There are several transmission mechanisms through which malnutrition could affect growth. A direct transmission mechanism has already been identified in the context of the simple theoretical models presented above : the productivity of the labour force operating through the efficiency effect of increased levels of nutrition. Before examining two indirect transmission mechanisms, a general framework is proposed that will facilitate the interpretation of the econometric results that will be presented below. Essentially, the empirical issue will be to disentangle direct from indirect effects of malnutrition on growth. Regression analysis is, of course, ideally suited to this exercise.
Consider a simple specification of a growth equation where the growth rate of per caput GDP (GROWTH) is a function of some "intermediate" variable x, a set of control variables, y, and a nutritional variable, denoted by m; thus:
(17)
Suppose now that the "intermediate" variable is, in turn, a function of the nutritional variable. This can be expressed by posing:
(18) x=x(m)
Substituting equation (18) into equation (17) yields:
(19)
Consider the total derivative of this last expression (equation (19)) with respect to m. One obtains:
(20)
Empirically, the implication is clear. If a regression of the growth rate is run on m, the estimated coefficient associated with this last variable gives us the value of the total derivative of growth with respect to m. In other words, the coefficient associated with m is equal to equation (20). It follows that a statistically significant coefficient associated with the DES per caput or the PFI can obtain for three reasons :
and
and
In order to distinguish between direct and indirect transmission mechanisms, the reduced form regression given by equation (19) is first run. As seen above in the results presented in Tables 1 to 6, the coefficient associated with the nutritional variable is indeed statistically significant. In order to test for whether this effect is associated with a direct or an indirect impact of malnutrition on growth, the "intermediate" variable is then introduced into the regression. Essentially, the regression given by equation (17) is run. If the coefficient associated with the intermediate variable is statistically significant and the coefficient associated with the DES per caput or the PFI becomes statistically insignificant (or, at least, falls in a statistically significant manner), it follows that there is an indirect impact of malnutrition on growth that is mediated by the intermediate variable. If it remains statistically significant, both a direct and an indirect effect of malnutrition on growth are at work.^{10}
In what follows, a first assessment is presented of the potential role played by two transmission mechanisms through which nutritional concerns may impact the growth rate of GDP per caput indirectly. The two transmissions mechanisms in question are life expectancy, which has been shown by a number of authors (e.g., Barro and Lee, 1993, Sachs and Warner, 1997a, 1997b) to be a significant determinant of growth, and schooling, which has been the focus of intense empirical research since the original contribution, based on an augmented Solow model, by Mankiw, Romer and Weil (1992).
As has already been seen, in the context of the empirical results based on the Sachs and Warner (1997) dataset, both life expectancy and nutritional variables are statistically significant when entered into a longrun growth regression based on thirty year averages. The question is whether this result will hold up within the context of our pooled countrydecade dataset.
Empirical results concerning life expectancy based on the same dataset as that used in the results presented in Tables 1, 3, 4 and 5 are presented in Table 7. Given our previous findings using both the between and the within estimator, three sets of results are presented, corresponding to pooled timeseries cross section (columns (1), (4) and (7)), OLS on country means (columns (2), (5) and (8)), and panel estimation which controls for countryspecific fixed effects (columns (3), (6) and (9)). The results are particularly revealing.
First, the coefficient associated with life expectancy is statistically significant at the usual levels of confidence in those six cases in which either pooling or the between estimator is applied, while its effect vanishes once countryspecific fixed effects are controlled for. Second, the coefficient associated with the PFI is statistically significant in all three methods of estimation. Third, the coefficient associated with the DES per caput in the linear specification becomes statistically insignificant in the pooling and between results, but is highly significant when one controls for countryspecific fixed effects. Fourth, and in contrast to the linear specification, the DES per caput and the DES per caput squared are significant determinants of growth in the pooling and between results, but vanish almost entirely when one uses the within procedure. Fifth, a specification in terms of countryspecific random effects is soundly rejected by the usual Hausman test in favour of the fixedeffects specification in all cases.
The contrast with the results obtained using the SachsWarner dataset are striking. In the long run, or when using either pooling or the between estimator, the impact of life expectancy on growth is statistically significant, but this effect disappears when one uses the within estimator. This suggests that the impact of life expectancy on growth is essentially a longrun phenomenon, and that its impact on growth obtains because it is controlling for other, unobserved, country characteristics that are purged once fixed effects are included. This disappearance of what was otherwise a highly significant variable is typical of results using panel data with countryspecific fixed effects. The PFI results are encouraging in that they imply that there is a statistically significant impact of malnutrition on growth irrespective of the time frame of analysis. Since life expectancy is included in the three regressions reported in columns (1), (2) and (3), it follows (based on the analytical framework outlined above) that there is a direct impact of the PFI on the growth rate of GDP per caput.
TABLE 7
PFI, DES per caput, and economic growth
Transmission mechanisms : life expectancy
(tstatistics below coefficients)
Dependent variable : 
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
(8) 
(9) 
Method of estimation 
OLS 
between 
within 
OLS 
between 
within 
OLS 
between 
within 
Intercept 
0.048 
0.071 
0.002 
0.020 
0.104 
0.141 

2.367 
2.091 
0.149 
0.900 
3.745 
3.045 

1960s dummy 
0.024 
0.007 
0.025 
0.006 
0.024 
0.005 

9.200 
0.885 
9.465 
0.737 
9.269 
0.655 

1970s dummy 
0.019 
0.012 
0.020 
0.012 
0.019 
0.012 

6.601 
3.331 
6.961 
3.409 
6.731 
3.267 

Africa dummy 
0.006 
0.005 
0.007 
0.007 
0.008 
0.007 

1.351 
0.932 
1.667 
1.258 
1.941 
1.479 

Latin America dummy 
0.015 
0.015 
0.015 
0.016 
0.016 
0.018 

5.332 
3.733 
4.580 
3.647 
5.304 
4.138 

Log of initial GDP (by decade) 
0.010 
0.009 
0.028 
0.010 
0.007 
0.033 
0.010 
0.007 
0.033 
3.714 
2.702 
3.914 
3.312 
1.788 
4.325 
3.385 
2.028 
4.155 

Life expectancy at age zero 
0.001 
0.001 
0.000 
0.001 
0.001 
0.001 
0.001 
0.001 
0.001 
4.467 
3.241 
4.321 
3.460 
0.476 
4.045 
3.094 
0.544 

Nutritional variables 

100  PFI (%) 
0.001 
0.001 
0.001 

2.937 
2.073 
2.167 

DES per caput (kcal/day) 
4.61E06 
1.40E07 
2.41E05 
8.80E05 
1.03E04 
5.29E05 

1.134 
0.021 
3.286 
4.444 
2.907 
1.521 

DES per caput, squared 
1.53E08 
1.84E08 
5.72E09 

4.361 
2.949 
0.852 

Mean of dependent variable 
0.019 
0.018 
0.019 
0.018 
0.018 
0.018 
0.018 
0.018 
0.018 
Adjusted R^{2} 
0.392 
0.432 
0.540 
0.367 
0.389 
0.547 
0.391 
0.436 
0.546 
0.019 
0.014 
0.017 
0.020 
0.014 
0.017 
0.019 
0.014 
0.017 

Hausman test : Random effects 
0.040 
0.001 
0.007 

Number of observations 
292 
100 
292 
291 
100 
291 
291 
100 
291 
Note : standard errors are White heteroskedasticityconsistent; threshold value of DES per caput in quadratic specifications where coefficients are statistically significant (columns (7) and (8)) : 2875 and 2798 kcal/day, respectively. Data source. Life expectancy at age zero : Barro and Lee (1993).
In contrast to the results based on the PFI, our results for the DES per caput suggest : (i) that in the long run (i.e., using the between estimator), the impact of the DES per caput on growth obtains indirectly through its effect on life expectancy; and (ii) that in the medium run, and when one accounts for unobserved countryspecific heterogeneity, there is a direct impact of the DES per caput on growth that is not mediated through life expectancy.
A potential solution to the paradox regarding the low rate of growth of SSA also appears in the results presented in Table 7. This is because, in contrast to our earlier results, the magnitude of the coefficient associated with the SSA dummy variable is halved when life expectancy is included in the regression and it is marginally significant at the usual levels of confidence (one exception to this is given by the quadratic specification presented in column (7), where the associated tstatistic is equal to 1.941). This is in sharp contrast to the usual results reported in the literature concerning African growth (e.g. Easterly and Levine, 1997), where the dummy variable remains highly significant. This result, it should be obvious from our results that include nutritional variables, is robust to the inclusion of the PFI or the DES per caput. Alternative explanations for the poor growth performance of SSA, such as those based on the high degree of ethnolinguistic fragmentation of the continent, never allow one to "kill the dummy".
Since the appearance of Lucas's (1988) seminal article on learning or doing, the importance of human capital in the growth process has been intensely studied by economists. Mankiw, Romer and Weil (1992) constitutes the bestknown quantitative assessment of the validity of the augmented Solow model in which human capital enters the production as a complementary factor input.
Empirical results corresponding to the hypothesis that schooling is one of the transmission mechanisms through which nutritional concerns impact the growth rate of GDP per caput are presented in Table 8. As with the case of life expectancy, results are presented based on simple pooled estimation, the between estimator, and the within estimator which controls for countryspecific fixed effects. The results are similar to those in the case of life expectancy, although a number of specificities emerge.
First, the coefficient associated with schooling is generally statistically significant in the basic pooled regression results (columns (1), (4) and (7)), and its standard error increases when one moves to results based on the between estimator (columns (2), (5) and (8)); it becomes negative, though statistically indistinguishable from zero, once the within estimator results are considered (columns (3), (6) and (9)). This result is wellknown in the context of panel growth regressions which control for unobserved countryspecific effects, and it is sometimes seen as something of a puzzle. It should not be. Indeed, as noted by Barro and Lee (1993), the neoclassical growth model would predict, in its closed economy form, a negative and statistically significant coefficient on schooling (the initial level of schooling, that is), just as one expects a negative coefficient on the initial level of GDP per caput if convergence effects are present. As they put it : "if there are diminishing returns to reproducible factors, as in the usual neoclassical growth model for a closed economy..., then an equiproportionate increase in [initial GDP per caput, initial schooling, and initial life expectancy] would reduce [the growth rate of per caput GDP]."
In this context, it is interesting to note that Barro and Lee (1993) themselves, when considering a panel regression using 3SLS over two decades in which male and female schooling appear separately, find a negative and statistically significant coefficient associated with female schooling, which they ascribe to "less female [schooling] attainment [signifying] more backwardness and accordingly higher growth potential through the convergence mechanism." (p. 277). Be this as it may, it will be seen below that the coefficient associated with schooling is negative and statistically significant when it is endogenized within the context of GMM estimation.
TABLE 8
PFI, DES per caput, and economic growth
Transmission mechanisms : schooling
(tstatistics below coefficients)
Dependent variable : 
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
(8) 
(9) 
Method of estimation 
OLS 
between 
within 
OLS 
between 
within 
OLS 
between 
within 
Intercept 
0.091 
0.113 
0.017 
0.021 
0.154 
0.199 

3.522 
2.620 
1.034 
0.831 
4.861 
3.486 

1960s dummy 
0.021 
0.007 
0.023 
0.008 
0.022 
0.007 

7.275 
1.174 
8.022 
1.296 
7.848 
1.253 

1970s dummy 
0.017 
0.011 
0.020 
0.012 
0.019 
0.012 

5.162 
2.979 
6.170 
3.367 
5.787 
3.179 

Africa dummy 
0.011 
0.011 
0.013 
0.013 
0.013 
0.013 

2.423 
2.153 
3.118 
2.355 
3.409 
2.579 

Latin America dummy 
0.014 
0.014 
0.014 
0.014 
0.016 
0.017 

5.005 
3.370 
4.342 
3.009 
5.178 
3.776 

Log of initial GDP (by decade) 
0.006 
0.006 
0.022 
0.006 
0.005 
0.025 
0.007 
0.007 
0.023 
2.411 
1.719 
2.694 
1.865 
1.147 
2.810 
2.247 
1.588 
2.651 

Log schooling 
0.008 
0.006 
0.011 
0.010 
0.012 
0.013 
0.010 
0.010 
0.013 
1.972 
1.123 
0.957 
2.719 
2.050 
1.163 
2.789 
1.927 
1.107 

Nutritional variables 

100  PFI (%) 
0.002 
0.002 
0.001 

5.383 
3.924 
2.449 

DES per caput (kcal/day) 
1.0E05 
9.25E06 
1.94E05 
1.46E04 
1.84E04 
7.69E05 

2.411 
1.258 
2.583 
6.484 
4.394 
2.238 

DES per caput squared 
2.46E08 
3.14E08 
1.14E08 

6.075 
4.22721 
1.7037 

Mean of dependent variable 
0.021 
0.020 
0.021 
0.020 
0.019 
0.020 
0.020 
0.019 
0.020 
Adjusted R^{2} 
0.383 
0.416 
0.590 
0.333 
0.329 
0.584 
0.390 
0.440 
0.586 
0.020 
0.015 
0.016 
0.021 
0.016 
0.016 
0.020 
0.015 
0.016 

Hausman test : Random effects 
0.000 
0.027 
0.046 

Number of observations 
261 
94 
261 
258 
93 
258 
258 
93 
258 
Note : standard errors are White heteroskedasticityconsistent; threshold value of DES per caput in quadratic specifications where coefficients are statistically significant (columns (7) and (8)) : 2967 and 2929 kcal/day, respectively. Data source. Log of 1 + average years of school attainment, quinquennial values (196065, 197075, and 198085) : Barro and Lee (1993).
The second result presented in Table 8 that is worthy of mention is that the PFI is statistically significant in all three specifications in which it appears ((columns (1), (2) and (3)). Since schooling is included in all three regressions, it follows that, as with life expectancy, there is a direct impact of the PFI on growth that is not mediated through its impact on schooling. In fact, compared with the results presented in column (3) of Table 3 (within estimation of the same equation without including schooling), the impact of the PFI on the growth rate of GDP is of the same order of magnitude and is estimated more precisely. In the case of the DES per caput, much the same obtains. The associated coefficient remains statistically significant in the pooling results, and does so in the context of "within" estimation as well (the coefficient is of the same order of magnitude as that presented in column (5) of Table 3). As with life expectancy, the quadratic specification with respect to the DES per caput remains robust to the inclusion of schooling for the pooling and between results, while the coefficients are estimated less precisely once one moves to countryspecific fixed effects. In contrast to the results based on life expectancy, it is interesting to note that the SSA dummy remains statistically significant, indicating that it is differences in terms of life expectancy that explain the slow growth of SSA economies, while differences in schooling do not.
These results imply that there is a potentially interesting story regarding life expectancy as a transmission mechanism whereby nutritional concerns indirectly affect the growth rate of GDP per caput, although it is clear that the direct impact of nutritional variables on growth through their effect on the productivity of labour will remain important since the fall in the coefficient associated with the DES per caput or the PFI when schooling or life expectancy are introduced into the equation is negligible. In the case of schooling as a transmission mechanism, on the other hand, the results are less promising. Disentangling the contribution of the indirect impact from the direct impact of nutritional variables on growth will be dealt with at greater length below in the context of the estimation of structural model by instrumental variable techniques.
9 Of course, the absence of a statistically significant coefficient associated with the nutritional variable in the reduced form regression could obtain because the two terms on the righthandside of equation (20) are of opposite sign and simply cancel out.
10 This line of reasoning is explained at greater length in Arcand, Guillaumont and Guillaumont Jeanneney (2000) in terms of Montecarlobased simulations, though the basic intuition should be obvious.