better at the math and science components, while women score score better at Indonesian language.

Are these point estimates large or small? What would we expect a priori of a bachelor’s education for example? Of those without a bachelor’s degree, about two-thirds has a 2- year post-secondary diploma, and the rest, one-third, has only a secondary education. This heterogenous group scores .4 of a standard deviation below the group with a bachelor’s degree on average. Not very much perhaps. Another way of looking at this is by looking at the _R_<sup>2</sup> of these regressions. They are around 0.05, showing that only 5% of the variance of the (noisy) test score data is explained by these characteristics. Discounting the fact that test scores are noisy, we can estimate an alternative _R_<sup>2</sup> , measuring what the _R_<sup>2</sup> ’s would have been if the testing data would have been noise-free.<sup>23</sup> Even these alternative _R_<sup>2</sup> ’s are not very big, indicating that these background characteristics do not explain much of the variation in subject-matter knowledge of teachers. Apparently there are many teachers without university diplomas who do very well on the test, and, similarly, many teachers with university diplomas who do badly. This suggests that Indonesia’s teacher training programs – on average – do not manage to lift teacher subject-matter knowledge to a much higher level.

With more flexible regression models we can explain much more of the variation in test scores than the models presented in table 1. School fixed-effects models (where the teacher test score is regressed on a full set of school dummy variables) have _R_<sup>2</sup> ’s in the neighborhood of 0.60, indicating that 60% of the variance of (noisy) test scores can be explained at the school level. (We note that these school fixed-effects models are prone to overfitting, as the number of teachers per school is probably too small. I ran a bootstrap analysis to investigate the extent of the overfitting problem in this setup.<sup>24</sup> The findings indicate that a more conservative estimate of the _R_<sup>2</sup> of the school fixed-effects model would be 0.45 or 45%. Still much higher

> does not favor teachers with higher levels of subject-matter knowledge. See also World Bank (2015).

> 23The standard _R_ 2 is defined as the variance of the prediction, divided by the variance of the left hand side variable. The alternative _R_<sup>2</sup> reported in table 1 is calculated as the variance of the prediction, divided by 1, the variance of the true score.

> 24For the bootstrap, the teacher’s test scores are randomly, reallocated across teachers after which we estimate the school fixed-effects model again. This procedure is repeated 1,000 times and the _R_<sup>2</sup> ’s of these regressions are stored. I find that on average, these artificial regressions have _R_<sup>2</sup> ’s of around 0.15. The overfitting alone therefore already accounts for 15% of the variance in the test scores. These _R_<sup>2</sup> ’s however are much lower than the _R_<sup>2</sup> of 0.60 we find in the data, suggesting that there is a lot of real clustering of subject-matter knowledge in schools left.

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