# **3. Methodology**

## **3.1 Models and Data**

The magnitude of SSA’s future demographic dividend depends on a range of economic variables that are not easily understood through analysis of only _ex post_ data or without consideration of the range of possible influencing factors in the global economy. A dynamic simulation model that can capture these diverse global behaviors in general equilibrium is thus necessary. LINKAGE, the recursive dynamic computable general equilibrium (CGE) model of the global economy at the World Bank (van der Mensbrugghe, 2011), is ideally suited for this task,<sup>7</sup> supported by globally consistent data on production, consumption, investment, and trade from the GTAP Database V8.1 (Narayanan, et al., 2012). For computational purposes, the database is aggregated to consider 30 countries and regions (17 of which are individual countries of SSA and one of which is a residual for the rest of the region) and seven sectors.<sup>8</sup> LINKAGE is a multi-sectoral, multi-country and multi-agent dynamic recursive CGE model that assumes perfect competition, with equilibria in a given year being dependent on current year prices and quantities, and the previous year’s equilibria. Household demand behavior is modeled using the Constant Difference of Elasticities (CDE) function, while production is assumed to be based on a multinested CES function. At the top of the multi-nested structure, an aggregate of intermediate inputs is combined with an aggregate value added under Leontief technology. Unskilled labor is substitutable for a skilled labor and capital composite, while skilled labor and capital are themselves complementary. The model takes a vintage approach to capital in production, so production can occur with either ‘old capital’ or ‘new capital’. The key difference being that ‘new capital’ is slightly more substitutable (or slightly less complementary) with skilled labor than ‘old capital’.

LINKAGE also considers segmented labor markets in developing countries, i.e. there are separate labor markets for unskilled labor in agriculture and non-agriculture. Endogenous migration of unskilled labor from one market to another within a country is modeled as a function of the wage of unskilled workers in agriculture relative to the wages received by unskilled workers in the nonagriculture market.

Since LINKAGE is a structural micro-foundations model that is consistent with neo-classical growth theory, aggregate growth depends on changes in the labor force, the capital stock, and total factor productivity. The economic impact of demographic change must therefore occur through one of these channels, and the key neo-classical growth drivers in LINKAGE that will be sensitive to demographics are the labor force and the capital stock. As a simulation is implemented over time, the skilled and unskilled labor forces for a given country are exogenously changed. At the same time, the model keeps track of the young (less than 15 years of age), working age (15-64 years of age), and aged (over 64 years of age) populations, following the values of the medium fertility scenario of the United

> 7 It must be noted that LINKAGE is able to support alternative assumptions about production and consumption behavior, factor market segmentation, _inter alia_ . This section describes the assumptions considered in the application of LINKAGE specific to this paper. Details on LINKAGE can be found in van der Mensbrugghe (2011). 8 GTAP regions aggregated to 28 economies (Table A1). GTAP 57 sectors aggregated to seven sectors: agriculture, fishing and forestry, natural resources, food, manufacturing, infrastructure, and services.

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