���� = ∝ + ������� ∗����� + ������� ∗����� + ∑�������� ���� + ���� + ��� + ���� (1) In equation (1), ���� denotes the UN score of school _s_ in district _d_ in year _t_ .<sup>9</sup> �� denote year dummies. ����� is a dummy variable that takes the value of 1 if the school is a government school and therefore eligible to compete for the performance grant, and takes the value of 0 if the school is a non-government school. ����is a vector of observable time-varying characteristics for school s in district d in year t. These are (i) the share of teachers with a bachelors’ degree or higher, (ii) the number of students in the graduating class and (iii) the number of students per classroom. ��� are school fixed effects, and ���� is the error term. Adding school fixed effects absorbs any timeinvariant school-level characteristics that may be correlated with UN scores and allows estimates of within school score changes before and after the introduction of the performance grant. The school fixed effects also control for any sub-district level factors that may drive differences in UN scores. In addition, the dummy variable for government schools (�����) is also subsumed in the school fixed effects. The coefficients of interest are �� and ��; �� is the estimate of the impact of the performance-based grant in 2015 while �� is the estimated impact in 2016. In other words, �� (��) denotes the gap between the change in scores among Jakarta government schools from 2014 to 2015 (2016) and the analogous change among non-government schools in Jakarta. We test the difference between �� and �� to assess whether the impact of the program changes over time.

# **_Validity of Difference-in-Differences_**

A key underlying assumption of the DD approach is that the size of the examination score gap between government and non-government schools was similar and remained relatively stable in the years prior to the introduction of the performance-based grant. This parallel trend assumption is tested in two ways. First, a test is performed to check whether the gap between examination scores in government and non-government schools before the program differed over time on average (denoted by �� in equation _i_ ).<sup>10</sup> This test does not reject the parallel trends assumption at the 5% significance level. Second, a test is performed to examine whether the score gap stayed the same across each year before the announcement. To test this assumption, examination scores are regressed on year dummies and interactions of year dummies with school type.<sup>11</sup> While the results

> 9 Every year, some primary schools are merged. To compare test scores over time, this paper uses the UN score of the “mother” school (that exists in the database after the merge) for the periods before the merge as “mother” schools tend to be larger on average than the other schools that are annexed in the consolidation.

> 10 A similar approach is adopted in Muralidharan, K. and N. Prakash (2013). Cycling to school: increasing secondary school enrollment for girls in India, National Bureau of Economic Research.

A DD model using UN scores data for 2012 to 2014 using the following equation, where _Year_ is a categorical variable from 1 to 3. The full results of this test are shown in Annex Table A1.2 – Panel A. The coefficient of interest in that table is Jakarta Government*Year.

11 A DD model using UN scores data for 2012 to 2014 of the following form is estimated where �� (��) denotes the difference in the government vs non-government score gap in 2013 (2012) relative to the analogous gap in 2014: ���� = �+ ���2013 ∗����� + ���2012 ∗����� + ∑�������� �� �� + ��� + ���� ( _ii_ ) 11