# **3. ANALYTICAL FRAMEWORK**

## **3.1 Models and data**

The magnitude of SACU’s future demographic dividend depends on a range of economic variables that are not easily captured without consideration of the range of possible influencing factors in the global economy, their impact on the economies and households. LINKAGE, the recursive dynamic CGE model is well suited for this task.<sup>9</sup> It is supported by globally consistent data on production, consumption, investment, and trade from the GTAP Database V8.1 (Narayanan et al. 2012). 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 function, while production is assumed to be based on a multi-nested 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.

Output is produced by different production streams—differentiated by capital vintage. Each production stream has an identical production structure based on a multi-nested Constant Elasticity of Substitution functional form, but with different technological parameters and substitution elasticities. At the top of the nest, a value-added bundle is combined with an intermediate inputs bundle under the Leontief technology assumption. The intermediate inputs bundle is combined with different inputs, with an Armington assumption applied to specific inputs. That is, for a given type of intermediate input, there is substitutability between domestic and imported inputs, and then again between imported inputs from different source countries. The value added bundle is made up of unskilled labor being slightly substitutable with a capital and skilled labor bundle. Skilled labor and capital are substitutable.

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 non-agriculture 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

> 9 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).

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