# **4.5 Choosing the right instruments**

The validity of the conditional LATE approach—and to a lesser extend of the narrow bounds approach—crucially depends on the choice of instruments. We adopt two strategies for this choice. First, we use an _ad hoc_ strategy in which we select a number of variables at the village and at the household level likely to affect the share of _a-compliers_ (within the group of compliers). For instance, we include the province fixed effects under the expectation that some provinces may have provided, before the beginning of the intervention, better preschool infrastructure than others without necessarily affecting the treatment effects. Using the same logic we include population size and land area of the villages<sup>35</sup> and whether the village has a primary and/or a secondary school. In a second specification within this same strategy, we add caregiver level variables (education and poverty level as well as caregiver cognitive test scores).

In a second strategy, we improve the transparency of the variable selection by implementing a machine learning algorithm to determine which variables should be included in equation (10) as X instruments to predict ASP attendance. We leverage the large baseline dataset composed of variables at the province, village, household, caregiver and child levels. Our objective is to predict the probability that a child will be enrolled in an ASP using baseline variables following the procedure implemented in Belloni et al. (2013) and Chernozhukov et al. (2018). We start the procedure by selecting all covariates available at baseline (1354 in our case). We exclude free-text variables, variables with very low response rate,<sup>36</sup> and variables without variation, which results in 224 eligible variables. We then create dummy indicators for categorical variables, compute the square of each covariate, and then remove perfectly collinear variables.<sup>37</sup> We use the resulting 493 baseline variables to predict ASP enrollment status at follow-up in the control group using LASSO.<sup>38</sup> To select the penalty term, we compare three different approaches: cross-validation, adaptive (Zou (2006)), and plug-in (Belloni et al. (2014)). Comparing the postestimation deviance ratio, we conclude that the plug-in LASSO fares slightly better and is much more parsimonious: in addition to the 12 province fixed effects, the plugin LASSO identifies five baseline variables that best predict midline ASP enrollment in the control group (whether the child attended preschool at baseline, whether he/she attended more than 30 days, baseline cognitive scores, age squared and one variable taking value one when the baseline infrastructure information is missing).<sup>39</sup>

> 35Under the expectation that population density may have an effect on alternative preschool availability

> 36We exclude variables with response rate lower than 70% in the control group with non missing ASP attendance information.

> 37To avoid dropping too many valuable observations, we impute baseline missing values using the median variable value. When we impute values, we create a dummy variable that takes value 1 for the imputed observation and 0 otherwise.

> 38We partial out the LASSO with stratification variable i.e. province fixed effect.

> 39The LASSO that uses the data-dependent penalty developed by Belloni et al. (2012) (some-

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