## 7. Concluding remarks

The basic story told by the empirical results reported in this paper is that nutrition matters, and that inadequate nutrition, as measured by positive values of the PFI or shortfalls in the DES per caput, significantly reduces the growth rate of per caput GDP. In contrast to much of the recent literature, that has identified increasingly esoteric variables as pieces of the explanation for cross-sectional differences in growth performance, it is clear that differences in nutrition constitute one of the fundamental, and eminently reasonable, explanations for the observed heterogeneity in growth rates across countries.

It is worth noting, however, that an alternative interpretation of the results is possible. This alternative interpretation stems from the manner in which the PFI, in particular, is calculated. Analytically speaking, the point of departure for the calculation of the PFI is necessarily the consumer's optimization problem. Write the solution to this problem as:

(60) ,

where c is the consumer's vector of consumption, p is the price vector, and y is the consumer's income.

Let c*f = c*f (p, y) denote the consumer's optimal level of food consumption, which is simply one of the elements of c*, and which will be measured in kcal/day. Let income in the population concerned be distributed according to the probability density function f(y) over the interval . Then by the usual theorem concerning the distribution of the transformation of a random variable (Roussas, 1997, Theorem 2, p. 216), food consumption will be distributed according to the probability density function g (c*t, where:

(61)

where c*-1f (p, c*f ) is the partial inverse of optimal food consumption with respect to y. It follows that, when one chooses a calorie cutoff point, denoted by cf, below which an individual is assumed to be inadequately fed, one is, in fact, choosing a threshold level of income, given by y = c* -1f (p, cf ) . This implies that computing a measure of the prevalence of food inadequacy is equivalent, analytically, to computing a poverty rate, since establishing a calorie cutoff point is equivalent to setting a poverty line.

The consequence is that the empirical results reported in this paper suggest that eliminating, or at least significantly reducing, poverty, will have an important quantitative impact on the growth rate of GDP per caput. From the empirical standpoint, it is clear that data corresponding to a greater number of country-decades is available when one works with the DES per caput or the PFI than when one works with the best data regarding income inequality available, recently pieced together by Deininger and Squire (1996). Indeed, replacing the DES per caput with the share of national income accounted for by the first quintile of the income distribution in the growth regressions presented in Table 1 of this paper reduces the number of observations from 314 to 151. In the case of the Gini coefficient, the corresponding number is 185. While the PFI or the DES per caput are not perfect measures of the incidence of poverty, they are perhaps adequate, and our empirical results show that the goals of "a world free of poverty" (The World Bank) or "a world free of hunger" (FAO) are complementary, and may not only improve human welfare in the static sense, but contribute to raising the rate of economic growth.