THE IMPACT OF INFRASTRUCTURE SPENDING IN SUB-SAHARAN AFRICA

# 3   The model

The basic elements of the model are drawn from the EXTER model of Decaluwé and others (2001) which we adjusted in order to introduce infrastructure externalities so that there is a function with sector-specific elasticity for infrastructure investment. We therefore prepared the model to consider four types of investment: road infrastructure, health, education, and telecom.

The main hypothesis of our model is that production is determined by a three-way system: total production of the branch ( _XS_ ) comprises fixed value-added shares ( _VA_ ) and intermediate consumptions ( _CI_ ), as is generally assumed in CGE modeling. The relationship determining the level of _VA_ is a CobbDouglas function between composite labor ( _LD_ ) and capital ( _KD_ ). This value-added function is multiplied by the externality, which is a ratio of new investment over past investment with a sector-specific elasticity. Producers minimize their cost of producing _VA_ subject to the production function (CobbDouglas). Optimal labor-demand equations are derived from this minimization process. We assume that capital is partly fixed among sectors because after a policy shock in Africa it is difficult in the short to medium term to convert capital for use in a new production sector. Intermediate consumption is modeled as fixed shares from input/output ratios calculated on the basis of SAM. This modeling is typical.

This is a small, open-economy model to which world prices of imports and exports are exogenous. We posed the Armington hypothesis (1969) for import demand whereby domestic consumers can substitute domestically produced goods with imports (imperfectly) by relying on a sector-specific elasticity of substitution. In sectors where local consumers are indifferent to imported versus local goods, one sees high elasticity of substitution and, inversely, a small elasticity of substitution, where consumers prefer one good versus the other. A high elasticity in one sector implies that a change in relative price between the locally produced good (competing with the imported good) and the imported good will have a strong substitution effect. For example, if the price of the locally produced good increases compared with the price of the imported good, local consumers will substitute the imported good. If the elasticity of substitution is low, this same change in relative price will have only a slight substitution effect. The elasticity of substitution depends _inter alia_ on differentiation between the goods and on the preference of local consumers. The relative price of the two goods is the other determinant of the ratio of demand between imported goods versus local goods. On the export side, producers can sell goods on the local market or export their production; they are influenced by relative prices in each market and by their elasticity when the good is transformed for one market or the other.

The different agents’ income equations are consistent with the structure presented in the SAM. In this model, factor allocations are exogenous while factor payments are endogenous. Because capital is fixed by sector, we have six capital payments and one wage. Dividends paid to households are also endogenous and depend on a firm’s income after taxes. The private firm’s income is the balance of capital remuneration not paid to households, to which must be added government subsidies and transfers from the rest of the world. Government revenue comprises production taxes, customs duties, household, and private firm taxes as well as transfers from the rest of the world (budgetary assistance). The government spends its budget on consumption of public goods, transfers to households, subsidies to private firms, and transfers to the rest of the world and savings.

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