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60 SAMUEL BENIN, SHENGGEN FAN, AND MICHAEL JOHNSON


3A.2, and 3A.5 for measures of these variables. This aggregation simplifi es the appli- cation of Equation 13 further and is, in fact, how the formula is usually applied in the case studies (specifi cally, those for Ghana, Kenya, Malawi, Nigeria, Rwanda, Uganda, and Zambia). Details of exactly how aggregation is done as well as the parameters and sources of data used are discussed in the specifi c cases. We summarize the key similarities and differences here, however. The analyses for Ghana, Malawi, Nigeria, Uganda, and Zambia are most similar in terms of applying the formula as it has been presented. It was applied using simple spreadsheet analysis. The main differences are the sources of information on expenditure–growth elasticities. In the cases of Ghana and Uganda, we draw on elasticities from previous work carried out by others in the respective countries. In the case of Malawi, Nigeria, and Zambia, we rely on parameters estimated at the pan-African level, also from previous work done by others using cross-country regression techniques. Although the case study on Kenya also uses parameter estimates from other studies, specifi cally those esti- mated for Uganda, the resource requirements are simulated by directly integrating the formula in the DCGE model for Kenya through a set of nested linear equations. The approach used in the case study on Rwanda is similar to the formula presented here, although in addition it used data on expenditures of specifi c agricultural sub- sectors in the scenarios (as was done to some extent in the case study on Kenya). In applying the formula, there are some simple assumptions to be borne in


mind. The main one is that the estimated elasticities are assumed to be valid outside the range of the data used in estimating them. This assumption is used to infer outcomes associated with large changes in required growth of PAE, which is due to the large gap between the observed and target agricultural GDP growth rate in most of the case studies. In reality, elasticities may change over time to refl ect increasing or decreasing returns to public spending. These dynamic effects are diffi cult to implement in the formula adapted here, and so we assume that the values of the parameters remain unchanged over the simulation period. Although this assump- tion may seem extreme and unrealistic in some cases, the results based on it have useful implications for reforming fi scal policy and public spending to raise and maintain high agricultural productivity. Another important consideration of the results not dealt with is how the addi- tional spending will be funded and implications of different fi nancing arrangements on the outcomes, with the exception of the Kenyan case study to some extent. One possible source of fi nancing for additional spending is from domestic sources through increased taxation of or borrowing from the savings of the private sector. Raising taxes can have negative total investment effects (that is, by crowding out private investment) to the extent that public and private spending is a zero-sum game. For example, in response to higher taxes, households may adjust their savings downward to maintain their current consumption levels, leading to a reduction in


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