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.

## 3.1 Direct versus indirect transmission mechanisms

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 :

1. there is a direct relationship between growth and malnutrition but no indirect link, i.e.,
2. and

3. there is an indirect relationship between growth and malnutrition but no direct effect, i.e.,
4. and

5. both (i) and (ii) obtain.9

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).

## 3.2 Life expectancy

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 long-run growth regression based on thirty year averages. The question is whether this result will hold up within the context of our pooled country-decade 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 time-series cross section (columns (1), (4) and (7)), OLS on country means (columns (2), (5) and (8)), and panel estimation which controls for country-specific 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 country-specific 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 country-specific 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 country-specific random effects is soundly rejected by the usual Hausman test in favour of the fixed-effects specification in all cases.

The contrast with the results obtained using the Sachs-Warner 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 long-run 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 country-specific 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

(t-statistics below coefficients)

 Dependent variable : growth rate of per caput GDP (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) 4.61E-06 1.40E-07 2.41E-05 8.80E-05 1.03E-04 5.29E-05 1.134 0.021 3.286 4.444 2.907 1.521 DES per caput, squared -1.53E-08 -1.84E-08 -5.72E-09 -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 R2 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 (H0) vs Fixed effects (H1), p-value 0.040 0.001 0.007 Number of observations 292 100 292 291 100 291 291 100 291

Note : standard errors are White heteroskedasticity-consistent; 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 country-specific 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 t-statistic 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".

## 3.3 Schooling

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 best-known 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 country-specific 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 well-known in the context of panel growth regressions which control for unobserved country-specific effects, and it is sometimes seen as something of a puzzle. It should not be. Indeed, as noted by Barro and Lee (1993), the neo-classical 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 neo-classical 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

(t-statistics below coefficients)

 Dependent variable : growth rate of per caput GDP (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) 1.0E-05 9.25E-06 1.94E-05 1.46E-04 1.84E-04 7.69E-05 2.411 1.258 2.583 6.484 4.394 2.238 DES per caput squared -2.46E-08 -3.14E-08 -1.14E-08 -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 R2 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(H0) vs Fixed effects (H1), p-value 0.000 0.027 0.046 Number of observations 261 94 261 258 93 258 258 93 258

Note : standard errors are White heteroskedasticity-consistent; 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 (1960-65, 1970-75, and 1980-85) : 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 country-specific 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 right-hand-side 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 Montecarlo-based simulations, though the basic intuition should be obvious.