possible control variables for the analysis in São Tomé and Príncipe. The variables in the control vector are also subject to some pre-selection as in the ad-hoc specification, based on the criterion that these variables are not likely to be correlated with the error term (i.e. they are exogenous). This is done in ZZ order to ensure that the conditional mean-zero assumption is more likely to hold 1 2] = 0 . Based on this criterion, variables such as whether the child is attending an early childhood development EE[εε|ZZ, DD , DD program and variables measuring the quality of care, such as the availability of playthings, or books, or the child being left alone in the care of another child, all available in the MICS, are excluded from the vector of controls. These variables are likely to be determined at the same time as early childhood development as well as child undernutrition (stunting), and thus likely to be correlated with the error term if they were included in the set of controls.<sup>12</sup>

The list of potential control variables includes, the young and old dependency ratio (ratio of household members younger than 15 years old or older than 64 and the total number of working age members 1564 years old), child gender, child age (in months) and age squared, whether the child is the son/daughter of the household head, the level of education of the head of the household, household size, the mother’s age at birth, the birth order of the child, the number of mosquito nets, the ethnicity and religion of the household, whether the mother believes that wife beating is acceptable on some occasions, whether at least once per week the mother reads a newspaper, listens to radio daily , or watches TV, the type of union between the mother and her spouse, all of the components of the household’s wealth index included as separate binary or continuous variables (see footnote 4 for a complete list), a binary variable for rural areas and a set of binary variables for regions. Except for age and age-squared, in the case of the Republic of Congo all of the preceding variables are also interacted with the binary variable for rural areas to allow for possible differences between urban and rural areas.

The analysis is carried out using the _regress, logit, xporegress_ and _xpologit_ commands in Stata v16.1. The two latter commands apply the DML (cross-fit partialing out) method for continuous and binary dependent variables, respectively.<sup>13</sup> The selection of the controls in the DML is based on LASSO by splitting the sample randomly into 10 parts (i.e., LASSO is estimated 10 times). In addition, the 10-part

> 12 This also supported by Loizillon et al. (2017) who in their report of the development of the ECD index state that “having books and participating in early learning programs were the strongest predictors of children’s outcomes as measured by the ECDI. Also, children with more books, playthings from more sources, and left alone less had higher mean item values on the ECDI than children with fewer books, playthings from fewer sources, and left alone more often. The differences were statistically significant.”

> 13 In addition, models were also estimated using the double selection ( _dsregress_ ) and partialing-out ( _poregres_ s) commands in STATA for the purpose of validating the inferences made based on the cross-fit partialing out (DML) method.

13