# **III. The Distribution of Education Matters**

# _Aggregation, Asset Distribution, and Economic Growth_

Most assets are tradable across firms or individuals. This tradability in a context of competitive markets provides a powerful justification for aggregating assets into an aggregate production function. If physical capital, for example, is freely traded across firms in a perfectly competitive environment, then the contribution of physical capital to aggregate output will not be affected by its distribution across firms or individuals. The reason is straightforward: since the marginal product of physical capital is equal for all firms, reducing the capital of one firm and increasing it for another by the same amount will not affect the aggregate output of the economy. If an asset is not traded or is imperfectly traded, however, then the marginal product of the asset across individuals is not generally equalized. In this case aggregate production depends not only on the total level of the asset but also on its distribution. These insights have been well known at least since Gorman's work in 1950. It is surprising, however, that they have not been exploited systematically in growth models.

The assumption of tradability is probably reasonable for most assets, including physical capital, land, and other resources (although tradability may not always be sufficient to equalize asset returns across firms or households). Where this assumption is probably least reasonable is for the distribution of education across individuals. Education and skills cannot be directly traded: only certain services of these skills are traded. This impose restrictions that may ultimately imply systematic heterogeneity of the marginal product of education across individuals.

The vast variability of natural abilities across individuals and the fact that the education children received depends on factors other than their abilities (parents' income, regional location, availability of schools) and is largely determined by nonmarket mechanisms (including government allocation of educationl services) imply that education levels are not necessarily highly correlated with abilities. That is, the limited role of the market in allocating education may imply large divergence in the value of the marginal products of education across individuals, beyond differences that could be explained by differences in ability.

The importance of these imperfections in the allocation of education and the consequences of such misallocations for aggregate income are examined in this section. We first set up a theoretical framework that integrates asset distribution in the derivation of an aggregate value added or GDP function yielding a structural empirical model. Next we estimate such a model for a group of middle-income developing countries using panel data for 1970-94.

# Consider the following production function of individual i,

## yi = Ak[Paih

(1.1) where yi is value added of individual i, _A_ is the coefficient of total factor productivity associated with the overall conditions of the economy, _ki_ is the share of total capital that corresponds to the individual, ai is a parameter reflecting the level of ability of individual i and hi is the level of education of individual i. The variable k represents the tradable factors that have equal marginal products across individual. Thus we assume that k can be aggregated without consideration of its distribution across individuals.

10