Abstract
Interactions between knowledge and health are studied in a three-period overlapping generations model with health persistence. Agents face a non-zero probability of death in adulthood. In addition to working, adults allocate time to child rearing. Growth dynamics depend in important ways on the externalities associated with knowledge and health. Depending on the strength of these externalities, increases in government spending on education or health (financed by a cut in unproductive spending) may have ambiguous effects on growth. Trade-offs between education and health spending can be internalized by solving for the growth-maximizing expenditure allocation. With an endogenous adult survival rate, multiple growth paths may emerge. A reallocation of public spending from education to health may shift the economy from a low-growth equilibrium to a high-growth equilibrium.
I am grateful to Barış Alpaslan and an anonymous reviewer for helpful comments on a preliminary draft. However, I bear sole responsibility for the views expressed here. The technical appendix is available upon request.
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Notes
- 1.
Two comprehensive composite measures of human capital have been published recently. The first, by the Institute for Health Metrics and Evaluation, covers 195 countries, whereas the second, by the World Bank, covers 157 countries. See https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(18)31941-X/fulltext and http://www.worldbank.org/en/publication/wdr2019.
- 2.
Among available studies, Baldacci et al. (2004), using cross-country regressions, found that health outcomes (as proxied by the under-five child mortality rate) have a statistically significant effect on school enrollment rates.
- 3.
- 4.
See for instance the results of Powdthavee and Vignoles (2008) for Britain.
- 5.
Tang and Zhang (2007) develop an OLG model with education and health but do not account for direct interactions between them. Tamura (2006) and Ricci and Zachariadis (2013) develop OLG models where schooling exerts external effects on health, in the form of a negative effect on adult mortality in the first case and a positive effect on longevity in the second. In the models of Galor and Mayer-Foulkes (2004) and Hazan and Zoabi (2006), health is, in addition to education, an input in the production of human capital. However, none of these contributions fully examines bidirectional effects, and the role of public policy, as is done here. Finally, Agénor (2011) do account for bidirectional effects in a continuous time, infinite-horizon setting, but in their model health is not stationary.
- 6.
- 7.
The assumption that the survival rate is constant initially is for expositional reasons. It helps to clarify the role of externalities and the fundamental trade-off between spending on education and spending on health.
- 8.
- 9.
See Bleakley (2010b) for an overview of the evidence on the impact of health and education.
- 10.
Research at the National institute of Health in the United States has also shown that the children of mothers who did not eat food with ample omega-3 fatty acids had a lower IQ than children who did.
- 11.
- 12.
At the same time, child development may also be related to a child’s socioeconomic background (see Taylor et al., 2004). If so then children from disadvantaged families may fall behind early in life and may be unable to catch up later.
- 13.
See also Oreopoulos et al. (2008), who found in a study for Canada that poor infant health is a strong predictor of future education outcomes.
- 14.
- 15.
As noted by Kohler and Soldo (2004) for instance, it is useful to separate two potential channels that may relate parents’ education to their children’s health and offsprings’ late life health outcomes. The first is the father’s education, which likely operates through economic circumstances (because fathers may be those who were the primary suppliers of economic resources in the family). The second is the mother’s education, which operates through knowledge about health care and health behavior that are essential determinants of children’s health outcomes.
- 16.
- 17.
The gender dimension of the interactions between education and health is further discussed in the concluding remarks.
- 18.
For simplicity, the direct cost of schooling and the cost of keeping children healthy (medicines, and so on) are abstracted from.
- 19.
If parents care equally about the health and education of their child, η E = η H.
- 20.
Alternatively, it could be assumed that the saving left by individuals who do not survive to old age is confiscated by the government, which transfers them in lump-sum fashion to surviving members of the same cohort. The effective rate of return to saving would thus be (1 + r t+1)∕p, which would yield an equation similar to (8.4). See Agénor (2012, Chapter 3) for a simple derivation.
- 21.
A more general specification would be to set \(A_{t}=E_{t}^{\chi }h_{t}^{1-\chi }\), where χ ∈ (0, 1).
- 22.
This assumption is consistent with the evidence for Sub-Saharan Africa for instance, which suggests that only 6.8 percent of youth engage in tertiary education, compared to a world average of 30 percent (United Nations, 2016, p. 46).
- 23.
See Osang and Sarkar (2008) and Agénor (2015). Of course, a similar argument could apply for the production of education services in (8.11). However, unlike health, knowledge does grow without bounds and the specification adopted in that equation is sufficient to ensure constant growth in the steady state.
- 24.
Activity in that case could of course be measured by the level of final output, but given the linear relationship between Y t and K t implied by (8.10) the use of the latter is mainly a matter of convenience.
- 25.
- 26.
Using θ 1 = 0.55, as in Osang and Sarkar (2008, Table 4) for instance, and a standard value of β = 0.65, this condition implies that θ 4 cannot be higher than 0.64.
- 27.
Note that Case 2 is qualitatively very similar to Case 1. An exhaustive analysis of all cases would require a numerical calibration.
- 28.
There are also intermediate cases, where one type of externality is high and the other low, which are ignored for the moment to facilitate the exposition of the graphical analysis.
- 29.
Curve HH can be either concave or convex, depending on whether \([1-(\beta \theta _{1}+\theta _{4})]/(\beta \theta _{1}+\theta _{3})\gtrless 1\). For illustrative purposes, it is shown as concave in Fig. 8.1. The difference between Cases 1 and 4, of course, is that the slopes of the two curves would be different, depending on the values of ν 3 and θ 3. However, this difference is inconsequential for a qualitative analysis.
- 30.
Note that if ϕ 2 = β then a 12 = 0 and system (8.24) is recursive; the dynamics are in terms of \(\hat {x}_{t}\) only. Then stability requires a 11 = 1 − β + ϕ 1 < 1, or ϕ 1 < β. If ν 3 = 0, then this condition becomes β(ν 1 − 1) < 1 which is always satisfied.
- 31.
A variety of other experiments could also be conducted, such as for instance a change in parental time allocated between the health and education needs of their children, that is, a change in χ. These experiments are left to the interested reader.
- 32.
The focus on growth could be because the economy considered is poor and the priority is to raise living standards. More formally, differences between the growth- and welfare-maximizing solutions can lead to relatively small differences in growth rates, and possibly welfare levels. See Misch et al. (2013) for a discussion.
- 33.
Some other contributions which focus on knowledge accumulation, such as Blackburn and Cipriani (2002), Cervellati and Sunde (2005), Castelló-Climent and Doménech (2008), for instance, have assumed that life expectancy is related to education. This can be justified by arguing that, as noted earlier, improved knowledge can lead to changes in lifestyle that may translate into better health outcomes. In the present setting, a more general approach, of course, would be to consider jointly education and health status as determinants of life expectancy. However, this would complicate significantly the analysis and would detract from the main contribution of this chapter.
- 34.
A simple functional form for f could be the exponential function, that is, \(p_{t}=1-1/\exp (h_{t})\).
- 35.
As noted in Agénor (2015), in the model health status can be interpreted as a broad measure of health, such as the body mass index (BMI). From that perspective, the thresholds h L and h H can be thought of as the lower and upper bounds of the BMI Chart, which are commonly used to measure the ranges for underweight (up to h L in the model), healthy weight (between h L and h H), and overweightandobesity (above h H), based on a person’s height. The last threshold is, in practice, further decomposed into separate thresholds for overweight and obesity but this does not matter from the perspective of this discussion.
- 36.
Based on the previous discussion, if the increase in public spending on health is financed by a cut in spending on education, the possibility of an adverse effect on growth would be magnified.
- 37.
Hazan and Zoabi (2006), however, focus on private expenditure on health and education, not public spending.
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Agénor, PR. (2019). Health and Knowledge Externalities: Implications for Growth and Public Policy. In: Bucci, A., Prettner, K., Prskawetz, A. (eds) Human Capital and Economic Growth. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-21599-6_8
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