indicator is a determinant specific to education; it is expressed as the ratio between the wages for labor at the next higher and current levels of education for the student in question (an indicator of payoff from continued education). MDG 2 – the objective of making sure that each child completes primary education -- is measured by the net (on-time) primary completion rate expressed as a period measure, i.e. the share of the population that enters the first primary grade in the relevant year that would graduate on time if the rates of net intake and promotion in the year in question were to prevail throughout their primary cycle (in the case of Pakistan a total of five years).<sup>9</sup> In MAMS, primary education is an integral part of a broader education module tracks base-year stocks of students and new entrants through the different grades of the three cycles (primary, secondary, and tertiary). In each year, students will successfully complete their grade, repeat it, or drop out of their level. A share of labor-force-age students exiting from the school system enters the labor force in the segment that matches their educational background. Similarly, a share of the non-school population (perhaps drop outs at an earlier age) that each year reaches labor force age enters the labor force, typically in its least educated segment.

# _Database_

The database for the MAMS application to Pakistan consists of an extensive data set for the simulation base-year – a social accounting matrix (SAM);<sup>10</sup> stocks for production factors (including different types of labor and capital), population, and school enrollment; indicators for selected MDGs and the educational system – as well as a set of elasticities (for production, consumption, trade, and human development relationships), and projections into the future (for growth in GDP at factor cost and the evolution of disaggregated MDG and education 9 More specifically, the net completion rate is defined as net completion rate expressed as a period measure, i.e. the share of the population that enters the first primary grade in the current year that would graduate on time given the current rates of net entry (neting1) and promotion (prom), i.e. the measure uses current rates assuming that the rate of promotion of the current year prevails throughout their primary cycle (for Pakistan the current year and four more years). Mathematically, _NPCR_ t = _NIR_ t∙( _PR_ t)<sup>_y_</sup> where _NPCR_ = net primary completion rate; _NIR_ = net intake rate (0 ≤ _NIR_ ≤ 1); _PR_ = promotion rate (0 ≤ _PR_ ≤ 1); and _y_ = number of grades in the primary cycle. As a simplification, MAMS assumes a uniform _PR_ for all primary grades. Compared to alternative indicators, the gross completion rate or the gross or net enrollment rates, the net completion rate provides a better measure of the performance of primary education in terms of ensuring completion of the full cycle for each child. Gross completion rates (the total number of students completing primary education, irrespective of age, as a share of the total population in the theoretical graduation age) may reach above 100 percent at the same time as far from all children manage to complete the full primary cycle; enrollment rates do not provide information about completion of the cycle.

10 A SAM is a square matrix with identical row and column accounts, providing a comprehensive representation of payments flows in the economy of a geographical unit (typically a country) during a period of time (typically one year). Cell entries represent payments from its column account to its row account. In a SAM without errors, row and column totals are equal. SAMs appear with widely varying degrees of disaggregation. The payments flows are expressed in current local currency or some transformation thereof – in Table 3.3, the value of each cell has been transformed into percent of GDP at market prices in the same year. For more on SAMs, see for example Reinert and Roland-Holst (1997) and Round (2003). The detailed Pakistan MAMS SAM for this application is available on request.

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