6. The efficiency cost of hunger: a quantitative assessment

Given the plethora of results concerning the impact of nutrition on the growth rate of GDP per caput, corresponding to different estimation methods, it is time to present a quantitative assessment of the impact of a reduction in the PFI or an increase in the DES per caput. Results of these simulation exercises are summarized in Table 14 for the PFI and in Table 15 for the DES per caput.

In each Table, four sets of results are presented. The first column reports the impact on the mean rate of growth in the sample used in the corresponding estimation, while including those countries in which the PFI is zero or the DES per caput is above 2770 kcal / day. The second column focuses attention on a subsample comprising those countries in which the PFI is positive or in which the DES per caput is below 2770 / day. The third column narrows the focus even further, and considers the impact on the mean rate of growth of those countries belonging to SSA. Finally, the fourth column presents results for the same set of African countries as the third column, but takes the Svedberg critique into account by assuming that the PFI is overestimated in the FAO data by a factor of 20 percent or that the DES per caput is underestimated, also by a factor of 20 percent.

Several results are worthy of mention. First, note that the impact on growth has been classified in the Tables in ascending order on the basis of the first column. That is, the outcomes of simulations are reported starting with the estimation method that produces the lowest impact on growth, and progressively move up to the estimation method that produces the greatest impact on growth. In Table 14, country-specific fixed effects produce the lowest impact of the elimination of food inadequacy on growth, ranging from 0.34 percentage points in the case of the full sample to 0.64 percentage points in the case of SSA.

TABLE 14
The (efficiency) cost of hunger : a quantitative assessment
Impact on the growth rate of per caput GDP of eliminating food inadequacy

 Sample Full sample PFI > 0 Africa, PFI > 0 Africa, PFI assumed overestimated by 20%, PFI > 0 Country specific fixed effects: column (3) of Table 3 0.0034 0.0047 0.0064 0.0051 Country-specific fixed effects, life expectancy included: column (3) of Table 7 0.0046 0.0063 0.0087 0.0069 Country-specific fixed effects, schooling included: column (3) of Table 8 0.0055 0.0075 0.0103 0.0083 Benchmark pooling results: column (4) of Table 1 0.0064 0.0087 0.0120 0.0096 Between estimator: column (1) of Table 5 0.0093 0.0127 0.0174 0.0140 Sachs-Warner model, logistic specification: column (3) of Table 6 0.0145 0.0253 0.0310 0.0285 Augmented Solow model, logarithmic specification: column (2) of Table 2 0.0182 0.0253 0.0310 0.0285 GMM estimation with first-differencing: column (8) of Table 4 0.0294 0.0401 0.0578 0.0463

TABLE 15
The (efficiency) cost of hunger : a quantitative assessment
Impact on the growth rate of per caput GDP of raising DES per caput
to 2770 kcal /day in countries in which it is below that level

 Sample Full sample DES per caput < 2770 Africa, DES per caput < 2770 Africa, DES per caput assumed underestimated by 20%,DES per caput < 2770 Single equation specifications Sachs-Warner model (column (2) of Table 6) 0.0023 0.0034 0.0039 0.0016 Pooling results, quadratic specification, life expectancy included (column (7) of Table 7 0.0048 0.0069 0.0086 0.0027 Between estimator, linear specification (column (3) of Table 5) 0.0050 0.0071 0.0085 0.0038 Benchmark pooling results, linear specification (column (7) of Table 1) 0.0050 0.0072 0.0086 0.0038 Country-specific fixed effects, linear specification, schooling (column (6) of Table 8) 0.0070 0.0101 0.0120 0.0053 Country-specific fixed effects, linear specification (column (5) of Table 3) 0.0080 0.0115 0.0137 0.0060 Augmented Solow model, logarithmic specification (column (3) of Table 2) 0.0080 0.0123 0.0112 0.0045 Benchmark pooling results, quadratic specification (column (8) of Table 1) 0.0083 0.0119 0.0147 0.0051 Country-specific fixed effects, linear specification, life expectancy (col. (6) of Table 7) 0.0088 0.0126 0.0150 0.0066 Pooling results, quadratic specification, schooling included (column (7) of Table 8) 0.0091 0.0130 0.0162 0.0053 Switching regression specification, high PFI regime (column (1) of Table 9) 0.0093 0.0133 0.0159 0.0070 Between estimator, quadratic specification (column (4) of Table 5) 0.0103 0.0148 0.0183 0.0062 GMM estimation with first-differencing (column (6) of Table 4) 0.0476 0.0704 0.0875 0.0404 Simultaneous equation specifications Direct effect, no feedback (column (3) of Table 11) 0.0031 0.0043 0.0054 0.0010 Indirect effect through life expectancy, no feedback (column (3) of Table 11) 0.0024 0.0033 0.0039 0.0013 Direct effect, feedback included (column (3) of Table 11) 0.0040 0.0055 0.0070 0.0013 Indirect effect through life expectancy, feedback included (column (3) of Table 11) 0.0030 0.0042 0.0050 0.0017 Direct effect, schooling included, no feedback (column (3) of Table 13) 0.0023 0.0034 0.0041 0.0005 Indirect effect through life expectancy, schooling, no feedback (column (3) of Table 13) 0.0031 0.0045 0.0053 0.0015 Direct effect, schooling, feedback included (column (3) of Table 13) 0.0036 0.0053 0.0064 0.0008 Indirect effect through life expectancy, schooling, feedback incl. (col. (3) of Table 13) 0.0048 0.0070 0.0082 0.0024

Second, in the case of the results based on increasing the DES per caput to 2770 kcal / day (Table 15), the estimation method that produces the lowest estimated impact on growth is given by the Sachs-Warner model. In both Tables, it is GMM with first differencing that produces the greatest impact on growth. For the PFI, the shortfall in the annual growth rate of GDP per caput caused by hunger is equal to 2.94 percentage points, rising to 4.63 percentage points in the case of SSA even when one assumes that the PFI, as currently measured by the FAO, is overestimated by 20 percent. For the DES per caput, the corresponding figures are 4.7 and 4.04 percentage points, respectively. These are extremely large numbers, and it is ironic that they correspond to an estimation procedure, as well as an assumption regarding the levels of the DES per caput and the PFI, that answer those (eminently valid) criticisms regarding the data enunciated by Svedberg (1999). Figure 7 provides an illustration of the evolution of the mean level of African GDP per caput as it appears in the data, as it would have appeared in the absence of malnutrition using the lowest estimate of the impact of food inadequacy on growth reported in Table 14 (fourth column), and as it would have appeared using the highest estimate reported in Table 15.

Figure 7
The (efficiency) cost of hunger : a quantitative assessment
Evolution of mean GDP per caput in sub-Saharan Africa If the range of figures generated by the econometric work makes one uncomfortable and one wishes to stick to a single number, caution and those estimation techniques that are most commonly utilized in the econometric literature suggest formulating a quantitative assessment based upon (i) simple pooling results or (ii) simple country-specific fixed effects (the latter at least control for unobserved country-specific heterogeneity). It also turns out that these two estimation techniques produce results that correspond to the mid-point between the highest and lowest estimates reported. Estimates are presented in Table 16, where countries are classified differently with respect to Tables 14 and 15. Here, the division is between countries with above-median levels of the PFI versus countries with below-median levels of the PFI. The mean loss in the annual growth rate of GDP per caput caused by the DES per caput being below 2 770 kcal/day is reported. If the vision concerning the cost of hunger is based on the simple pooling results with the quadratic term in the DES per caput, then it is seen that the annual growth rate of GDP per caput was reduced by 1.6 percentage points by an inadequate level of DES per caput. This is illustrated graphically in Figure 8. From a mean difference of just less than \$US 3 000 in 1960, the mean difference in GDP per caput between below-median PFI countries and above-median PFI countries had grown to \$US 5 000 by 1990.

TABLE 16
The (efficiency) cost of hunger : a quantitative assessment
Loss in annual growth rate of GDP per caput caused by DES per caput being below 2 770 kcal/day

 Loss in annual growth rate of GDP per caput caused by DES per caput being below 2,770 kcal / day Estimation method Countries withabove-median PFI Countries withbelow-median PFI Pooling results with quadratic term in DES per caput 1.597 0.122 Country-specific fixed effects, linear in DES per caput 1.137 0.128

Note: average annual growth rate of GDP per caput of countries with below-median PFI is 1.134%; for countries with above-median PFI, it is 2.950%.

Figure 8
The efficiency cost of hunger : a quantitative assessment
Change in difference in mean income between above-median and below-median PFI countries Had the DES per caput been raised to 2 770 kcal / day in all countries, this difference would have only increased to \$US 3 250. This result illustrates dramatically how inadequate nutrition contributes to widening the income gap separating rich and poor countries.