less year of free schooling; therefore, on-time entrants in the 1986 cohort benefited only after completing at least grade one. Finally, on-time entrants born in 1977 or earlier would have completed all ten grades prior to 1995 and so gained zero years of free schooling.<sup>2</sup> Assuming on-time entrance into school and continuous progression, the maximum benefit of the FPE reform for each cohort is as follows: Data from the Ethiopian census provide zone-specific information on the actual starting age of children in Ethiopia, allowing the on-time entry assumption to be relaxed. Because students often enter school at ages other than the legal starting age of seven, an individual’s year of birth does not determine their year of school entry but rather a possible range of years in which the individual could enter school. The calculation of the reform’s impact can be adjusted to take into account the possibilities of starting school as early as age six, one year early, and as late as age 12, five years late. The central assumption made regarding variation in entry probability is that the relative age distribution within each zone is constant over time; this means that even though all ages are more likely to enter school in the post-reform period, if a seven-year-old is twice as likely to enter school relative to a six-year-old in the census data, then a seven-year-old remains twice as likely to enter school in both the pre- and the post-reform states of the world.<sup>3</sup> Following the removal of school fees, the maximum impact of the reform would be that every student could potentially enter school. To represent this possibility, the starting probabilities, _Sz,a_ , are assumed to sum to 1, holding the relative probabilities from the data constant across each age: The following set of equations (4) uses the 1985 cohort as an example to illustrate how starting ages are included in the calculation of the impact of FPE on each cohort. First, some fraction of the cohort, _Sz,_ 6,

> 2The timing of the impact on each cohort, assuming on-time entry, is shown in Appendix Table A.1.

> 3Justification for this assumption is shown in Appendix Figure B.1; when scaled to full entry, age specific probabilities yield a consistent pattern (Appendix Figure B.1c). Data from the 1984, 1994, and 2007 rounds of the census are compared. The 1984 census is the only fully pre-reform round of the census, but the administrative boundaries were changed at the beginning of the transitional administration. The starting-age probabilities in the 1994 census were likely directly affected by the ongoing reforms. Therefore, the 2007 census, which is made up of a set of respondents whose entry decisions were made after the post-reform equilibrium had been established, is used in the main body of the article to calculate starting ages. Under the assumption that relative starting ages should be consistent over time, this round of the survey provides the clearest representation of the equilibrium relative starting ages within the current administrative boundaries. Estimates using alternative starting-age calculations from the other census rounds, with the 1984 values weighted by overlapping area into the 1994 boundaries (panel F) and the 1994 start values (panel G), can be found in Appendix Section D.2.

5