Despite the substantial progress that has been made in recent years in explaining crosssectional differences in growth performance, as well as the plethora of variables that are advanced by different authors as providing a piece of the explanation, remarkably little has been done lately in terms of aggregate crosssectional econometrics in order to evaluate the impact of nutritional concerns on economic growth.
The converse, of course, is not true. In a recent paper, one of the most prominent authors associated with the new empirical growth literature, William Easterly, finds, among a multitude of other indicators of the quality of life, that daily calorie intake increases with per caput GDP, the coefficient associated with the latter, when estimating in firstdifferences (in order to control for unobserved, time invariant, countryspecific effects) and instrumenting using GDP per caput lagged two periods (in order to control for random measurement error or potential endogeneity) is equal to 538 with a corresponding tstatistic of 3.22. This implies that an increase in GDP per caput of 1 percent is associated with an increase in daily calorie intake of 538 kcal / day. The purpose of the present paper is essentially to reverse the causality in a regression such as Easterly's in order to assess the contribution of nutritional concerns to the growth rate of GDP per caput. As such, the prevalence of hunger is not only an indicator of what Amartya Sen would refer to as "deprivation" which is, of course, an extremely important cost in and of itself but also potentially a fetter that moves one away from the efficient frontier.
One of the main findings of this paper is that there is a statistically significant, and quantitatively important impact of nutrition on growth, and that this result is robust to the use of three different datasets and to the application of a multitude of different econometric procedures, ranging from simple pooled timeseries crosssection regressions estimated using ordinary least squares (OLS), the inclusion of countryspecific fixed effects, a switching regression specification with unknown sample separation estimated by Maximum Likelihood, Generalized Method of Moments (GMM) estimation preceded by firstdifferencing, and GMM estimation in which a growth regression is paired with a life expectancy equation. Interestingly, it would appear that the effect of nutrition on growth operates in part directly, probably through its impact on labour productivity, as well as indirectly, through improvements in life expectancy which, in turn, spur faster growth.
In theoretical terms, these econometric results concerning the direct effect of nutrition on growth are easy to justify on the basis of the substantial literature that goes back to Leibenstein (1957), Mazumdar (1959), Mirlees (1975), Stiglitz (1976), Bliss and Stern (1978), or Dasgupta and Ray (1984), linking better nutrition to higher labour productivity. In terms of the ample, though sometimes controversial, microeconometric evidence regarding the impact of nutrition on labour productivity, our results should also come as no surprise. A number of papers from the 1980s all find substantial effects of nutrition on labour productivity (for the standard surveys, see Barlow, 1979, Martorell and Arrayave, 1984, Strauss, 1985, Srinivasan, 1992, Behrman and Deolalikar, 1988), although these results would appear to be extremely sensitive to specification and, in particular, to controlling for householdspecific fixed effects.^{1} The results presented in what follows would appear to indicate that many of the findings reported at the microeconomic level translate into statistically discernible effects at the aggregate level.
The paper which is perhaps the closest in spirit to what follows is Wheeler (1980) (see Gwatkin, 1983, for a survey of the crosscountry work that was done in the late seventies and early eighties), who estimated, using the relatively scarce data available twenty years ago, a system of four equations using threestage least squares (3SLS).^{2} His system comprised an output equation, a nutrition equation, a health equation, and an education equation, with the three latter variables all appearing in the production function as determinants of "effective labour". All equations were specified in terms of growth rates. Wheeler found an elasticity of output with respect to daily calorie availability of 2.652, which was significant at the usual levels of confidence (standard error of 0.391). While his results are easy to criticize today given the advances in data availability and in econometric technique, they do indicate that a statistically significant impact of nutrition on growth had been identified twenty years ago.
The results should also come as no surprise in light of recent work undertaken by the Development Research Group of the World Bank: McCarthy, Wolf and Yu (2000) find, for a substantial number of countries in subSaharan Africa, that the presence of malaria reduces the annual growth rate of GDP per caput by 0.25 percentage points. Thus, a disease that has an important direct effect on human welfare also entails important efficiency losses. The results presented in the present paper suggest that the costs associated with hunger, in terms of lost growth, are probably significantly greater than those associated with malaria.
The structure of the paper is as follows. In the remainder of part 1, the stylized facts concerning the relationship linking the growth rate of GDP per caput to two measures of nutritional status are established, namely (i) the prevalence of food inadequacy (PFI) and (ii) the dietary energy supply (DES) per caput, as reported in the Sixth World Food Survey of the FAO. A pooled timeseries crosssection dataset is used in which each observation corresponds to a countrydecade as well as with the standard longrun dataset, covering a thirtyyear time span, first analysed by Levine and Renelt (1992). A theoretical interpretation of the results is provided in the context of an extremely simple endogenous growth model of the "AK" variety, and in a neoclassical model in the tradition of Solow. The potential existence of (i) nonlinearities in the relationship and (ii) threshold effects of the impact of the DES per caput on growth which depend upon the initial level of GDP per caput are established.
Part 2 considers the robustness of the preliminary results presented in part 1. Loosely speaking, the basic empirical results are subjected to a battery of statistical procedures with the aim of destroying them. In particular, the criticisms of FAO data recently formulated by Svedberg (1999) are taken into account, and the basic specification is estimated using a firstdifferencing procedure followed by Generalized Method of Moments (GMM) estimation which corrects, simultaneously, for the problems of countryspecific and random measurement errors raised by Svedberg. The result is that the statistically significant impact of the DES per caput and the PFI on the growth rate of per caput GDP is not only robust to this procedure but also increases in quantitative terms. The initial results are reestimated using countryspecific fixed effects, using the between estimator, and using an alternative dataset due to Sachs and Warner (1997a, 1997b). As with the GMMfirstdifferencing procedure, the basic result of a statistically significant impact of the DES per caput and the PFI on the growth rate remains.
Part 3 begins investigating those indirect transmission mechanisms by which nutritional status might affect the growth rate of GDP per caput, in contrast to the direct effect that operates through the productivity of the labour force. Two potential indirect transmission mechanisms based on human capital arguments are considered: schooling and life expectancy. Including measures of both of these variables in the basic specification, regardless of the estimation procedure that is chosen, yields roughly the same, statistically significant, coefficient on the nutritional variables. The conclusion is that, while an indirect effect of nutrition on growth operating through the impact of the human capital variables cannot be excluded, the direct effect (operating through labour productivity) is an important transmission mechanism in and of itself. Disentangling the relative contributions of the indirect versus the direct effects is dealt with in part 5.
Part 4 is motivated by the threshold effect and nonlinearities uncovered in the analysis of the preliminary results. Therefore, it examines the possibility of the existence of nutritionallygenerated "growth traps", in the sense that a country whose population is inadequately fed may be unable to emerge from a low level equilibrium onto a balanced growth path. A simple endogenous growth model is thus formulated that can, potentially, generate such nutritional growth traps. This theoretical model is then parameterized, using a switching regression specification with unknown sample separation, in which countries are divided into a high PFI and a low PFI regime, the distinguishing feature of the former being that convergence effects are absent and that the impact of the DES per caput is present, the distinguishing feature of the latter being that convergence effects are present and nutritional effects are absent. This model is estimated by Maximum Likelihood, and shows that a shortfall of two percentage points in the annual growth rate of GDP per caput can be accounted for by a country belonging to the high PFI regime. The issue of how countries are classified into the two regimes by the switching regression procedure is addressed. Perhaps the most interesting finding is that a group of five Near East and North Africa countries (Algeria, Morocco, Tunisia, Syria and Egypt) managed to emerge from the high PFI regime into the low PFI regime during the 1970s.
Part 5 returns to the issue of identifying the relative magnitudes of the direct effect of nutrition on growth versus its indirect effect mediated by human capital variables. To that effect, the section begins with the estimation, by GMM, of a system of two equations in which a growth regression is paired with a life expectancy equation. The DES per caput enters the growth regression directly, but also impacts growth indirectly through its effect on life expectancy, which itself is included in the growth equation and is assumed to be endogenous. It is found that a more complex specification in which a threeequation system is considered in which the additional regression is given by a schooling equation is statistically fragile. Therefore, settle on a twoequation system comprising a growth equation and a life expectancy equation is chosen, but where schooling appears in the growth equation and is assumed to be endogenous (the hypothesis that schooling is exogenous is strongly rejected by a test of this overidentifying restriction). This specification allows me to empirically separate the direct from the indirect impact of the DES per caput on growth. In quantitative terms : an increase of the DES per caput to 2770 kcal/day in those countries where it is below that level would increase the annual growth rate of GDP per caput by 0.53 percentage points directly and by 0.70 percentage points indirectly, yielding a total increase in the annual growth rate of 1.23 percentage points.
Part 6 provides a quantitative assessment of the impact on the annual growth rate of GDP per caput of eliminating food inadequacy or increasing the DES per caput to 2770 kcal/day, based on 8 different estimation procedures for the case of the PFI and 17 different estimation procedures for the case of the DES per caput. For subSaharan Africa, the estimated shortfall in the annual growth rate of GDP per caput caused by inadequate nutrition ranges from 0.64 percent to 4.04 percent, even when one assumes that the PFI is overestimated or the DES per caput is underestimated by 20 percent. Ironically, the higher figure corresponds to the estimation procedure (GMM with firstdifferencing) that directly addresses the concerns regarding the data that were raised by Svedberg (1999). These figures imply, over a 30 year period, that the mean GDP per caput of subSaharan African nations would have been between 200 and 2 500 dollars higher had food inadequacy been eliminated. The sample is then divided into countries with abovemedian and belowmedian PFI. Using the simple pooling results that are probably the least controversial in terms of the existing growth literature, it is found that the gap in the mean GDP per caput between these two groups of countries would have been narrowed from $US 5 000 to $US 3 250 in 1990 had the DES per caput been raised to 2 770 kcal / day in the abovemedian PFI countries. Part 7 concludes, and offers some thoughts regarding the implications concerning poverty that can be drawn from my results.
Figure 1
Log of GDP per caput as a function of the DES per caput (kcal/day)
Figure 2
Growth rate of GDP per caput as a function of the DES per caput
As illustrated by Figure 1, which plots the logarithm of per caput GDP against the dietary energy supply (henceforth, DES) per caput in kcal/day, the correlation between income and nutrition is a wellestablished empirical regularity (see, for example, the paper by Easterly alluded to above). Each observation in Figure 1 corresponds to a countrydecade. While the link between income and nutrition is clear even in a one dimensional plot, this cannot be said of the relationship linking the DES per caput to the growth rate of per caput GDP, as illustrated in Figure 2.
Nevertheless, moving to elementary regression analysis suggests that a link does indeed exist. Indeed, if one regresses the growth rate of GDP per caput on two decade dummies, two continent dummies and 100 minus the prevalence of food inadequacy (henceforth, PFI), the coefficient associated with the PFI is positive and significantly different from zero at the usual levels of confidence.^{3} The estimated relationship is given in column (3) of Table 1. In column (6) of the same table, a similar relationship is considered, where the proportion of the PFI is replaced by the DES per caput. Again, the coefficient associated with the nutritional variable is statistically significant at the usual levels of confidence.^{4}
It is, of course, possible to argue that the observed correlation between the growth rate of per caput GDP and the nutritional variables is merely a statistical artefact that stems from the exclusion, in the two regressions, of GDP per caput. That is, it may be that the nutritional variables, given their high level of correlation with GDP per caput, are simply picking up the latter's impact on growth. Columns (4) and (7) of Table 1 show that this is not the case. When one includes the initial level of GDP per caput in both specifications, the coefficient associated with the nutritional variables remains statistically significant and of the same order of magnitude. These preliminary results suggest that nutritional concerns have an impact on economic growth, and that this effect does not stem from omitted variables bias. Indeed, the coefficients associated with log GDP per caput are negative, though statistically insignificant at the usual levels of confidence. This corresponds to the wellknown absence of unconditional convergence : when additional explanatory variables, such as measures of human capital (health or schooling) are included in the regression, as shall be seen below, the conditional convergence effects are, as expected, negative and statistically significant.
TABLE 1
Prevalence of food inadequacy (PFI), dietary energy supply (DES) per caput, and economic growth
Benchmark results and nonlinearities in the relationship
Method of estimation : OLS (tstatistics below coefficients)
Dependent variable : growth rate of 
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
(8) 

Nutritional variable 
none 
PFI 
DES per caput 

Intercept 
0.018 
0.008 
0.060 
0.056 
2.755 
0.012 
0.003 
0.120 

8.124 
0.604 
2.776 
2.468 
2.232 
1.463 
0.242 
4.033 

1960s dummy 
0.021 
0.022 
0.022 
0.020 
0.019 
0.023 
0.022 
0.021 

8.001 
8.141 
8.188 
7.437 
6.969 
8.432 
8.147 
7.867 

1970s dummy 
0.019 
0.019 
0.019 
0.018 
0.017 
0.020 
0.019 
0.018 

6.234 
6.407 
6.038 
5.868 
5.769 
6.396 
6.297 
6.033 

Africa dummy 
0.022 
0.020 
0.014 
0.016 
0.011 
0.014 
0.016 
0.015 

7.586 
5.039 
3.653 
3.726 
2.478 
4.075 
4.190 
4.316 

Latin America dummy 
0.019 
0.019 
0.016 
0.017 
0.010 
0.014 
0.013 
0.015 

6.635 
6.329 
5.568 
5.614 
3.195 
4.546 
4.068 
4.893 

Log of initial GDP (by decade) 
0.001 
0.003 
0.008 
0.003 
0.004 

0.733 
1.594 
3.395 
1.392 
1.589 

Estimated annual rate of 
1.16E04 
2.82E04 
7.59E04 
3.24E04 
3.58E04 

convergence 
0.725 
1.488 
3.324 
1.334 
1.505 

Nutritional variables 

100  PFI (%) 
0.001 
0.001 
0.104 

3.659 
4.113 
2.336 

(100  PFI (%)) ^{2} 
0.0013 

2.428 

(100  PFI (%) )^{3} 
5.23E06 

2.539 

DES per caput (kcal/day) 
9.59E06 
1.38E05 
1.11E04 

3.957 
3.432 
5.201 

DES per caput, squared 
1.81E08 

4.725 

Mean of dependent variable 
0.020 
0.020 
0.020 
0.020 
0.020 
0.019 
0.019 
0.019 

Adjusted R^{2} 
0.293 
0.294 
0.322 
0.326 
0.350 
0.306 
0.309 
0.340 

F test (zero slopes), pvalue 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 

0.022 
0.022 
0.021 
0.021 
0.021 
0.021 
0.021 
0.021 

Number of observations 
330 
328 
322 
320 
320 
316 
314 
314 
Note: each observation corresponds to a countrydecade; standard errors are White heteroskedasticityconsistent; threshold value of DES per caput in quadratic specification (column (6)) : 3066 kcal/day. Data source. Growth rate of GDP per caput : World Bank National Accounts; initial GDP per caput: Summers and Heston (1991); DES per caput and PFI : The Sixth World Food Survey (Rome: FAO, 1996).
It is worth putting these initial results in perspective from the quantitative standpoint : an increase of one standard deviation (508 kcal/day) from the mean DES per caput in the sample (2535 kcal/day) increases the annual growth rate of GDP per caput by 0.7% : over the medium to long term, it is safe to say that this is a substantial effect, the mean annual growth rate of GDP per caput in the sample being 2.0%. Similarly, a decrease of one standard deviation in the PFI (7.05) would also increase the annual growth rate of GDP per caput by 0.7%. Eliminating food inadequacy entirely would raise the growth rate of per caput GDP by 0.64% (the mean value of food inadequacy being of 6 percent in the full sample). These numbers would of course be even larger if one confined one's attention to those countries where the PFI is particularly large. Note finally that the dummy variable indicating that an observation corresponds to a subSaharan African (henceforth, SSA) country is negative and highly significant at the usual levels of confidence. This corresponds to the wellknown puzzle of the lower rate of economic growth of SSA which is usually robust to the inclusion of additional explanatory variables (see, e.g. Easterly and Levine, 1997, although Sachs and Warner, 1997b, claim to have solved the puzzle). As will be shown below, in contrast to the usual findings of the literature, that the Africa dummy will become insignificant once health indicators and nutritional variables are both included in the specification. It would therefore seem that African specificity in terms of health and nutrition lie behind the puzzle of the low growth rate of SSA.
The most obvious manner of formalizing the preceding empirical results is within the context of the simplest endogenous growth model of the "AK" variety in the tradition of Rebelo (1991). Let the effective labour input be given by:
(1)
where L_{t} is the labour force, m is the PFI and is a parameter; therefore represents the productivity of labour. For the time being, m will be treated as an exogenous parameter with respect to the dynamics of the model. Let K_{t } represent the stock of physical capital. As is usual in endogenous growth models, the labour force is normalized to one (L_{t }= 1)and zero population growth is assumed.^{5} Assuming an additively separable intertemporal utility function with preferences that satisfy constant relative riskaversion (CRRA) and exponential discounting (at rate ), the representative consumer's optimization problem is given by :
(2) s.t.
(3)
(4)
where the first constraint represents the AK production technology with constant returns to physical capital (Y_{t } is simply aggregate output and A represents total factor productivity) and the second constraint gives us the law of motion of the stock of physical capital.^{6} The corresponding Hamiltonian is given by:
(5)
where is the costate variable. By an elementary application of Pontryagin's Maximum Principle and the usual manipulations, the steady state growth rate of consumption, the capital stock, and the growth rate are obtained as:
(6)
The steadystate growth rate of per caput GDP will thus be a decreasing function of the PFI, as we found empirically in columns (3) and (4) of Table 1. If 1  m is replaced by the DES per caput, a similar model corresponding to the results presented in columns (6) and (7) of Table 1 nis obtained. One manner of interpreting the preceding formalization (and, for that matter, the neoclassical model that follows below) is in terms of the nutritional efficiency wage model, first suggested by Harvey Leibenstein (1957). As noted by Bliss and Stern (1981), nutritional levels are sufficiently low in many LDCs for workers' productivity to be significantly increased by an increase in food consumption.
An alternative formalization of the empirical regularities uncovered in our initial empirical analysis is provided by a simple neoclassical growth model in the tradition of Solow. Assuming a constant returns to scale CobbDouglas production technology with aggregate capital and effective labour as inputs, one obtains, using the same parameterization of the effective labour input as above (see equation (1)) :
(7)
where is a parameter. Assuming neoclassical saving behaviour , where s denotes the investment rate, one obtains the usual equation for the rate of growth of the capital stock, per caput:
(8) ,
where k_{t} = K_{t} / L_{t} denotes capital per caput and
n denotes the (constant) growth rate of the population .
In steadystate , the level of the capital stock per caput is thus given by:
(9)
which implies that output per caput in steadystate is given by:
(10)
Taking logarithms, one obtains an "augmented" Solow equation for the determinants of the steadystate level of per caput GDP :
(11)
Linearizing around the steadystate, one obtains the standard convergence specification for the neoclassical growth model :
(12)
where represents the annual rate of convergence. Simple estimations based on equation (12) are presented in Table 2, where the Levine and Renelt (1992) datasetis used.^{7} Again, as with the initial results presented in Table 1, the PFI as well as the DES per caput are both found to be highly significant variables, in this case in logarithmic form within the context of the standard Solow neoclassical model. The estimated annual rate of convergence obtained in these regressions ranges from 0.6 percent in the absence of nutritional variables in the unrestricted specification, to 3 percent in the restricted specification which includes the PFI.
It is of course quite possible that the empirical regularity uncovered with the simple linear relationships estimated above hides more complex phenomena linked to threshold effects or nonlinearities in the effect of the PFI or the DES per caput on growth. Consider an alternative specification of the regression presented in column (7) of Table 1 in which DES per caput appears in quadratic as well as in linear form. Results for this specification are presented in column (8) of Table 1. It is clear that both the linear and quadratic terms are highly significant at the usual levels of confidence; moreover, the estimated coefficients yield an "invertedU" relationship between the growth rate of per caput GDP and the DES per caput once decade and continent dummies and a convergence effect are controlled for.
The threshold level of the DES per caput at which the impact of daily calorie intake on growth begins to become negative is equal to 3066 kcal/day. Sixty observations out of the 314 used in the regression presented in column (8) of Table 1 correspond to countrydecades with a level of the DES per caput greater than this threshold value. The mean value of per caput GDP for this subsample is equal to US$ 6 447, whereas the full sample mean is US$ 1 993.
Figure 5 illustrates the change in the marginal impact of the DES per caput, expressed in kcal/day, on the growth rate of per caput GDP, as the marginal impact is evaluated between 1500 and 4000 kcal / day. As shall be seen below, the quadratic specification in the context of the DES per caput variable is often robust to changes in specification or estimation procedure. For the PFI, on the other hand, experimentation revealed that a cubic specification, presented in column (5) of Table 1, offered the best fit to the data. This polynomial form is, however, not robust to the battery of tests that will be presented below. A graphical illustration of the quadratic relationship in terms of the DES per caput in provided by Figure 4, whereas the cubic representation in terms of the PFI is illustrated in Figure 3. Note that the values on the vertical axis in both Figures 3 and 4 are per caput growth rates net of the values predicted by the regressors other than nutritional variables. Thus, differences between GDP growth rates in the two figures are due tot he different scales in which the variables are measured. The lines in the two figures correspond to the functional forms in which the nutritional variables enter the "chosen" regressions.
TABLE 2
PFI, DES per caput and economic growth : Augmented Solow model
Method of estimation : OLS (tstatistics below coefficients)
Dependent variable : 
(1) 
(2) 
(3) 
Intercept 
4.775 
7.193 
27.576 
3.190 
5.435 
2.897 

Log of initial GDP per caput 
0.177 
0.492 
0.371 
1.672 
4.966 
3.306 

Log of investment share 
3.687 
2.154 
2.840 
5.681 
2.725 
3.616 

Log of growth rate of population 
0.874 
0.239 
0.469 
4.392 
1.210 
2.067 

Nutritional variables 

Log PFI (%) 
1.264 

5.313 

Log DES per caput 
4.198 

3.720 

Estimated annual rate of convergence 
0.006 
0.023 
0.015 
in unrestricted specification 
1.502 
3.296 
2.317 
Estimated annual rate of convergence 
0.010 
0.031 
0.023 
in restricted specification 
1.962 
3.473 
2.679 
Estimated capital share 
0.601 
0.350 
0.476 
in restricted specification 
15.751 
3.503 
6.270 
Mean of dependent variable 
2.020 
2.029 
1.971 
Adjusted R^{2} 
0.430 
0.598 
0.478 
1.400 
1.187 
1.358 

Number of observations 
100 
98 
94 
Note: restricted specification corresponds to imposing that the coefficients associated with log investment share and log growth rate of the population are equal and of opposite sign; the restriction is rejected in all cases with an associated pvalue that is smaller than 0.001.
Data source: Initial GDP per caput: Summers and Heston (1991); investment share of GDP : World Bank National Accounts; growth rate of population : World Bank Social Indicators. Same data as that used by Levine and Renelt (1992); data currently available at: http://www.worldbank.org/html/prdmg/grthweb/ddlevren.htm.
In addition to nonlinearities, threshold effects are also a possibility. In columns (7) and (8) of Table 3, estimates are presented corresponding to the inclusion of an interaction term given by the product of the DES per caput by the logarithm of initial GDP per caput (column (8)). In column (7) it is 100 minus the PFI that is multiplied by the logarithm of initial GDP per caput. In both cases, the multiplicative term is significant at the usual levels of confidence. In the case of the DES per caput, the value of initial GDP per caput at which the marginal impact of the DES per caput becomes negative is equal to $US 10 853. For the PFI, on the other hand, there is the somewhat surprising result of a marginal impact of the prevalence of food adequacy increasing with the level of income, indicating that the positive impact on growth of reductions in the PFI is larger at higher levels of income.
Figure 3
Impact of the PFI on the growth rate of per caput GDP
Source : regression 5 of Table 1; vertical axis corresponds to growth rate of GDP per caput, purged of impact of the intercept, two continent dummies, log of initial GDP per caput, and two decade dummies.
Figure 4
Impact of the DES per caput on the growth rate of per caput GDP
Source : regression 8 of Table 1; vertical axis corresponds to growth rate of GDP per caput, purged of impact of the intercept, two continent dummies, log of initial GDP per caput, and two decade dummies.
Figure 5
Quadratic specification
Marginal impact of the DES per caput on the growth rate of per caput GDP
Note : computed from the estimates presented in column (8) of Table 1; the solid line corresponds to the point estimate of the marginal impact of the DES per caput on the growth rate of GDP per caput, evaluated between 1500 and 4000 kcal / day ; dotted lines correspond to the one standarddeviation confidence interval around this point estimate.
Interestingly, this result will find some support in the context of the regressions run using the Sachs and Warner (1997a, 1997b) dataset that will be presented below. Both the results in terms of the quadratic specification and those in terms of interaction variables indicate that some form of conditional impact of nutrition on growth is at work. In section 4, this possibility in the context of a switching regression specification will be formally investigated.
TABLE 3
PFI, DES pe caput, and economic growth
Controlling for unobserved, countryspecific heterogeneity and interaction effects
(tstatistics below coefficients)
Dependent variable : 
(1) 
(2) 
(3) 
(4) 
(5) 
(6) 
(7) 
(8) 

Method of estimation 
"within estimator" 
OLS 

Intercept 
0.270 
0.195 

1.717 
3.250 

1960s dummy 
0.021 
0.008 
0.008 
0.009 
0.009 
0.008 
0.020 
0.022 

8.330 
2.223 
1.918 
2.119 
2.213 
2.140 
7.349 
7.928 

1970s dummy 
0.019 
0.013 
0.013 
0.013 
0.013 
0.013 
0.018 
0.018 

7.598 
4.890 
4.314 
4.499 
4.804 
4.699 
5.779 
6.144 

Africa dummy 
0.016 
0.015 

3.637 
4.042 

Latin America dummy 
0.014 
0.016 

4.510 
4.854 

Log of initial GDP per caput (by decade) 
0.026 
0.027 
0.027 
0.032 
0.032 
0.052 
0.022 

4.569 
3.779 
3.824 
4.113 
3.962 
2.184 
2.753 

Estimated annual rate of 
0.003 
0.003 
0.003 
0.003 
0.003 

4.510 
4.515 
4.548 
5.120 
5.006 

Nutritional variables 

100  PFI (%) 
0.001 
0.065 
0.002 

1.717 
1.300 
1.495 

(100  PFI (%))^{2} 
8.05E04 

1.312 

(100  PFI (%))^{3} 
3.29E06 

1.334 

100  PFI (%) X Log of initial GDP 
0.001 

2.125 

DES per caput (kcal/day) 
2.20E05 
4.34E05 
9.19E05 

3.227 
1.311 
4.209 

DES per caput, squared 
4.28E09 

0.655 

DES per caput X Log of initial GDP 
9.89E06 

3.555 

Mean of dependent variable 
0.020 
0.020 
0.020 
0.020 
0.018 
0.018 
0.020 
0.019 

Adjusted R^{2} 
0.483 
0.534 
0.532 
0.532 
0.529 
0.527 
0.331 
0.330 

0.019 
0.018 
0.018 
0.018 
0.018 
0.018 
0.021 
0.021 

Hausman test : Random effects (H0) vs Fixed effects (H1), pvalue 
0.000 
0.000 
0.000 
0.000 
0.000 
0.000 
n.a. 
n.a. 

Number of observations 
330 
328 
320 
320 
314 
314 
320 
314 
Note: each observation corresponds to a countrydecade; standard errors are White heteroskedasticityconsistent; threshold value of log GDP per caput in multiplicative specification with DES per caput (column (6)) : 9.29221 (i.e., 10,853 US$). Data source : same as Table 1.
1 The comparison between the papers of Strauss (1986) and Deolalikar (1988), which use the same dataset, but where Deolalikar uses fixed effects and instrumental variables, is striking in this respect. Strauss finds effective family labour input to be increasing in daily calorie availability while Deolalikar finds that output is not affected by daily calorie intake. Mark Rosenzweig (1988), in his survey of labour markets in lowincome countries in the Handbook of Development Economics, is less convinced of the impact of daily calorie availability on labour productivity, stating that both of these studies "do not find much, if any, rigorous supporting evidence." (p. 727) For a more recent effort in this direction, see Haddad and Bouis (1991).
2 Fogel (1989) also considers the impact of nutrition, from an historical perspective, although the focus is more on the reverse causality.
3 The chosen continent dummies (subSaharan Africa and Latin America) are included so as to make the results directly comparable to much of the work undertaken by the Development Research Group of the World Bank.
4 It has correctly been pointed out by Ali Gürkan that statistical inference in growth regressions can be rendered dubious because of the potential heteroskedasticity induced by the very calculation of growth rates of GDP per caput. All pooling regression results reported in this paper were therefore run while correcting for this specific form of heteroskedasticity. Results do not differ in any significant manner from those obtained using a White correction, and the latter are therefore presented in order to render the findings more readily comparable with the existing literature.
5 This is to avoid the counterintuitive result, that obtains is most endogenous growth models, in which the steadystate growth rate of GDP per caput would be an increasing function of the growth rate of the population; indeed, the steadystate growth rate of GDP per caput would be an increasing function of the labour force itself in most endogenous growth models.
6 The usual notation is used whereby a "dot" above a variable indicates its derivative with respect to time; that is K_{t} = dK_{t} / dt.
7 See Levine and Renelt (1992) for the original contribution using this data, as well as Mankiw, Romer and Weil (1992) for the standard assessment of the neoclassical model.