To account for differences in cohort sizes over time, we consider the fertility rate at each cohort’s year of birth, which is unchanged through the life cycle. To account for cohort composition effects we compute the proportion of individuals in the lower 40 percent of the income distribution (summarized in Table 4) that attended LS at the official LS age in each cohort. To avoid endogeneity with the dependent variable -which includes the same cohort of reference in its measurement- we instrument this variable by using the lagged value of the same variable, which refers to an earlier cohort. For the macroeconomic environment, we use the growth rate of GDP per capita and the inflation rate, from the World Development Indicators.

The rest of the variables are obtained directly from our household survey database. To characterize labor market dynamics we compute the average wage and the proportion of individuals that are employed under a remunerated activity, for individuals in the 25-45 age brackets in each country and year. These age groups are always above the USE ages considered in the dependent variable and so can be considered as exogenous. Returns to schooling are estimated for the population aged 25-55 in each case, which also avoids potential endogeneity.

Our base estimates are obtained through panel difference in difference regressions with Hubercorrected robust standard errors and country-year dummies, so our results control for time variant and invariant country characteristics and for non-observable cohort characteristics simultaneously. All regressions are performed for the total population and for males and females separately. All in all, we observe 226 episodes of change in the pooled data of the 18 countries over the decades between the early 1980s and 2012. We test with a series of specifications and report the models to verify the stability and consistency in the coefficient estimates.

# **4.1 Base results**

Table 3 presents the base regression for our analysis by introducing each group of variables parsimoniously. The first estimation shows a negative and statistically significant relationship between changes in school enrollment shares at USE ages for each cohort, and cohort size as measured by the fertility rate in the cohort’s birth year. Similarly, as expected, there is a negative and significant relationship with changes in the (instrumented) share of LS enrolled individuals belonging to the poorest 40 percent in the income distribution, and changes in USE enrollment.

The second estimation incorporates the variables measuring economic growth and macroeconomic stability. According to our results, the relation between changes in enrollment and GDP per capita growth is positive, but not statistically significant. However, there is a strong negative and significant association with the inflation rate which suggests that USE enrollment declines when instability in the economic environment increases, as would be expected.

The third estimation incorporates labor market variables characterized by the average wage and employment levels for the population in the 25-45 age brackets in each year. Interestingly the coefficient for the wage and employment variables are positive and statistically significant, which 21