The resulting measure of expected school years approximates the number of years of school that a child can expect to attain by her 18<sup>th</sup> birthday if she starts school at age 4, for a maximum of 14 years. Data on this measure of expected years of school are reported in the top panel of **Figure 2** .

Conceptually this calculation corresponds to the measure of “school life expectancy” (SLE) calculated by UNESCO Institute for Statistics.<sup>6</sup> However, the implementation here differs in that UIS uses gross enrollment rates to calculate school life expectancy, whereas here total net enrollment rates are used wherever possible. This reflects a tradeoff. On the one hand, gross enrollment rates are more widely available and typically have longer time‐series coverage in the UIS data. On the other hand, total net enrollment rates conceptually correspond more closely to the age‐specific enrollment rates in Equation (5). A further reason to use total net enrollment rates is that for some countries the repetition‐adjusted gross enrollment rates reported by UNESCO are – sometimes implausibly – well above 100 percent. While gross enrollment rates (the number of students enrolled at a given grade level as a fraction of children of the theoretical age for that grade level) can in principle exceed 100 percent if some children start school early or late, it is difficult for this timing effect to generate gross enrollment rates that are persistently much above 100 percent.<sup>7</sup> A practical consequence of using gross enrollment rates above 100 percent to calculate SLE is that SLE can then exceed the statutory duration of school. This is the case for primary and secondary SLE as reported by UIS for about one‐quarter of 6 When more granular data such as enrollment rates by age are available, UNESCO uses them to calculate SLE. When they are not, UNESCO calculates SLE using school level‐specific gross enrollment rates (which are the most widely available in the UNESCO data), using Equation (5). Whether age‐specific or level‐specific enrollment rates are used makes little practical difference for the calculations. Using the data on gross enrollment rates and duration by level of school as reported by UNESCO in Equation (5), and restricting attention to primary and secondary, reproduces the UNESCO estimates of SLE for primary plus secondary almost exactly.

> 7 To see why, consider an education system in which a fraction a� of each cohort of students start school at the official age; a fraction l� starts one year late and therefore are above age‐for‐grade; and a fraction 1 �a� �l� students do not start school at all.   Gross enrollment in first grade at time t is the number of students in first grade divided by the cohort of children aged 6 who are supposed to be in first grade, i.e. GER� � �� ���������� ����� where

N� is the number of children in the cohort of new six year‐olds at time t . With a stationary population N� �N��� and stationary starting age shares a� �a and l� �l , it follows that GER�a�l�1 , even though there could be many over‐aged children in the grade. With stationary starting age shares the only way to generate GER�1 is if a�l is close to one (i.e. near‐universal enrollment) and N��� �N� i.e. a shrinking school‐aged population. The other way to generate GER�1 is with time‐varying starting age shares. If for example there is a big expansion in enrollment to include children who should have started in the previous year but did not, then with stable cohort size it follows that GER�a� �l��� and it is possible that a� �l��� �1 if enough children from the previous cohort who did not enroll at the correct age now enroll, i.e. if l��� is large enough. One factor contributing to high gross enrollment rates in some countries is that they can include adults who are returning to complete secondary school, which can inflate gross enrollment rates beyond 100 percent, making it a poor proxy for enrollment rates among 14‐17 year‐olds 27