discussed in Section 1, Grade 4 students in these schools were administered two rounds of tests (each covering the subjects of mathematics, Kiswahili, and English) and we use these to calculate an overall score averaging over subjects and the two rounds.<sup>34</sup> Specifically, we estimate two-parameter IRT models for each subject and each round separately. We then extract the latent ability parameter from each model, average across these, and normalize the resulting variable so it has mean 0 and standard deviation 1.<sup>35</sup> We estimate a series of regression models with the student test score as the dependent variable against various combinations of the variables that emerge from the observation instruments. We include two variables related to the share of time spent in teaching and learning: the Share of Time Teaching and a separate variable equal to the share of time lost due to students being off-task.<sup>36</sup> In addition, we include a test score for the teachers’ subject content knowledge. This is derived from a test administered as a part of the national SDI survey structured as a teacher correcting mock student tests in language and math. The test covered material at all grades of primary school.<sup>37</sup> The score we use is based on an item response theory analysis of these data.<sup>38</sup> We estimate each model first without controlling for other variables, and second including a set of student, household, teacher, and school characteristics. Student and household characteristics include age, gender, whether the student had eaten before school on the day of the test, and a number of characteristics that reflect socioeconomic status (having a separate room to sleep in at home; having electricity at home; having running/tap water at home; living in a dwelling with concrete/cement/stone walls; living in a dwelling with a metal roof; living in a dwelling with a toilet; household ownership of various assets—bed, mosquito net, books, mobile phone, computer).<sup>39</sup> Teacher characteristics include variables reflecting gender, age, education, and training. School characteristics include indicators for whether the school has a way of “recognizing” teacher performance, availability of piped water at the school, accessibility to a road, the ratio of students to teachers, and the location of the school (urban/rural). We also control for the subject being taught during the observation.

> 34 Results disaggregated by subject are qualitatively similar (these are available online via a link on - <u>https://sites.google.com/site/decrgdeonfilmer/working papers).</u>

> 35 We also estimated results using a Rasch model, as well as simply the percent correct and results are qualitatively similar (these are available online via a link on <u>https://sites.google.com/site/decrgdeonfilmer/working-papers).</u>

> 36 This is calculated as Share of Time Teaching minus Share of Time Teaching and Learning.

> 37 See Bold et al. (2019) for further description of the teacher test.

> 38 The specific measure we use comes from an analysis of pooled data from a number of Sub-Saharan African countries.

> 39 In a number of cases, some of these variables are missing.  In such cases we replace the value by the mean across the sample, and include a dummy variable in the model that is equal to 1 if the value was originally missing.

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