7. Contribution of Health to Income Differences Among Countries
7.1 Robustness and Sensitivity
My estimates of the proximate effects of health on GDP differences among countries are built up from data on how health indicators vary among countries and estimates of the return to health. In the case of health as measured by ASR, the health indicator itself is of relatively high quality and is measured on a uniform basis, and so the most likely source of error is in the calculation of the return to health. This is particularly true because in this case the return to health is itself the product of two other estimates: the return to height and my estimated mapping between changes in ASR and changes in height.
One of the two measures of health’s importance that I use, the fraction of variance explained by health, is by construction linear in the estimated return to health. Thus, it easy to
results. For example, if instead of my baseline estimate of the return to height (7.2% per
centimeter) I use the estimate derived from the Behrman and Rosenzweig data on twins (3.3% per centimeter), the fraction of the variance in log GDP explained by health will fall from 22.6% to 10.3%. Using the highest estimated return to height in my data (9.4% per centimeter), the fraction of variance in log income explained would be 29.5%. The estimated fraction of variance in log GDP explained by health is also linear in the estimate of – that is, the mapping from
changes in ASR into changes in height. In the calculations above, I use the estimate of this ratio excluding a time trend (26.4). Using instead the estimate including a time trend (16.6), along with the baseline estimate of the return to height, the fraction of variance of log GDP accounted for by health falls from 22.6% to 14.2%. Using the lowest combination of estimates (3.3% for the return to height and 16.6 for the mapping from ASR to heigh), the fraction of log variance of output explained by health is 6.5%.
The other measure of health’s importance that I construct, the reduction in the variance of log income that would result from equating health among countries, is not linear in the return to health. However, because the bulk of this term is due to the covariance of health with other inputs rather than health’s own variance (see equations 17 and 18), in practice this measure also varies roughly linearly with the return to health. Moving from the low to the benchmark estimates of the return to height (3.3% to 7.2% – a factor of 2.18), the reduction in log variance of output that results from an elimination of health gaps among countries rises from 18.9% to 36.6% – a factor of 1.94. Using the lowest combination of estimates of the return to height and the mapping from ASR to height, the reduction in the variance of log output that would result from an elimination of health gaps is 12.3%.
In the case of health as measured by age of menarche, the estimated return to menarche is arguably less likely as source of error than mismeasurement of menarche itself. As mentioned above, my data on menarche come from a variety of years, and in some cases refer to the median
rather than the mean. A regression of age of menarche on a dummy for median and year of measurement yields the following (standard errors in parentheses):
Age of Menarche = 51.98 -0.105 median -0.0195 year R2=.054
(25.46) (0.264) (0.0128) N = 49
Using the residuals from this regression in the accounting exercise above implies that age at menarche explains 10.6% of the variance in the log of GDP per capita, which is hardly different from my original estimate of 10.8%.
7.2 The Changing Relationship Between ASR and Income
As mentioned in Section 3.3, my method for finding the return to a health outcome, D, is biased in the case where the ratio of changes in worker productivity to changes in the indicator induced by the experiment used to measure D is different then the ratio of changes in worker productivity to changes in the indicator in cross-country data. In the case of the Adult Survival Rate, there is reason to worry that just such a bias may be present, due to AIDS. As shown in Figure 1, a significant fraction of the variance in ASR in the year 1999 is due to high AIDS mortality in developing countries. Young (2004) argues that, in comparison to other diseases, AIDS has a disproportionally large effect on mortality in comparison to its affect on morbidity (that is, the health of workers). Specifically, in the case of sub-Saharan Africa, where advanced medical treatment for AIDS is rare, individuals infected with HIV experience a long asymptomatic period during which their labor productivity is unaffected by the disease, following which they sicken and rapidly die. If this is the case, my estimates of the variation in human capital in the form of health among countries, using adult survival to measure health, will be overstated.
18GDP per worker is the variable RGDPWOK from Heston, Summers, and Aten (2002). Adult Survival is from the World Development Indicators database of the World Bank.
look at data from the period before AIDS became widespread. Specifically, using data on output per worker and ASR, I construct the same two measures of health’s importance that were
examined in Table 3 – the fraction of the variance of log GDP per worker that is attributable to health and the reduction in the variance of log GDP per worker that would result from an elimination of health gaps – for every decade over the period 1960-2000. In the year 2000, there were 2.4 million AIDS deaths in Africa, compared to 450,000 in 1990 and almost none in 1980.
The data are a panel of 80 countries for which data on GDP per worker and Adult Survival were available over the period 1960-2000.18 I use the benchmark estimate of the return to adult survival of D = 1.9 derived above. Figure 6 shows the results. There is indeed a
significant rise (5.4 percentage points, or 29%) in the implied effect of health on GDP between 1990 and 2000. If we assume that this entire rise was due to AIDS, and that AIDS had no effect at all on the labor input of workers, then the fraction of income variance explained by health calculated in Table 3 would have to be reduced to 17.4%, which is still quite large. Even if this adjustment is applied to the lowest estimated return to ASR discussed in Section 7.1 (that is, the combination of the lowest estimates of the return to height and the mapping from ASR to height), the implied fraction of the variance in log GDP explained by health is 9.5%, which is hardly insignificant.
Besides addressing the issue of bias induced by AIDS, Figure 6 is interesting in its own right. It shows that in the period prior to 1990, convergence in health among countries
significantly reduced the fraction of world income variation attributable to health. Because this reduction in mortality was due to progress against a number of diseases, it is less likely that the bias in measuring the return to health discussed above is present, and thus it is less likely that decline in health’s importance as a determinant of GDP variation is a statistical illusion.
8. Conclusion
People in rich countries are on average healthier than people in poor countries. In this paper I have sought to determine the extent to which these gaps in health can help explain the income gaps themselves. Knowing the role that health plays in explaining income differences among countries is important both for policy makers who are considering interventions to improve health in poor countries and for economic researchers seeking a fuller picture of how income gaps arise.
Determining health’s role in accounting for income differences among countries is made difficult by the endogeneity of health. In particular, the endogeneity of health makes it almost impossible to use aggregate data to estimate the structural effect of health on income. In this paper I have presented a methodology by which properly-identified estimates of the effect of variation in health inputs on individual income and health outcomes can be applied to cross- country data on health indicators in order to estimate the effect of health on income. In other words, I use microeconomic results to answer the macroeconomic question of how much of income variation among countries is explained by health. My methodology has the advantage of being able to incorporate and compare results from a large number of microeconomic studies that have examined different health interventions and different health indicators. The methodology can also encompass historical data on health and labor productivity.
The effects of health on income that I estimate are large. My baseline estimate, using the Adult Survival Rate for men as a measure of health, is that health explains 22.6% of the variance of log GDP per worker, and that eliminating health gaps among countries would reduce the variance of log GDP per worker by 36.6%. A parallel set of estimates, using the age of
menarche as a health indicator, are slightly less than half as large. The conclusion that health is an important determinant of income variation is robust to using a variety of different microeconomic and historically calibrated estimates of the return to health, as well as to using alternative
estimates of the mapping between different health indicators and adjusting for the role of AIDS in affecting mortality in the 1990s.
A limitation of the methodology that I present is that it can only examine the proximate effect of health – that is, people working harder, longer, or more intelligently – on GDP per worker. In addition to this proximate effect, there are a number of indirect channels through which health affects a country’s output. As discussed in the introduction, it is conceptually difficult, if not impossible, to answer the question “how much of the variation in income among countries is explained by health?” in a framework that takes account of these indirect effects. On the other hand, the question “how much would the variance of income fall if health gaps were eliminated?” raises no such conceptual problem. Nor is there any doubt that accounting for health’s indirect effects would yield a larger answer than the one I have presented here. How much larger remains a question for future work.
Appendix: Allowing Latent Health to be Two Dimensional
As a way of thinking about the biases resulting from the assumption that latent health is uni-dimensional, I here consider the case in which there are two latent health characteristics, one of which, z, is relevant to an individual's productivity in the labor market, and the other of which, ., is not. I assume that both aspects of health can affect the observed health indicator, I. Specific variations in the vector of health inputs, X, will affect one or both of the aspects of underlying health.
Consider two countries with vectors of health inputs X1 and X2. The true difference in their levels of human capital in the form of health will be
(A.1)
let (Iz be the coefficient giving the effect of the latent health measure z on the observable health outcome I, and similarly (I. be the coefficient giving the effect of the latent health measure . on the observable outcome I. The difference in I is given by
(A.2)
Using microeconomic data in which one element of the health input vector, x, is varied exogenously, the estimated return to characteristic I is
(A.3)
Thus the estimated difference in human capital in the form of health is
(A.4)
which can be rearranged to give
(A.5)
The term in square brackets in this expression is the actual gap in human capital in the form of health between the two countries from equation (A.1). The other part of the expression is the bias in estimating this gap. Several points can be noted about this bias term:
• If (I. = 0, that is, the aspect of health that is irrelevant for v is also irrelevant for the indicator I, then there is no bias.
• If (I. > 0, then the sign of the bias will depend on how the variation in the two dimensions of health induced by the experiment being used to estimate the return to the characteristic (that is, the ratio of d./dx to dz/dx ) compares to the actual variation in the two dimensions between two countries (that is, the ratio of (.(X1) - .(X2)) to (z(X1) - z(X2)). If these two ratios are equal, then once again there is no bias. The gap in v between two countries will be overstated in cases where variation in the aspect of health that is irrelevant for producing output (.) , relative to variation in the relevant aspect of health (z), is larger among countries than the variation induced by the experiment being used to estimate the return to health.
• If there is bias present from the above cause, then the absolute size of this bias will be magnified the greater is the ratio (I. / (Iz, that is, the more that the aspect of health that is irrelevant to output affects the observable health indicator relative to the effect of the relevant measure of health on the observable indicator.
One can do similar algebra to deal with the case (described in Section 3.2 and applied in Section 5.3) where the return to health is calibrated by examining changes over time in v within a single country. The estimated gap in v between countries will be biased if the ratio of changes in the different elements of latent health (z and .) that took place in the relevant historical
experiment does not match ratio of differences in these two elements of latent health between countries.
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