Health and Economic Growth: Reconciling the Micro and Macro Evidence

Abstract

Economists use micro-based and macro-based approaches to assess the macroeconomic return to population health. The macro-based approach tends to yield estimates that are either negative and close to zero or positive and an order of magnitude larger than the range of estimates derived from the micro-based approach. This presents a micro-macro puzzle regarding the macroeconomic return to health. We reconcile the two approaches by controlling for the indirect effects of health on income per capita, which macro-based approaches usually include but micro-based approaches deliberately omit when isolating the direct income effects of health. Our results show that the macroeconomic return to health lies in the range of plausible microeconomic estimates, demonstrating that both approaches are in fact consistent with one another.

1. Introduction

Health is an essential component of human capital that supports worker productivity by enhancing physical capacity and mental capabilities. Health improvements influence economic growth through many pathways: better health increases labor market participation and worker productivity (Strauss and Thomas 1998; Bloom and Canning 2000; Schultz 2002); higher life expectancy creates incentives to invest in education, innovation, and physical capital and attracts inflows of foreign direct investment (Bloom et al. 2003, 2007; Alsan et al. 2006; Cervellati and Sunde 2013; Prettner 2013); and better health, particularly that of women, reduces fertility and spurs an economic transition from a state of stagnating incomes toward sustained economic growth (Galor and Weil 2000; Galor 2011; Cervellati and Sunde 2005, 2015; Bloom et al. 2020). In contrast, epidemics and pandemics can take an enormous human toll and impose a massive burden on economies (Bloom et al. 2022).

Economists use two methods to assess the macroeconomic return to population health, which measures how much improvements in population health increase economic growth in terms of income per capita or income per worker. Micro-based approaches derive the macroeconomic return to health by aggregating the estimates of Mincerian wage regressions that explain variation in wages by differences in individual health holding other factors constant. Macro-based approaches estimate a generalized aggregate production function that decomposes human capital into its components, including not only population health but also other factors. While most studies based on these methods indicate a positive macroeconomic return to health, the size of the return remains subject to intense debate. In particular, the macro-based approach tends to find estimates that are either negative and close to zero (Caselli et al. 1996; Acemoglu and Johnson 2007, 2014; Hansen and Lønstrup 2015) or 2.5 to 18.5 times larger than micro-based estimates (Barro and Lee 1994; Barro 1997, 2013; Bloom and Williamson 1998; Gallup and Sachs 2001; Bloom et al. 2004, 2014; Sala-i-Martin et al. 2004; Lorentzen et al. 2008; Aghion et al. 2011). This presents a micro-macro puzzle of the macroeconomic return to health. On the one hand, the small negative estimates suggest that health is irrelevant or even detrimental to economic development, which seems to conflict with evidence of a positive return of health on economic outcomes at the individual level (Miguel and Kremer 2004; Bleakley 2007; Bleakley and Lange 2009; Field et al. 2009; Baird et al. 2016). On the other hand, the large positive estimates far exceed the macroeconomic return to health that results when aggregating the microeconomic returns to the macro level (Shastry and Weil 2003; Weil 2007; Bleakley 2010).¹

One might suspect this puzzle emerges because isolating causal pathways from health to income is challenging. This concern especially applies to early contributions, which use cross-sectional variation to compute the macroeconomic return to health. However, even recent contributions that leverage natural experiments and instrumental variables find estimates that are negative or 2.5 to 10 times larger than micro-based estimates. Hence, the discrepancy between micro-based and macro-based estimates of the macroeconomic return to health must have a different explanation.

This paper aims to reconcile micro-based and macro-based approaches by showing that estimates derived from a well-specified macroeconomic analysis are compatible with estimates based on well-identified microeconomic results. We argue that the gradient between micro-based and macro-based estimates emerges because these approaches measure conceptually different aspects of the macroeconomic return to health. While micro-based approaches abstract from indirect effects of health on growth—for example through the effects of education, capital accumulation, or population dynamics, which may be positive or negative—, macro-based approaches include these indirect effects to estimate the overall effect of health. We overcome this difference by estimating a macro-based model incorporating a Mincerian wage regression that is consistent with the micro-based evidence on the direct effect of health on growth. To this end, we develop a production function model of economic growth, keeping our specification as close as possible to a generalized Mincerian wage equation as proposed by micro-based approaches. This permits us to compare our macro-level estimates and the results from micro-level calibrations directly. This comparison is not possible for other macro-based models that lack the conceptual link between microeconomic and macroeconomic determinants of economic performance through the Mincer equation.

We estimate our macro-based model for 133 countries observed every five years from 1965 to 2015. The specifications use within-country variation of predetermined measures of human capital in a dynamic cross-country panel controlling for past economic development, institutions, demographic structure, and time trends. We show that our results are stable with respect to i) changes in the specification by including country-specific growth trends and additional control variables, ii) changes in the estimation method, and iii) changes in sample composition and sample length. All approaches yield similar estimates of the macroeconomic return to health that quantitatively match the well-identified evidence from the micro-based approach. Moreover, our additional estimates for physical capital, human capital, and convergence all fit the stylized facts in the literature.

According to Weil’s (2007) micro-based approach, a 10-percentage-point increase in adult survival rates raises labor productivity by 6.7 or 13.4 percent, depending on the microeconomic estimates used for calibration. Given the conservative estimate of 6.7 percent, health differentials account for about 9.9 percent of the variation in income per worker across countries (Weil 2007). Our macro-based analysis implies that a 10-percentage-point increase in adult survival rates is associated with a 10.6-percent increase in labor productivity. Weil’s estimates fall within the 95-percent confidence interval of our estimate, suggesting that the two models’ results are compatible. Likewise, our estimate falls within the interval of values consistent with Weil’s micro evidence. Because we include physical capital and education in our empirical framework, the resulting estimate excludes indirect effects such as the role of better health in increasing the incentives for investment, saving, and education, and its role in reducing fertility and spurring a takeoff toward sustained growth. Hence, we can interpret our estimate as a measure of the direct productivity benefits of health as estimated in micro-based approaches.

This paper contributes to the literature in two ways. First, our results show that micro-based and macro-based estimates of the macroeconomic return to health are consistent with one another, once we adopt a conceptually comparable framework. The consistency between both estimates suggests that scale effects do not impair aggregation of well-identified microeconomic estimates through a macroeconomic production function. This result justifies using the micro-based approach to estimate the direct economic benefits of specific health interventions at the macro level. If these results were inconsistent with one another instead, micro-based approaches would not credibly gauge the macroeconomic return to health interventions. Second, our results shed new light on the interpretation of the macro-based evidence in the literature. The sizable gradient between the direct effect of health and the total effect of health indicates that health can have significant positive and negative indirect effects on growth. Successful development policies should thus account for both direct and indirect effects of health interventions by devising complementary policies that also target the indirect effects of health.

2. The Effect of Health on Economic Growth: From Theory to Empirics

2.1. Theoretical Framework

To derive the direct effects of health on economic growth, we develop a production function model that decomposes human capital into its components, building on a generalized Mincerian wage equation. Assume time $t=1,2,\dots ,T$ evolves discretely and consider the production function

$$Y_t=A_t{K}_t^{\alpha }{H}_t^{1-\alpha },$$ (1)

where $Y_t$ denotes aggregate output (which is equivalent to aggregate income in a closed economy), $A_t$ denotes total factor productivity (which reflects the economy’s technological level in a broad sense), $K_t$ is the physical capital stock, $H_t$ is the aggregate human capital stock, and $\alpha$ constitutes the elasticity of aggregate income with respect to physical capital. This functional form has been widely applied in literature that estimated the macroeconomic return to health, such that a comparison between our results and the various macro-based estimates requires us to do the same.² The sum of individual levels of human capital $v_{j,t}$ of workers $j=1,2,\dots ,J$ in the economy—that is, $H_t={\sum }_j^J{v}_{j,t}$—describes the aggregate stock of human capital. Expressing income in per worker units and per capita units yields (2) and (3):

$$y_t=A_t{k}_t^{\alpha }{v}_t^{1-\alpha }$$ (2)

$${\tilde{y}}_t=\frac{Y_t}{N_t}=\frac{L_t}{N_t}{A}_t{k}_t^{\alpha }{v}_t^{1-\alpha },$$ (3)

where $L_t$ refers to the size of the workforce, $N_t$ to the total population size, and $v_t$ to the average human capital stock of workers.

In a competitive labor market, one unit of composite labor $v_t$ earns the wage $w_t$, which equals its marginal product:³

$$w_t=\frac{\partial {\tilde{y}}_t}{\partial v_t}=(1-\alpha )\frac{{\tilde{y}}_t}{v_t}.$$

Furthermore, we assume individual human capital follows a generalized Mincerian wage equation along the lines of Hall and Jones (1999), Bils and Klenow (2000), and Weil (2007). Specifically, we model individual human capital $v_{j,t}$ as an exponential function:

$$v_{j,t}=\text{exp}\left({\varphi }_h{h}_{j,t}+{\varphi }_s{s}_{j,t}\right),$$ (4)

where $h_{j,t}$ denotes the state of health, $s_{j,t}$ denotes educational attainment, ${\varphi }_h$ is the semi-elasticity of human capital with respect to health, and ${\varphi }_s$ is the semi-elasticity of human capital with respect to educational attainment. Conceptually, $h_{j,t}$ and $s_{j,t}$ need not represent all aspects of health and educational attainment: only those that are relevant to produce final output. We also consider an augmented version of this model in which we add experience and experience squared to account for a positive but diminishing marginal return to experience. As we show subsequently, however, including experience does not significantly alter the estimated macroeconomic return to health. Accordingly, a worker $j$ with $v_j$ units of human capital earns a wage of

$$w_{j,t}=w_t\cdot v_{j,t}=w_t\cdot \text{exp}\left({\varphi }_h{h}_{j,t}+{\varphi }_s{s}_{j,t}\right).$$ (5)

This notation normalizes the effective labor input of a hypothetical worker without any health capital and education to one. Meanwhile, workers with better health and higher education are equivalent in productivity to more such baseline workers. Logarithmic wages at the individual level thus take the well-known Mincerian form:

$$\text{ln}\left(w_{j,t}\right)=\text{ln}\left(w_t\right)+\text{ln}\left(v_{j,t}\right)=\text{ln}\left(w_t\right)+{\varphi }_h{h}_{j,t}+{\varphi }_s{s}_{j,t}.$$ (6)

Hence, the aggregate production function in (1) with our measure for human capital in (4) is consistent with wage equations used in the microeconomic literature.

The Mincerian wage form implies that the aggregate human capital stock is given by

$$H_t=\sum _j^J{v}_{j,t}=\sum _j^J\text{exp}\left({\varphi }_h{h}_{j,t}+{\varphi }_s{s}_{j,t}\right).$$ (7)

Aggregating human capital requires exponentiating a standard function of individuals’ health and educational attainment. This complication in the aggregation vanishes if human capital and thus wages follow a lognormal distribution.⁴ In this case, the log of the average wage corresponds to the average of $\mathrm{l}\mathrm{o}\mathrm{g}$ wages plus one-half of the variance of $\mathrm{l}\mathrm{o}\mathrm{g}$ wages ${\sigma }_t^2$. Therefore, the log of human capital per worker simplifies to

$$\begin{gathered} \text{ln}\left(\frac{H_t}{L_t}\right)=\text{ln}\left(\frac{{\sum }_j^J{v}_{j,t}}{L_t}\right)=\frac{{\sum }_j^J\text{ln}\left(v_{j,t}\right)}{L_t}+\frac{{\sigma }_t^2}{2} \\ =\frac{{\sum }_j^J{\varphi }_h{h}_{j,t}+{\varphi }_s{s}_{j,t}}{L_t}+\frac{{\sigma }_t^2}{2} \\ ={\varphi }_h{h}_t+{\varphi }_s{s}_t+\frac{{\sigma }_t^2}{2}. \end{gathered}$$ (8)

In this framework, a marginally better health status (for example, an increase in the adult survival rate by 1 percentage point) raises labor productivity and wages by $100\cdot {\varphi }_h$ percent. Analogously, additional marginal investment in education (for example, one year of schooling) raises labor productivity and wages by $100\cdot {\varphi }_s$ percent. This effect is larger for highly educated high-wage workers than for poorly educated low-wage workers. Likewise, an extra year of education for a highly educated worker also represents a greater investment because the worker forgoes a higher wage for extra schooling.

2.2. Empirical Framework

Suppose the production function in (3) applies to $i=1,\dots ,I$ countries. Taking the logarithm of the production function and using the result from (8), the log of income per capita is given by

$$\text{ln}\left({\tilde{y}}_{i,t}\right)=\text{ln}\left(\frac{L_{i,t}}{N_{i,t}}\right)+\text{ln}\left(A_{i,t}\right)+\alpha \text{ln}\left(k_{i,t}\right)+(1-\alpha )\left({\varphi }_h{h}_{i,t}+{\varphi }_s{s}_{i,t}+\frac{{\sigma }_{i,t}^2}{2}\right).$$ (9)

In equation (9) income per capita could be estimated directly if all right-hand-side variables were available. In practice, however, total factor productivity is not observed. Several approaches can address this problem. We follow Bloom et al. (2004) and model technological development as a diffusion process across countries, which allows for the possibility of long-run differences in total factor productivity even after the diffusion is complete. The change in total factor productivity is then

$$\text{Δ}\text{ln}\left(A_{i,t}\right)=\lambda \left[\text{ln}\left(A_{i,t}^{\ast }\right)-\text{ln}\left(A_{i,t-1}\right)\right]+{\epsilon }_{i,t},$$ (10)

where ${\epsilon }_{i,t}$ constitutes an idiosyncratic shock to technological development. Each country has a period-specific bound, given by $\mathrm{l}\mathrm{n}\left(A_{i,t}^{\ast }\right)$. A country’s total factor productivity adjusts toward this bound at rate $\lambda$. We assume this bound depends on country characteristics $x_{i,t}$ and on the worldwide technology frontier ${\mu }_t$. Moreover, schooling in previous periods may facilitate the diffusion and adoption of existing technologies (Nelson and Phelps 1966) or spur novel innovation (Romer 1990; Strulik et al. 2013). Hence, lagged schooling $s_{i,t-1}$ constitutes another determinant of potential total factor productivity. Neglecting one of these channels might bias the empirical estimates, as Sunde and Vischer (2015) demonstrate. Because technological gaps are not directly observed, we follow Baumol (1986) and use lagged income per capita as a proxy (see also Fagerberg 1994; Dowrick and Rogers 2002). The change in total factor productivity thus reads

$$\text{Δ}\text{ln}\left(A_{i,t}\right)=\lambda \left[{\mu }_t+x_{i,t}^{\prime }\text{Θ}+\rho s_{i,t-1}-\text{ln}\left({\tilde{y}}_{i,t-1}\right)\right]+{\epsilon }_{i,t}.$$ (11)

Alternatively, a richer model derives the log of lagged total factor productivity $\mathrm{l}\mathrm{n}\left(A_{i,t-1}\right)$ directly from the production function such that

$$\begin{gathered} \text{Δ}\text{ln}\left(A_{i,t}\right)=\lambda \left[{\mu }_t+x_{i,t}^{\prime }\text{Θ}+\rho s_{i,t-1}-\text{ln}\left({\tilde{y}}_{i,t-1}\right)+\alpha \text{ln}\left(k_{i,t-1}\right)\right] \\ +\lambda (1-\alpha )\left({\varphi }_h{h}_{i,t-1}+{\varphi }_s{s}_{i,t-1}\frac{{\sigma }_{i,t-1}^2}{2}\right)+{\epsilon }_{i,t}. \end{gathered}$$ (12)

This slightly more comprehensive modeling approach, however, suffers from including additional highly correlated explanatory variables that inflate the estimated standard errors without providing additional insights into the parameters of interest. We provide estimates for both models and show that they are qualitatively and quantitatively similar.

First-differencing (9) and inserting (11) provides our estimation equation:

$$\begin{gathered} \text{Δ}\text{ln}\left({\tilde{y}}_{i,t}\right)=\text{Δ}\text{ln}\left(\frac{L_{i,t}}{N_{i,t}}\right)+\lambda \left[{\mu }_t+x_{i,t}^{\prime }\text{Θ}+\rho s_{i,t-1}-\text{ln}\left({\tilde{y}}_{i,t-1}\right)\right] \\ +\alpha \text{Δ}\text{ln}\left(k_t\right)+(1-\alpha )\left({\varphi }_h\text{Δ}\left(h_{i,t}\right)+{\varphi }_s\text{Δ}\left(s_{i,t}\right)+\frac{\text{Δ}{\left({\sigma }_{i,t}\right)}^2}{2}\right)+{\epsilon }_{i,t}. \end{gathered}$$ (13)

According to this specification, growth of income per capita $\mathrm{\Delta }\mathrm{l}\mathrm{n}\left({\tilde{y}}_{i,t}\right)$ can be decomposed into four components. The first component represents growth of the working-age population relative to the total population, which concomitantly controls for both population growth and growth of the working-age population and thereby accounts for dynamics in demographic structure. The second component is a catch-up term that captures the reduction of the technological gap between country $i$ and the leading countries in each time period, which depends on the world technology frontier ${\mu }_t$, country-specific characteristics $x_{i,t}$, past levels of education $s_{i,t-1}$, and income per capita $\mathrm{l}\mathrm{n}\left({\tilde{y}}_{i,t-1}\right)$. The third component comprises growth of capital per worker $\mathrm{\Delta }\mathrm{l}\mathrm{n}\left(k_{i,t}\right)$, changes in the input factors health $\mathrm{\Delta }\left(h_{i,t}\right)$ and education $\mathrm{\Delta }\left(s_{i,t}\right)$, and the change in wage dispersion $\mathrm{\Delta }{\left({\sigma }_{i,t}\right)}^2$ that arises when aggregating human capital. The fourth component is an idiosyncratic shock ${\epsilon }_{i,t}$ to the country’s technological development.

When estimating our model, changes in input factors might respond to technological shocks ${\epsilon }_{i,t}$. We address this concern in several ways. First, we use within-country variation of predetermined measures of human capital in a dynamic cross-country panel controlling for past economic development, institutions, demographic structure, and time trends. Specifically, we measure changes in health and education of the working-age population, which reflect changes in health and education inputs of the potential workforce rather than health and education inputs of the actual workforce, which might react sensitively to variations in labor supply over the business cycle. In additional specifications, we also include country-specific growth trends, lagged input factors, population growth, geography, trade, and ethnic fractionalization to account for unobserved heterogeneity with a persistent effect on technological development.

Second, we take advantage of the data’s time structure to estimate the parameters via dynamic panel generalized method of moments (GMM) models, thereby eliminating potential correlations that arise mechanically through a link between the lagged dependent variable and technology shocks in the error term. Specifically, this approach instruments potentially endogenous regressors by their lagged values, thereby also accounting for a reverse effect from income growth to changes in population health. If individuals do not systematically anticipate deviations from country-specific long-run growth trends (which are captured by the model), this approach precludes the possibility that random future productivity shocks influence past input factors in a Granger-causal sense.

Third, we assess the stability of our results with respect to changes in sample composition and sample length. This exercise addresses concerns regarding result heterogeneity with respect to economic development, institutional environment, and period-specific events. Moreover, these specifications serve as a robustness test: if changes in input factors were to respond to country-period-specific technology shocks, obtaining systematically similar results across different samples and time periods would be unlikely.

2.3. Data

We estimate our equation for 133 countries observed every five years over the period 1965–2015. Data on income and physical capital are from the Penn World Tables (Feenstra et al. 2015).

Health measures are obtained from United Nations (2017). We use adult survival rates, which measure the probability of surviving from age 15 to 60. We use this measure to compare our results directly with those of Weil’s (2007) micro-based approach. Conceptually, this measure may relate more closely to adult health and worker productivity than life expectancy, which is sensitive to changes in infant mortality rates. We report results for an alternative specification using life expectancy in the robustness section. However, both adult survival rates and life expectancy only proxy for workforce health as they measure mortality rather than morbidity.

The mean of the adult survival rate in the sample is 0.8, which implies that the average probability of surviving from age 15 to 60 across all countries and periods is 80 percent. To get an idea of the variation in survival rates, consider an increase in the adult survival rate of 10 percentage points—our measure for interpreting the effect of population health on labor productivity. Between 1970 and 2015, adult survival rates rose on average by 10 percentage points (from 0.7 to 0.8) in non-advanced economies and by 8 percentage points (from 0.84 to 0.92) in advanced economies.

Data on education are obtained from Barro and Lee (2013). We proxy education by years of secondary schooling for the working-age population 15–64. We focus on secondary schooling because it accounts for most of the variation in education in our sample and provide results for total years of schooling in the Appendix.

In extended specifications, we augment the modeling of human capital with respect to experience. To this end, we construct experience as the median age of the population (United Nations 2017) net of the labor market entry age as measured by an intercept of six years corresponding to early childhood plus years of compulsory schooling (UNESCO 1997, 2017). This correction is necessary because countries with higher life expectancy and older populations tend to have later workforce entry due to longer schooling. As experience enters the regression framework in differences, this measure takes up variation from changes in median age and compulsory schooling following educational reforms.⁵ In additional extended specifications, we approximate changes in wage dispersion by changes in income inequality. We measure inequality by pre-tax, pre-transfer income Gini coefficients (Solt 2020), which are standardized and thus comparable across countries and over time. We do not include experience and inequality in the baseline specification, as this reduces the sample size by up to 340 observations without improving the model’s explanatory power and does not change the main findings considerably.

We also control for variables that might affect a country’s technological development. Specifically, we add time effects for the world technology frontier and a country-specific control for institutional quality, which captures i) the size of government, ii) the quality of the legal system and property rights, iii) monetary stability, iv) freedom to trade internationally, and v) regulation of businesses and credit and labor markets (Gwartney et al. 2017). Institutional quality is particularly important, as it may simultaneously raise income growth, health outcomes, and education (Weil 2014). Because our models include lagged variables and because the data on institutional quality are available only from 1960 onward, they restrict the estimation sample to the time period 1965–2015.

In robustness tests, we add further controls for population growth (United Nations 2017); geography in terms of tropical land area and land area within 100 km of a coast, both measured as a share of the country’s territory (Gallup et al. 1999); trade openness, defined as the ratio of imports and exports relative to gross domestic product (Feenstra et al. 2015); and ethnic fractionalization (Alesina et al. 2003).

Table A.2 in the Appendix reports descriptive statistics for the estimation sample, and Table A.3 lists all countries in the sample.

3. The Estimated Macroeconomic Return to Health

Table 1 presents estimation results for the macroeconomic return to health. Specification (1) reports estimates of the baseline model, which are derived from ordinary least squares. The estimates show the signs expected from theory. Lagged income per worker negatively relates to growth, which implies conditional convergence across countries as predicted by growth theory (Solow 1956; Cass 1965) and as established empirically (Caselli et al. 1996; Barro 1997; Sala-i-Martin et al. 2004; Islam 1995; Durlauf et al. 2005). In turn, capital accumulation positively relates to growth, again conforming to the literature’s results. Changes in human capital positively affect income per capita: the estimates for changes in adult survival and in secondary schooling both have a positive sign. Hence, health and education both constitute important dimensions of human capital. Finally, economic growth increases with the ratio of the working-age to the total population, which captures dynamics in demographic structure. All estimates differ from zero at conventional significance levels.

Table 1:

Estimated Macroeconomic Return to Health

Dependent variable	Growth rate of income per capita
	Baseline controls	Including working experience	Including income inequality	Including lagged controls	Country growth trends	Panel GMM
	(1)	(2)	(3)	(4)	(5)	(6)
Log income per capita (t − 1)	−0.070*** (0.009)	−0.071*** (0.009)	−0.073*** (0.011)	−0.158*** (0.014)	−0.270*** (0.034)	−0.060*** (0.023)
Growth of capital per worker	0.344*** (0.049)	0.355*** (0.048)	0.284*** (0.058)	0.343*** (0.059)	0.257*** (0.082)	0.364*** (0.051)
Change in adult survival	0.698*** (0.258)	0.899*** (0.238)	0.792*** (0.301)	0.694*** (0.253)	0.394* (0.220)	0.653** (0.271)
Change in secondary schooling	0.068*** (0.024)	0.065*** (0.024)	0.057** (0.023)	0.030 (0.023)	0.049* (0.026)	0.062** (0.028)
Growth of working-age population/total population	1.043*** (0.306)	1.051*** (0.345)	0.989** (0.405)	0.983*** (0.291)	0.231 (0.415)	0.968*** (0.361)
Countries	133	131	131	133	133	133
Observations	1020	948	731	1020	1020	1020
R 2	0.29	0.30	—	0.34	0.33	—
AR(2) p-value	—	—	—	—	—	0.10
Hansen p-value	—	—	—	—	—	0.15
Diff.-in-Hansen p-value	—	—	—	—	—	0.97

Note: Estimation results for five-year panels of 133 countries over the period 1965–2015. Estimates are derived from ordinary least squares in specifications (1) to (5) and system GMM in (6). All specifications include time fixed effects, controls for lagged years of secondary schooling, and quality of economic institutions. Specification (2) includes controls for experience and experience squared; specification (3) includes the pre-tax, pre-transfer Gini coefficient; and specification (4) includes lagged controls for physical capital per worker, population health, and the size of the working-age population relative to the total population. Specifications in (5) and (6) account for country-specific growth trends by including country fixed effects. The panel GMM specification in (6) uses the first lag of the endogenous variables in the difference equation and the first difference of the endogenous variables in the level equation as instruments; standard errors in this specification are computed with the two-step procedure and corrected with respect to finite sample size (Windmeijer 2005). Standard errors are clustered at the country level and reported in parentheses. Asterisks indicate significance levels:

^*p < 0.1;

^**p < 0.05;

^***p < 0.01.

Further specifications show that these results are stable to extensions of the baseline model with respect to additional controls and country-specific growth trends. Specification (2) augments the modeling of human capital with experience and experience squared to account for a positive but diminishing return to worker experience. The corresponding estimates show similar influences of physical and human capital on growth based on a reduced sample of 948 observations. In contrast, the coefficients for experience are small and statistically insignificant (see Table A.4 in the Appendix for the coefficients of all control variables). Because experience varies strongly across individuals but little across countries, obtaining a precise estimate of the macroeconomic return to worker experience is difficult (Bloom et al. 2004). Specification (3) controls for changes in income inequality to approximate dynamics in wage dispersion over time. The sample shrinks to 731 observations because of data availability⁶. Again, the estimates take similar values as in the baseline specification and confirm our qualitative findings.

Specification (4) presents results for a comprehensive model, which derives lagged total factor productivity directly from the production function according to equation (12). This specification includes lagged controls for physical capital per worker, population health, and the size of the working-age population relative to the total population. The estimated coefficients for the adult survival rate resemble those for the baseline specification. Specification (5) contains country-specific growth trends, which take up unobserved heterogeneity that persistently affects technological development. This specification is more restrictive than the previous models because it relies only on variation in the deviations of input factors from their long-run growth trends. The estimates shrink slightly in size but are still reasonably close to the baseline results.

Another way to assess the results’ stability is to exploit the data’s time structure to estimate a dynamic panel GMM model to eliminate potential correlations between lagged income per capita, changes in input factors, and technology shocks in the error term. Specifically, we estimate a system GMM model (Arellano and Bover 1995; Blundell and Bond 1998), in which we instrument lagged income per capita, growth of capital per worker, and changes in adult survival and in secondary schooling by their first lag. Specification (6) in Table 1 reports the corresponding estimates. The coefficients resemble the baseline estimates and confirm the qualitative findings. By relying on lagged variation in the variables, this specification accounts for a potential reverse effect from income growth to changes in population health.⁷ The AR(2) test shows no second-order autocorrelation in the non-demeaned error terms, which indicates that the lagged independent variables can be used as instruments. In addition, the Hansen J-test does not reject the null hypothesis that the instrument set is exogenous.

In addition to these different specifications, the coefficients for growth of the working-age population relative to the total population provide an internal specification test. By construction, these coefficients should not differ from one. None of the coefficients is significantly different from one, and they are all close to one except for the imprecisely estimated coefficient accounting for country-specific growth trends. This imprecision is unsurprising as the demographic structure changes only slowly and shows little variation above and beyond its long-run growth trends.⁸.

A common concern regarding the macro-based approach is that decomposing production functions into their components might produce results that react sensitively to the sample composition both in the cross-sectional and in the time dimension. Table 1 addresses this concern, where we assess the stability of the results with respect to changes in sample composition and sample length.

While specification (1) shows the baseline results for the full sample of 133 countries, specification (2) reproduces the estimation for a balanced sample of 50 countries for which we have data over all 10 time periods after differencing and lagging. Because of data availability, the balanced sample is predominantly predicated upon advanced economies. Irrespective of the considerable change in the composition of countries and the reduction in the number of observations, the coefficients of all explanatory variables take similar values as in the baseline specification and remain statistically significant. In specification (3), we focus on developing and emerging countries and exclude all advanced economies. The coefficient of the adult survival rate has again a similar value as in the baseline specification, whereas the return to secondary schooling grows some what in size.⁹ Many socialist countries have undergone major social and economic transformations that considerably affected economic development and population health—for example, in the Russian Federation after the collapse of the Soviet Union. To account for the possibility that these countries drive our results, we exclude all countries that previously were or still are socialist in specification (4). Again, the results are quantitatively similar to our main results. Finally, specifications (5) and (6) reduce the observation period to 1965–2005 and 1975–2015, respectively. When excluding later periods, the coefficient estimate of the adult survival rate increases slightly. A potential explanation is that health improvements in later periods predominantly promoted older workers’ health, such that the macroeconomic return to health increases when excluding them. Nevertheless, excluding these time periods still produces quantitatively similar results to those of the full-length sample.

4. Consistency of Micro-Based and Macro-Based Estimates

How do these estimates relate to the microeconomic evidence in the literature? Table 3 compares the results of our baseline specification with those of Weil’s (2007) micro-based approach. Weil derives the macroeconomic return to health using microeconomic estimates of the return on height from childhood inputs, twin studies, and long-run historical data. According to Weil’s baseline calibration, an increase in adult survival rates of 0.1—or 10 percentage points—raises labor productivity by 6.7 percent. To obtain this figure, Weil uses the two lowest but arguably best-identified estimates at his disposal, stemming from twin studies in the developed world. These estimates are conservative insofar as “[…] nutrition primarily affects physical capabilities and […] these capabilities are less important in rich than in poor countries […]” (Weil 2007, p. 1288). Averaging over all estimates and study types would suggest a larger return on labor productivity of 13.4 percent. We deem values between 6.7 and 13.4 percent to be plausible.¹⁰ Our baseline estimate falls in this range: an increase in adult survival rates of 0.1 translates into a 10.6 -percent increase in labor productivity $\left(0.1\cdot {\varphi }_h\approx 0.1\cdot 0.698/0.656\approx 0.106\right)$. To obtain this figure, we need to divide the estimate of $(1–\alpha )\cdot {\varphi }_h\approx 0.698$ in Table 1 by $(1–\alpha )\approx 0.656$, see equation (13). The results do not change substantially when computing this value for the alternative specifications in Table 1 (see Table A.5 in the Appendix). The 95-percent confidence interval of our estimate ranges from 3.4 to 17.9 percent and accounts for uncertainty in the macroeconomic return to health that derives from dividing by $(1–\alpha )$, which we estimate. The confidence interval includes the calibrated return to health based on Weil’s micro evidence. Likewise, our estimate falls in the range of plausible values implied by Weil’s micro-based calibrations. Hence, macro-based and micro-based results conform quantitatively, implying that micro-based and macro-based approaches to estimating the macroeconomic return to health are consistent with one another after all.

Table 3:

Comparison of Our Estimates with Evidence in the Literature

Parameter	Estimate	Confidence interval	Evidence in literature
$\lambda$	< 0	—	< 0
$\alpha$	0.34	0.25–0.44	0.3–0.4
${\varphi }_h$	10.6%	3.4%–17.9%	6.7%–13.4%
${\varphi }_s$	10.4%	3.5%–17.3%	9.7%

Note: This table reports parameter estimates for the baseline specification (1) in Table 1. Estimates for the macroeconomic returns to health ${\varphi }_h$ and schooling ${\varphi }_s$ are obtained by dividing the estimates by $(1-\alpha )$, where $\alpha$ is the estimate of growth in capital per worker. The macroeconomic return to health ${\varphi }_h$ is multiplied by 10 to match a 10-percentage-point increase in the adult survival rate. The parameter $\lambda$ denotes convergence in income per worker.

Notably, our confidence interval excludes the point estimates from other macro-based approaches for which we were able to compute the macroeconomic return to health (see Table A.1 in the Appendix). This result demonstrates the conceptual and quantitative differences between micro-based and macro-based approaches that this paper addresses. We are able to reconcile the micro-based and the macro-based estimates because we control for a wide range of indirect effects that health has on other domains, which the micro-based approach excludes by design and which other macro-based approaches include to estimate the total effect of health. For example, i) better health may improve education outcomes of children; ii) better health may imply stronger incentives to save and invest in innovative projects; iii) a society with a better health status may have more incentives to establish inclusive institutions; iv) better health may spur population growth by improving mothers’ and infants’ health and thereby dampen income per capita growth; $v$) a better health status of the workforce may facilitate technology adoption through human capital and thus promote total factor productivity; and vi) better population health may accelerate the demographic transition and expedite dynamics in demographic structure beneficial to growth. Our framework controls for these channels and thus reduces the potential ways in which indirect health effects influence economic growth. While we cannot control for the indirect effects of immunization with respect to the spread of communicable diseases, the pathways by which these indirect effects could possibly affect productivity growth are widely controlled for as argued previously.

Overall, the consistency between the micro-based and macro-based approaches is reassuring because it would be highly implausible if our macro-based estimates were biased but simultaneously consistent with the micro-based estimates and stable across specifications, estimation methods, and samples. Moreover, our estimates also match the stylized facts of the empirical literature on the remaining explanatory variables. The estimate for growth of capital per worker $\alpha$ is 0.344. This value is in line with estimates of the elasticity of income with respect to physical capital, which tend to fall in the range 0.3–0.4 (Gollin 2002; Jones 2016). Dividing our estimate of education by $(1–\alpha )$ yields a macroeconomic return to secondary schooling of 10.4 percent $\left({\varphi }_s\approx 0.068/0.656\approx 0.104\right)$. This value is consistent with the range of plausible estimates in the literature reviewed in Psacharopoulos and Patrinos (2018), where the return on secondary schooling averages 9.7 percent in 224 studies across 70 countries between 1960 and 2014. Finally, the sign of our estimate on the convergence rate $\lambda$ accords with previous findings on conditional convergence.

5. Robustness

This section presents the results’ robustness to including additional controls; using different measures of income, health, and education; and to using alternative GMM specifications.

5.1. Additional Controls

A potential concern is that other factors not contained in our model may correlate with both economic development and population health. Table A.6 in the Appendix presents results for extended specifications that include additional variables suggested by the literature that might affect a country’s development. These specifications control for heterogeneity with respect to population size and growth, trade openness, geography, and ethnic fractionalization in addition to our baseline controls that capture past changes in economic performance, convergence in technology, and country differences in demographic structure and institutions. The corresponding estimates confirm the macroeconomic return to health from our main specification qualitatively and quantitatively. While geography, fractionalization, and to a lesser extent population growth correlate with economic development, including these variables neither significantly changes the explanatory variables’ coefficients nor improves the model’s fit.

5.2. Income per Worker

Table A.7 reports results for the growth rate of income per worker as the dependent variable instead of the growth rate of income per capita. In these specifications, we transform the dependent variable into per worker by removing the control for growth of the support ratio $\mathrm{\Delta }\mathrm{l}\mathrm{n}\left(L_{i,t}/N_{i,t}\right)$, thereby following the derivation of our model in equations (2) and (3). The estimated macroeconomic return to health is quantitatively similar to the main results.

5.3. Life Expectancy at Birth

Table A.8 presents results for empirical specifications in which we proxy health by life expectancy at birth instead of the adult survival rate. The estimates qualitatively confirm the empirical patterns in the main results. Using the correlation between adult survival and life expectancy in our sample, we can quantitatively compare the results for both health measures. The estimates for life expectancy are 1.8 times larger than those for adult survival. However, these estimates are not significantly different from one another. Moreover, both estimates differ from the various estimates of the macroeconomic return to health in the literature that are either negative and close to zero or positive and large. This evidence thus corroborates our main finding that micro-based and macro-based estimates of the macroeconomic return to health are consistent.

5.4. Total Years of Schooling

Table A.9 reports the results of an empirical model that proxies education by average years of total schooling instead of average years of secondary schooling. Qualitatively and quantitatively, the results conform closely to our main results. In particular, the estimated macroeconomic return to health is quantitatively almost identical to the main results and lies in the range of plausible microeconomic estimates. At the same time, the estimated macroeconomic return to an additional year of schooling is statistically insignificant in some specifications; however, with values of 5 percent, it still lies at the lower end of the range of plausible values of microeconomic estimates. The variation in this regressor may be less informative than the variation in years of secondary education because primary education and tertiary education vary less over the observation period than years of secondary schooling.

5.5. Alternative GMM Specifications

Table A.10 presents results for alternative GMM specifications. The rationale for these specification tests is that the empirical results in GMM models may react sensitively to changes in the instrument set (Roodman 2009). Specifically, we estimate models that differ from the baseline specification in the following dimensions: a model that eliminates fixed effects using forward orthogonal deviations instead of first differences, a model that instruments explanatory variables with second lags rather than first lags, and a model that collapses the instrument set. The corresponding results are qualitatively and quantitatively similar to our main findings and confirm that micro-based and macro-based estimates of the macroeconomic return to health are consistent.

6. Policy Implications

The growth literature has used micro-based and macro-based approaches to assess the macroeconomic return to health. Micro-based approaches aggregate the return on health obtained from Mincerian wage regressions to derive the macroeconomic return to health, whereas macro-based approaches estimate generalized production functions decomposing human capital into its components. Macro-based approaches tend to find estimates that are negative and close to zero or 2.5 to 18.5 times larger than micro-based estimates, thereby raising a micro-macro puzzle of the macroeconomic return to health. Our study shows that macro-based estimates of the macroeconomic return to health are compatible with micro-based estimates when we control for the indirect effects of health, which macro-based approaches usually capture but micro-based approaches omit by design. Our estimate indicates that an increase in the adult survival rate of 10 percentage points increases labor productivity by 10.6 percent. This estimate is consistent with the calibrated values of Weil’s (2007) micro-based approach, which range from 6.7 percent to 13.4 percent when averaging over all microeconomic estimates referenced in that work. Our results confirm the validity of the micro-based approach and justify its use when estimating the direct economic benefits of health interventions at the macro level.

Furthermore, our results indicate that population health can be an important source of cross-country differences in income per worker, suggesting that public health measures are an important lever for fostering economic development. Potential policies along these lines include vaccination programs, antibiotic distribution programs, and micronutrient supplementation schemes, which lead to large improvements in health outcomes for relatively low expenditures (World Bank 1993; WHO 2001; Field et al. 2009; Luca et al. 2018). However, our results also suggest that health improvements have sizable indirect effects on economic growth that can operate through mechanisms such as education, fertility, and saving. The neglect of these mechanisms in policy considerations could diminish the estimated economic return to population health. Hence, public health measures and related policies—such as those involving family planning and education (Bloom et al. 2020; Kotschy et al. 2020)—should account for both the positive and negative indirect effects of health on economic growth.

Table 2:

Stability across Samples and over Time

Dependent variable	Growth rate of income per capita
	Full sample	Balanced sample	Excluding advanced economies	Excluding socialist countries	Sample 1965–2005	Sample 1975–2015
	(1)	(2)	(3)	(4)	(5)	(6)
Log income per capita (t − 1)	−0.070*** (0.009)	−0.054*** (0.018)	−0.080*** (0.011)	−0.061*** (0.011)	−0.064*** (0.011)	−0.072*** (0.009)
Growth of capital per worker	0.344*** (0.049)	0.322*** (0.069)	0.336*** (0.056)	0.359*** (0.056)	0.313*** (0.060)	0.330*** (0.051)
Change in adult survival	0.698*** (0.258)	0.719*** (0.244)	0.639** (0.272)	0.663** (0.284)	0.976*** (0.312)	0.685*** (0.261)
Change in secondary schooling	0.068*** (0.024)	0.058** (0.027)	0.095** (0.037)	0.080*** (0.026)	0.080** (0.032)	0.071*** (0.025)
Growth of working-age population/total population	1.043*** (0.306)	1.614*** (0.505)	1.083*** (0.385)	1.097*** (0.336)	1.190*** (0.361)	1.100*** (0.317)
Countries	133	50	98	103	123	133
Observations	1020	500	700	868	756	970
R 2	0.29	0.31	0.33	0.26	0.26	0.28

Note: Results for different samples. Estimates are derived from ordinary least squares. Specification (1) reports results for the unbalanced full sample, whereas specification (2) reports results for the subset of countries that are observed in all periods from 1960 to 2015. Specifications (3) and (4) exclude advanced economies or countries that were or still are socialist. Specifications (5) and (6) report results for shortened samples over the periods 1965–2005 and 1975–2015. All specifications include time fixed effects, controls for lagged years of secondary schooling, and quality of economic institutions. Standard errors are clustered at the country level and reported in parentheses. Asterisks indicate significance levels:

^*p < 0.1;

^**p < 0.05;

^***p < 0.01.

Highlights.

• Micro-based and macro-based approaches to the assessment of the macroeconomic return to population health tend to produce substantially different results.

• Using a macro-based approach that incorporates a Mincerian wage equation, we show that micro-based and macro-based approaches are in fact consistent with one another.

• Our results indicate that population health can be an important source of cross-country differences in both income per worker and income per capita.

• Micro-based approaches can be used to estimate the direct economic benefits of health interventions at the macro level.

• The allocation of resources to public health should take account of the indirect effects of health on economic growth.