# **4   Calibration**

I now move on to the quantitative analysis and begin by discussing the calibration of the model.

## **4.1   Calibration of time-invariant parameters**

First, let me consider the parameters of the model that remain invariant over the decades. There are seven such parameters. Barring the elasticity of substitution across occupation-specific labor inputs , all time-invariant parameters are calibrated at the country level. For the baseline results, I assume 4 and report the responsiveness of the results by considering other values of in the appendix. σσ σσ= The preference parameter captures the trade-off between consumption and time dedicated in σσ accumulating human capital. I calibrate to match the Mincerian returns to schooling at the occupationββ group level after adding gender controls. ββ To calibrate the elasticity of human capital with respect to associated expenditures, I use the share of GDP (adjusted for the share attributed to labor) spent on education. The education expenditure ηη share includes both private and public spending. The World Development Indicators database (World Bank, 2019) contains annual series on the government expenditure on education as a share of GDP for many years since 1970. The average of this series serves as one component of the total education expenditure.<sup>12</sup> The OECD Indicators database (OECD, 2019) comprises some information on the private education spending across countries. However, the data are sparse both in terms of country and time coverage. The only CENAM for which the private education expenditures are available is Costa Rica. Moreover, this data is available only for 2013. The private education spending as a share of GDP stood at 2 percent in 2013 and I use this as a baseline for all countries.<sup>13</sup> Nonetheless, I note that this value is higher relative to many countries in the OECD database and it is likely that the actual values are lower. Finally, I use a labor income share of 0.65 to adjust the education expenditure share for all countries. There is a wide range of estimates of this parameter with many well-known measurement concerns. The chosen value lies within the range of the estimates and near the median and the average across countries and years (Gollin (2002), Guerriero (2019)).

The Fréchet shape parameter governs the skill dispersion and an increase in its value reduces the variability of innate talent. To estimate this parameter, I fit the residuals obtained after regressing the log of hourly wages on occupation-group-dummies to estimate in an intermediate step. The value of is recovered given the estimate of via the process discussed previously. θθ(1 −ηη) θθ The only time-invariant parameters that need calibration are the experience-related returns to ηη human capital . The parameters 0 1 2 relate to the young, middle and old cohorts and I normalize 0 to 1. To isolate the experience-related human capital gain for the other cohorts, I target the wage cc γγ γγ , γγ , γγ growth of young men over their lifetime after controlling for occupational choices. The average across all γγ occupations serve as the baseline for each country. Table 3 reports the time-invariant parameters for each country. The calibrated values of El Salvador are close to that of Panama. The preferences structure of

> 12 Another strategy is to use a long-term average considering data from the mid-1990s onward only. However, this truncated average is very close to the baseline considered here for each country.

> 13 The private education share consists of early childhood spending which is approximately 0.2 percent of GDP.

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