# **1. Introduction**

<mark>There is strong agreement that teachers matter a lot for student learning;</mark><sup>2</sup> <mark>but little agreement on which specific teacher factors matter most. Studies document wide variation in teacher effectiveness that is not well explained by observable teacher characteristics (e.g., McCaffrey et. al 2004; Jacob and Lefgren, 2005; Rivkin, Hanushek, and Kain, 2005; Gordon, Kane, and Staiger, 2006; Kane, Rockoff, and Staiger, 2008). Specifically, observable and widely available teacher characteristics such as teacher qualifications, test scores, training, and experience appear to be weak predictors of teacher contributions to student learning in high-income countries (Rockoff 2004; Rivkin, Hanushek and Kain 2005; Aaronson, Barrow and Sander 2007, Staiger and Rockoff 2010). This finding is mirrored in recent studies from low- and middle-income countries. Research from Pakistan and India does not find a strong relationship between teacher qualifications and teacher value-added in either government or private schools (Bau and Das 2020; Azam and Kingdon 2015); in Ecuador teacher entry-exam performance explains a small fraction of the variation in student learning (Cruz-Aguayo et al. 2017). Bau and Das (2020) find in Pakistan’s context that observed teacher characteristics account for less than 5 percent of the variation in teacher value-added.</mark> Using machine learning methods on a rich student-teacher data set from Tanzania, this paper identifies key predictors of teacher effectiveness, proxied through student learning gains linked to a teacher over an academic year, closely linked to the concept of teacher value-added (TVA).<sup>3</sup> Specifically, it explores which aspects of a teacher – who teachers are, what teachers know, what teachers do, or what teachers believe – are most predictive of student learning gains.

Machine learning (ML) is a well-suited (albeit novel) approach for identifying key predictors of teacher effectiveness from a large set of teacher, student, and school covariates since most studies in the TVA literature use linear modeling techniques (Koedel et al. 2015). ML applications, which are increasingly common in econometrics (Athey and Imbens 2016, Mullainathan and Spiess 2017), often involve predictions about some variables given others. They manage to uncover generalizable patterns and discover complex structures that were not specified in advance (Mullainathan and Spiess 2017). ML algorithms attempt to select flexible models that fit the data well, but not so well that out-of-sample prediction is compromised (Athey and Imbens 2016). They can be particularly successful on high-dimensional data where we observe many pieces of information on each unit (Athey and Imbens 2016).

In our case where data are relatively high dimensional (with 52 explanatory variables), using ML algorithms helps us avoid ad-hoc model selection. Instead, the ML algorithm helps show which teacher covariates matter more for predicting student learning gains, by allowing for highly flexible models that are evaluated on the basis of out-of-sample replicability. ML algorithms also help avoid the problem of multicollinearity

> 2 See for example: Hanushek and Rivkin 2010; Nye et al. 2004; Chetty et al. 2014a; 2014b; Buhl-Wiggers et al. 2017; Bau and Das, 2020.

> 3 Several studies show that teacher value-added measures, which control for a student’s prior-year test scores, provide unbiased forecasts of teachers’ causal impacts on student achievement (Bacher-Hicks et al 2017, Glazerman and Protik 2015, Chetty et al. 2014, Bacher-Hicks, Kane, and Staiger 2014, Rothstein 2014).

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