Geography, Health, and Demo-Economic Development

family size more easily in favorable locations. Figure 1 summarizes the results. The equilibria
y* and y will be explained later.

In order to investigate hump-shapednees of population growth and other correlations of demo-
economic development quantitatively, we consider a calibration of the model. For better inter-
pretation generational growth rates are transformed into annual ones. Thus, y is measured as
adult income per year. Let ψ denote the length of adulthood measured by the fecundity period.
Annual population growth is then γL ≡ (1 + gL)¹∕^ψ — 1. We set ψ to 25.

Fundamental child survival is parameterized as π = a ∙ (1 — e~^b'^y) so that mortality decays
exponentially at rate b when income rises. In other words, survival π is a concave function of
income, reaching a maximum at a. The functional form is taken from Kalemli-Ozcan’s (2002)
empirical work. Yet, we cannot adopt his parameter estimates one-to-one because now π is
only the first of two parts of total child survival. Survival is also determined by individual
health expenditure i.e. parameters of the utility function. Therefore a and b are determined in
an iterative way together with preference parameters so that the endogenously generated total
survival rate corresponds with the actually observed data. This leads to an estimate of a = 0.72
and b = 0.004.

Preference parameters are set so that parents in a fully developed country (where c/y is
negligible small and fundamental survival is at the highest level) show the following behavior: a
savings rate of 0.16, a total child survival rate close to one hundred percent, a child expenditure
share of 0.2 per child per parent, and families consisting of 1.13 children per parent (implying
a population growth rate of 0.5 percent). These values are chosen to reflect approximately
the demo-economic performance of the United States. They lead to an estimate of β1 = 0.32,
β2 = 0.09, β3 = 0.12, β4 = 0.087, and λ = 5.⁷

The subsistence level c is calibrated as a parameter that shapes the income elasticity of child
demand according to the demo-economic history. We set c so that population growth peaks
at a value of 2.0 percent per year (see Lucas, 2002). The resulting income correlations are
displayed by solid lines in Figure 4. Parental behavior generates a positive correlation of income
with the rates of human capital expenditure and savings and an inverted-u shaped correlation
of income and population growth. The dotted line in the y — π-diagram represents Kalemli-
Ozcan’s estimate of the survival function (2002, Table 3, survival probability to age 5 in 1997 for

⁷Data Sources for calibration are USDA (2004), World Bank (2004).

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