Chapter 5. Estimation Results: New Evidence from Cross-Country Data, 1970-96

Descriptive Analysis

Child malnutrition prevalences and means of the explanatory variables are presented in Table 4 by developing region and decade.²⁵ The numbers for the developing countries as a whole are given in Table 5. Figures 2-7 show the country-level data: child malnutrition prevalences are plotted against each variable using data pooled across all countries and time periods. The fitted lines in each figure are arrived at using a Lowess smoothing technique.²⁶

²⁵ The measures of the explanatory variables are used in the tables and figures throughout this report. For example, "female-to-male life expectancy ratio" is given instead of "women's status relative to men's."

²⁶ The Lowess smoother produces locally weighted regression smoothing, using iterative weighted least squares (SPSS 1993).

The regional trends and levels of child malnutrition in the sample closely follow those for the developing countries as a whole in Table 1. South Asia had the highest prevalence of child malnutrition during the period, with a rate roughly double that of the next highest region, Sub-Saharan Africa (Table 4). More than half of all South Asian children under five were underweight for their age. Roughly one-third were underweight in Sub-Saharan Africa and one-fifth in East Asia. NENA and LAC had the lowest underweight rates. The regions whose rates have declined the most are South Asia and East Asia. Sub-Saharan Africa is the only region for which underweight rates have increased.

Turning to the underlying-determinant explanatory variables, NENA and LAC had the highest overall rates of access to safe water, more than 70 percent, while Sub-Saharan Africa had the lowest at 37.5 percent, illustrating the high degree of inequality across the regions (Table 4, column 2). Improvements in access to safe water during the study period have been extraordinary. For the full sample, the percentage of people having access to safe water more than doubled, starting at 36.3 percent in the 1970s, increasing quickly to 61.6 percent in the 1980s, and rising to 69 percent by the 1990s (Table 5). The rates of improvement were greatest for East Asia and South Asia. Figure 2 illustrates that the negative association between national rates of access to safe water and child malnutrition is fairly strong, especially after a safe water access rate of 40 percent has been reached.

Table 4 - Regional comparison of sample child malnutrition (underweight) prevalences and explanatory variable means, 1970s, 1980s, and 1990s

Region/decade		Child malnutrition (1)	Access to safe water (2)	Female secondary school enrollment (3)	Female-to-male life expectancy ratio (4)	Per capita dietary energy supply (5)	Per capita GDP (6)	Democracy (7)
		(percent)	(percent)	(percent)		(kilocalories)	($PPP)	(1= least democratic)
South Asia		61.0	60.5	23.8	1.010	2,187	863	4.59
	1970s (n= 4)	69.1	29.8	16.3	0.987	2,023	728	4.38
	1980s (n=6)	61.8	51.9	14.2	1.020	2,042	719	3.25
	1990s (n=6)	55.7	81.3	31.5	1.022	2,332	990	5.16
Sub-Saharan Africa		31.0	37.5	15.6	1.061	2,164	879	2.57
	1970s (n=10)	27.2	24.7	8.5	1.069	2,207	1,358	1.77
	1980s (n=26)	26.5	35.0	14.6	1.066	2,117	1,031	2.02
	1990s (n=29)	33.7	40.4	17.0	1.060	2,184	740	2.96
East Asia		23.0	64.5	47.9	1.051	2,595	1,874	1.69
	1970s (n=2)	45.0	19.7	25.8	1.050	2,007	1,402	3.0
	1980s (n=13)	26.8	63.8	39.2	1.053	2,502	1,483	2.30
	1990s (n=11)	19.4	67.8	54.4	1.049	2,686	2,132	1.25
Near East and North Africa		11.0	75.5	52.5	1.043	3,058	2,527	2.81
	1970s (n=3)	16.5	72.5	34.0	1.042	2,710	1,547	3.32
	1980s (n=4)	10.1	69.3	46.4	1.043	3,018	2,746	3.09
	1990s (n=7)	10.8	79.4	59.7	1.043	3,157	2,637	2.55
Latin America and the Caribbean		12.0	71.8	44.8	1.094	2,647	4,740	4.73
	1970s (n=12)	18.9	59.5	33.3	1.086	2,620	4,713	4.06
	1980s (n=26)	11.4	79.0	47.2	1.096	2,675	4,871	5.14
	1990s (n=20)	8.3	73.3	51.4	1.098	2,636	4,607	4.79

Notes: The means reported in this table are calculated based only on the country-year pairs included in the study data set. They are population-weighted.

Table 5 - Child malnutrition (underweight) prevalences and explanatory variable means, 1970s, 1980s, and 1990s

Variable	1970s	1980s	1990s	Change 1970s to 1990s	Percent change 1970s to 1990s
Child malnutrition (percent)	50.7	29.0	28.5	-22.2	-43.8
Access to safe water (percent)	36.3	61.6	69.0	32.7	+90
Female secondary school enrollment (percent)	21.7	34.5	45.0	23.3	+107
Female-to-male life expectancy ratio	1.024	1.055	1.047	0.023	+2.25
Per capita dietary energy supply (kilocalories)	2,187	2,440	2,564	377	+17.2
Per capita GDP ($)	1,772	1,871	1,904	132	+7.45
Democracy (1 = least democratic)	3.96	2, 86	2.66	-1.3	-32.8
Number of observations	31	75	73	...	...
Number of countries	29	54	58	....	...

Note: The means reported in this table are calculated based only on the country-year pairs included in the study data set, and therefore must be considered illustrative (see Table 10 for an alternative estimation of the changes in time using data on all of the study countries for consecutive five-year intervals). They are population-weighted.

With respect to women's education, Sub-Saharan Africa had the lowest rate of enrollment in secondary school, at 15.6 percent (Table 4, column 3). South Asia's rate, at only 23.8 percent, was also very low. For the full sample, female secondary school enrollment rates improved steadily during the period, rising from 21.7 percent in the 1970s to 45 percent in the 1990s. Nevertheless they remain quite low, with less than half of the age-eligible women in developing countries entering secondary school. Figure 3 shows the negative association between female secondary school enrollments and child malnutrition rates. The association is especially strong where female enrollment rates are very low (below 40 percent).

The indicator of women's status relative to men's was the lowest by far in South Asia, with female and male life expectancy being roughly equal (Table 4, column 4). Women's life expectancy in the developed countries is on average six to seven years longer than men's (Mohiuddin 1996). The ratio in Norway, for example, is 1.08. Thus South Asia's ratio of 1.01 is extremely low. Sub-Saharan Africa, East Asia, and NENA have ratios of 1.06, 1.05, and 1.04, respectively, still below what is common in developed countries. LAC had the highest ratio of the developing-country regions, which at 1.09 is on a par with the developed-country level. Over time, the ratio for the developing countries as a group increased from 1.02 in the 1970s to 1.05 in the 1990s (Table 5). This change, while small in absolute terms, is equal to about one-eighth of the variable's entire range (0.97 to 1.12 - see below). The ratio has improved or remained fairly steady in all regions except Sub-Saharan Africa. The negative association between life expectancy ratios and child malnutrition prevalences is fairly strong for the sample as a whole (Figure 4). The relationship appears to be very strong at lower life expectancy ratios, where most of the South Asian data points fall, flattening out after about 1.05.

Figure 2 - Prevalence of underweight children by access to safe water, by region, 1970-96

Source: IFPRI Cross-Country Child Malnutrition Determinants Data Set, 1997/98.

Per capita DESs were lowest in South Asia and Sub-Saharan Africa during the period. The minimum daily dietary energy requirement for an active and healthy life is about 2, 150 kilocalories (FAO 1996). Supplies (not intake) in these regions barely surpassed this requirement (Table 4, column 5). The minimum DES considered necessary (but not sufficient) for bringing the share of food insecure to a very low 2.5 percent of a country's population is 2, 770 kilocalories (FAO 1996). The dietary energy supplies of East Asia and LAC neared this level; NENA's surpassed it. From the 1970s to the 1990s, DES increased in all regions except Sub-Saharan Africa. Figure 5 points to a strong negative association between DES and child malnutrition rates.

Figure 3 - Prevalence of underweight children by female secondary school enrollment, by region, 1970-96

Source: IFPRI Cross-Country Child Malnutrition Determinants Data Set, 1997/98.

Per capita GDP was lowest for South Asia and Sub-Saharan Africa and highest for LAC (Table 4, column 6). From a descriptive standpoint, Figure 6 indicates a negative relationship between per capita national incomes and child malnutrition in developing countries. However, at the extremes there is much less correspondence. Two observations are worth noting. First, above a per capita GDP threshold of $3, 000, it is rare to find a child underweight rate above 25 percent. Most of the LAC and NENA data points fall into this category. Second, below a per capita GDP of $2, 000, where most of the Sub-Saharan African and South Asian data points lie, there are striking differences in the prevalences, ranging from 12 percent to 71 percent. While high income and high child malnutrition generally do not coexist, it is possible - and not uncommon - for countries to achieve low levels of child malnutrition even with low per capita incomes. Some countries in the sample for which this is the case are Cd'Ivoire (in 1986), Lesotho (in 1981), Nicaragua (in 1993), and Zimbabwe (in 1994).

Figure 4 - Prevalence of underweight children by female-to-male life expectancy ratio, by region, 1970-96

Source: IFPRI Cross-Country Child Malnutrition Determinants Data Set, 1997/98.

The region that has been least democratic during the study period is East Asia (Table 4, column 7). Interestingly, South Asia and LAC, while at opposite extremes on underweight rates, appear to have been equally democratic over the 25-year period. These regions had the highest democracy index scores. Democracy has improved for South Asia, Sub-Saharan Africa, and LAC; it has deteriorated for East Asia and NENA. It is the only explanatory variable that has declined for the developing-country sample as a whole, falling from about 4.0 in the 1970s to 2.7 in the 1990s (Table 5). Figure 7 illustrates that the regions vary widely around the regional means reported in Table 4, and that the association between democracy and underweight is distinctly negative, especially at the democracy index extremes.

Figure 5 - Prevalence of underweight children by per capita dietary energy supply, by region, 1970-96

Source: IFPRI Cross-Country Child Malnutrition Determinants Data Set, 1997/98.

Multivariate Analysis

According to the descriptive analysis of the last section, improvements in all of the hypothesized explanatory variables lead to reductions in child malnutrition. However, the bi-variate relationships identified may mask the variables' confounding influences. The goal of this section is to single out the independent effect of each variable, while controlling for the others. In the section, the parameter estimates for the static models and the results of the specification tests are first presented. Next, the practical significance of the parameter estimates are discussed, and the possibility of significant regional differences is investigated. Finally, the determinants of child malnutrition are explored from a dynamic perspective.

Figure 6 - Prevalence of underweight children by per capita GDP, by region, 1970-96

Source: IFPRI Cross-Country Child Malnutrition Determinants Data Set, 1997/98.

Estimation Results for Static Models

Parameter Estimates. The pooled OLS and country FE estimation results are presented in Table 6. Here all independent variables are assumed to enter into equations (8) and (9) linearly. Tests for nonlinearities in the FE estimating equations reveal a curvilinear relationship between child malnutrition prevalence and two variables: per capita DES and per capita GDP. The estimation results when these relationships are taken into account are given in Table 7. The final preferred estimates are those generated using FE estimation and three-segment linear splines to represent the CM-DES and CM-GDP relationships. Nevertheless, the other estimations are presented and discussed in order to demonstrate a number of methodological points.

Figure 7 - Prevalence of underweight children by democracy index, by region, 1970-96

Source: IFPRI Cross-Country Child Malnutrition Determinants Data Set, 1997/98.

Table 6 compares the pooled OLS and FE estimation results for both the underlying-determinants model and the basic-determinants model. The only difference between the OLS and FE estimating equations is the inclusion of 63 country-specific dummy variables in the latter. F-tests for the joint significance of the dummy variables strongly reject the null hypothesis that they have no impact on child malnutrition.

A comparison of the pooled OLS and linear FE parameter estimates points to some important differences. First, for the underlying-determinant specifications, once the country fixed-effects terms are included, the magnitudes of the coefficients on safe water access (SAFEW), the female-to-male life expectancy ratio (LFEXPRAT), and DES drop substantially, and they lose statistical significance. This finding indicates that OLS estimates of the effects of these variables on child malnutrition are biased upward. Second, while the OLS estimates suggest that the effect of female secondary school enrollment (FEMSED) is statistically insignificant and small, the FE results indicate strong statistical significance and a much stronger effect (the coefficient on FEMSED is 150 percent higher). OLS estimates of the effects of female education are thus biased downward. For the basic determinant specifications, the OLS coefficient estimate for GDP is biased upward; that for democracy (DEMOC) is biased downward. These differences illustrate the strong biases that result when unobserved country-specific, time-invariant factors are omitted from regression analysis of the determinants of child malnutrition.

Table 6 - Child malnutrition regressions: Ordinary least squares and country fixed effects, linear specifications

	Pooled ordinary least squares (OLS)		Country fixed effects (FE)
Variable	Underlying determinants (1)	Basic determinants (2)	Underlying determinants (3)	Basic determinants (4)	All determinants (5)
Access to safe water (SAFEW)	-.139 (2.7)***	...	-.085 (2.14)**	...	-.069 (1.7)*
Female secondary school enrollment (FEMSED)	-.068 (1.27)	...	-.167 (2.64)***	...	-.177 (2.78)***
Female-to-male life expectancy ratio (LFEXPRAT)	-177 (5.23)***	...	-93.45 (2,25)**	...	-111 (2.6)**
Per capita dietary energy supply (DES)	-.012 (3.65)***	...	-.0081 (2.48)**	...	-.0077 (2.21)**
Per capita GDP (GDP)	...	-.0048 (8.2)***	...	-.0023 (2.46)**	1.20 E-04 (.137)
Democracy (DEMOC)	...	-.274 (.44)	...	-.884 (1.67)*	-.779 (1.68)*
R2	.433	.346	.943	.916	.945
Adjusted R2	.420	.338	.910	.869	.910

Notes: The dependent variable is prevalence of underweight children under five. The number of observations for all regressions is 179 (63 countries). Absolute values of t-statistics are given in parentheses.

* Significant at the 10 percent level.

** Significant at the 5 percent level.

*** Significant at the 1 percent level.

Column (5) of Table 6 contains FE estimation results when both underlying and basic determinants are combined in the same estimating equation. While the parameter estimates of the four underlying determinants and DEMOC differ little from the FE separate-model estimates, the magnitude of the coefficient estimate for GDP declines substantially and becomes statistically insignificant. The combined-model specification suggests a weak relationship between per capita national income and child malnutrition.

Table 7 - Child malnutrition regressions: Country fixed effects, nonlinear specifications

		Quadratic DES and GDP curves		Three-segment linear spline DES and GDP curves
Variable		Basic determinants (2)	Underlying determinants (1)	Underlying determinants (3)	Basic determinants (4)
Access to safe water (SAFEW)		-.072 (1.84)*	...	-.076 (1.95)*	...
Female secondary school enrollment (FEMSED)		-.232] (3.51)***	...	-.220 (3.41)***	...
Female-to-male life expectancy ratio (LFEXPRAT)		-74.89 (1.83)*	...	-71.8 (1.74)*	...
Per capita dietary energy supply (DES)		-.067 (3.00)***	...	...	...
DES2		1.24E-05 (2.66)***	...	...	...
DES spline
	DES £ 2, 300 (n= 93)	...	...	-.0170 (3.41)***	...
	2, 300 < DES £ 3, 120 (n= 83)	...	...	-.0024 (2.16)**	...
	DES>3, 120 (n=3)a	...	...	.0405 (1.35)	...
Per capita GDP (GDP)		...	-.0121 (4.68)***	...	...
GDP2		...	9.67 E-07 (4.03)***	...	...
GDP spline
	GDP £ 800 (n=37)	...	...	...	-.0444 (3.15)***
	800 < GDP £ 4, 725 (n= 118)	...	...	...	-.0067 (2.63)***
	GDP > 4, 725 (n= 24)	...	...	...	.0006 (3.37)***
Democracy (DEMOC)		...	-1.45 (2.81)***	...	-1.27 (2.51)**
R2		.947	.927	.947	.930
Adjusted R2		.914	.884	.914	.889

Notes: The dependent variable is prevalence of underweight children under five. The number of observations for all regressions is 179 (63 countries). Absolute values of t-statistics are given in parentheses. ^a The choice of spline segments is the result of a grid search with minimum sum of squared residuals as the criterion. The coefficient on the third segment remains positive and statistically insignificant even when the cut-off point is lowered considerably (which would make the number of data points sufficient for the estimation of a significant coefficient).

* Significant at the 10 percent level.

** Significant at the 5 percent level.

*** Significant at the 1 percent level.

The separate-model specification, on the other hand, suggests a statistically significant and practically strong relationship. These contrasts illustrate the dangers of combining variables at very different levels of causality in the same regression when the intention is to estimate the independent effects of the variables.

Starting from the FE models, tests for the significance of all quadratic and interaction terms are undertaken to determine whether any nonlinear relationships exist between child malnutrition and its determinants.²⁷ No statistically significant interaction terms were detected.²⁸ However, coefficients on quadratic terms for both DES and GDP are statistically significant and positive, indicating that they work to reduce child malnutrition but have a declining marginal effect. Along with the quadratic, a number of alternative functional forms were fitted to determine which best captures the curvature.

²⁷ Other available tests of nonlinearities are based on comparisons of subsamples of data across the range of an independent variable (Chow F tests for structural change, Utts Rainbow test, the CUSUM test, see Green 1997; Haddad et al. 1995). Because subsamples of data in the set do not contain the same countries, the same fixed-effects terms do not apply to them all. Thus the tests are not valid for detecting nonlinearities in country fixed-effects analysis.

²⁸ Note, however, that micro-level studies have found evidence of significant interactions between the various determinants of child malnutrition, for example between food security and health (Haddad et al. 1996).

For DES, the quadratic provides a better fit than both reciprocal and linear log specifications. The estimation results for the quadratic specification are given in column (1) of Table 7. The turning point in the CM-DES curve is 2, 727 kilocalories per capita. The result suggests that, after the turning point, increased per capita DES works to worsen child malnutrition. The study sample contains 29 data points (mostly in the Latin America and Caribbean and Near East and North Africa regions) that fall above this number. While a declining marginal effect is intuitive, a positive one is not.

To test whether the quadratic upturn is in fact implied by the data rather than "forced" on it by the functional form, the curve was fitted as a linear spline. An extensive grid search was undertaken to locate the knot combinations yielding the smallest sum of squared residuals. The best fitting function was a three-segment spline with optimal knots at 2, 300 and 3, 120 kilocalories.²⁹ Next, with the lower knot anchored at 2, 300, a spline function with the second knot at 2, 727 kilocalories was estimated. The coefficient on the third segment of the spline was positive but insignificant (t = 1.0). Hence, the upturn implied by the quadratic function is not substantiated by the data, and the spline-generated estimates are preferred.

²⁹ Two knot sets proved to fit the data equally well: (2, 300; 3, 120) and (2, 280; 2, 940) For both, the coefficients on the third segment were statistically insignificant (n.b. the number of sample data points with DES 3, 120 is 3; the number with DES 2, 940 is 13). The former was chosen because it allows more data from the sample to be used for estimations of the coefficients for the usable (first two) segments, thus producing more efficient parameter estimates for them.

The linear spline estimates are reported in Table 7, column (3). The first and second segments of the spline have negative and significant slopes, with the second having a much smaller slope than the first. The coefficient of the third segment is not statistically different from zero. The quadratic and spline specifications differ little in terms of overall fit and in the coefficients on the non-DES explanatory variables. However, their shape differs substantially at high levels of DES, as illustrated in Figure 8.

Figure 8 - Prevalence of underweight children and per capita dietary energy supply (DES): Linear, quadratic, and spline curves

Source: IFPRI Cross-Country Child Malnutrition Determinants Data Set, 1997/98.

As for DES, the quadratic form of the CM-GDP relationship provides a better fit than other nonlinear specifications. The estimation results for the quadratic specification are given in column (2) of Table 7. The turning point in the function is $6, 250. Linear spline fitting results in a three-segment spline with optimal knots at $800 and $4, 750. The estimation results are presented in column (4) of Table 7. As for DES, the first and second segments of the spline have negative and significant slopes, with the second having a much flatter slope than the first. The last segment has a positive (though very small) and statistically significant slope, suggesting the possible existence of a slight upturn in the function after its second knot (Figure 9).

In addition to the estimated quadratic and spline curves, Figures 8 and 9 show the estimated CM-DES and CM-GDP functions when a linear form is assumed. For the underlying-determinants model, an F-test of the hypothesis that the actual slope of the function is constant is rejected at the 5 percent level; for the basic-determinants model, the hypothesis is rejected at 1 percent. These results confirm substantial nonlinearity in the CM-DES and CM-GDP relationships.

Figure 9 - Prevalence of underweight children and per capita gross domestic product (GDP): Linear, quadratic, and spline curves

Source: IFPRI Cross-Country Child Malnutrition Determinants Data Set, 1997/98.

The parameter estimates derived from the spline specifications in columns (3) and (4) of Table 7 are adopted as the preferred estimates for the policy analyses of Chapters 6, 7, and 8. However, the quadratic estimations are employed for the specification tests (see the next section) due to greatly reduced time costs.

In Figure 10, the predicted child malnutrition prevalences generated from pooled OLS and the preferred spline-generated FE estimations are plotted against the actual prevalences for the underlying-determinants model. Figure 11 shows the same comparison for the basic-determinants model. As both figures illustrate, the preferred estimates yield much more accurate in-sample predictions. Most of the difference is due to the inclusion of the fixed-effects terms (rather than the allowance of nonlinearities). It is interesting to note that the data points exhibiting the greatest error in the OLS estimates relative to the FE estimates are mainly from South Asia.³⁰ This suggests that the importance of country-specific, time-invariant factors in influencing child malnutrition in South Asian countries is greater than that for the other regions, a finding that will be addressed in more detail later.

³⁰ In Figure 8, the OLS data points exhibiting the greatest error are for Bangladesh (4), India (2), Sri Lanka (2), and Viet Nam (1). In Figure 9, the data points are Bangladesh (4), India (2), Sri Lanka (1), Nepal (1), Philippines (1), and Guatemala (2).

Figure 10 - Actual underweight prevalences, by predicted prevalences for OLS and country fixed effects, underlying determinant models

Source: IFPRI Cross-Country Child Malnutrition Determinants Data Set, 1997/98.

According to the conceptual framework (Figure 1) and comparison of the separate-model and combined-model specification presented earlier, the basic determinants affect child malnutrition through their influence on the underlying determinants. Table 8 gives country fixed-effects regression estimates of the impact of GDP and DEMOC on each underlying determinant using the quadratic form for the CM-GDP curve. All parameter estimates are statistically significant except for DEMOC in the FEMSED (column 2) and LFEXPRAT (column 3) equations.

Specification Tests. Ramsey RESET test for Omitted Variables (OV) bias. The FE basic-determinants model weakly rejects the null hypothesis that the Z matrix proxy variables are zero, that is, that no OV bias exists. The null hypothesis is rejected at the 5 percent level but not at the 1 percent level. For the underlying-determinant FE model the null hypothesis is not rejected. This indicates that the preferred FE specifications are probably not plagued by serious OV bias, but with more confidence in the underlying-determinant than basic-determinant specification. Note that the OLS basic-determinants model strongly rejects the null hypothesis, suggesting that there is strong OV bias in the parameter estimates. For the underlying-determinant model the null is weakly rejected (at a 5 percent significance level).

Figure 11 - Actual underweight prevalences, by predicted prevalences for OLS and country fixed effects, basic determinant models

Source: IFPRI Cross-Country Child Malnutrition Determinants Data Set, 1997/98.

Hausman-Wu endogeneity tests. The instrumental variable candidates for the Hausman-Wu tests are listed in Table 9, Only one instrument each is identified for SAFEW and LFEXPRAT. Multiple instruments are available for FEMSED, DES, and GDP. The rationale for selection of each instrument is given in the table, along with the data sources. The instruments "arable land per capita" and "economic openness" are not significantly correlated with DES and GDP, respectively (see last column). They are thus excluded from further testing. No instrument is identified for DEMOC.

Table 8 - Underlying-determinant variable regressions with basic-determinant variables as independent variables

Variable	Access to safe water (SAFEW) (1)	Female secondary school enrollment (FEMSED)(2)	Female-to-male life expectancy ratio (LFEXPRAT) (3)	Per capita dietary energy supply (DES) (4)
Per capita GDP (GDP)	.0174 (2.85)***	.0148 (371)***	1.0E-05 (1.90)*	.4105 (6.26)***
GDP2	-1.31E-06 (2.31)**	-9.32 E-07 (2.53)**	-8.2E-10 (1.67)*	-2.79 E-05 (4.59)***
Democracy (DEMOC)	3.49 (2.87)***	.981 (1.23)	-.002 (1.57)	26.28 (2.0)**
R2	.835	.922	.901	.902
Adjusted R2	.740	.877	.845	.846

Notes: The number of observations for all regressions is 179 (63 countries). Absolute values of t-statistics are given in parentheses. The regressions are estimated using a country fixed-effects specification.

* Significant at the 10 percent level.

** Significant at the 5 percent level.

*** Significant at the 1 percent level.

Table 10 reports the results of the relevance, overidentification, and Hausman-Wu tests for the FE model specifications. The tests for SAFEW and LFEXPRAT are restricted to subsamples of the full sample because data on their instruments are scarce.

The instrument for LFEXPRAT (percent of births attended by health staff) does not pass the relevance test. Therefore, the Hausman-Wu test cannot be performed for the women's relative status indicator. One set of instruments for DES - land in cereal production, fertilizer use, and irrigated land - also does not pass the relevance test. Fortunately, another set, that containing only fertilizer use and irrigated land, passes the test at a 5 percent significance level. One set of instruments for FEMSED - male primary enrollments and public expenditures on education - also does not pass the relevance test. Two other sets do, however. The instrument for SAFEW (water resources) and the instrument set for GDP (investment share of GDP and foreign investment share of GDP), also pass the relevance test. For all relevant instrument sets, F >1. Thus IV estimates, if deemed preferable, would be less biased than the FE estimates.

The overidentification test cannot be performed for SAFEW as only one instrument is available. While there is no statistical evidence that this variable is not correlated with the error term in the CHMAL equation, intuition suggests that it is not (see "Rationale for Instrument Choice" in Table 9). Therefore, the Hausman-Wu test is performed, assuming that the water resource instrument is valid despite its limitations. for FEMSED, only the instrument set containing the availability of secondary school teachers and public expenditures on education passes the test. It is this set that is used for the Hausman-Wu test. For DES and GDP the test is undertaken for the linear models in columns (3) and (4) of Table 6.³¹ Both sets of instruments easily pass the test: the null hypothesis that the instruments should not be included in the list of original explanatory variables and are not correlated with the error term in the CHMAL equations is not rejected. Therefore, it is assumed that the instrument sets satisfy these conditions for the nonlinear model as well, and that they are valid for performing the Hausman-Wu test.

³¹ The test is not performed using the quadratic model because DES and GDP are too highly correlated with their squares, such that the test's power is diminished. For the interested reader's information, a relevance test for DES and DES-squared using an instrument set made up of fertilizer use, irrigated land, and these variables squared is not passed (p=0.163 for DES, p=0.11 for DES-squared). The overidentification test using this instrument set gives a p-value of 0.87.

Table 9 - Instrumental variable candidates for endogeneity tests

Explanatory variable	Candidate instrument	Rationale for instrument choice	Data source	Correlation between instrument and variablea
Access to safe water (SAFEW)	Annual internal renewable freshwater resources per capita	Fresh water availability is unlikely to affect child malnutrition other than through provision of safe water.	World Resources Institute (various years)	0.19 (p=.043)
Female secondary school enrollment (FEMSED)	Male gross primary school enrollment	Current male primary school enrollment unlikely to be contemporaneously correlated with malnutrition of children under five, yet to be correlated with female secondary school enrollment through the value placed on education and through its availability.	UNESCO 1998	0.55 (p=.000)
	Secondary school teachers per capita	Number of teachers available per person directly constrains the ability of parents to send their children to secondary school. However, could also affect child nutrition through male enrollment.	UNESCO 1998. Population data from World Bank 1997a	0.80 (p=.000)
	Public expenditures on education as a percentage of GNP	Public investment in education is positively correlated with the availability of educational facilities and teachers, which directly constrains the ability of parents to send their children to secondary school. However, could also affect child nutrition through male enrollment.	UNESCO 1998	0.29 (p=.000)
Female-to-male life expectancy ratio (LFEXPRAT)	Percent of births attended by health staff	Births attended by health staff are likely to be positively correlated with female life expectancy through reduced maternal mortality, yet the nutritional status of surviving children may not be affected.	UNICEF various years. World Bank 1997a	0.39 (p=.000)
Per capita dietary energy supply (DES)	Arable land per capita	Land availability is a constraining factor in agricultural production; however, it could affect child malnutrition by raising incomes from nonfood production.	FAO 1998. Population data from World Bank 1997a	-0.10 (p=.17)
	Land under cereal production per capita	Land employed as an input into cereal production raises food production. May affect child malnutrition other than through DES by raising incomes.	FAO 1998. Population data from World Bank 1997a	-0.19 (p=.014)
	Fertilizer use per hectare of arable land	Fertilizer use increases agricultural yields. May affect child malnutrition other than through DES by raising incomes or causing illness in children due to leakage of contaminants into water tables.	FAO 1998	0.49 (p=.000)
	Irrigated land per capita	The use of irrigation increases agricultural yields; however, it could affect child malnutrition other than through DES by raising household incomes.	FAO 1998	0.20 (p=.009)
Per capita GDP (GDP)	Real investment share of GDP	As per Pritchett and Summers 1996.	World Bank 1997a, 1998a	0.31 (p=.000)
	Foreign investment share of GDP	As per Pritchett and Summers 1996.	World Bank 1997a, 1998	0.25 (p=.001)
	Economic openness measure	Economic openness may improve national income but not otherwise affect child malnutrition.	Heston and Summers 1998	0.07 (p=.367)
Democracy (DEMOC)	No candidate identified	...	...	...

^a Pearson correlation coefficient. If the p-value (given in parentheses) is greater than 0.1, the correlation is considered to be statistically insignificant.

Table 10 - Results of endogeneity tests

			Relevancea (3)		Overidentificationb (4)		Hausman-Wuc (5)
Potentially endogenous explanatory variables	Instrumental variable set (1)	Number of observations (2)	F- statistic	Test passed?	c2 statistic	Test passed?	t-statistic	Test passed?
Access to safe water (SAFEW)	Water resources	94	3.4*	Yes	...	...	1.2d	Yes
Female secondary school enrollment (FEMSED)	Male primary school enrollments, public expenditures on education	152	1.0	No	...	...	...	Not performed
	Male primary school enrollments, secondary school teachers per capita	136	6.0***	Yes	3.40	No	...	Not performed
	Secondary school teachers per capita, public expenditures on education	119	4.5**	Yes	0.11	Yes	-0.97	Yes
Female-to-male life expectancy ratio (LFEXPRAT)	Birth attendance by health staff	92	0.6	No	...	...	...	Not performed
Per-capita dietary energy supply (DES)	Land in cereal, fertilizer use, irrigated land	163	2	No	...	...	...	Not performed
	Fertilizer use, irrigated land	177	3.1**	Yes	0.71	Yes	1.5	Yes
Per capita GDP (GDP)	Investment share and foreign investment share of GDP	164	8.9***	Yes	0.35	Yes	-0.27	Yes

Notes: These tests are only performed for the fixed-effects model specifications, with quadratic terms representing nonlinearities.

^a The null hypothesis is that the instrument set z in a regression of the potentially endogenous variable on the exogenous variables and z is not significant. If F is greater than the critical value of the F-distribution for 1 percent (***), 5 percent (**), or 10 percent (*) significance tests, then the null hypothesis is rejected.

^b The null hypothesis is that the model is correctly specified (the instruments should not be included in the list of explanatory variables) and the instruments z are uncorrelated with the error term in the CHMAL equation. The c² statistic is equal to N × R², where N is the number of observations, and R² is from a regression of the predicted residuals from two-stage least squares estimation of the original CHMAL regression on the exogenous variables plus z. This test can only be performed when there is more than one instrument available for the variable being tested. It is not possible to perform the test using the nonlinear (quadratic) specifications because DES and GDP are too highly correlated with their squares. The test results reported are for the associated linear models. This assumes that if the instruments for the variables pass the test in the linear models, then they are uncorrelated with the error term in the nonlinear models.

^c The null hypothesis being tested is that the instrumental variable and fixed-effects estimates are different, indicating endogeneity of the variable. The null hypothesis is rejected if the predicted residuals from a regression of the endogenous variable on the exogenous variables and instruments are insignificant when included in a regression of CHMAL on all explanatory variables.

^d This t-statistic is corrected using a procedure laid out in Haddad et al. 1995. The correction is not needed for the other t-statistics because the test was passed using the uncorrected statistic (the correction reduces the size of the t-statistic).

The variables SAFEW, FEMSED, DES, and GDP all pass the Hausman-Wu test. The t-statistics on h in equation (12) (reported in column 5) are all statistically insignificant.³²

³² An attempt was made to undertake the tests for multiple independent variables. However, the sample sizes for the tests proved to be too small for most combined instrument sets. The only variables for which sufficient data exist to perform a dual test are DES and FEMSED. Two instrument sets passed the relevance and overidentification tests for the variables. Using the first set (fertilizer use, irrigated land, male primary enrollments, and public education expenditures), the Hausman-Wu test was passed when a 5 percent significance level criterion was employed, but not when a 10 percent criterion (more stringent) was employed (p=.07, n=152). For the second instrumental variable set (in which secondary school teachers replaces education expenditures), the test was passed, employing the 10 percent level criterion (p=.11, n=136). The test statistics are uncorrected. If they were corrected, the p-values would be even higher, giving added support to the finding that FEMSED and DES are not endogenous in the fixed-effects CHMAL equation.

The above test results indicate that (1) these variables are likely not endogenous, (2) the direction of causality runs from the variables to child malnutrition (and not vice versa), and (3) the fixed-effects (FE) estimates are not seriously plagued by measurement error problems for the variables. In light of the results, one can proceed under the assumption that the FE estimates are as accurate as possible given current data constraints. Since SAFEW, DES, and GDP are the variables for which there is most concern about reverse causality and (in the case of SAFEW) measurement error, the more efficient FE estimates are used rather than the IV estimates for the remainder of this analysis. In addition, that the estimations are based on a sound conceptual framework (Figure 1) and are undertaken with respect to changes over time in the variables provides further assurance that a causal, rather than merely associative, relationship between child malnutrition and the explanatory variables has been identified.

Hausman test for fixed-effects versus random effects (RE). As discussed in Chapter 4, FE estimates are preferred to RE estimates. Here the results of a Hausman (1978) test are given for information only. The test evaluates the null hypothesis that the country-specific effects and the regressors are correlated, in which case RE estimation is inappropriate. The null is rejected (p = .39), indicating that the assumption of no correlation between the effects and the regressors is correct, and RE estimation would be a valid procedure. For the interested reader, a comparison of the FE and RE estimates for the underlying-determinants quadratic model is presented in Appendix Table 30.

Interpretation of the Parameter Estimates. Returning to the preferred estimates in column (3) of Table 7, the coefficients on the first three of the hypothesized underlying-determinant variables are statistically significant and negative. Increased access to safe water, increased education of women, and increased relative status of women all work to reduce prevalences of child malnutrition in developing countries, while increased quantities of food available at a national level do so as well. The strength of their effect declines as they increase. According to the data in the sample, they have no effect after a DES level of about 3, 120 kilocalories.

Consider next the basic-determinant results in column (4). The coefficient on DEMOC is negative and statistically significant, suggesting that increased democracy serves to reduce child malnutrition in developing countries. As indicated by the statistically significant and negative coefficients on the first two segments of the GDP linear spline, increased national incomes per capita also work to reduce child malnutrition. The strength of the effect declines, however, as they increase. After a level of about $4,725, they no longer contribute to reductions in child malnutrition.

The estimation results in Table 8 clarify the means through which GDP and DEMOC affect child malnutrition. The coefficient on GDP in all equations is significant and positive. The coefficient on GDP-squared is significant and negative. The results suggest that per capita national income is probably an important resource base for investment - both public and private - in health environments, women's education, women's relative status, and food availabilities. However, the impact of incremental increases in national income tends to decline as incomes rise (as reflected in both quadratic and spline estimation results when CHMAL is the dependent variable). The coefficient on DEMOC is significant and positive in the SAFEW and DES equations. This result implies that democratic governments are more likely to direct their budgets to improvements in health environments and food availabilities. They are not more likely to direct public resources toward women's education or to women vis-is men.³³

³³ The GDP coefficient(s) in the basic-determinant model (s) captures both the indirect effect of per capita national income on CHMAL and any direct effects that may exist. The value of the total differential of CHMAL with respect to GDP captures both effects. For the quadratic specification, at the sample mean the total differential is -0.0076 (calculated from Table 7, column 2). The value of the indirect effects of GDP on CHMAL through the underlying determinants is -0.006 (calculated from the coefficients in Table 7, column 1 and Table 8, columns 1-4). The small difference between the two gives further evidence that GDP mainly has its effects on child malnutrition through the underlying determinants. The similar comparison for DEMOC indicates that democracy most likely has effects on CHMAL through other means than the underlying determinants. For the quadratic specification, the value of the total differential of CHMAL with respect to DEMOC is -1.45. The value of the indirect effects through the underlying determinants is -0.55, about one-third of the total.

How substantial, in a practical sense, are the estimated effects of the determinants on child malnutrition and how do they compare across determinants? In making such comparisons, again, it is important to consider the underlying- and basic-determinant variables separately since the determinants lie at different levels of causality.

To start with the underlying determinant variables, Table 11, column (2), reports elasticities derived from the coefficient estimates of the FE basic- and underlying-determinant child malnutrition regressions. These numbers give the percentage of reduction in the prevalence of developing-country child malnutrition that can be expected from a 1 percent increase in each variable.³⁴ Among the underlying-determinant variables, by far the largest reduction in the child malnutrition prevalence - 3.1 percent - is predicted to come from a 1 percent increase in the ratio of female-to-male life expectancy. This amounts to a decline of 0.8 percentage point in the sample mean prevalence of 24.6 percent, about two-and-a-half times the annual decline in the last decade. The expected effect is thus quite large. Per capita DES has the next highest elasticity, at -0.95. The elasticity for the first segment of the DES spline function is even higher, while that for the last is zero. The elasticity of FEMSED is -0.3. That of SAFEW is the lowest among the underlying-determinant variables, at -0.174.

³⁴ Full sample elasticities for DES and GDP are estimated using (1) a weighted average of regression coefficients for each of the three spline segments, where the weights are the proportion of the sample data points falling into each segment; and (2) sample variable means. Segment-specific elasticities are calculated using segment-specific regression coefficients and segment-specific variable means.

Table 11 - Elasticities and related statistics for interpreting the strength of the effects on child malnutrition

Variable			Sample (or segment) mean (1)	Elasticity evaluated at sample meana (2)	Developing-country rangeb (3)	Increase in variable needed to reduce prevalence of child malnutrition by percentage pointc (4)	Number in (4) as a percent of developing-country range (5)
Underlying determinant variables
	Access to safe water (SAFEW)		56.2	-0.174	1-100	13.1	13.2
	Female secondary school enrollment (FEMSED)		33.8	-0.302	0.5- 100	4.6	4.6
	Female-to-male life expectancy ratio (LFEXPRAT)		1.0624	-3.092	0.97-1.12	0.0139	9.3
	Per capita dietary energy supply (DES)		2,360	-0.949	1,522-3,605	101	4.9
		DES £ 2,300	2,106	-1.150	...	59	2.8
		2,300 < DES £ 3,120	2,613	-0.343	...	425	20.4
		DES > 3,120	3,230	0	...	...	...
Basic determinant variables
	Per capita GDP (GDP)		2,306	-1.26	300-8,612	74.1	0.89
		GDP £ 800	645	-0.740		23	0.3
		800 < GDP £ 4, 725	2,102	-0.605		150	1.8
		GDP > 4, 725	5,867	0.329
	Democracy (DEMOC)		3.5	-0.181	1-7	0.79	13.1

Note: The numbers in column (5) provide a scale-neutral measure of the strength of impact of each variable, which allows comparison across the variables. The lower the number, the greater the strength of impact of the variable.

^a Estimated percent change in CHMAL resulting from a 1 percent increase in the explanatory variable based on estimates of Table 8, columns (3) and (4). The segment elasticities for DES and GDP are evaluated at the variable and CHMAL means for the data falling within the segments.

^b The end points of the developing-country ranges are for the following countries and years (minimum, maximum): SAFEW (Gabon 1970; Barbados 1990s), FEMSED (Mauritania 1970; Bahrain 1993); LFEXPRAT (Nepal 1975, maximum: Brazil 1996 and El Salvador 1993. Note that these numbers are only based on this study's sample and the maximum value for the sample, that of 1.15 for El Salvador in 1988 is excluded); DES (Ethiopia 1977, Turkey 1995); GDP (Ethiopia 1992; Chile 1995); DEMOC (see Table 3 for examples from this study's sample).

^c Calculated as 1 divided by the regression coefficients of Table 7, columns (3) and (4).

Compared to the elasticities of LFEXPRAT and DES (for the full sample), those of FEMSED and SAFEW are quite small. However, the variables are all measured in different units. In comparing the strengths of their effects, attention must be paid to the range of numerical values each actually takes on. These ranges, based on the minimum and maximum values observed among developing countries over the period 1970-95, are given in Table 11, column (3). The ranges for SAFEW and FEMSED are roughly equal, at about 1 to 100. The comparison of their elasticities is thus straightforward. However, it is difficult to compare the variable SAFEW with LFEXPRAT; the latter takes on values from 0.97 to 1.12. A 1 percent increase in SAFEW over the sample mean would raise it from 56.2 percent to 56.8 percent, quite a small change in terms of its 1 to 100 percent range (only 0.6 of a percent of the range). A 1 percent increase in the variable LFEXPRAT over its sample mean (1.062 to 1.071), by contrast, represents 6 percent of its entire range. Thus, while the variable LFEXPRAT has a large elasticity and SAFEW a small one, it would take quite a large increase in the former, compared with the latter, to raise the variable by 1 percent.

Taking this scaling factor into account, the relative strengths of impact of the variables can be seen from the standpoint of how much an increase in each would be required to bring about the same change in child malnutrition. For example, how much would each have to be increased (holding the others constant) to reduce the malnutrition prevalence by 1 percentage point? These increases are given in Table 11, column (4). They are translated into "scale neutral" numbers that are comparable across variables by calculating each number as a percent of its range (column 5).

A 13.1 percentage-point increase in population with access to safe water would be required to bring about a 1 percentage-point reduction in the prevalence of child malnutrition. This represents 13.2 percent of the variable's range. By contrast, the required increase in female secondary school enrollments is only 4.6 percentage points, representing only 4.6 percent of its range. Thus the required increase in safe water access to bring about the same reduction in child malnutrition is much higher than the required increase in female school enrollments. The required increase in per capita DES for the full sample (101 kilocalories) is 4.9 percent of its range; that of the female-to-male life expectancy ratio (0.0134) is 9.3 percent of its range. Therefore a rough ranking of the underlying determinant variables in terms of their potency in reducing child malnutrition is women's education (greatest potency), followed closely by food availability, followed by women's relative status in third place, and safe water access in fourth place. Note that for countries falling into the low DES range (£ 2, 300) food availability is ranked first and women's education second. For countries falling into the medium and high (>3, 120) DES ranges, however, women's education is ranked first and food availability last. The policy implications of these rankings will be drawn out more fully in Chapter 8.

For the basic determinant variables, national income appears to be a more potent force for reducing child malnutrition than is democracy. The full sample elasticity of GDP per capita, at -1.26, is much higher than that of DEMOC (-0.18). The required increase in GDP to reduce the child malnutrition prevalence by one percentage point is $74. This is a very small proportion of the variable's range, less than 1 percent. By contrast, a very large change in democracy would be required to bring about the same change, an increase in the index of 0.8 points (13 percent of its range). The stronger impact of national income than democracy holds even for the medium GDP segment (between $800 and $4, 725). For the high GDP group ($4, 725), however, democracy prevails as the most potent basic determinant.

Differences Across Regions. Past studies suggest that there may be differences across the developing regions in the determinants of child malnutrition or in the magnitude of their effects, especially for South Asia (see Chapter 3). For the underlying-determinants FE model, a Chow F-test of parameter stability across the regions does not reject the null hypothesis that all the coefficients are identical across regions.³⁵ While some regional differences probably do exist, they are not strong enough to detect given the data in the sample. Thus, it is assumed that the underlying-determinant parameter estimates given in Table 7, columns (3) and (4) apply to all of the regions.

³⁵ The test statistics for the hypothesis that the slope coefficients are equal across all regions is F=1. 15, which is not even significant at the 10 percent level. The highest F-statistic for the five tests of the hypothesis that individual regions differ is 1.54 (for South Asia), which is also not significant.

While from a structural standpoint the child malnutrition-DES relationship does not differ substantially across the regions, the regions do differ greatly in terms of the levels of their per capita DESs. Because the strength of this variable depends on its level, the regions thus differ greatly in the strength of impact of DES on child malnutrition. Table 12, column (2), reports estimates of the DES regression coefficients for each developing-country region.³⁶ Corresponding to their low per capita DESs over the study period, the effects for Sub-Saharan Africa and South Asia are the highest in magnitude, both at about -0.01. The other regions have substantially higher DESs per capita, and thus their coefficient estimates are much lower in magnitude.

³⁶ These coefficients are calculated as a weighted average of the segment parameter estimates, where the weights are the proportion of the sample data points of the region falling into each segment.

Table 12 - Estimated child malnutrition regression coefficients for per capita dietary energy supply and per capita gross domestic product by region, 1970-95

	Per capita dietary energy supply		Per capita gross domestic product
Region	Mean (1)	Coefficient (2)	Mean (3)	Coefficient (4)
South Asia	2,187	-0.0133	863	-0.0255
Sub-Saharan Africa	2,164	-0.0140	879	-0.0222
East Asia	2,595	-0.0085	1,874	-0.0090
Near East and North Africa	3,058	-0.0019	2,527	-0.0067
Latin America and the Caribbean	2,647	-0.0069	4,740	-0.0040
Full samplea	2,360	-0.0099	2,306	-0.0135

Notes: The regression coefficients are calculated using the country fixed-effects coefficient estimates of Table 7, columns (3) and (4). They are calculated as a weighted average of the segment coefficients, where the weights are the proportion of the sample data points of the region falling into each segment.

^a While the regional means are population-weighted, the full sample means are not (see Table 3).

For the basic-determinants FE model, the Chow F-test for parameter stability rejects the null hypothesis that all the coefficients are identical across regions. The test results suggest that there are significant structural differences across the regions in the effects of national income or democracy or both and, in particular, that South Asia differs fundamentally from the others.³⁷

³⁷ For the hypothesis that the slope coefficients are equal across all regions, F=3.09, which is significant at the 1 percent level. The test statistic for the null hypothesis that South Asia differs from the others is F=6.4, which is significant at the I percent level. The test statistic for the null hypothesis that LAC differs from the others is F=3.8, which is significant at the 5 percent level Those for all other regions are statistically insignificant.

As for food availability, the effect of per capita national incomes on child malnutrition for any region depends on its level. Table 12 reports the estimated regional per capita GDP regression coefficients (column 4). In South Asia and Sub-Saharan Africa, which had the lowest GDPs per capita over the study period, the effect of national income is relatively strong. It is much weaker for East Asia, NENA, and LAC.

Note that the regression coefficients reported in Table 12 reflect the regions' average DES and GDP positions as they stood over 1970-95. In Chapter 8, regional differences are discussed in the context of the regions' current positions, which differ substantially from the 25-year study period.

The final clue as to whether there are substantial regional differences in the causes of child malnutrition lies in the magnitudes of the country FE terms included in the regression equations. These terms represent the effects of factors that do not change very much over time (over 13-year periods). A very clear result from the analysis is that the influence on child malnutrition of these unobserved factors is much stronger for South Asia than for the other regions. The mean of the FE coefficients in the underlying-determinants model is 9.6; the mean for South Asia is far above that for the sample and the other regions, at 33.3.³⁸

³⁸ The average FE coefficients for the other regions are Sub-Saharan Africa, 6.3; East Asia, 19.3; NENA, 2; and LAC, 5.7 percentage points.

Estimation Results for Dynamic Models

Tables 13 and 14 present the results of the dynamic estimations for the basic and underlying determinant models, respectively. Consider first the OLS-estimated basic-determinant results (Table 13, column 1). Controlling for current levels of per capita GDP and democracy, child malnutrition in the previous period is estimated to have a highly statistically significant effect on current levels of child malnutrition. This result suggests a strong link between current and past levels of child malnutrition, either through cumulative effects on children over time or intergenerational linkages. The OLS estimates for the underlying determinants (Table 14, column 1) also indicate a strong positive relationship between current and past child malnutrition. SAFEW is the only other variable whose parameter estimate is statistically significant.

In the country FE estimates for both basic- and underlying-determinant models, the coefficient on lagged CHMAL is not statistically significant. Note, however, that the t-statistics on the coefficients are fairly high. The FE estimations require that three data points in time be available for any country included: the current observation, the lagged observation, and a twice-lagged observation (as an instrumental variable). Thus the estimations were limited to 36 countries (54 data points). Only as more data become available will it be possible to determine in a robust manner whether the relationship is statistically significant.

Overall, this analysis indicates, but is not able to give strong evidence in support of, the possibility that child malnutrition may have substantial "feedback" effects. The coefficient estimates on lagged child malnutrition reported in Tables 13 and 14 range from a low of 0.28 to a high of 0.838. If these estimates can be verified, they indicate that a 1 percentage-point increase in the prevalence of child malnutrition today contributes to an increase of between 0.3 and 0.8 percentage points in child malnutrition in the future, regardless of the current state of safe water access, women's education, women's status, food availability, national income, and democracy.

Table 13 - Child malnutrition dynamic regressions, basic-determinant variables

		Country fixed effects
Variable	Ordinary least squares (1)	Without time trend and initial conditions (2)	With time trend and initial conditions (3)
Lagged child malnutrition	.76 (19.3)***	.290 (1.41)	.454 (.941)
Per capita GDP (GDP}	-.001 (2.92)***	-.745 (1.0)	-.0016 (.95)
Democracy (DEMOC)	-.931 (2.64)***	-.0008 (.61)	-1.27 (1.32)
Time trend (t)	...	...	.52 (1.33)
t × GDP0	...	...	.0006 (.87)
t × DEMOC0	...	...	-.903 (1.57)
R2	.856	.0605	.1102
Number of countries	63	36	36
Number of observations	116	54	54