## EMPIRICAL RESULTS

Introduction

The economic history of the post-Second World War period has been full of growth miracles and disasters. Since Solow’s (1956) seminal work, economists have made significant progress in understanding differences in cross-country economic growth. Most of this new understanding, including the so-called unconditional and conditional convergences, can be illustrated by the following simple model, which we use as the starting point for our empirical analysis.[25]

Assume that each economy has a balanced growth path in which every variable grows at a constant rate, and this steady-state value of physical capital is equal to ki*, where subscript i represents the country concerned. At any point of time t, the deviation of actual k from the steady-state value will generate the following convergence growth:

 (48)

where a dot on top of a variable represents the time derivative of that variable, and l is the rate of convergence. Consider between time 0 and T that we have:

 (49)

Equation 49 decomposes the potential sources of economic growth into two parts. The first term on the right-hand side captures the pure convergence effect: i.e. growth rate depends on the country’s initial position relative to its (initial) balanced growth path. The second term captures the changes to steady state that may also spur growth. Earlier changes have greater effects than later changes.

The above example is given in the form of physical capital, but the same idea can easily be extended to include human capital and efficiency. The basic conclusion is that a country’s growth depends on its starting points relative to balanced growth paths, as well as on changes in those balanced growth paths. The variables included in the first term, those used to represent the initial state of the economy, are called “state variables”. Variables included in the second term, which are used to represent the subsequent changes in the steady state, are called “control”, “environmental” or “fundamental” variables. Work that assumes a common steady state for all countries is called “unconditional convergence analysis”, while a study that controls for a country-specific steady state is called a “conditional convergence analysis”.

Most of the current literature that adopts the convergence analysis approach to explain cross-country growth differences varies only in its choices of state and control variables. However, it is not uncommon to see results based only on the variables of specific interest. This is problematic because omitted variables, especially those that are found to exert a significant effect on growth, will produce biased (inconsistent) and inefficient estimates on the parameters of interest. However, we have no intention of listing all of the important variables that can explain growth because, unless a simultaneous system is adopted, the inclusion of variables that are closely related to nutritional status will obscure the full effect. Fortunately, several recent works have been successful in defining an appropriate list of variables that should be included in the regression. We draw heavily on these works in the following analysis. Barro and Sala-i-Martin (1999) describe the choice of these variables in detail. Among other authors, Islam (1995) discusses the methodology of using panel data for growth convergence analysis and Arcand (FAO, 2001) shows a battery of econometric methods to correct for potential problems.

Regression results

We are interested in heterogeneities in two dimensions. First, we aim to define the role that is played by the time frame in the estimated effect. As already mentioned, better nutritional status may improve growth gradually. As a result, the short- and long-run impacts may be different. Investigating different time frames produces a better exposition of the overall dynamics. Second, we are interested in how different countries (or groups) perform differently in terms of improved nutrition. Identifying the causes of such distinctions can help to create understanding of the differences in cross-section growth performances.

We start with the long-run case of 40 years, from 1960 to 1999, before moving on to the ten- and five-year samples. In each case, we divide the countries into subgroups, so that the sources of cross-section differences can be identified.

Pooled regressions: 1960-1999

Table 1a summarizes the results of the 40-year long-run analysis. We first calculated the growth rate of real GDP per capita from the latest World Bank data set. Initial per capita GDP is real GDP per capita for the year 1960. Initial DES is DES for 1961, as reported on FAO’s Web site.[26] In order to mitigate the effect of random measurement error in DES and real GDP per capita, we also studied the effects of using the average for 1961 and 1962 as the initial value.

In order to take “environment” changes into account, we added some popular variables to the right-hand side of the regression. Investment share, trade share and population growth rate all come from the latest World Bank dataset. Since investment share is the real investment share of GDP, it serves as a proxy for the saving rate in the augmented Solow model. Everything else holds constant, a higher saving rate results in a higher steady state, thus faster growth, given the same initial position. Population growth has exactly the opposite effect. None of these variables is expected to affect the long-run growth rate in a Solow framework.

If we deviate from the exogenous growth framework and adopt an endogenous growth model, such as the AK model or the human capital accumulation model discussed in the previous chapter, the saving rate and the population growth rate may have a long-run effect. In any case, their impact on economic growth is predictable.

TABLE 1A
DES and long-run economic growth (1960-1999): OLS

 Dependent variable: annual growth rate of per capita GDP 1960-1999 (1) (2) (3) Intercept -0.0050 0.0142 0.0057 (-0.34) (0.97) (0.33) Log of initial per capita GDP -0.0026 -0.0048 -0.0041 (-1.59) (-3.23) (-2.22) Initial DES 4.10e-6 6.35e-6 7.40e-6 (0.74) (1.28) (1.55) Investment share 0.0019 0.0016 0.0016 (5.72) (5.13) (4.94) Population growth rate -0.0051 -0.0028 -0.0035 (-2.24) (-1.51) (-1.65) Sub-Saharan Africa dummy -0.0163 -0.0171 (-3.75) (-3.78) Latin America and Caribbean dummy -0.0088 -0.0108 (-2.60) (-2.23) South Asia dummy -0.0053 -0.0059 (-1.29) (-1.36) Developing country dummy 0.0056 (0.79) Number of observations: 87 87 87 Adjusted R2: 0.48 0.55 0.55

Note: t-values in parentheses calculated with White-heteroscedasticity-consistent standard error.

We also used variables as proxies for the “fundamental” changes that enhance long-run growth permanently. One of these is DES. We speculated that better nutrition may improve the quality of labour and expedite the accumulation of human capital, thus the country may enjoy faster long-run growth. We also experimented with the trade share of GDP to check whether foreign trade serves as an additional growth engine. It turned out that foreign trade does not add significantly to the model, and so it is not reported in the results.

Finally, we added some dummy variables to account for regional effects. We also added a dummy for developing countries to check whether any effect for this specific group of countries had been omitted.

Evidence for conditional convergence is only weakly significant. After controlling for the “fundamentals”, we found that countries with lower initial incomes tend to grow faster. If a country’s initial income is 1 percent less than that of another country with the same fundamentals, it will grow 0.3 to 0.5 percentage points faster every year. Investment share contributes positively, and population growth negatively, to economic growth. Quantitatively, if the investment share increases by 10 percentage points, the long-run growth rate will increase by 1 to 2 percentage points, while a 1 percentage point increase in population will reduce economic growth by 0.3 to 0.5 percentage points. This is consistent with most other research findings.

Initial DES has a modest positive effect on economic growth. The estimates imply that an increase of 500 kcal/day of energy intake will increase the annual growth rate by 0.4 percentage points. Over 40 years, this represents a 17 percent difference.

If we use location dummies to represent specific fundamentals for countries within an area, it seems that all three regions (sub-Saharan Africa, Latin America and the Caribbean, and South Asia) converge to a relatively lower steady state. If we take 40 years as representing the long-run situation, these groups of countries have permanently lower growth rates. As discussed by Cho and Graham (1996), the poorest countries converge to lower steady states from above, while the richest countries converge to higher steady states from below. This explains why the growth rate is stalled for some developing countries. In fact, these countries are very close to their (low) steady state; the only factor that can boost their economic growth is having improved "fundamentals". As Table 1a shows, increasing DES has the potential to achieve that goal.

After adding the three location dummies, the developing country dummy has a negligible effect on growth. This implies that other developing countries are growing at a rate that is comparable with that of developed countries, after controlling for the first four variables (initial log GDP, initial DES, investment share, and population growth).

We also applied the variables column 1 to the subgroups of developing and developed countries. The results are reported in Table 1b. Although the convergence effect, savings and population growth assume the usual signs, initial DES does not contribute further to long-run growth. The null of constant parameters across these two groups of countries cannot be rejected at the usual confidence level.[27]

TABLE 1B
DES and long-run economic growth (1960-1999): OLS

 Dependent variable: annual growth rate of per capita GDP 1960-1999 (1) Developing country (2) Developed country Intercept -0.0063 0.0598 (-0.36) (2.22) Log of initial per capita GDP -0.0030 -0.0040 (-1.50) (-1.26) Initial DES 5.16e-6 4.63e-6 (0.78) (-0.60) Investment share 0.0020 0.0008 (5.36) (1.63) Population growth rate -0.0053 -0.0043 (-1.63) (-1.54) Number of observations: 65 22 Adjusted R2: 0.43 0.31

Notes: t-values in parentheses calculated with White-heteroscedasticity-consistent standard error. 114 countries total; 22 out of 27 developed countries and 65 out of 87 developing countries provide sufficient information for estimations.

TABLE 1C
DES and long-run economic growth (1960-1999): OLS

 Dependent variable: annual growth rate of per capita GDP 1960-1999 (1) Sub-Saharan Africa (2) Latin America and Caribbean (3) East and Southeast Asia Intercept 0.0011 -0.0014 0.0379 (0.05) (-0.03) (3.41) Log of initial per capita GDP -0.0064 0.0002 -0.0054 (-2.13) (0.03) (-2.19) Initial DES 6.94e-6 3.07e-6 3.42e-5 (1.04) (0.31) (4.19) Investment share 0.0021 0.0004 0.0009 (4.57) (0.57) (2.05) Population growth rate -0.0039 -0.0015 -0.0274 (-0.63) (-0.33) (-7.83) Number of observations: 26 21 7 Adjusted R2: 0.48 -0.19 0.82

Notes: t-values in parentheses calculated with White-heteroscedasticity-consistent standard error. 26 out of 36 countries in sub-Saharan Africa, 21 out of 21 in Latin America and the Caribbean and seven out of 11 in East and Southeast Asia provide sufficient information for estimations.

For Table 1c we estimated separately for the subgroups of sub-Saharan Africa, Latin America and the Caribbean, and East and Southeast Asia. Inonly the last group does initial DES show a positive impact on long-run growth. This group of countries also experienced the fastest growth in DES during the four-decade period. In particular, the impact of DES on economic growth for this group is almost five times as large as the full sample average reported in Table 1a, column 3. This translates into an increase of 1.7 percentage points in annual economic growth, amounting to a 96 percent difference over 40 years.

For this section we divided the sample period into four decades: 1960-1969, 1970-1979, 1980-1989 and 1990-1999. We used the DES for 1961, 1970, 1980 and 1990, respectively, and the logarithms of real GDP per capita in 1960, 1970, 1980 and 1990, respectively, as the initial values for each decade. The investment shares and population growth rates are averages for the respective decade.

Table 2a reports the OLS results. Column 1 gives pooled regressions, while columns 2 to 5 give independent regressions for each decade. The null that the four decades have the same coefficients is rejected at the usual level of confidence.[28]

Location dummies indicate that the sub-Saharan African growth rate was particularly low in the 1960s, the 1970s and the 1990s. While in Latin America and the Caribbean the worst periods were the 1960s and the 1980s. For South Asia, the 1970s and the 1990s saw the worst growth rates. Investment share showed constantly significant positive effects, while population growth had a mostly negative impact on growth.

The effect of the initial log GDP is mostly insignificant. The convergence effect is not significant for three out of four decades. The initial value of DES is even more puzzling because none of the positive effects are significant, and the negative effects are quite significant for the 1980s. In the pooled estimation, the initial impact of DES is significantly negative. This is drastically different from the long-run result. This difference implies that the short- and long-run impacts may diverge. In theory, given initial GDP, the positive effect of initial DES on growth derives from its positive impact on the quality of human capital. However, if initial DES also serves as a good proxy for initial GDP, it could yield a negative effect. These mixed and puzzling effects call for more elaborate estimation procedures.

TABLE 2A
DES and medium-run economic growth (by decade): OLS

 Dependent variable: annual growth rate of per capita GDP by decade (1) Pooled (2) 1960-1969 (3) 1970-1979 (4) 1980-1989 (5) 1990-1999 Intercept 0.0426 -0.0020 0.0354 0.0461 -0.0196 (2.94) (-0.08) (1.40) (1.98) (-0.78) Log of initial per capita GDP -0.0017 -0.0010 -0.0060 -0.0021 -0.0008 (-1.11) (-0.24) (-2.80) (-0.88) (-0.31) Initial DES -1.08e-5 6.77e-6 1.76e-6 -1.13e-5 4.11e-6 (-2.45) (0.69) (0.22) (-1.64) (0.60) Investment share 0.0014 0.0011 0.0017 0.0016 0.0014 (6.06) (2.64) (3.58) (3.81) (3.23) Population growth rate -0.0054 0.0034 -0.0015 -0.0126 -0.0017 (-2.88) (1.24) (-0.46) (-7.97) (-0.57) Sub-Saharan Africa -0.0151 -0.0174 -0.0173 -0.0033 -0.0100 (-3.72) (-2.59) (-2.46) (-0.41) (-1.45) Latin America and the Caribbean -0.0096 -0.0159 -0.0054 -0.0155 0.0020 (-2.82) (-3.26) (-0.84) (-2.88) (0.36) South Asia -0.0037 -0.0110 -0.0217 0.0106 -0.0161 (-0.83) (-1.27) (-2.71) (1.11) (-2.16) Number of observations: 380 75 89 103 113 Adjusted R2: 0.24 0.31 0.26 0.50 0.25

Notes: t-values in parentheses calculated with White-heteroscedasticity-consistent standard error. F(8,348) = 14.86, thus the null of constant coefficient across all four decades is rejected.

We used the least square dummy variable (LSDV),[29] the iterative generalized method of moment (ITGMM) with instrumental variables and iterative two-stage least squares (IT2SLS) to estimate the four-decade panel. The purpose of LSDV is to account for unobservable individual heterogeneity, while ITGMM can correct for possible measurement error problems. Iterative algorithms are adopted to improve the estimates’ small sample properties. In both the ITGMM and the IT2SLS procedures we took first difference across time, and then used the GDP and DES values lagged for two periods as instruments.

TABLE 2B
DES and medium-run economic growth (by decade): LSDV, ITGMM, IT2SLS

 Dependent variable: annual growth rate of per capita GDP by decade (1)LSDV (2)ITGMM (3)IT2SLS Log of initial per capita GDP 0.0230 -0.0155 -0.0228 (-4.97) (-0.90) (-1.37) Initial DES 73e-6 -4.00e-5 -4.00e-5 (-1.76) (-1.66) (-1.66) Investment share 0.0016 (7.42) Population growth rate -0.0067 (-2.43) 1970-1979 -0.0002 (-0.06) 1980-1989 -0.0100 (-2.96) 1990-1999 -0.0065 (-1.81) Number of observations: 380 181 181 Adjusted R2: 0.70 0.11 0.15

Notes: t-values in parentheses. Column 1: null of no fixed effect is rejected with F(113 259) = 2.69. Random effect model is rejected with a Wald statistic (c2) equal to 22.67. Column 2: overidentification restriction has c2 with degree of freedom equal to 2. P-value = 0.41.

The results reported in Table 2b reinforce those in Table 2a. LSDV estimation reveals faster convergence than that derived from the OLS method. This implies that the unobservable individual effect contaminated the estimates in Table 2a, column 1. However, the negative coefficients for initial DES are very similar to those in Table 2a. Moreover, both ITGMM and IT2SLS find significantly negative coefficients on initial DES.

Parallel to the long-run analysis, we also ran separate regressions on developing and developed countries, and the results are reported in Table 2c. Neither group shows initial DES to have a positive impact on growth.

TABLE 2C
DES and economic growth (by decade): OLS

 Dependent variable: annual growth rate of per capita GDP 1960-1999, by decade (1) Developing country (2) Developed country Intercept 0.0230 -0.0184 (2.23) (-0.46) Log of initial per capita GDP -0.0029 0.0038 (-1.65) (1.37) Initial DES 3.50e-6 -5.06e-7 (0.72) (-0.06) Investment share 0.0017 0.0011 (6.25) (2.85) Population growth rate -0.0080 0.0013 (-4.47) (0.59) 1970-1979 -0.0044 0.0194 (-1.09) (-3.73) 1980-1989 -0.0249 -0.0236 (-6.65) (-4.72) 1990-1999 -0.0201 -0.0284 (-5.37) (-4.44) Number of observations: 293 87 Adjusted R2: 0.34 0.37

Notes: t-values in parentheses calculated with White-heteroscedasticity-consistent standard error. 87 observations out of 108 (27 × 4) for developed countries, and 293 out of 348 (87 × 4) for developing countries provide sufficient information for estimations.

The negative aggregate shocks of the 1980s and 1990s seem to be quite evenly distributed.

Table 2d shows the group-wise result for sub-Saharan Africa, Latin America and the Caribbean, and East and Southeast Asia. Similar to the findings for long-run growth, the positive impact of initial DES shows up only for East and Southeast Asian countries. The magnitude of this effect is also quite large, and implies that a 500-kcal/day increase in DES will increase the average growth rate of the following ten years by 1.9 percent. On the other hand, the DES coefficients for the sub-Saharan Africa, and Latin America and the Caribbean groups are negligibly small and insignificant.

TABLE 2D
DES and economic growth (by decade): OLS

 Dependent variable: annual growth rate of per capita GDP by decade (1) Sub- Saharan Africa (2) Latin America and Caribbean (3) East and Southeast Asia Intercept 0.0167 -0.0125 -0.0255 (0.78) (-0.48) (-0.72) Log of initial per capita GDP -0.0034 0.0029 -0.0074 (-1.11) (0.73) (-1.92) Initial DES 2.38e-7 6.53e-7 3.73e-5 (0.03) (0.09) (3.27) Investment share 0.0016 0.0005 0.0016 (4.06) (1.27) (2.58) Population growth rate -0.0029 -0.0004 -0.0003 (-0.65) (-0.14) (-0.04) 1970-1979 -0.0050 0.0024 -0.0016 (-0.79) (0.41) (-0.17) 1980-1989 -0.0186 -0.0295 -0.0159 (-3.46) (-6.20) (-1.17) 1990-1999 -0.0226 0.0091 -0.0292 (-3.94) (-1.86) (-2.25) Number of observations: 20 82 32 Adjusted R2: 0.28 0.32 0.29

Notes: t-values in parentheses calculated with White-heteroscedasticity-consistent standard error. 120 observations out of 144 (36 × 4) for sub-Saharan Africa, 82 out of 84 (21 × 4) for Latin America and the Caribbean and 32 out of 44 (11 × 4) for East and Southeast Asia provide sufficient information for estimations.

Panel regressions: by five-year period

We further divided our sample into eight five-year intervals. Estimation results are reported in Tables 3a and 3b, and are generally consistent with the estimations for each decade.

In the pooled regressions, the impact of initial DES on the average growth rate of the following five years is not significantly different from zero. When five-year dummies and country group dummies are included, more detailed information about the aggregate shocks and (group) idiosyncratic shocks can be derived. The aggregate shock turned strongly negative from 1975 to 1979, and reached its lowest point during 1980-1984. Since then it has subsided, but was still significantly negative in 1999. When these aggregate shocks are included, some of the country group dummies are no longer significant: the sub-Saharan Africa dummy, for example, becomes insignificantly different from zero. This indicates that there was no particular negative idiosyncratic shock in this group of countries. An interesting finding is that the East and Southeast Asia group of countries experienced significantly positive idiosyncratic shocks.

TABLE 3A
DES and GDP growth rate (in five-year periods): full sample

 Dependent variable: five-year average growth rate of per capita GCP (1) OLS (2) LSDV (3) ITGMM Intercept 0.0123 (0.92) Log initial per capita GDP -0.0013 -0.0222 -0.0132 (-0.99) (-4.93) (-0.74) Initial DES 1.81e-6 -9.56e-6 -2.00e-5 (0.44) (-1.66) (-0.60) Investment share 0.0015 0.0019 0.0006 (7.39) (9.41) (0.63) Population growth -0.0044 0.0003 -0.0085 (-3.38) (0.21) (-0.75) 1965-1969 -0.0035 0.0003 (-0.86) (0.06) 1970-1974 -0.0009 0.0056 (-0.20) (1.31) 1975-1979 -0.0157 -0.0070 (-3.39) (-1.60) 1980-1984 0.0316 -0.0183 (-7.02) (-4.07) 1985-1989 -0.0200 -0.0048 (-4.67) (-1.08) 1990-1994 -0.0277 -0.0120 (-5.69) (-2.60) 1995-1999 -0.0171 -0.0004 (-3.95) (-0.08) Sub-Saharan Africa -0.0031 (-0.72) Latin America and the Caribbean -0.0016 (-0.48) South Asia 0.0093 (1.82) East and Southeast Asia 0.0155 (3.60) Number of observations: 757 114 × 8 528 Adjusted R2: 0.28 0.50

Notes: t-values in parentheses. Column 1: t-values calculated with White-heteroscedasticity-consistent standard error. Total number of countries is 114. Column 2: no-fixed-effect is rejected with F(113,632) = 2.63 (p-value < 0.0001). Column 3: overidentification condition has c2(1) equal to 2.05.

TABLE 3B
DES and GDP growth rate (in five-year periods): by country group

 Dependent variable: five-year average growth rate of per capita GDP (1) Sub- Saharan Africa (2) Latin America and Caribbean (3) East and Southeast Asia Intercept -0.0087 -0.0215 -0.0396 (-0.36) (-0.88) (-1.04) Log initial per capita GDP -0.0030 0.0046 -0.0046 (-0.98) (1.12) (-1.27) Initial DES 2.69e-6 -3.47e-6 3.47e-5 (0.30) (-0.45) (2.49) Investment share 0.0016 0.0009 0.0012 (4.82) (2.38) (2.45) Population growth 0.0043 0.0005 0.0001 (0.79) (0.18) (0.02) 1965-1969 -0.0013 -0.0054 0.0107 (-0.16) (-1.00) (0.86) 1970-1974 0.0059 0.0066 0.0102 (0.66) (0.90) (0.79) 1975-1979 0.0202 -0.0086 0.0048 (-2.08) (-1.01) (0.36) 1980-1984 -0.0323 -0.0383 -0.0096 (-3.47) (-6.12) (-0.58) 1985-1989 -0.0131 -0.0241 -0.0052 (-1.54) (-3.23) (-0.34) 1990-1994 -0.0392 -0.0095 -0.0117 (-4.33) (-1.34) (-0.63) 1995-1999 -0.0107 -0.0134 -0.0250 (-1.26) (-2.03) (-1.55) Number of observations: 238 164 66 (number of countries) (36) (21) (11) Adjusted R2: 0.25 0.24 0.20

Notes: t-values in parentheses. Column 1: t-values calculated with White-heteroscedasticity-consistent standard error. Total number of countries is 114. Column 2: no-fixed-effect is rejected with F(113,632) = 2.63 (p-value < 0.0001).

When a fixed-effect model (LSDV) is used, the initial DES impact becomes negative, albeit not very significantly. The income convergence effect is surprisingly strong given the short time horizon. The dummy for 1995-1999 is no longer significant, indicating that there was no negative shock at the global level and that it was individual (country) heterogeneity that was affected.

We also estimated the model for some subgroups of developing countries, and obtained results that are similar to others: initial DES shows a significantly positive impact for East and Southeast Asian countries only. The magnitude of the estimate is also very similar to those of the 40-year and ten-year estimates. Another interesting finding is that, although sub-Saharan African, and Latin American and the Caribbean countries suffered negative shocks from the late 1970s until the present, East and Southeast Asian countries seem to have managed to avoid such shocks. An appreciably negative shock for this group of countries appears only in the last five-year period.

A simple Granger causality experiment

Convergence regression is suitable for revealing only long-run relations, so we had to deviate from this method in order to find out more about short-run relations. In particular, we used the simple Granger causality model to focus on the two time series, i.e. DES and GDP, on an annual basis.

Table 4 reports the seemingly unrelated regression (SUR) result of a Granger causality test. We chose an arbitrary five-year time lag for both equations. In terms of “time precedence”, we cannot reject the fact that causality runs in both directions. Relatively speaking, the impact of growth on DES is more significant than that of DES on growth, at least in the short run.

The accounting identity critique

The growth of real GDP per capita is calculated by a weighted sum of the growth in agricultural, industrial and service sector GDP. Running a regression of “total” growth on its component is therefore spurious because of this identity relationship. Since DES is calculated from the food consumption balance sheet, it is highly correlated to a country’s agricultural productivity. As a result, regressions of “total” growth may fall into the accounting identity critique.

TABLE 4
Granger causality test: seemingly unrelated regression (SUR)

 Dependent variable Growth rate of real GDP per capita (y) Log DES (des) Intercept -0.0677 0.1025 (-2.01) (4.67) y-1 0.2494 0.0485 (14.20) (4.24) y-2 0.0428 -0.0032 (2.38) (-0.27) y-3 0.0880 0.0136 (4.99) (1.18) y-4 0.0157 0.0120 (0.91) (1.07) y-5 0.0439 0.0092 (2.76) (0.89) des-1 0.0296 0.8659 (1.10) (49.33) des-2 -0.0385 0.0681 (-1.09) (2.95) des-3 0.0033 0.0729 (0.09) (3.19) des-4 -0.0024 0.0103 (-0.07) (0.45) des-5 0.0177 -0.0300 (0.67) (-1.75) F-test: coefficients of y lags = 0 19.44 (p-value) (0.000) coefficients of des lags = 0 4.98 (p-value) (0.026) Adjusted R2 (OLS): 0.10 0.97 Cross-correlation: 0.22 Number of observations: 3 386

Note: t-values in parentheses

We proposed two methods to evaluate the validity of this critique. First, we removed the agricultural component from total growth, and re-estimated the model. That is, we used only the industrial and the service sector shares of real GDP to evaluate the impact of initial DES. Thus, if DES is shown to have a positive impact on growth, it cannot be a mirage effect from agricultural growth. Second, we maintained the integrity of the variable on the left-hand side, but purged DES of any information about agricultural growth and used only information that is orthogonal to agricultural growth in the estimation. In particular, we replaced DES with the residual from a first-step regression of DES on agricultural GDP. The agricultural, industrial and service sector shares in GDP are available for each country on an annual basis from the World Bank data set. We re-estimated both the long-run (40 years) and the medium-run (ten years) models.

TABLE 5A
Growth without agriculture sector

 Dependent variable: growth rate of real non agricultural GDP per capita (1) 1960- 1999 (OLS) (2) by decade (OLS) (3) by decade (LSDV) Intercept 0.0248 0.0652 (0.92) (3.43) Log of initial GDP -0.0081 -0.0041 -0.0385 (-3.97) (-2.49) (-6.44) Initial DES 1.00e-5 -5.25e-6 -1.00e-5 (1.43) (-0.95) (-1.51) Investment share 0.0020 0.0018 0.0019 (4.85) (5.54) (5.85) Population growth -0.0022 -0.0082 -0.0105 (-0.48) (-4.56) -2.44) Sub-Saharan Africa -0.0182 -0.0101 (-2.96) (-1.84) Latin America and the Caribbean -0.0095 -0.0063 (-1.71) (-1.53) South Asia -0.0096 0.0014 (-1.60) (0.20) 1970-1979 -0.0109 0.0057 (-1.83) (1.09) 1980-1989 -0.0298 -0.0020 (-5.27) (-0.34) 1990-1999 -0.0293 0.0004 (-4.88) (0.06) Number of observations: 42 311 109 Adjusted R2: 0.53 0.30 0.70

Notes: t-values in parentheses calculated with White-heteroscedasticity-consistent standard error. Total number of countries is 114.

Growth without the agricultural component

Table 5a, column 1 reports the long-run (40-year) convergence regression with OLS. As data on the share of agriculture for the starting year of 1960 are missing for many countries, only 42 (out of 114) countries are included in the final estimation. This sample size is too small to use for further subgroup analysis, so we used only the decade panel for subgroup estimations.

Compared with Table 1a, column 2, income convergence is faster, and the initial DES effect is twice its previous magnitude and more significant. So, in the long-run regression, removing the agriculture sector enhanced the effect of initial DES.

Column 2 is comparable with Table 2a, column 1. Income convergence is faster, and the effect of initial DES changes from significantly negative to insignificantly negative, while the magnitude drops by half. This also indicates that, rather than weakening the positive effect, removing the agriculture sector weakens the negative effect.

Column 3 is comparable with Table 2b, column 1. The initial DES coefficients, both the estimate and the t-value, are very similar. Removing the agriculture sector does not have a significant effect on the impact of initial DES on growth.

Table 5b is parallel to Table 2d. We ran separate regressions for the subgroups of developing countries (sub-Saharan Africa, Latin America and the Caribbean, and East and Southeast Asia). For the first two groups, the negative initial DES coefficient is ten times larger in absolute value, but it is still statistically insignificant. For the last group, i.e. East and Southeast Asia, the rate of convergence is higher, and the positive effect of initial DES on growth is larger. This enforces the finding that the positive effect exists for this group of countries only.

To summarize, most of the regressions indicate that removing the agricultural component from real GDP per capita does not change the basic findings. In particular, for the group that shows initial DES to have a significant positive effect on growth, the effect is actually increased. Moreover, in the long-run (40-year) regression, the positive effect is larger and more significant. By attempting to correct for the identity problem, we actually reinforced our previous findings.

TABLE 5B
Growth without agriculture sector

 Dependent variable: annual growth rate of non-agricultural GDP per capita, by decade (1) Sub- Saharan Africa (2) Latin America and Caribbean (3) East and Southeast Asia Intercept 0.0631 0.0374 -0.0330 (2.10) (1.14) (-0.60) Log of initial per capita GDP -0.0081 0.0006 -0.0120 (-2.06) (0.13) (-2.73) Initial DES -3.99e-6 -5.82e-6 5.24e-5 (-0.32) (-0.66) (2.74) Investment share 0.0022 0.0004 0.0013 (3.82) (0.79) (1.57) Population growth rate -0.0023 -0.0043 0.0022 (-0.33) (-1.28) (0.22) 1970-1979 -0.0253 0.0013 0.0091 (-2.14) (0.18) (0.52) 1980-1989 -0.0394 -0.0305 -0.0059 (-3.67) (-5.30) (-0.31) 1990-1999 -0.0474 -0.0122 0.0223 (-4.00) (-2.19) (-1.15) Number of observations: 110 70 30 Adjusted R2: 0.28 0.25 0.13

Notes: t-values in parentheses calculated with White-heteroscedasticity-consistent standard error. 110 observations out of 144 (36 × 4) for sub-Saharan Africa, 70 out of 84 (21 × 4) for Latin America and the Caribbean and 30 out of 44 (11 × 4) for East and Southeast Asia provide sufficient information for estimations.

DES orthogonal to agricultural productivity

DES is closely related to a country’s real agricultural GDP per capita. This is the source of the possible identity problems that have already been mentioned. For this section, we purged DES of the component of real agricultural GDP and used only the residual in the growth regression. This residual could reflect the distributional properties of the food supply in a country, and we believe that it is not correlated to the level of agricultural development. In a way, this resembles an exogenous DES shock, such as food aid from abroad.

We first regressed DES on real agricultural GDP per capita, and saved the residual. The footnote to Table 6a reports this first-step regression for the long-run and the ten-year samples. Both quadratic functions show the usual concave shape. We used the residual from these quadratic regressions as the DES in the second-step estimation.

TABLE 6A
DES orthogonal to agricultural GDP

 Dependent variable: average annual growth rate of per capita GDP (1) 1960- 1999 (OLS) (2) by decade (OLS) (3) by decade (LSDV) Intercept 0.0277 0.0365 (1.54) (2.64) Initial per capita GDP -0.0048 -0.0033 -0.0286 (-3.66) (-2.57) (-5.63) Initial DES (residual) 1.15e-5 -6.53e-6 -7.58e-6 (1.85) (-1.61) (-1.32) Investment share 0.0018 0.0016 0.0016 (4.39) (6.08) (6.55) Population growth -0.0026 -0.0069 -0.0061 (-0.95) (-4.31) (-1.88) Sub-Saharan Africa -0.0184 -0.0091 (-3.54) (-2.12) Latin America and the Caribbean -0.0108 -0.0054 (-2.23) (-1.66) South Asia -0.0077 0.0006 (-1.55) (0.13) 1970-1979 -0.0056 0.0032 (-1.36) (0.80) 1980-1989 -0.0231 -0.0083 (-5.97) (-1.92) 1990-1999 -0.0205 -0.0041 (-5.34) (-0.90) Number of observations: 42 311 109 Adjusted R2: 0.58 0.36 0.73

Notes: t-values in parentheses calculated with White-heteroscedasticity-consistent standard error (columns 1 and 2 only). Column 1 first step result is:

 DES = 1946 + 0.2188 * yagr - 1.168e-5 * yagr2 (39.71) (2.95) (-1.15)

Adjusted R2 = 0.51. “yagr” stands for real agriculture GDP per capita.

Columns 2 and 3 first-step result is:

 DES = 2204 + 0.1181 * yagr - 2.95e-6 * yagr2 (94.19) (10.36) (5.98)

Column 3: F-test for the null of no fixed effect is equal to 2.39 (p-value < 0.0001).

TABLE 6B
DES orthogonal to agricultural GDP

 Dependent variable: annual growth rate of per capita GDP, by decade (1) Sub- Saharan Africa (2) Latin America and Caribbean (3) East and Southeast Asia Intercept 0.0199 0.0085 0.0311 (0.90) (0.24) (0.94) Log of initial per capita GDP -0.0029 0.0010 -0.0011 (-0.97) (0.26) (-0.40) Initial DES 3.36e-7 -7.96e-7 2.76e-5 (0.04) (-0.04) (2.74) Investment share 0.0016 0.0006 0.0014 (3.86) (1.30) (1.94) Population growth rate -0.0032 -0.0029 0.0055 (-0.69) (-0.92) (-0.86) 1970-1979 -0.0100 0.0034 0.0004 (-1.30) (0.54) (0.04) 1980-1989 -0.0238 -0.0282 -0.0118 (-3.45) (-5.14) (-0.81) 1990-1999 -0.0276 -0.0096 -0.0242 (-3.85) (-1.85) (-1.73) Number of observations: 110 70 30 Adjusted R2: 0.29 0.28 0.22

Notes: t-values in parentheses calculated with White-heteroscedasticity-consistent standard error. 110 observations out of 144 (36 × 4) for sub-Saharan Africa, 70 out of 84 (21 × 4) for Latin America and the Caribbean and 30 out of 44 (11 × 4) for East and Southeast Asia provide sufficient information for estimations.

Table 6a is parallel to Table 5a. There is little difference between the corresponding columns in the two tables. In particular, for the long-run sample shown in column 1, the contribution of initial DES to long-run growth is in the range of 1e-5, and both estimates are slightly significantly different from zero. Columns 2 and 3 of the two tables are also quite similar. One interesting observation is that when the individual unobservable effect is included, dummies for the 1980s and the 1990s are far less significant. This indicates that the negative shocks during these two decades were country-specific, and not time-specific.

Table 6b once again focuses on the three subgroups of developing countries. The only substantial change is in East and Southeast Asian countries, where the impact of initial DES on growth is cut in half, but remains very significant. In addition, these two estimates are much larger than those obtained from the long-run regression. This difference has two potential causes: this group of countries might be enjoying a higher rate of return from improved nutritional status; and the short-run effect may be different from the long-run effect. We return to this point in the Nutrition and population growth section.

Simultaneous estimations[30]

Empirical results from the previous section revealed two features of the relation between nutritional status (in particular, DES) and GDP growth: DES and GDP growth are jointly determined; and lagged effects exist - i.e. the economy may have to grow for a while before the population’s nutritional status improves,[31] and nutritional status has to improve substantially before its effect on economic growth shows up. For this section we combined the growth equation with a simple nutrition equation in a simultaneous equation-type model. Both structural parameters and, most probably, lags can be recovered from this estimation.

We postulated the following equation system:

 (50)
 (51)

where git is the growth rate of real GDP per capita for country i at time t; sit is the investment share of GDP; nit is the population growth rate; and des{L=tg} is a lag indicator function. For example, iftg = 2, this formula is equal to dest-2. That is, the impact of DES on growth has a lag of two years.[32]g{L=td} has a similar interpretation: we assumed that growth impact has a tdperiod lag on nutritional status. a’s and b’s are parameters to be estimated. We further assumed that the error terms, egit and edit, follow a bivariate normal distribution with zero means, standard deviations sgand sd, respectively, and correlation coefficient rgd. Two-equation joint estimation is more efficient than single-equation estimation, as long as the correlation coefficient is not equal to zero.

First, assuming that we know (tg,td), the log likelihood of the bivariate normal distribution is:

 (52)

where:

 (53)
 (54)

For each given pair of (tg, td) we found the set of parameter values that maximize Equation 52, given the data on GDP growth rate, DES, investment share and population growth rate.[33] Then we chose the pair of (tg, td) that has the maximal log likelihood as the most probable value of lags.

Three types of regression results are reported in Table 7. Column 1 is a standard regression with Equations 52, 53 and 54. Population growth has been dropped from column 2 for reasons that will become clear. In column 3, we added an additional lag to the right-hand sides of both Equations 50 and 51 to see the robustness of the results reported in column 1.

Coefficients in column 1 are consistent with our previous results. Note that in order to facilitate computation, we multiplied the GDP growth rate by 100. Thus, in comparable terms, the coefficient for investment share is about 0.002, and for population growth it is about -0.0013. Both have the usual signs, and their magnitudes are very close to those found in previous estimates. Since this is basically a short-run model, the coefficient for lagged log DES is significantly negative. The most probable DES lag for this equation is two years. For the second equation, i.e. the DES equation, lagged growth rates improve DES significantly, and the most probable lag for this effect is five years. This result is consistent with Figure 7.

TABLE 7
Simultaneous equations: maximum likelihood estimation

 (1) (2) (3) Growth equation Constant 1.9263 1.9176 1.9257 (1.05) (31.8) (0.46) Investment share 0.1969 0.1962 0.1975 (15.72) (18.30) (15.83) Population growth -0.1324 -0.1385 (1.51) (1.63) Lag(t) log DES -0.6142 -0.6452 -0.6143 (2.57) (20.23) (1.14) Log DES equation Constant 7.8344 7.8345 7.8308 (2056.28) (2061.71) (2007.90) Lag(t) growth rate 0.0049 0.0048 0.0074 (6.93) (6.86) (8.60) sg 1.59 1.59 1.59 (117.08) (120.20) (113.57) sd -1.65 -1.64 -1.65 (-121.18) (-124.49) (-165.00) rgd 0.0513 0.0689 0.0500 (2.07) (3.74) (1.67) tg 2 2 2 td 5 5 4 Number of observations: 2 717 2 717 2 717 Mean log likelihood: -0.9403 -0.9408 -0.9357

Notes: t-values in parentheses. Growth rates are multiplied by 100 to facilitate numerical calculation (same reason for taking logarithms of DES). In order to bound the variances and correlation coefficient, exponential function is used to transform the standard deviations and (exp(x) - exp(-x))/(exp(x) + exp(-x)) to transform the correlation coefficient function. The purpose is to bind standard deviation above zero, and correlation coefficient within (-1,1). Thus, for column 1 the standard deviations and correlation coefficients are (4.90, 0.19, 0.05), for column 2 they are (4.90, 0.19, 0.07), and for column 3 they are (4.90, 0.19, 0.05).

As already mentioned, forcing the correlation to be fixed at one period may be problematic. We thus added an additional lag to the right-hand sides of both Equations 50 and 51. That is, g depends on both the log DES lagged tg period and the tg+1 period, but in order to maintain easy computability we restricted these so that they have the same coefficients. That is, we assumed that g depends on the average of log DES of period tg and tg+1. In Equation 51, we added the growth rate of GDP for period td+1 to the right-hand side, with the same coefficient as for the period td. Column 3 reports the results. With the exception of the negative sign for the coefficient of lagged log DES - which has become insignificant - these results are almost the same as those reported in column 1. Another minor change is that the most probable lag for the second equation is four years instead of five years. As, in this specification a four-year lag includes the five-year lag by construction, this does not pose a contradiction to the previous result.

Figure 8: Log likelihood

Why would an increase in DES decrease the economic growth rate in the short run? We suggest the following explanation: An increase in DES can improve the health condition of the population, thus reducing its mortality rate. A decrease in the child mortality rate, coupled with elderly people living longer, is equivalent to population growth. Although better nutrition is expected to raise labour productivity and accelerate human capital accumulation, such long-run effects will not override short-run effects on the mortality rate. As a result, the mortality effect will dominate in the short run, and accelerated population growth will soon cancel out any modest amount of productivity growth. This could create a negative short-run coefficient for DES. In the long run, the mortality effect will diminish, while child mortality and life expectancy will remain at their “natural” rates. The productivity effect becomes the dominant force, and this renders a positive coefficient for the long-run model.

This argument is at least partially supported by the regression results shown in Table 7, column 2. We dropped population growth, so the DES coefficient should pick up both the mortality and the productivity effects. The coefficients in column 2 are mildly more negative and drastically more significant than those in column 1. Comparison of column 2 with column 3 shows that inclusion of the population growth variable makes the lagged DES coefficient insignificantly negative. This indicates that the negative short-run effect of DES on growth is mainly due to its impact on short-run population growth.

Figure 8 is a three-dimensional graph on the choice of (tg, td) for column 1. The final choice of (2,5) is obviously the peak of the surface. However, the lag in the growth equation (with lagged log DES) seems to be far more robust than it is in the DES equation (with lagged growth) because the likelihood does not change much from changes in log DES lags. As a result, td = 5 may be a fragile result.

Nutrition and population growth

Two puzzles come to mind from the full spectrum of regression results. First, why is the impact of nutrition on growth negative (or close to zero) in the short run but positive in the long run? Second, why is this effect positive for some countries and negative for others?

We believe that the answer lies in the long- and short-run relations between population growth and nutrition and between productivity growth and nutrition. In a typical developing economy in which there is severe food shortage, population growth is low owing to high child mortality and widespread malnutrition-related illness (or starvation). An improvement in nutritional status will have an instant impact on these two factors, thus population growth will increase. Unless improved nutrition can also enhance food production immediately, the previous nutritional status will not be sustainable. That is, the increased population will quickly "consume" the additional nutrition, thereby reducing the overall nutritional status. This constitutes a "nutrition trap".[34] If the improvement in nutrition is not large enough, or cannot be transformed into productivity quickly enough, the nutritional status will be stuck in the low equilibrium, thus its impact on productivity will be negligible.

We used the decade information on initial DES and population growth for the following ten years to estimate a quadratic function. The result is:

 n = -350.5426 + 92.9095 (log DES) - 6.1106 (log DES)2 (-4.29) (4.44) (-4.56) Adj. R2 = 0.19

which implies an "inverse-U-shaped” relation between population and DES. Figure 9 shows the estimated function for DES from about 1 500 to 4 000 kcal/day.[35] Before reaching the peak of the function, an increase in DES will increase population growth, thus the population is likely to be stuck in the low nutrition trap. This function reaches its peak at about 7.6, which is about 2 000 kcal/day. Table 8 reports countries that fell into this category during the four decades covered in the sample. Sub-Saharan Africa accounted for about one-third of the countries in this category, and little has changed over the past four decades. In the meantime, most East and Southeast Asian countries have escaped from the trap.

Figure 10 shows the decade and country group nutritional level changes and the population growth rate. Each pair of twin bars is for a country group and a specific decade. The left-hand bar is the DES level, and the right-hand bar is the population growth rate (multiplied by 1 000). It is obvious that sub-Saharan African countries have experienced substantial increases in population growth, and this should be an important reason for the almost constant DES level during the four decades. On the other hand, economies in both Latin America and the Caribbean, and East and Southeast Asia are able to reduce their population growth rates continuously, thus their per capita DES is constantly improving.

In the long run, both nutrition (as measured by DES) and the population growth rate will stabilize at a constant level. For example, there is an optimal nutritional intake in terms of biological and anthropological factors, and the birth/death rate will also be determined by "natural" forces. All of these factors are beyond the scope of economics, and we can treat them as exogenous. Once this stage has been reached, DES should not have much impact on economic growth, even though other measures of better nutrition may have. However, for most developing countries, especially those that have been plagued with serious malnutrition problems, an increase in DES is most likely to increase population immediately and significantly. As a result, it should not be surprising to see a slow improvement of nutritional status and sluggish economic growth at the very beginning. Once this short-run population effect is exhausted, the long-run productivity effect will become the dominant force. This explains why the short-run effect can be negative while the long-run effect is positive.

Figure 9: DES and population growth

TABLE 8
Developing countries in nutrition trap: by group

 Country group 1960- 1969 1970- 1979 1980- 1989 1990- 1999 Sub-Saharan Africa (36) 12 8 7 12 Latin America and the Caribbean (21) 7 4 0 2 East and Southeast Asia (11) 6 2 1 1

Notes: For 1990-1999, 12 sub-Saharan African countries are AGO, BDI, CAF, ETH, GHA, GIN, KEN, MOZ, MWI, RWA, SLE, and TCD. Two Latin American and the Caribbean countries are HTI and PER. One East and Southeast Asia country is KHM.

Finally, why does an improvement in DES have a positive impact in East and Southeast Asia but not in sub-Saharan Africa? We believe that the population effect plays a major role in explaining this. If population growth follows the trajectory shown in Figure 9, it may take a long time for a developing country to emerge from the nutrition-growth trap. However, if proper population control is implemented with a nutrition improvement plan, the effect of the latter will be more prominent.

Figure 10: DES and population growth

## CONCLUSIONS AND POLICY IMPLICATIONS

Improving the nutritional status of developing countries is important for many reasons. First, better nutrition leads to better health and is, itself, a key indicator of a country's welfare. Second, a healthier labour force is more productive, in terms of both physical production and human capital production. Hence, better nutrition helps capacity building for human capital. This is an important driving force for improving the standard of living. Developed countries can also benefit directly from a more integrated and vibrant global economy.

Our empirical results lead to the following conclusions:

• Better nutrition is associated with faster economic growth in the long run. The magnitude of this effect, taken at the current sample mean, is about 0.5 percentage points for a 500-kcal/day increase in DES.

• The short-run effect is, however, rather ambiguous. It is not uncommon to observe a negative short-run effect, especially when the positive impact of nutrition on population growth is strong.

• In both the short and the long runs, we find evidence that nutrition's contribution to growth can be positive, if the population growth effect is properly controlled.

• Since nutrition contributes to economic growth in the long run, any policies to improve nutritional status have to have a long-run provision. Corollary to this, a country that implements such policies must commit to them for the long run.

• Results show that the presence of hunger in a country is costly in terms of economic growth, in the short as well as the long run.

• We find evidence that there are strong associations in both direction, i.e. nutrition effects growth and growth effects nutrition. However, both associations seem to show significantly lagged and asymmetric effects. This calls for further detailed modelling of the short-run dynamics of both time series.

## REFERENCES

Arora, S. 2001. Health, human productivity, and long term economic growth. Journal of Economic History, 61(3): 699-749.

Barro, R.J. 1991. Economic Growth in a Cross Section of Countries. Quarterly Journal of Economics, 106 (May): 407-443.

Barro, R.J. & Sala-i-Martin, X. 1991. Convergence across states and regions. Brookings Papers on Economic Activity, 1: 107-182.

Barro, R.J. & Sala-i-Martin, X. 1992. Convergence. Journal of Political Economy, 100 (April): 223-251.

Barro, R.J. & Sala-i-Martin, X. 1999. Economic growth. Cambridge, MA, USA, MIT Press.

Baumol, W. 1986. Productivity growth convergence, and welfare. American Economic Review: 76 (December): 1072-1085.

Bils, M. & Klenow, P.J. 2000. Does schooling cause growth? American Economic Review: 90 (December): 1161-1183.

Cho, D. & Graham, S. 1996. The other side of conditional convergence. Economics Letters, 50: 295-290.

De Long, J.B. 1988. Productivity growth, convergence, and welfare: comment. American Economic Review: 78 (December): 1138-1154.

Easterly, W. 1999. Life during growth. Journal of Economic Growth, 4(3): 239-276.

FAO. 1996. The Sixth World Food Survey. Rome, Italy, Food and Agriculture Organization of the United Nations.

FAO. 2001. Undernourishment and economic growth: the efficiency cost of hunger, by Jean-Louis Arcand. FAO Economic and Social Development Paper No. 147. Rome, Italy.

Grossman, M. 1972. On the Concept of Health Capital and Demand for Health. Journal of Political Economy, 80 (March-April): 223-255.

Hanushek, E.A. & Kimko, D.D. 2000. Schooling, labor-force quality, and the growth of nations. American Economic Review, 90 (December): 1184-1208.

Islam, N. 1995. Growth empirics: a panel data analysis. Quarterly Journal of Economics, 110(4): 1127-1170.

Leibenstein, H. 1957. Economic Backwardness and Economic Growth. New York, John Wiley.

Lucas, R.E. 1976. Econometric policy evaluation: a critique. Carnegie-Rochester Conference Series on Public Policy, 1: 19-46.

Lucas, R.E. 1988. On the mechanism of economic development. Journal of Monetary Economics, 22 (July): 3-42.

Mankiw, G.N., Romer, D. & Weil, D.N. 1992. A contribution to the empirics of economic growth. Quarterly Journal of Economics, 107 (May): 407-437.

Romer, D. 2001. Advanced macroeconomics. Second Edition. McGraw-Hill.

Romer, P.M. 1986. Increasing returns and long run growth. Journal of Political Economy, 94 (October): 1002-1037.

Sachs, J.D. & Warner, A.M. 1997a. Fundamental sources of long-run growth. American Economic Review, 87 (May): 184-188.

Sachs, J.D. & Warner, A.M. 1997b. Sources of slow growth in African economies. Journal of African Economies, 6: 335-376.

Sachs, J.D. et al. 2001. Macroeconomics and health: investing in health for economic development. Report for the Commission on Macroeconomics and Health of the World Health Organization (WHO).

Solow, R.M. 1956. A contribution to the theory of economic growth. Quarterly Journal of Economics, 70 (February): 65-94.

Solow, R.M. 2000. Growth Theory: An Exposition. Second Edition. Oxford University Press.

Svedberg, P. 1999. 841 million undernourished. World Development, 27: 2081-2098.

Uzawa, H. 1965. Optimum Technical Change in an Aggregative Model of Economic Growth. International Economic Review, 6 (January): 12-31.

World Bank. 2001.World Development Indicators. Washington D.C., USA.

Ward, M.P. & Jones, M.C. 1995. Kernel smoothing. Monographs on Statistics and Applied Probability, 60.

Zon, A. & Muysken, J. 2001. Health and endogenous growth. Journal of Health Economics, 20: 169-185.

 [25] This part follows Romer (2001) and Barro and Sala-i-Martin (1999).[26] FAOSTAT is on the Internet at: apps.fao.org/[27] F(5,77) = 0.65. Not reported in the table. [28] F(8,348) = 14.86.[29] Also called the “within” or “fixed effect” estimator.[30] It will become clear that this is a misnomer because only lagged dependent variables enter as independent variables. [31] This could be owing to a growth trap.[32] This specification has the problem of ignoring anything beyond period tg, although adding more lagged variables quickly increases the computation burden. We report the case that includes an additional lag.[33] The maximum likelihood estimation routine we used is GAUSS MAXLIK.[34] Technically, a nutrition trap can be defined as a phenomenon of mildly decreased DES after a one-off increase in DES. [35] ln(1 500) » 7.3, ln(4 000) » 8.3.