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The physiological foundations of the wealth of nations

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Abstract

In the present paper we advance a theory of pre-industrial growth where body size and population size are endogenously determined. Despite the fact that parents invest in both child quantity and productivity enhancing child quality, a take-off does not occur due to a key “physiological check”: if human body size rises, subsistence requirements will increase. This mechanism turns out to be instrumental in explaining why income stagnates near an endogenously determined subsistence boundary. Key predictions of the model are examined using data for ethnic groups as well as for sub-national regions.

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Notes

  1. See e.g., Fogel (1994) and Weil (2007) for evidence on the positive link between body size and labor productivity. Note that a virtuous circle of rising nutrition and attendant increases in body size and income could in principle be quantitatively significant. Fogel (1997) calculates that about 30% of UK growth 1780–1979 can be accounted for by improvements in nutrition.

  2. A related contribution by Abdus and Rangazas (2011) does allow subsistence consumption to be endogenously determined by body size and activity level. In contrast to the present paper, however, individuals do not take their metabolic needs into account when optimizing (and metabolism does not increase with fertility), nor does physical stature matter to productivity. Rather than focusing on the causes of stagnation, Abdus and Rangazas use their their model to show a long-run constancy of calorie consumption during roughly the last two centuries; in their model increasing demand for food as a source of utility is off set by a declining activity level at work.

  3. More broadly, the anthropometric literature has long observed a link between changes in body size and movements in fertility, since nutrition during childhood influences not only adult stature but may also have a direct effect on fertility. For example, the age of menarche is reached earlier within well fed populations. A careful discussion is found in Komlos (1989), analyzing the period of take-off in the Habsburg Monarchy. Extending the theory below to include some of these additional mechanisms could be a potentially interesting topic for future work.

  4. See Cole (2000) and Silventoinen (2003) as well.

  5. In the “upper middle class” we find parents with a secondary education, families where the father has a non-manual occupation, and where at least one of the parents was brought up in a middle class family with similar characteristics. In contrast, the “lower manual” group is characterized by the father being a manual laborer, by both parents only having primary education, and by upbringing; both parents were raised in a working-class family. Between these two extremes we find the “lower middle class” and “upper manual class”; these groups are differentiated from “upper middle class” and “lower manual class” mainly by their educational attainment.

  6. From now on we refer to \(m_t \) as body size rather than body mass. This is done for semantic reasons. The term “body size” is closer to the the literature in anthropology and economic history, which focusses on human height. It also avoids confusion with the body mass index.

  7. “Ontogeny” describes the origin and the development of an organism from the fertilized egg to its mature form.

  8. A physiological explanation for this observation is that child development until weaning depends on energy consumption in utero and during the breastfeeding phase. Since larger mothers consume absolutely more energy the offspring should be larger at this point as it receives a fraction thereof.

  9. Notice that this claim is based on the observation that instability does exist for some \(\alpha <1 \), which can be verified numerically. Of course, the numerical analysis cannot substitute for a theoretical proof of stability of the equilibrium of stagnation.

  10. Alternatively, it appears to be plausible that there exist a physiologically determined upper limit of body size that humans can attain. In that case, instability would imply that the representative individual is of maximum feasible size, an equally unobserved phenomenon in the history of mankind.

  11. In a previous draft we examined a cross-section of 38 LDCs that underwent the demographic transition in 1980 or later, according to the “dates” for the fertility decline established by Reher (2004). This is the sample within which the average female weight is 54.3 kg; see Dalgaard and Strulik (2010, Table 2).

  12. This standard is documented in de Onis et al. (2007). It is worth observing that the basis for the weight-for-age curve is solely US children. Since US children may not be an accurate description of less developed economies we chose to use the 25th percentile, rather than the median. The choice of the 25th percentile is admittedly a somewhat arbitrary choice. In any event, the calibrated parameter values are not very sensitive to the exact choice of weight-for-age curve. For instance, \(\mu \) (and \(d\) below), only changes to a very minor degree if we use the 50th percentile instead.

  13. The continuous time ontogenetic growth equation is given by \(\dot{m} = \delta m^b + d m \), where \(d\) is the energy used for cell maintenance relative to cell creation (West et al. 2001). From that we obtain \( d=\log \left( { [1-(m_0 /m^*)^{1/4} ] / [ 1-(m_v/m^*)^{1/4}] }\right) \cdot {4 /v}\). Accordingly, \(m_0 = 9.4\), \(m_v = 16.5, v=3.5\) and \(m^{*}=54.3\).

  14. Long-lasting effects of droughts and famines during childhood on adult height and weight have been established in previous research; see e.g. Alderman et al. (2006), Meng and Qian (2009), Maccini and Yang (2009).

  15. The BMI is defined as height (in m) divided by the square root of weight (in kg). Ideally we would like to compare the models’ predictions directly to historical data on body size in the sense of weight; to our knowledge such data does not exist, unfortunately.

  16. Details of the method are found at http://ianmorris.org/socdev.html.

  17. Ideally, we would want data on female body weight. These data are, however, are a lot scarcer than male weight for which reason we use the latter. Still, it is worth noting that male and female weight appears to be highly correlated across ethnic groups. A regression of female body weight on male body weight (N = 33) returns a slope estimate of 0.99, significant at the 1 % level, and a statistically insignificant intercept of \(-0.15\).

  18. The DHS surveys that we employ were conducted around the year 2,000, and contain information about the weight of females in the age group 15–44. Accordingly, all the surveyed individuals were born prior to the fertility decline.

  19. See the Online Appendix for further details.

  20. The measure discussed in Nunn and Wantchekon (2011) is calculated as the ratio between the point estimate given a full set of controls (here: column 6 of Table 2), \(\beta _{f}\), and the difference in estimates between a restricted set of controls, \(\beta _{r}\) and the full set of controls: \(\beta _{f}/(\beta _{r}-\beta _{f})\). To calculate the measure we ran a stripped down regression of density on rainfall and soil quality, controlling only for language fixed effects and ensuring that the sample is identical to the one from column 6 of Table 2 (N = 190). This returns a point estimate for log rainfall of 0.97, and 1.67 for soil quality. The relevant measure for rainfall is thus \(0.81/(0.97-0.81) = 4.8\).

  21. One new result, though, is that the joint significance of our productivity proxies in Table 2 (column 10), evaporates in the more limited sample, demonstrating its non-robustness.

  22. Michaelopolous and Papaioannou (2012) document that the “lights data” predicts livings standards measured by a wealth index available from DHS.

  23. The standard reference on pre-industrial development is of course Maddison (2003). Yet the accuracy of these data are often questioned by economic historians. See e.g. Persson (2010) and references cited therein.

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Acknowledgments

We would like to thank Jeanet Bentzen, Oded Galor, Mark Gradstein, Nicolai Kaarsen, John Komlos, Omer Moav, Fidel Perez-Sebastian, Karl-Gunnar Persson, seminar participants at the 2010 AEA meeting; Brown, Ben-Gurion, Copenhagen, Cypress, Vienna, Hannover, Fribourg, and Utrecht Universities for helpful comments. We also thank Doug White and Frank Marlowe for kindly sharing their data.

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Appendices

Appendix 1: Proof of Proposition 3

The proof inspects the derivatives of (13) with respect to the physiological parameters \(a\), \(d\), \(\mu \), \(B_0\), and \(\rho \). For body size we observe immediately \({\partial m^*/ \partial a } >0 \), \({\partial m^* /\partial B_0 } > 0\), \({\partial m^* /\partial \mu } > 0\), \({\partial m^*/ \partial \rho } >0 \), and \({\partial m^*/ \partial d } <0\). For income we have \({\partial y^* / \partial a } = \omega b m^{b-1} {\partial m^* / \partial a } >0 \), \({\partial y^* / \partial \mu } = \omega b m^{b-1} {\partial m^* / \partial \mu } >0 \), \({\partial y^* / \partial d } = \omega b m^{b-1} {\partial m^* / \partial d } <0\), \({\partial y^* / \partial B_0 } =\omega /B_0 m^b+ \omega b m^{b-1} {\partial m^* / \partial B_0>0 }\), and \({\partial y^* / \partial \rho } = (\beta +\gamma )\tau B_0 / \left[ \gamma -1-(\beta +\gamma ) \tau \right] /\epsilon m^b + \omega b m^{b-1} {\partial m^* / \partial \rho }>0\), in which we have defined \(\omega \equiv {\left[ (\beta + \gamma ) \rho +\gamma -1 \right] B_0 / \{ \left[ \gamma -1 - (\beta +\gamma ) \tau \right] \epsilon } \} \). Notice the positive relationship between potential income \(y^*\) and income per capita \(\tilde{y}^*\).

For population density we have \({\partial (L^*/X) / \partial a } = - \theta \sigma m^{-\sigma -1} {\partial m^* / \partial a }<0\), \({\partial (L^*/X) / \partial \mu } = - \theta \sigma m^{-\sigma -1} {\partial m^* / \partial \mu }<0\), \({\partial (L^*/X) / \partial d } = - \theta \sigma m^{-\sigma -1} {\partial m^* / \partial d } > 0\), \({\partial (L^*/X) / \partial B_0 } = -\theta /[(1-\alpha )B_0] m^{-\sigma } - \theta \sigma m^{-\sigma -1} {\partial m^* / \partial B_0 }<0\), and \({\partial (L^*/X) / \partial \rho } = - (A/\omega )^{ {1\over 1-\alpha }-1} / (1-\alpha ) (\beta +\gamma ) \cdot \left[ \gamma -1 - (\beta +\gamma ) \tau \right] / \left[ \gamma -1 + (\beta +\gamma ) \rho \right] m^{-\sigma } - \theta \sigma m^{-\sigma -1} {\partial m^* / \partial \rho }<0\), with \(\theta \equiv (A/\omega )^{1/(1-\alpha )}>0\) and \(\sigma \equiv (b-\phi )/(1-\alpha )>0\).

Appendix 2: On the numerical analysis of the model

1.1 Stability

We evaluate the Jacobian determinant of system (12) numerically. Given the value of \(b\) fixed by nature, we have identified the elasticities \(\alpha \) and \(\phi \) whose change induces the strongest reaction of dynamic behavior. Figure 6 shows the eigenvalues of the Jacobian and alternative \(\alpha \). White dots on the left hand side demonstrate stability of our benchmark calibration (parameter values from Table 1). Black dots reflect results for the case of \(\phi =1.5\) indicating a strong violation of the physiological check (all other parameter values from Table 1). The Malthusian equilibrium is now unstable for \(\alpha >0.40\), i.e. for any reasonable labor share.

Fig. 6
figure 6

Eigenvalues. Parameters from Table 1 and alternative values of \(\alpha \). White dots benchmark case from Table 1. Black dots violation of the physiological check: \(\phi =1.5\)

1.2 An evolutionary argument for the size of \(\gamma \)

In light of the models’ sensitivity to the value of \(\gamma \) it is of interest to try to gauge a likely size of this parameter. As it turns out, the weight of child quantity in the utility function can be given an evolutionary motivation, from which a magnitude is implied.

Suppose nature maximizes genetic fitness, given by the total number of descendants produced. Denote by \(\pi _t \) the fraction of surviving children. Then genetic fitness of the current generation is given by \(\prod _{t=0}^{\infty } \pi _t n_t\). As the solution of the maximization problem is invariant to a monotonous transformation of the objective function, we let nature maximize the logarithm of genetic fitness so that the objective becomes \(\max \sum _{t=0}^{\infty } \log \pi _t + \sum _{t=0}^{\infty } \log n_t\). From the allometric literature we know that longevity (survival probability) of free living animals scales with body mass at factor \(1/4 \) (e.g., Brown et al. 2004), i.e. \(\pi _t \propto m_t^{\psi }, \psi = 1/4 \). Evaluating (6) at the steady-state, we find that \(m_t \propto c_t \) and thus \(\log \pi _t \propto \psi \cdot \log c_t \). Inserting this information into “nature’s objective function” and dividing through by \(\psi \), we find that maximizing genetic fitness is tantamount to maximizing \(\sum _{t=0}^{\infty } \left[ \log (c_t) +(1/\psi ) \cdot \log (n_t) \right] \). This is fulfilled when parents’s of each generation maximize (7) for \(\beta =0\) and \(\gamma =1/\psi \). Note that evolutionary considerations thus predict \(\gamma \approx 4\). This is the value we will use in our calibrations. Note that this relatively high value for \(\gamma \) serves to stabilize the economic systems (cf above).

Observe, finally, that this argument precludes that parents derive utility from own consumption, beyond metabolic needs. In a previous version of this research (Dalgaard and Strulik 2010) we show that all our key results go through if \(\beta = 0\), i.e. if parents only care about child nutrition and family size, but not about own consumption beyond metabolic needs.

Appendix 3: Body size of the grown up child in the utility function

This section develops a version of the model where parents derive utility from child body size (instead of food expenditure for children). Parents now maximize (17) subject to (6) and (8).

$$\begin{aligned} U(c_{t},n_{t})=\beta \log (p_t) + \log (m_{t+1})+\gamma \log (n_{t}) \end{aligned}$$
(17)

By contrast to the baseline model, sophisticated parents take the law of motion for body size into account in their maximization of utility i.e. they understand how child nutrition affects ontogenetic growth. Solving the first order conditions for the variables of interest leads to the solution (18) .

$$\begin{aligned} p_t&= {\beta \left[ y_t- (B_0/\epsilon ) m_t^b\right] \over \beta +\gamma } \end{aligned}$$
(18a)
$$\begin{aligned} c_{t}&={a \epsilon \left[ \tau y_t +\rho (B_0/\epsilon ) m_t^b\right] -\gamma (1-d) \mu m_t \over (\gamma -1) a \epsilon } \end{aligned}$$
(18b)
$$\begin{aligned} n_{t}&= {(\gamma -1) \left[ y_t - (B_0/\epsilon ) m_t^b\right] \over (\beta +\gamma ) [a \epsilon (\tau y_t + \rho (B_0/\epsilon ) m_t^b] - (1-d) \mu m_t} \end{aligned}$$
(18c)

Inserting nutrition expenditure (18b) into (6) provides the law of motion for body size (19a) and inserting fertility (18c) into (11) provides the law of motion for population size (19b).

$$\begin{aligned} m_{t+1}&= {a (\tau \epsilon y + \rho B_0 m_t^b) - (1-d) \mu m_t \over \gamma -1} \end{aligned}$$
(19a)
$$\begin{aligned} L_{t+1}&= {(\gamma -1) a (\epsilon y - B_0 m_t^b) \over (\gamma +\beta ) \left[ a (\rho B + \tau \epsilon y) - (1-d) \mu m_t \right] } \cdot L_t , \end{aligned}$$
(19b)

with \(y\) determined by (10). At the steady-state, \(n_t=n^*=1\). Using this information in (18c) and solving for \(y\) provides (20).

$$\begin{aligned} y^* = {\gamma +\beta \over a \epsilon } m^* + {B_0 \over \epsilon } (m^*)^b. \end{aligned}$$
(20)

The utility-from-child-size model thus preserves the positive association of income and body-size. Since \(y^*\) does not directly depend on \(a\), \(d\), or \(\rho \), the model preserves the feature of a positive association across steady-states when countries differ (genetically) in stature of their inhabitants. Substituting (20) into (19a) provides body size at the steady-state.

$$\begin{aligned} m^* = \left[ (\tau + \rho ) a B_0 \over \gamma -1 - (\gamma +\beta ) \tau + (1-d) \mu \right] ^{1/(1-b)}. \end{aligned}$$
(21)

This expression looks very similar to the original \(m^*\) from the baseline model. Inserting \(y^*\) into (19b) provides population density at the steady-state.

$$\begin{aligned} \left( L \over X \right) ^* = \left( { a \epsilon A \over (\gamma +\beta ) (m^*)^{1-\phi } + a B_0 (m^*)^{b-\phi }} \right) ^{1 \over 1-\alpha }. \end{aligned}$$
(22)

Note that population density does not directly depend on \(a\), \(d\), or \(\rho \). This means that the utility-from-child-size model preserves the feature of a positive association between body size and income across country-specific steady-states when countries differ (genetically) in stature of their inhabitants. The expression (22) is less compact than in the baseline model. But visual inspection reveals that the utility-from-child-size model preserves the features of the baseline model stated in Proposition 23 and in Corollary 1.

Appendix 4: Data sources

See Table 4.

Table 4 Summary statistics: main variables

1.1 Ethnic-groups sample

  • Population density Average population density. See Online appendix for detailed sources.

  • Body size Average male weight (kg). See Online Appendix for details.

  • Rainfall Average precipitation for the period 1900–2000 in a 200 km radius around the center of the ethnic group defined by lat/lon as reported in the Ethnographic Atlas (EA). Source: http://www.cru.uea.ac.uk/cru/data/hrg/.

  • Soil quality Fraction of land area (200 km radius around center of ethnic society) which that is not “unsuitable” for crop growth based on soil conditions. Plate 27 of FAO’s 2002 GAEZ database http://webarchive.iiasa.ac.at/Research/LUC/SAEZ/.

  • Land quality Share of total area, which is arable according to the impact class measure (impact classes 1+2+3+4+5). Source: Plate 47 of FAO’s 2002 GAEZ database: www.iiasa.ac.at/Research/LUC/SAEZ/.

  • Temperature Average precipitation for the period 1900–2000 in a 200 km radius around the center of the ethnic group. Source: http://www.cru.uea.ac.uk/cru/data/hrg/.

  • Continent dummies Include Europe, Asia, North America, South America, Africa, and Oceania.

  • Distance to coast or river Distance to nearest coast or ocean from center of society.

  • Percent near coast Percent of total area which lies within 100 km of icefree coast or navigable river, defined by Center for International Development, Harvard. Shapefile: www.hks.harvard.edu/centers/cid.

  • Days without Frost Based on climate information during the period 1901–1930. Source: http://www.ipcc-data.org/obs/cru_ts2_1.html.

  • Absolute latitude V104 in the EA.

  • Settlement patterns 1–8 indicator, with 1 being nomadic and 8 being complex settlement. V30 in the EA.

  • Jurisdictional Hierarchy Beyond Local Community Following Michaelopolous and Papaioannou (2012), this is an ordered variable ranging from 0 to 4 indicating the number of jurisdictional levels (political complexity) in each society above the local level. Based on V33 in the EA.

  • Language fixed effects Based on V99 in the EA.

  • Agricultural dependence Dependence on animal husbandry and agriculture. V4 and V5 in EA.

1.2 Pixel-level sample

  • Body size Average female weight (kg). The basic data is collected by DHS http://www.measuredhs.com/data/available-datasets.cfm. Some of the surveys are labelled “GPS datasets”. Access can be obtained for the purpose of research upon request. In these data sets the place of data collection is linked to coordinates. With this data in hand we aggregated across enumeration areas to obtain the (weighted) average female body weight by (1 degree latitude, 1 degree longitude) pixel in the countries under consideration.

  • Population density, Land quality, Malaria ecology, distance to capital, distance to border, “earthlights” Source: Michaelopolous and Papaioannou (2012) (MP). MPs data is found at a resolution of 0.125 * 0.125 decimal degrees. For present purposes the data was “aggregated” to a 1 * 1 resolution by taking an area weighted average.

  • Latitude (degrees), elevation (m above sea level), temperature (average annual level 1980–2008, C degrees), precipitation (average annual level 1980–2008, ’000 mm), area (sq km), distance to ice-free ocean or major navigable river (km). Source: Yale University Geographically based Economic (G-Econ) data version 3.4. Data are available at http://gecon.yale.edu.

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Dalgaard, CJ., Strulik, H. The physiological foundations of the wealth of nations. J Econ Growth 20, 37–73 (2015). https://doi.org/10.1007/s10887-015-9112-5

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