well. However, lagged GDP caused severe multicollinearity with lagged HCE, forcing a simplified specification with current GDP. Based on the Hausman test, we choose an optimal lag length of 10 years for HCE and ALC in Eq. (4) and 5 years for HCE in Eq. (5), values that seem to be reasonable in view of earlier research. Second, realizing a health profile as shown in Figure 1 calls for investment in (the control of) health over the life-cycle in response to age-dependent mortality. However, the corresponding health production function would require life-cycle measurements of HCE and other inputs, which are not available internationally at this time.^b The third issue is endogeneity. Remaining life expectancy and VAD may feed back to HCE. Countries where individuals live shorter or face higher uncertainty with regard to longevity may spend more on HCE than countries where individuals live longer or face less uncertainty. Such a feedback would likely occur through the political process, in analogy to the feedback relationship found by [11]. However, the Durbin-Wu-Hausman test ([23] and [24]) for endogeneity does not reject the null hypothesis of exogeneity of HCE at the one percent level.

Based on the econometric specification of [20] and the conventional health production approach (see e.g. [11]) the following specification is estimated (note that the variables in Eq. (2) are in logarithms):

The dependent variables are,

Both variables are calculated from period life tables as follows (this type of life tables is discussed at the beginning of the next section). LE ₆₀ is the weighted average of age at death above 60, x - 60, with weights given by the number of individuals dying at the respective age, d _x , relative to the number of survivors at age 60, l ₆₀

The overall sd of age at death is given by

with le symbolizing life expectancy at birth. In keeping with Figure 1, perfect rectangularization means a vertical drop of the health (and hence survival) profile. The age at which the greatest number of a cohort's members die approximates best this vertical drop. Therefore, the standard deviation above the modal year will be used to measure compression of mortality, which increasingly occurs at higher ages (see the example of Sweden again in Figure 1). The sd above the modal year is calculated in analogy to the overall sd,

The independent variables are,

This study addresses an issue that has been overlooked in the production of health literature with its emphasis on flat-of-the-curve medicine. For risk-averse individuals, not only the level of health but also its variability is important. However, improved control over health status is reflected in an increased rectangularization of the survival curve, indicating a reduced variability of age at death (VAD). Since this rectangularization can indeed be observed in OECD countries, this raises four research questions. Are the countries of our sample characterized by flat-of-the-curve medicine (Q1)? Do medical or non-medical factors contribute more to reducing VAD (Q2)? Do these effects differ among the elderly, where rectangularization has been prominent (Q3)? Is flat-of-the-curve medicine wasteful (Q4)?

The standard deviation (sd) of age at death serves as an indicator of overall uncertainty concerning health status and the sd above the modal year (where the number of deaths in adulthood reaches its maximum) as an indicator of uncertainty surrounding health status among the elderly. Between 1960 and 2005 both measures decreased for the 24 OECD countries sampled, pointing to reduced VAD. However, sd above the modal year began to fall in the early 1980s only. These two indicators are related to HCE as a proxy of medical inputs to the production of health and to GDP and alcohol consumption as a proxy of non-medical ones. Based on a specification that takes account of hidden heterogeneity through random effects, the four research questions can be answered as follows.

Q1: According to our estimates the critical value of HCE beyond which its marginal effect ceases to be positive can be put at USD 2,116. With a mean value of USD 3,436 as of 2005, the OECD countries of our sample are on average well within the flat-of-the-curve range.

Q2: The reduction of VAD (indicating better control over health status) is importantly due to both, HCE and GDP.

Q3: Significant effects of HCE and GDP on VAD among the elderly are found for the time period between 1983 to 2005 only, of a magnitude comparable to Q2.

Q4: Comparing the marginal cost in terms of HCE with the willingness-to-pay values for the United States and Switzerland, we find that the benefits in terms of reduced VAD exceed the extra cost. Therefore, flat-of-the-curve medicine may be worthwhile as "real insurance" serving to reduce uncertainty of health status.

However, several limitations of this study need to be pointed out. First, variability of health status as experienced by individuals is only crudely measured by cross-sectional measures such as the standard deviation of age at death. Tracking individual's health status over time would be preferable, but availability of panel data would restrict the analysis to a few countries only. Second, medical and especially non-medical inputs to the production of health are not very well captured by HCE and GDP and alcohol consumption per capita, respectively. Unfortunately, measures of education and other indicators of lifestyle do not date back sufficiently far for many OECD countries. Third, we used a coefficient of absolute risk aversion derived from U.S. data. Its value likely differs between countries.

However, the findings on the whole do suggest that variability of health status can be influenced. This has important implications. First, reduced uncertainty about age at death likely has been modifying the decisions especially of older individuals concerning savings, consumptions, and the purchase of life and long-term care insurance. Quite generally, it helps risk-averse individuals to optimize lifetime consumption, permitting them to reduce precautionary saving (see [32] and [33]). Second, knowing the extent and determinants of variability of health status enables insurers and reinsurers to calculate more accurate values of the financial risk they are exposed to and expected to face in the future in different countries. Finally, our study suggests complementing the economic evaluation of medical interventions (such as cost-utility or cost-effectiveness analysis) with possible reductions in the uncertainty of outcomes.

^aThese are Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Finland, France, Germany, Hungary, Iceland, Italy, Japan, Luxembourg, the Netherlands, New Zealand, Norway, Portugal, Slovak Republic, Spain, Sweden, Switzerland, United Kingdom, and the United States.

^bWe owe this important point to an anonymous referee.

^cA disadvantage of period life tables is that they are based on one-year age intervals and that it is assumed that infants born today will experience the same mortality risks over their lifetimes as do the various age groups in the current population (see [18]). In times of decreasing mortality rates, period life tables underestimate life expectancy.

^dE.g. premiums for the basic mandatory coverage are not risk-rated.

^eThey included consumption of kilocalories per capita as an additional lifestyle variable, which however turned out to be not significant.

^fFrom Table 2, one obtains the critical value beyond which e(LE, HCE) decreases: . This yields HCE = 2.116 or 2,116 USD respectively, which is in the same range as the critical value estimated in [11].