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close this bookReversing the Spiral - The Population, Agriculture, and Environment Nexus in Sub-Saharan Africa (WB, 1994, 320 p.)
close this folder4. The Nexus of population growth, agricultural stagnation, and environmental degradation
View the documentThe main linkages
View the documentTraditional crop cultivation and livestock husbandry methods
View the documentLand and tree tenure systems and the Nexus
View the documentDeforestation, fuelwood, and the Nexus
View the documentLogging
View the documentNotes
View the documentAppendix to chapter 4

Appendix to chapter 4

Statistical Analysis to Explain Intercountry Variations in Crop Yields

As in the case of the analysis of total fertility rates, two independent statistical investigations were undertaken to explain the cause of variation in yields per hectare of various crops, between countries and over time. (Both are described more fully in the Supplement.) Unfortunately, some of the relationships discussed in Chapter 4 could not be investigated due to lack of suitable data. However, limited testing may establish the plausibility of the hypotheses

· Incidence of drought will significantly affect crop yields.

· Crop yields should be higher where population is growing most rapidly relative to cultivated land. People begin to intensify agricultures cultivable area per person declines. Hence, statistical analysis should show an inverse relationship between area cultivated per person and crop yields (all other things being equal). However, the rate of growth in yields stimulated by declining availability of cultivable land per person will be significantly lower than the rate of population growth.

· Efforts to stimulate intensification (use of fertilizer, for example) will significantly accelerate the increase in crop yields beyond the growth rate stimulated by rising population density alone. This should be observed as higher yield growth rates in countries using more fertilizer (all other things being equal).

· Primary school of males and females, should facilitate farmer adoption of intensive farming techniques and therefore be associated with higher crop yields.

· Countries with more rapid degradation of their natural resource endowment, as reflected in higher rates of deforestation, should have lower crop yields, other things being equal

· Countries with a policy environment more accommodating for profitable market-oriented farming should have higher crop yields than countries with less conducive policies.

Pooled Cross-Country Time Series Analysis

The pooled cross-country time series analysis investigated the determinants of crop yields for cereals as a whole, as well as separately for rice, maize, sorghum, wheat, and cassava. The independent variables were drought, the nominal protection coefficient (representing the adequacy of agricultural policy), primary education, and cultivated area per capita. The higher the nominal protection coefficient, the higner is the farmgate price of the commodity relative to the world price. This is a proxy for the quality of the agricultural policy environment.

In summary, the following results were obtained (see the Supplement for details):

· Crop yields are negatively related to drought the coefficient on drought is negative for all crops and in all cases except for rice significant at the 10 percent level (this is the 2-tail significance test, meaning that there is a 90 percent probability that the coefficient is different from zero).

· Crop yields are positively related to good agricultural price policy the coefficient on the nominal protection coefficient is positive and in the case of cereals and sorghum significant at the 10 percent level. It shows no impact on cassava yields, however; this makes sense because cassava is a subsistence crop which is least affected by price policy.

· Crop yields are positively related to primary education the coefficient on primary education is positive, except for cassava and maize where it is highly insignificant. In the cases of rice and sorghum, it is significant at the 10 percent level.

· As hypothesized, yields are higher as the availability of cultivated land per capita declines: the coefficient on per capita land under annual and permanent crops is negative, except for cassava where it is highly insignificant. In the cases of rice and maize' it is significant at the 10 percent level. This means that for the crops which are most commercialized, the smaller the land holdings, the higher the yield (other things being equal).

· The for cassava are strikingly different from those for the cereal crops. Neither the nominal protection coefficient, nor primary education, nor per capita farm size affect cassava yields. Cassava is a subsistence crop and rarely traded on international markets.

Single-Observation Cross-Country Analysis

A separate analysis was undertaken of the causes for variations in crop yields using a different data set with single observations for each country. The main drawback of this approach is that it eliminates the time dimension from the analysis and that there are fewer observations. On the other hand, it allows a larger number of independent variables to be included. This analysis tested the statistical relationship between cereal yields (averages far 1984-1986) as the dependent variable, using as independent variables: cultivated area per person (average 1965-1987), fertilizer use per hectare m 1987/88 (fertilizer use remained fairly stable in the 1980s), percentage of the school-age population in primary school (average 1965-1987), the rate of deforestation in the 1980s, and the general "appropriateness" of agricultural policy during the period 1980 to 1987. Except for the rate of deforestation, the values for each variable were converted to their natural logarithm and a regression equation was fit to these data, the coefficients reported below therefore represent elasticities. Policy appropriateness is represented by a dummy variable having the value 1 for countries where policy is judged to have been conducive to profitable agriculture, and 0 where it is judged to have been inappropriate: Of the thirty-eight countries considered, twentyfour were judged to have pursued inappropriate policies, fourteen appropriate. This rating of countries is consistent with the categorization by the World Bank; it is, however, highly subjective. The role of women in agriculture and the effect of the land tenure situation could not be quantified and therefore were not tested in their impact on yields.

The equation, with the dependent variable being average cereal yields in 1984/86 (natural logarithm), is as follows:

Independent Variable

Coefficient t-statistic

2-Tail Significance Test





Cultivated ha per persona




Fertilizer use per haa




Primary school enrollment ratea




Deforestation rate




Agricultural policy dummy




Adjusted R squared = 0.45

F Statistic = 7.0

a. Converted to natural logarithm.
b. Represents elasticity.

The equation explains about 45 percent of the differences in cereal yields among the thirty-eight countries; this is not as good as the pooled time series cross-country equation.

Consistent with the hypotheses and with the results from the pooled time series cross-country data, the smaller the cultivated area per person, the higher are cereal yields, all other things being equal. The coefficient (0.3) is identical using the two sets of data. The statistical relationship is highly significant, with a t-statistic of 2.5, and with a 2-tail significance test of 2 percent (indicating only a 2 percent probability that the coefficient is actually zero). It suggests that the pressure to intensify farming mounts with increasing population density on cultivated land; it is true even when the use of fertilizer and other modern inputs, the policy environment and primary school enrollment rates are held constant. This reflects farmers' ability to respond to rising population density with simple technological innovations. But, also consistent with the hypotheses, the coefficient is less than 1, suggesting that a decline in cultivated area per person (due to population growth) will only stimulate people to intensify farming at a rate of about one-third that of population growth itself. Historically, this is what happened. Cropland expanded at a rate of less than 1 percent per year, and yields increased on average by slightly more than I per year, giving an agricultural output growth of only about 2 percent per year for SSA as a whole for the 1965 1990 period.

A 1 percent increase in fertilizer intensity is associated with a 0.1 percent increase in cereal yields. The coefficient is significant statistically (2-tail test of 10 percent, indicating a 90 percent probability that the coefficient is not zero). Since fertilizer use is extremely low in SSA (averaging 85 grams per ha in 1987/88, compared to China, for example, where * is 2,360 g/ha), there is vast scope for increasing its use. This is also true for other modern tools and inputs, with which fertilizer use is highly correlated; given this correlation, the fertilizer variable also picks up the effect of the use of other modern inputs. Growth rates of fertilizer use (and other modem inputs) of 10-15 percent per year during the next decade are feasible. This would stimulate growth of cereal yields, according to this equation, by 1.0-1.5 percent per year.

A 1 percent increase in the share of prirnary school-age children enrolled in school is associated with an 0.17 percent increase in cereal yields. The statistical relationship is weak, but when added to the evidence cited in the text and the significance of this variable in the pooled cross-country time series tests, it suggests that better overall educational attainment has a positive impact or farm productivity This makes sense, since in most SSA countries the majority of the adult popuIation works in agriculture and associated activities.

The dummy variable representing agricultural policy adequacy is statistically significant in explaining cereal yield variation among countries. A better policy environment is associated wit., higher yields, all other things being equal This is consistent with the pooled cross-country time series analysis showing the significance of the nominal protection coefficient.

Consistent with the hypothesis, countries experiencing the most rapid deforestation have lower cereal yields, all other things being equal But the statistical relationship shows no significance The problem may be that deforestation is endogenous. The statistical tests summarized in Box 4A.2 suggest that deforestation itself is related to population density on cultivated land, intensity of fertilizer use, and agricultural policy. Therefore, when assesing the determinants of crop yields across countries, these other factors already pick up the impact of deforestation, thus leaving deforestation as such with a coefficient not significantly different from zero.

The above analysis also suggests the plausibility (though not the likelihood) of achieving 4 percent per year average growth of agriculture in SSA. This could occur from: more late or use per hectare facilitated by continued population growth (causing a 1 percent increase in annual output growth), 15 percent annual yield growth attributable to a 15 percent annual increase in the use of fertilizer (and of other modern inputs); and a rate of expansion in the cropped area of 05 percent per year This gives a total output growth rate of 35 percent per year An increase in the number of countries with appropriate agricultural policy and with primary school enrollment increasing at 2 percent per year should suffice to provide the additional 05 percent annual growth rate required to reach the postulated aggregate growth target. However, in the long run, as population growth slows, the scope for policy improvement narrows, and further expansion of cropped area becomes less feasible, sustaing 4 percent annual growth wilI become more difficult. It will depend increasingly on greater use of modern inputs and equipment, genetic improvements in crops and livestock, and improvements in people's educational attainment. Hence the importance of improved agricultural research and extension and of general education

Statistical Analysis to Explain Intercountry Variations in the Rate of Deforestation

The analysis in Chapter 4 suggests that deforestation is related positively to population pressure on cultivated land (the smaller the cultivated area per person, the higher the rate of deforestation), the rate of population growth (the higher population growth rate, the higher the rate of deforestation due to land clearing and fuelwood provision), and policies favorable to agriculture (the more profitable agriculture and logging, the more rapid the clearing of forests). It is negatively related to the use of modern farm inputs such as fertilizer (the greater the use of modern farm inputs, the lower the need to clear more land for farming). Open-access land tenure situations were also hypothesized to stimulate deforestation, but this cannot be quantified.

To test these hypotheses, regression analysis was undertaken with the rate of deforestation as the dependent variable. Two separate data sets were used, as described for the analysis of crop yields (seethe Supplement for details).

The nominal protection coefficient has no statistically significant relationship with deforestation, contrary to the hypothesis.

Using the data set with single observations per country, the dummy variable distinguishing countries with good agricultural policy (the variable has a value of 1) from those having poor policy (value 0) is nearly significant (2-tail test of 11 percent, or significance at the 89 percent level). The coefficient is positive, as hypothesized. The result is therefore ambiguous. Even if poor agricultural policy were to reduce the rate of conversion of forest to cropland, it would not be appropriate to pursue poor agricultural policy to conserve forest resources, because the objective of accelerating agricultural growth will override that of reducing the rate of deforestation in every country. However, this finding does suggest the need for mitigating actions to retard deforestation when agricultural policy is good. Land use planning will be important in this context.

The hypothesis that population pressure on cultivated area increases the rate of deforestation could not be confirmed. In the pooled cross country time series analysis, the relationship is not statistically significant In the simple cross-country sample, this variable had the expected negative coefficient (the smaller the cultivated area per person, the higher the rate of deforestation), but the significance level was very marginal (2-tail significance test of 15 percent). The result is therefore ambiguous and unconfirmed.

Drought proved to increase the rate of deforestation significantly.

As hypothesized, the use of modem farm inputs such as fertilizer is negatively related to the rate of deforestation. Intensifying agriculture slows the rate of deforestation This is likely to be the most important policy available to deal with this problem.