parents may not need their children to work). The aggregate measure is strictly increasing in all of its components, and does not capture potential bottlenecks and/or the decreasing returns to scale as the target approaches (due to the difficulty of reaching the most remote parts of the population or, for example, necessity of high-level medical care to reduce maternal mortality beyond a certain threshold). In order to account for these effects, the top level of the MDG production nest links this aggregate measure of MDG service delivery to actual MDG outcomes by requiring greater and greater improvements in the former for the same rate of improvement in the latter. This is accomplished by using a logistic function with the MDG outcome as a dependent variable and the aggregate measure of MDG service delivery as an independent variable.

The treatment of the education sector slightly differs from other MDGs. The model explicitly tracks base-year stocks of students and new entrants through three education cycles: primary, secondary, and tertiary. In each year, students can successfully complete their grade, repeat it, or drop out of their cycle. Similar to other MDGs, student performance depends on educational quality (growth in spending per student), improvements in household welfare (per-capita household consumption, which captures the demand side), growth in public infrastructure spending, and other MDGs. However, educational outcomes are also positively influenced by good returns to education (proxied by the wage premium paid to skilled workers).<sup>6</sup> The achievement of MDG 2 requires that all students in the relevant age cohort enter the primary cycle and successfully complete each year within this cycle. In the model, this is translated into requiring that the rates of 1st grade entry, graduation, and continuation to next grade within the primary cycle are at or very close to 100 percent for a six-year period prior to 2015.

A major advantage of MAMS is its ability to simultaneously determine MDG progress, supply and demand of private goods and services, and factor markets equilibrium. In the model, this is accomplished through several links between the MDG module and the rest of the economy. Firstly, the increase in government service provision needed to reach the MDGs requires additional resources—capital and investment, labor, and intermediate inputs—that become unavailable to the rest of the economy. As an example, this link allows the model to capture the wage hikes for skilled labor that may stem from the combination of its small supply and rapid demand expansion (from MDG services that are intensive in skilled labor). These demand increases are likely to reduce the number of skilled workers available to the private sector even as increased school enrollment reduces the overall labor force. On the other hand, by allocating graduates and dropouts from the education system to different segments of the labor force (as a function of the highest degree achieved), MAMS captures the supply side of expanding education services, which works in the opposite direction by depressing relative wages of labor categories with the most rapid growth. If government services rely heavily on these labor types, government costs and financing needs decline. Moreover, a higher average level of education raises the productivity and the wages of the labor force, with a positive feedback on growth, private incomes, government revenues, and MDG achievements.

> 6 A large micro-econometric literature exists on how to model the production and the demand for education. MAMS simply summarizes the most salient points of this literature in a simple reduced form equation. The main advantage of this approach is its general equilibrium method but it is not at all a substitute to more detailed sectoral analyses.

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