2.2.1. Deriving education-specific life tables from Eurostat

Eurostat does not provide complete period life tables by level of education, which are required to estimate education-specific HLY indicators. However, Eurostat publishes single age-specific estimates of remaining life expectancy by gender and educational attainment (as defined by the ISCED) for several European countries. We derived the missing life table function (i.e., the number of person-years lived between age x and x + 1(Lx)) as the main life table function of interest for obtaining HLY based on the Sullivan method) from their single age-specific e_x estimates. Usually, e_x is the outcome of a complete life table. In this paper, we use e_x to reconstruct the (complete) life table, i.e., we calculated the life table in reverse. After assuming that in each age interval x to x + 1, people dying within this period live an average 1/2 person-years (ax=0.5), and using the life table function relationships (see Preston et al., 2001), we can express life table survivors l_x+1 as:

where lx refers to the life table survivor at age x. Please note, l0 denotes the life table radix (usually defined as 100,000) and does not require estimation. Thus, the Eurostat education-specific life tables can be recreated by an iterative process starting with l1. Once all lx are estimated on the basis of equation (1), the remaining life table functions can be easily derived, such as Lx (Lx=(lx+lx+1)/2). Theoretically, equation (1) enables us to reconstruct life table functions based on e_x values (under the a_x = 0.5 assumption). In practice, however, the reconstruction might require additional steps, which we describe in more detail in the supplementary material. In general, the proposed method leads to life tables, which produce accurate e30 estimates, i.e., the difference between derived e30 and original e30 is mostly smaller than ±0.1 years. We focus on e30 and HLY at age 30 as it is not only favorable from a technical point of view, but also theoretically: Very young persons have not usually finished their educational attainment (Connelly, Gayle, & Lambert, 2016).