captures the traditional Katz and Murphy (1992) college premium, while the second term represents the high school premium – the difference in wages within the two groups that constitute the unskilled aggregate. Large values for the elasticities of substitution _σ_ suggest that the two types of labor are close to perfect substitutes, and relative wages would then be uncorrelated with relative quantities.

The model from which these equations are derived captures the intuition of the Tinbergen’s framework: for instance, the wage skill premium between skilled and unskilled labor will decline when the relative supply of skilled labor _St/Ut_ increases, and it will rise with positive changes in the relative demand parameter. Moreover, the greater the elasticity of substitution between two factors, the greater must be the fluctuations in their relative demand to explain any given time series of relative prices for a given time series of observed relative quantities.

A limitation of the Tinbergen framework and its subsequent applications, however, is that for all its emphasis on both supply and demand factors, it does not provide for an unambiguous way to approximate changes in demand. This limitation is due to the difficulty of identifying simultaneous demand and supply movements from observed quantities and prices which are, by definition, equilibrium points resulting from the intersection of the two corresponding curves. While the constructed supply and wage skill premiums also result from market equilibrium, it is plausible to argue that the supply index, based on population stocks, represents the actual relative supply. Katz and Murphy (1992) and the subsequent studies in this literature use observed wage premiums and relative changes in quantities of skilled and unskilled labor as measures of relative prices and supply, respectively, and then compute the changes to the relative demand of skilled labor as a residual – that is, as the figures that would be compatible with the observed changes in prices and supply for a given levels of the elasticity of substitution between both factors (see Appendix B).

# **_3.2 Estimation of wage skill premia, relative supply, and relative demand factors_**

This section presents results using the approach described in the previous section for 16 countries in Latin America from 1989 to 2009. The analysis is based on a careful process to construct country and time consistent aggregate measures of labor supply and wages by skill level.<sup>6</sup> The two wage skill premiums (left hand side terms on equations 1 and 2) and the relative supplies of labor (last terms on the right hand side) are constructed from household survey data for each country. Intuitively, the skill premiums are derived from wage differentials in Mincer-type wage regressions, while the relative supplies are weighted functions of the proportions of each group of workers in the population.<sup>7</sup> More specifically and following Katz and Murphy (1992), this study derives the relative supply _St_ / _Ut_ by dividing the population of each country into 24 groups according to its educational level, gender, and potential experience, and then computes the average wage for all years with respect to the wage

> 6 The specific details on the construction of these variables are presented in Data Appendix B.

> 7 As in Manacorda _et al._ (2010), the whole population between 25 and 55 years old is used to construct our measures of labor, although all the results are qualitatively and quantitatively similar if the supplies are derived from those in the labor force, from those working, or from the proportion of total hours worked by each skill group. Manacorda _et al._ (2010) also find no qualitative difference when using these four alternative definitions of supply.

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