Among the non-SAM data, labor, population and school enrollment stocks were readily available (World Bank 2011a; World Bank 2011b). Private capital stocks were estimated on the basis of capital value-added in the SAM, a net profit rate of 16 percent (Nehru and Dhareshwar 1993, p. 53), and a depreciation rate of 4.5 percent based on a review of the literature (Goldman-Sachs 2006, p. 5; Nehru and Dhareshwar 1993, p. 46). Government capital stocks were estimated on the basis of the assumption that base-year investment levels (in the SAM) matched what was required to ensure that these capital stocks grow at the same rate as GDP, after adjustment for depreciation, compared to cross-country data to verify aggregate plausibility (Arslanalp _et al_ . 2010).<sup>23</sup> Drawing on surveys of econometric evidence, standard values for developing countries were used for elasticities in trade and production (Annabi _et al_ . 2006). Income elasticities for household consumption (entering a linear expenditure system) are from the database of the ENVISAGE model; for details see van der Mensbrugghe (2010). For the poverty module, initial rural and urban consumption poverty rates and Gini coefficients are medians for LICs from the World Bank (2011b) and World Bank (2012).<sup>24</sup> MAMS was parameterized to replicate _base_ -run projections for MDGs 4, 5, 7s, and 7w (underfive mortality, maternal mortality, water access, and sanitation access, each of which was disaggregated into rural and urban) as well as a wide range of education indicators (with data available for a wider range of indicators the lower the level of education), generated on the basis of constant-elasticity regressions of these indicators on gross national expenditure (or absorption) per capita and the simulated evolution of GNE per capita under the _base_ run (Quijada 2012). The definitions of individual elasticities, which drive the relative importance of the different determinants in Table 2.1 (indicated by decompositions) was informed by a survey of cross-country studies, complemented by judgment calls (Lofgren 2010); in this application, roughly 30-40 percent of the changes in MDG and education indicators is attributed to changes in services and private per-capita consumption with the remainder due to the other determinants (cf. Table 2.1). Econometric estimation of the details of these relationships remains very challenging for a number of reasons: causality may go in both directions (higher incomes improve health and better health improves incomes) and include complex time lags; many of the variables (determinants and outcomes) are highly correlated; relationships may vary over time and space; and data is imperfect. To provide an example with regard to the latter point: it near impossible to determine the levels of real supplies of government education or health services in the absence of relevant price indices and a separation of spending data into current and capital.

This MAMS application includes links between growth in TFP and growth in government capital stocks in agriculture and public infrastructure; drawing on available evidence (see for example Foster and Briceño-Garmendia, 2010, p. 71; IMF 2008, p. 20; and World Bank 2007a, p. 65), the

> 23 Cross-country data on total private and government capital stocks (with values expressed as shares of GDP) constitute a source of checks on initial estimates. As an additional check on initial capital stocks and depreciation rates, dynamically one would expect a growing developing economy with investment rates that match historical data to see its private capital stocks grow faster than its labor force, i.e. to experience a process of capital deepening in its private sector (as well as in the economy in general).

> 24 Israel Osorio-Rodarte extracted the rural and urban poverty data from the I2D2 database.

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