metadata: authors: 0: author: Skoufias,Emmanuel
1: author: Vinha,Katja Pauliina
count: Congo, Republic of,Sao Tome and Principe
docna: 0: docna: Child Stature, Maternal Education, and Early
            Childhood Development
docty: Policy Research Working Paper
subtopic: Educational Sciences,Social Protections & Assistance,Nutrition,Reproductive Health,Early Childhood Development,Early Child and Children's Health
teratopic: Social Protections and Labor,Education,Health, Nutrition and Population
abstracts: cdata!: This paper uses Multiple Indicator
            Cluster Surveys data from the Republic of Congo and São Tomé
            and Príncipe to study the relationships between child
            stature, mother's years of education, and indicators of
            early childhood development. The relationships are
            contrasted between two empirical approaches: the
            conventional approach whereby control variables are selected
            in an ad-hoc manner and the double machine-learning approach
            that employs data-driven methods to select controls from a
            much wider set of variables. Overall, the findings based on
            the preferable double machine-learning approach differ
            across the two countries depending on the measures of early
            childhood development and child stature (height-for-age
            Z-score and stunting) used in the analysis. Double
            machine-learning estimates for the Republic of Congo suggest
            that height-for-age Z-score and stunting have a direct
            causal effect on early childhood development. In contrast,
            for São Tomé and Príncipe, no relationship is found. Thus,
            country-specific policy advice based on the relationships
            observed from data in other countries may be quite risky, if
            not misleading. Double machine-learning provides a practical
            and feasible approach to reducing threats to internal
            validity to derive robust inferences based on observational
            data for evidence-based policy advice.
geo_reg_key: 517196,1927320,517191
repnme: repnme: Child Stature, Maternal Education, and
            Early Childhood Development
display_title: Child Stature, Maternal Education,
            and Early Childhood Development
listing_relative_url: /research/2020/09/32403243/child-stature-maternal-education-early-childhood-development
topicv3: Nutrition m1326779 644,Education m1327048 470,Stunting m1327504 1445,Early Child Development m1327727 479,Early Childhood m1582438 4408
publishtoextweb_dt: 2020-09-14T00:00:00Z
historic_topic: Social Protections and Labor,Education,Health, Nutrition and Population
origu: EFI-AFR1-POV-Poverty and Equity (EAEPV)
no_of_pages: 29
author_keys: 0: author_key: 177660
1: author_key: 435289
model_extractions: Policy Research Working Paper 9396 Child Stature, Maternal Education, and Early Childhood Development _Emmanuel Skoufias Katja Vinha_ Poverty and Equity Global Practice September 2020
Policy Research Working Paper 9396

# **Abstract**

This paper uses Multiple Indicator Cluster Surveys data from the Republic of Congo and São Tomé and Príncipe to study the relationships between child stature, mother’s years of education, and indicators of early childhood development. The relationships are contrasted between two empirical approaches: the conventional approach whereby control variables are selected in an ad-hoc manner and the double machine-learning approach that employs datadriven methods to select controls from a much wider set of variables. Overall, the findings based on the preferable double machine-learning approach differ across the two countries depending on the measures of early childhood development and child stature (height-for-age Z-score and stunting) used in the analysis. Double machine-learning estimates for the Republic of Congo suggest that heightfor-age Z-score and stunting have a direct causal effect on early childhood development. In contrast, for São Tomé and Príncipe, no relationship is found. Thus, country-specific policy advice based on the relationships observed from data in other countries may be quite risky, if not misleading. Double machine-learning provides a practical and feasible approach to reducing threats to internal validity to derive robust inferences based on observational data for evidence-based policy advice.

This paper is a product of the Poverty and Equity Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at eskoufias@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Child Stature, Maternal Education, and Early Childhood Development**

**Emmanuel Skoufias* - The World Bank**

**Katja Vinha - Consultant**

**JEL Classification:** C18, C21, I15, I25, J13, J24

**Keywords:** inference, stunting, child height-for-age, education, double machine learning

> * _Corresponding Author_ : Emmanuel Skoufias, The World Bank, Mail Stop J5-504, 1818 H Street NW, Washington, DC 20433, USA. tel: (202) 458-7539; e-mail: eskoufias@worldbank.org _._

The findings, interpretations, and conclusions in this paper are entirely those of the authors and do not reflect the views of the World Bank.
# **Child Stature, Maternal Education, and Early Childhood Development**

In an ideal world, recommendations for social policies aimed at improving welfare and especially maternal and child outcomes would be based on well-established evidence on the causal relation between the variables of interest. In reality, however, this is not feasible. The increasing number of randomized controlled trials (RCTs) that are useful for establishing causal inferences, combined with the limited ability of RCTs to address every policy relevant question, has not been able to satisfy the increasing demand for evidence-based policy advice. At the same time, the higher standards for the internal and external validity of the empirical evidence generated have increased the urgency to extract credible causal relations, rather than just partial correlations, between variables of interest based on the already available and accessible cross-sectional surveys.

Yet, studies with credible causal inferences based on regression analysis using non-experimental household cross-sectional data are not common, or even purposefully avoided by young researchers in social sciences aspiring to establish their publication record in their respective fields in the context of a proliferation of RCTs as the standard for causal inferences. Instead, the common practice in fields such as maternal and child health is to present estimates from simple regression models with few chosen controls for confounding factors acknowledging the potential role of other confounding factors left out of the model and publish with the qualifying statement that such estimates establish significant partial correlations but not causation between the variables of interest (Miller et al, 2015). Frequently the acknowledged relative weaknesses in the internal validity of these studies is compensated by efforts to strengthen the external validity of the findings by carrying out the same regression (or partial correlation) analysis across different countries with the same type of survey (e.g., Li et al., 2020; Jeong et al., 2019; and Kang et al., 2018).

This paper applies recently developed methods to address threats to internal validity using individual child data from two countries, the Republic of Congo and São Tomé and Príncipe, for the purpose of deriving “causal” inferences about the effect of child stature and mother’s level of education on early childhood development (ECD). Stunting is the impaired growth and development that children experience from poor nutrition, and repeated infection, and is based on measuring the height (length) of children and comparing it to the height of well-nourished children of the same age. The level of education of a mother affects early childhood development through a variety of channels: improved child health and nutrition, increased labor force participation, and income earning opportunities 2
(income effects), greater empowerment and bargaining power within the household, complementarities with household characteristics and community services, access to information (i.e., exposure to media) and information processing (Aslam and Kingdon, 2012). ECD is defined to include the literacy/numeracy, as well as physical, social, emotional and learning/cognitive development of the child. Parental investments in the quantity and quality of ECD form both the basis for readiness as well as performance and achievement in education, leading to higher productivity. Thus, they are critical for the quantity and quality of the human capital of future generations (Daelmans et al., 2017).

Chronic malnutrition as measured by stunting is one important factor associated with early childhood development. Impaired growth in early life - particularly in the first 1,000 days from conception until the age of two - has adverse functional consequences on the child as these years contain the most rapid changes in brain development. Stunting is associated with concurrent and later cognitive delay or deficit (Powell, et al 1995; Crookston et al, 2011; Berkman et al. 2002), poor cognition (Shonkoff, 2003, and Shonkoff et al., 2012; Prado and Dewey, 2014) and educational performance (Glewwe et al., 2001), low earnings in adulthood (Hoddinott et al., 2008), a variety of adverse consequences over the life course on human, social, and economic capital (Hoddinott et al., 2013), and, when accompanied by excessive weight gain later in childhood, an increased risk of nutrition-related chronic diseases in adult life (Wells et al., 2020).

Given the difficulties involved in the measurement of developmental delays and some empirical evidence on the causal effect of stunting on early childhood development, stunting, which is more easily measured, is frequently used as a stand-in for developmental delay in cross-sectional population health (e.g. Jeong et al., 2019; and Kang et al., 2018). However, there is an ongoing debate about the relationship between child linear growth (height gain) and child development, especially based on the evidence from cross-sectional data. On the one hand, some researchers argue that there is a causal relationship between linear growth or stunting and childhood development, and especially their cognitive ability (Sudfeld et al., 2015a and 2015b). On the other hand, studies such as Tran et al (2019), based on data from 178,393 children aged 36 to 59 months from 55 countries, conclude that the “association between growth and development in early childhood appears to be primarily a cooccurrence because the magnitude of the association varies among settings from no association in higher-income countries to a moderate level in low-income countries, and that.....overall, growth is not a sensitive and therefore suitable indicator of child development.” 3
There is also plenty of empirical evidence available in the literature on the association between a mother’s education and different dimensions of child health such as infant mortality, the number of immunizations (e.g., Desai and Alva, 1998), child nutrition measured by height-for-age (HAZ) or stunting (e.g. Alderman and Heady, 2017), and fertility (e.g. Pop-Eleches, 2010; Kim, 2010; McCrary and Royer, 2011; Monstad et al., 2008). Yet, causal evidence on the effect of a mother’s education on ECD net of its effect of stunting is rather scarce. A better understanding of the channels through which maternal education affects ECD outcomes is essential for the prioritization of policies related to child health. Evidence of a direct effect of maternal education on ECD, separate from its potential effects on child stunting, would suggest that maternal education has the added advantage of compensating for the potentially negative effects of stunting on ECD and thus provide even stronger justification of the need to increase the quantity and quality of female education as an especially important factor in the development and economic growth of Sub-Saharan African countries undergoing a demographic transition.

With this background in mind, the analysis in this paper takes advantage of the variation across households in indicators of early childhood development and applies recently developed methods for more robust inferences based on observational data (Chernozhukov et al., 2018). The results from the conventional ad-hoc specification of a model, i.e., a regression model with the usual suspect confounding factors, chosen based either on custom or economic intuition, are contrasted to a more sophisticated approach, called double machine learning (DML). DML employs data-driven methods to select controls from a much wider set of variables available in the survey along with statistical learning methods that yield information that would not be available from fitting the model only once using the original sample (e.g. Hastie et al., 2009; James et al., 2013; Athey and Imbens, 2019).

# **Data**

The analysis relies on the cross-sectional variation across households in two Multiple Indicator Cluster Surveys (MICS): the 2014-15 MICS in the Republic of Congo and the 2014-15 MICS in São Tomé and Príncipe. The MICS is an international household survey program that collects information about health, nutrition, education, and early development of well-being of children and their families in developing countries.

4
In statistical terms, a child is stunted if his/her height-for-age Z-score (HAZ) is more than 2 standard deviations (SD) below the median height of a healthy reference population (that is, HAZ <-2).<sup>1</sup> The measure of HAZ and thus stunting used in this study is based on the new WHO child growth reference population. The incidence of stunting among children ages 36-59 months is a consequence of the growth faltering in first 1,000 days from conception. Growth faltering is the rapid decline in height- and weight-for-age of children in the first two years of life and is common in many developing countries. Growth faltering among children was first documented in a study by Shrimpton et al. (2001) and to a large extent, it is in response to these finding that several global health policy and information campaigns with emphasis on the first 1,000 days window have been initiated (Prentice et al., 2013).

Figure 1 presents the cross-sectional age profile of growth faltering (HAZ scores) for children between 0 and 59 months of age in the two countries analyzed in this paper. As is easily apparent, growth faltering in the first 1,000 days is prevalent among children in both the Republic of Congo and São Tomé and Príncipe, with growth faltering (or HAZ decreasing) accelerating rapidly with age in the first 21-24 months of life, somewhat recovering at a slower rate afterwards with minor fluctuations.<sup>2</sup>

**Figure 1: Growth faltering in the Republic of Congo and in São Tomé & Príncipe**

<!-- Start of picture text --> Congo: Average HAZ Sao Tome & Principe: Average HAZ<br>Children under 60 months Children under 60 months<br>0 20 40 60 0 20 40 60<br>Age in months Age in months<br>Source: Rep. of Congo MICS 2014-15 and São Tomé and Príncipe MICS 2014-15<br>-.2 0<br>-.4<br>-.5<br>-.6<br>Average HAZ -.8 Average HAZ -1<br>-1<br>-1.5<br><!-- End of picture text --> Much of the empirical literature on the role of a mother’s education focuses on children less than 60 months without making any distinction about the age of the child (exceptions are Skoufias et al., 2019;

> 1 A child is classified as severely stunted if HAZ<-3.

> 2 For a recent cross-country study on the determinants of growth faltering, see Rieger and Trommlevora (2016). The growth faltering curves are derived using a local polynomial smooth of HAZ with the Stata command lpoly.

5
Alderman and Heady, 2018). Given the rapid growth faltering in the first two years of a child’s life and the fact that measures of ECD are available only for children 36-59 months old, this study investigates not only whether there is a causal relationship in the full sample of children 0 to 59 months of age, but also whether there are any structural differences in the causal relation between maternal education and child stature separately in the sample of younger (0-35 months) and older (36-59 months) children.

A useful feature of the fourth round of MICS is the inclusion of 10 caregiver-reported questions with binary (0,1) responses aiming to measure the developmental status of children 36-59 months (or 3-5 years of age) within four domains. Specifically, the four domains include: (i) **literacy-numeracy** : children are identified as being developmentally on track _if they can do at least two_ of the following: identify/name at least 10 letters of the alphabet; read at least four simple, popular words; and/or know the name and recognize the symbols of all numbers from 1 to 10; (ii) **physical development** : If the child can pick up a small object with two fingers, like a stick or rock from the ground, and/or the mother/caregiver does not indicate that the child is sometimes too sick to play, then the child is regarded as being developmentally on track in the physical domain; (iii) **learning** : If the child follows simple directions on how to do something correctly and/or when given something to do, is able to do it independently, then the child is considered to be developmentally on track in the learning domain; and (iv) **social-emotional** : The child is considered developmentally on track if two of the following are true: the child gets along well with other children; the child does not kick, bite or hit other children; and the child does not get distracted easily.

According to UNICEF a child is developmentally on track if he or she is on track in at least three of the four domains (literacy-numeracy, physical, social-emotional and approaches to learning) (Loizillon et al., 2017).<sup>3</sup> This implies that affirmative responses to (any) 7 or more of the 10 questions are sufficient to classify a child as being on track in development. In this paper, an alternative composite score for early childhood development is the standardized Early Childhood Developmental Index (or ECDI), which is generated by simply summing the number of positive responses in any of the 10 questions without taking into consideration the domain of the questions (total score ranging from 0 to 10) and then normalizing to a z-score (mean of 0 and standard deviation of 1). This is a more sensitive, though less scientifically-based, measure of child development as it simply compares the developmental status of any given child to the developmental status of the average child in the sample.

> 3 The 10 items were determined through multi-country field tests, validity and reliability studies, and consultations with experts. For more details on the UNICEF method for constructing the ECDI see Loizillon et al. (2017).

6
Table 1 presents the mean values of the child outcomes analyzed, for the full sample of children and separately for children in urban and rural areas. The high proportion of children on track in physical development and low proportion of children on track in literacy/numeracy are similar to the patterns observed in other countries based on the MICS ECD module. McCoy et al. (2016), for example, argue that the questions designed to assess literacy/numeracy are too advanced for 3- and 4-year-old children and that the sensitivity of the physical domain module is low, detecting only more extreme conditions. The pincer grasp in the physical domain, in particular, represents a skill typically acquired before 12 months of age. The inability of a child in the 3- to 4-year age range to pick up a small object with two fingers captures only very severe developmental setbacks.

Another striking characteristic of the data is that the mean values of all the early childhood developmental indicators are lower in the rural areas, except for stunting whose incidence is considerably higher in the rural areas. The deprivations faced by children in rural areas early in life can disadvantage their physical and mental development in adulthood, resulting in the transmission of poverty across generations and in poverty traps.

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**Table 1:  Mean Values of key variables analyzed for children 36 to 59 months**

||**Re**<br>|**p. of Con**<br>|**go**<br>|**São T**<br>|**omé & Pr**<br>|**íncipe**<br>|
|---|---|---|---|---|---|---|
|**ECD Indicator**|**All**|**Urban**|**Rural**|**All**|**Urban**|**Rural**|
|**Child height-for-age (HAZ)**|-0.62|-0.18|-1.37|-0.87|-0.80|-1.00|
|**Child is stunted**(=1 if HAZ<-2, 0 otherwise)|19%|12%|31%|13.6%|13.2%|14.5%|
|**Child is underweight**(=1 if WAZ<-2, 0 otherwise)|10.7%|8.2%|15%%|5.7%|5.7%|5.9%|
|**Child is wasted**(=1 if WHZ<-2, 0 otherwise)|10.5%|8.0%|14.8%|2.73%|2.67%|2.83%|
|**Years of education of the mother**|7.5|8.8|5.1|6.8|7.2|6.2|
|**On track in ECD:**= 1 if child is on track in at least 3<br>of the 4 domains,= 0 otherwise|62%|69%|49%|58%|58%|59%|
|**Total score (ranging from 0 to 10) in 10 ECD**<br>**questions:**number of positive responses across the<br>literacy-numeracy, socioemotional, learning and<br>physical domain items|5.55|5.82|5.06|5.51|5.59|5.34|
|**On track in literacy/numeracy:**=1 if the child can<br>do at least two of the following: identify/name at<br>least ten letters of the alphabet; read at least four<br>simple, popular words; and/or know the name and<br>recognize the symbols of all numbers from 1 to 10;|16%|20%|8%|17%|20%|11%|
|**On track in physical development:**=1 If the child<br>can pick up a small object with two fingers, like a<br>stick or rock from the ground, and/or the<br>mother/caregiver doesnotindicate that the child is<br>sometimes too sick toplay|98%|99%|96%|97%|97%|97%|
|**On track in learning**=1 if on track if one or both of<br>the following are true: child follows simple<br>directions on how to do something correctly; when<br>given something to do, is able to do it<br>independently|86%|88%|82%|82%|83%|81%|
|**On track in social and emotional development:**=1<br>if two of the following are true: the child gets along<br>well with other children; the child doesnotkick,<br>bite or hit other children; and the child doesnot<br>get distracted easily|65%|70%|56%|65%|63%|70%|
|Source: Authors’ estimates based on the 2014-15 MIC|S from the|Rep. of Con|go and São T|omé & Prín|cipe||

# **Methods**

The main question addressed in this paper is an inference question: how does the predicted value of an indicator of early childhood development change if the incidence of stunting (a binary variable) or height-for-age-z score (a continuous variable) or a mother’s years of education are increased by one unit, holding other confounding factors fixed. This question can be answered within the context of a partially linear model, such as 1 1 2 2 , 1 2] = 0 (1) YY= ββ DD + ββ DD + ff(ZZ) + εε EE[εε|ZZ, DD , DD

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where denotes the ECD outcome, 1 is the HAZ score of the child (or a binary variable identifying whether the child is stunted), 2 is the years of education of the mother of the child, and is a YY DD possibly nonlinear function of the confounding factors or controls . In the discussion following it is DD ff(ZZ) assumed that inferences are desired on the two variables, 1 , 2 , whose respective coefficients 1 , and ZZ 2 provide an approximation of the long-run relationship between the variable and the outcome of DD DD ββ interest. ββ

# **_Conventional ad-hoc approach for choosing confounding variables_**

Traditionally, in the empirical literature in social sciences, the number of control variables in is determined by hand, or in an ad-hoc manner, rather than choosing the control variables in a dataZZ dependent manner. For example, in the health and nutrition literature (e.g., Alderman and Heady, 2017; Jeong et al., 2019; Kang et al., 2018) the conventional approach consists of selecting control variables based on common sense and/or the economic intuition derived from the human capital and health production function model summarized by Rosenzweig (1990).

The paper presents results following this ad-hoc approach, by assuming a small set of control variables entering equation (1) linearly, i.e., 1 1 2 2 + φ , (1a) YY= ββ In this setting, the coefficients DD + ββ DD + εε 1 , and 2 provide estimates of the partial correlation between 1 , and 2 , with the dependent variable net of the effect of all other confounding factors. The control variables ββ ββ DD in equation (1a) are denoted by instead of to make explicit the point that this is a subset of selected DD control variables from the wider set of control variables available in the survey and denoted in equation φφ ZZ (1) above by . The 23 control variables used in the regressions, include a binary variable for girls, child age (in months) and age squared, household size, the dependency ratio (separate for younger and older ZZ members in the Republic of Congo), four binary variables identifying the household’s wealth quintile,<sup>4</sup> a binary variable for rural areas and a set of binary variables for region of residence.

> 4 The wealth index is composed of: number of persons per room used for sleeping, primary material used for floor, roof, and walls, type of cooking fuel, ownership of household collective assets (electricity, radio, TV, fixed telephone, tables, chairs, beds, lamps, etc.), ownership of individual assets (watch, portable telephone, bicycle, motorcycle, car, etc.), ownership of house, bank account, agricultural land, animals (livestock, horses, goats, sheep, chicken, pigs, camels, guinea fowl, etc.), principal source of drinking water for the household and its geographic location, and type of toilet used by the household and whether it is shared or not.

9
It is well established in the literature that the coefficients estimated from a regression have a causal interpretation if the conditional mean independence assumption holds (e.g., Angrist and Pischke, 2009). The conditional independence assumption (CIA), in essence, requires that 1 and 2 are conditionally exogenous, which implies that that 1 and 2 are as good as randomly assigned conditional on the DD DD covariates .<sup>5</sup> Given that only a few controls are included in , there is a variety of threats to the DD DD internal validity of the causal interpretation of the estimated coefficients 1 , and 2 , arising from the φφ φφ potential of correlation between 1 and 2 and the error term . Omitted variable bias, for example, ββ ββ can lead to a nonzero correlation between the error term and 1 and 2 leading to a violation of the DD DD εε conditional independence assumption (as well as of the conditional mean-zero-assumption, i.e., DD DD 1 2] = 0 ). It is precisely for this reason that the estimates of the coefficients 1 , and 2 , from a regression model as (1a) based on the ad-hoc selection of a few controls, are typically interpreted as EE[εε|φφ, DD , DD ββ ββ estimates of the association or partial correlations of , 1 , and 2 , rather than as causal estimates of the effect of 1 , and 2 , on . YY DD DD DD DD YY

# **_Double Machine Learning (DML) Approach_**

To address the preceding concerns, the “double machine-learning” (henceforth DML) approach developed by Chernozhukov et al. (2018) for the purpose of making inferences is also explored as an alternative to the ad-hoc approach. Expanding the set of controls to a much larger set of variables, denoted by , minimizes potential omitted variable bias, and this in turn makes the conditional mean independence assumption required for causal inferences much more defensible than in the case of a ZZ few selected controls . As implied by the name, DML allows for a data-driven selection of controls from a wider set of variables based upon the combination of methods of statistical learning, such as φφ regularization, resampling (Hastie et al., 2009; James et al., 2013) and cross-fit partialing-out ZZ (Chernozhukov et al., 2018).<sup>6</sup> Regularization (or shrinkage) can fit a model containing a large number of regressors, even greater than the number of observations available, using a technique that constrains or regularizes the coefficient estimates, or equivalently, that shrinks the coefficient estimates towards zero

> 5 The conditional independence assumption for internal validity is weaker than the conditional mean zero assumption of 1 2] = 0 typically required for the OLS method. In fact, as long as 1 and 2 , conditional on a set control variables, happen to be independent of the error term, causal inferences could be made about 1 and 2 , even if some or all of the control variables were correlated with the error term. EE[εε|φφ, DD , DD DD DD 6 Cross-fit partialing-out is a recent innovation for using LASSO for inference improving upon related methods such as partialing DD DD out and double selection (Belloni et al., 2014a and 2014b).

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(e.g., LASSO).<sup>7</sup> Resampling methods that repeatedly draw samples from a training set and refit the model of interest on each auxiliary (test) sample, combined with cross-fit partialing-out that swaps the roles of training and auxiliary samples to obtain multiple estimates can provide additional information about the bias and efficiency of the fitted model. Such cross-validation sampling methods yield information that would not be available from fitting the model only once using the original training sample. In combination, the data-driven selection of control variables for the model from a much larger pool of variables combined with resampling and cross-fit partialing-out offer the opportunity to increase robustness reduces the variance of the coefficient estimates and to avoid overfitting (i.e., poor predictions on future observations not used in model training).

Specifically, the full partially linear model, is specified as 1 1 2 2 1 2] = 0 (2) YY= ββ1 DD + ββ 1DD + ff(ZZ) + εε EE[εε|ZZ, DD1 , DD (2a) DD2 = gg(ZZ) + vv2 EE[vv 2|ZZ] = 0 (2b) where DD = h(ZZ) + vv , 1 , 2 are as above, , and EE[vv |ZZ] = 0 are possibly nonlinear functions of the controls summarized by a “high-dimensional” vector of confounding factors that could include many, if not all, of YY DD DD ff(ZZ) gg(ZZ) ZZ the variables in the survey (and perhaps even greater than the number of observations in the survey). Equation (2) is the main equation, and 1 and 2 are the main regression coefficients for inference. If 1 and 2 are exogenous conditional on controls , 1 and 2 , have the interpretation of the treatment ββ ββ DD effect parameters. The second and third equations (2a) and (2b) keep track of confounding, namely the DD ZZ ββ ββ dependence of the treatment variables on controls, with the functions and h allowing for the possibility that the functional form summarizing the relationship between the treatment variables 1 gg and 2 and may differ.<sup>8</sup> DD DD ZZ

As pointed out by Chernozhukov et al. (2018), one naive approach trying to improve on the ad-hocspecification would likely ignore equations (2a) and (2b) and focus only on the first equation (2) by attempting to select control variables from a much wider pool of variables available in a survey, by applying LASSO to equation (2) above, forcing the treatment variables 1 and 2 to remain in the model DD DD

> 7 LASSO stands for the Least Absolute Shrinkage and Selection Operator (Tibshirani, 1996). In LASSO, coefficients are chosen to minimize the sum of the squared residuals plus a penalty term that penalizes the size of the model through the sum of absolute values of the coefficients.

> 8 Equations (2a) and (2b) are not of interest per se, but they are important for characterizing and removing regularization bias.

11
by excluding 1 and 2 from the LASSO penalty. One could then try to estimate and do inference about 1 and 2 by applying ordinary least squares with as the outcome, and 1 and 2 and any selected ββ ββ control variables as regressors. The problem with this approach can be seen by noting that, in LASSO, ββ ββ YY DD DD any variable that is highly correlated to the 1 or 2 treatment variables is likely to be dropped since including such a variable does not add much predictive power for the outcome given that the DD DD treatment variables 1 and 2 are already in the model. As a consequence, the exclusion of a variable YY that is highly correlated to the treatment variables 1 and 2 can lead to substantial omitted-variables DD DD bias in the coefficients 1 and 2 . Similarly, if one applied a variable selection method to only equations DD DD (2a) and (2b) for predicting 1 and 2 , one could miss variables that have moderate-sized coefficients in ββ ββ predicting 1 and 2 , but large direct effects on . Such an omission may again lead to non-negligible DD DD omitted-variable bias in the coefficients 1 and 2 .<sup>9</sup> DD DD YY In more intuitive terms, the DML method consists of estimating the coefficients ββ ββ 1 and 2 from the regression coefficients of the “residualized” on the “residualized” 1 and 2 variables, where the ββ ββ residuals are constructed from the difference between the actual value of (and the actual values of YY DD DD 1 and 2 ) and the fitted value from a regression of (and 1 and 2 ) on .<sup>10</sup> As in the conventional YY (or ad-hoc) approach summarized earlier, the maintained (and untested) assumption for causal DD DD YY DD DD ZZ inferences based on the DML regression equations (2), (2a) and (2b) is that 1 2] = 0 , and for .<sup>11</sup> The key difference between the ad-hoc approach and DML that allows for EE[εε|ZZ, DD , DD causal inferences is the assumption that ii 1 or 2 are conditionally exogenous (or as good as randomly EE[vv |ZZ] = 0 ii= 1,2 assigned conditional on the covariates ) is more defensible. The vector of the confounding variables DD DD is of much higher dimension than the vector which is composed of the few confounding variables ZZ ZZ chosen in ad-hoc manner. Thus, in the ad-hoc approach the estimates of 1 and 2 may subject to φφ omitted variable bias thus preventing one from making causal inferences. ββ ββ In contrast to the ad-hoc approach, the vector in the DML approach, as applied in this study, consists of 375 possible control variables for the analysis using the MICS from the Republic of Congo and 109 ZZ

> 9 The DML approach has a more relaxed sparsity requirement than double selection (Belloni et al. 2014b), that adds robustness since the sample is split and coefficients are obtained from one sample and used in another independent sample (see the Appendix for more details).

> 10 The sequence of steps involved in applying the DML method is presented in detail in the Appendix.

> 11 An alternative approach is to employ instrumental variables for the 1 and 2 treatment variables and apply a variant of the DML approach explored here. The difficulty common to most applications of the instrumental variable approach is to identify variables that are excluded from equation (2) but correlated with the treatment variables DD DD 1 and 2 and uncorrelated with the error term . DD DD εε

12
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
random splitting is repeated 10 times (and then averaged) to take into account the fact that the selection of variables introduces a new source of variability that may affect the standard errors of the estimates and thus inference.<sup>14</sup>

# **Analysis and Results**

Tables 2 and 4 present the estimates of the relationship between child nutrition and maternal education using the ad-hoc approach of selecting controls and the DML approach, for two alternative measures of ECD, the standardized ECD index and the binary variable identifying whether a child is on track in development, for the Republic of Congo and for São Tomé and Príncipe, respectively. Two alternative measures of the nutritional status of the child are explored. Specification A constrains the overall relationship between the ECD measure used and child HAZ, a continuous variable to be linear. This provides a useful characterization of the relationship between ECD and HAZ on average among all children and not necessarily among children who are stunted. Specification B provides more information on the relationship between ECD and child stature among undernourished children (at the lower part of the distribution of HAZ). The dichotomous variable on stunting allows for a direct comparison of the ECD measures between the groups of children with low HAZ scores (HAZ<-2) and higher HAZ scores (HAZ>=2).

The ad-hoc estimates in column 1 of Table 2 for the Republic of Congo suggest that there is a statistically significant association between child HAZ-scores as well as maternal education and the value of the ECD standardized index. In specification A, even after controlling for selected confounders, children with higher linear growth (higher HAZ) appear to have a higher value of the ECD standardized index. Moreover, even after controlling for HAZ, an extra year of education of the mother is associated with a higher value of the ECD standardized index. The same relation holds with specification B that compares stunted against non-stunted children. The value of the standardized index is lower on average among stunted children in comparison to non-stunted children. However, as discussed earlier, the variety of threats to the internal validity of estimates, as in column 1, typically prevent analysts from moving beyond correlations.

> 14 Thus, a total of 100 LASSOs are estimated. The variables selected based on LASSO in one sample may differ for the variables selected in another sample, which implies that the standard errors used for proper inferences would need to take into account that new source of variability.

14
The causal estimates based on the DML approach (column 2 of Table 2) reveal that there is a statistically significant causal effect between child linear growth (HAZ) or stunting and early childhood development as measured by the ECD index (specifications A and B). The DML estimate implies that being stunted “causes” a decrease in the value of the ECDI by 0.167 SD units (95% CI [-0.264, -0.069]). Also, based on the DML approach, after controlling for child HZA or stunting, and a variety of other confounders selected based on data-driven methods, maternal education does not have a direct causal effect on early childhood development in addition to any potential effect it may have on ECD through improved HAZ scores or decreased likelihood of stunting.

The estimates in Table 2 also reveal that the results are sensitive to the measure used for early childhood. Using the binary variable identifying whether a child is on track in development in 3 of the 4 domains of early childhood development, HAZ does not have a statistically significant effect on the OR of being on track in development (at the 5 percent level of significance) and neither does maternal education (see column2 in Table 2). Nevertheless, being stunted causes a statistically significant and large decrease in the odds ratio of a child being on track in development (OR= 0.758; CI [0.594, 0.966]) (see specification B column 2 Table 2).

**Table 2: Republic of Congo: Effects on Early Childhood Development (children 36-59 months)**

|||**(1)**<br>**Ad-hoc**<br>|||**(2)**<br>**DML approach**<br>||
|---|---|---|---|---|---|---|
|**Dependent variable: ECD Index**<br>**(standardized)**|**Coeff**|**95% CI**|**P-value**|**Coeff**|**95% CI**|**P-value**|
|**Specification A**|||||||
|Child HAZ score|0.059|[0.034,0.084]|0.000|0.055|[0.025,0.085]|0.000|
|Mother’syears of education|0.017|[0.005,0.029]|0.004|0.006|[-0.010,0.023]|0.477|
|**Specification B**|||||||
|Whether child is stunted|-0.167|[-0.246,-0.087]|0.000|-0.167|[-0.264,-0.069]|0.001|
|Mother’syears of education|0.018|[0.006,0.029]|0.003|0.007|[-0.010,0.023]|0.429|
|**Dependent variable: Binary (0,1)**<br>**variable on whether child is on track**<br>**in ECD**|**OR**|**95% CI**|**P-value**|**Coeff**|**95% CI**|**P-value**|
|**Specification A**|||||||
|Child HAZ score|1.065|[1.007,1.126]|0.028|1.072|[0.997,1.153]|0.061|
|Mother’syears of education|1.000|[0.975,1.025]|0.990|0.970|[0.933,1.009]|0.134|
|**Specification B**|||||||
|Whether child is stunted|0.803|[0.670,0.963]|0.018|0.758|[0.594,0.966]|0.025|
|Mother’syears of education|1.00|[0.975,1.025]|0.992|0.968|[0.930,1.007]|0.104|
|Shaded cells denote variables with signi<br>Confidence intervals reported are base<br>The control variables used in the ad-ho<br>squared, household size, the household<br>for region of residence.|ficant coef<br>d on robust<br>c model inc<br>’s wealth q|ficient estimates (P<br>standard errors<br>lude: the child gen<br>uintile, a binary var|-value < 0.05<br>der, child ag<br>iable for rur|)<br>e in mont<br>al areas an|hs and age in mont<br>d a set of binary v|hs<br>ariables|

15
The effect of maternal education on child HAZ and stunting is confirmed further in a separate analysis of the relation between HAZ and stunting and maternal education controlling for covariates based on the alternative approaches. Table 3 presents estimates of the relation between years of maternal education and different child anthropometric measures for the sample of all children less than 5 years of age (0-59 months) commonly used in the empirical literature as well as separately for the sample of children less than 36 months and the sample of children 36-59 months of age for which ECD indicators are also available. The estimates obtained using the ad-hoc approach to selecting controls, suggest that maternal education is significantly associated with child linear growth (HAZ), and with a child being stunted or underweight or wasted, irrespective of the age group of children analyzed. In contrast, the DML estimates reveal a much more intriguing picture. Maternal education has a significant effect on the linear growth of younger children (less than 36 months) and no significant effect on the odds ratio of being underweight or wasted among children in this age group. However maternal education has an effect on the odds of being underweight or wasted for the older age group.

Maternal education ceases to have a significant effect on the odds ratio of being stunted among older children (36-59 months) compared to the older children that are not stunted. However, maternal education has an effect on the HAZ of older children, on average, though this effect on linear growth is smaller among older than it is for younger children. For example, an increase in maternal education by one year results in an increase in child HAZ by 0.048 SD of HAZ among younger children, whereas this effect drops down to 0.027 SD of HAZ among older children. In contrast the point estimate of the coefficient of maternal education based on the ad-hoc approach is the same 0.048 SD for both age groups.

16
**Table 3: Republic of Congo: Child undernutrition and maternal schooling**

|||**(1)**<br>**Ad-hoc model**|||**(2)**<br>**DML approach**||
|---|---|---|---|---|---|---|
||**Odds**<br>**Ratio**<br>**(OR)**|**95% CI**|**P-value**|**OR**|**95% CI**|**P-value**|
|**Sample: Children 0-59 months**|||||||
|Child HAZ score|0.048<sup>a</sup>|[0.036,0.060]|0.000|0.041<sup>a</sup>|[0.024,0.058]|0.000|
|Whether child is stunted|0.936|[0.920,0.952]|0.000|0.952|[0.928,0.977]|0.000|
|Whether child underweight|0.945|[0.926,0.966]|0.000|0.958|[0.926,0.991]|0.014|
|Whether child is wasted|0.945|[0.925,0.965]|0.000|0.953|[0.920,0.987]|0.008|
|**Sample: Children < 36 months**|||||||
|Child HAZ score|0.048<sup>a</sup>|[0.032,0.064]|0.000|0.048<sup>a</sup>|[0.027,0.070]|0.000|
|Whether child is stunted|0.940|[0.920,0.961]|0.000|0.945|[0.912,0.979]|0.002|
|Whether child underweight|0.950|[0.921,0.971]|0.000|0.957|[0.913,1.003]|0.066|
|Whether child is wasted|0.945|[0.920,0.971]|0.000|0.955|[0.911,1.002]|0.059|
|**Sample: Children 36-59 months**|||||||
|Child HAZ score|0.048<sup>a</sup>|[0.030,0.065]|0.000|0.027<sup>a</sup>|[0.003,0.050]|0.026|
|Whether child is stunted|0.928|[0.901,0.955]|0.000|0.964|[0.923,1.007]|0.101|
|Whether child underweight|0.943|[0.911,0.977]|0.001|0.954|[0.922,0.987]|0.007|
|Whether child is wasted|0.943|[0.911,0.977]|0.001|0.959|[0.928,0.991]|0.014|
|Shaded cells denote variables with si<br>a: This is not an OR but simply the re<br>Confidence intervals reported are ba<br>The control variables used in the ad-<br>squared, household size, the young a<br>or older than 64 and the total numbe<br>wealthquintile,a binaryvariable for|gnificant coeff<br>gression coeffi<br>sed on robust<br>hoc model incl<br>nd old depend<br>r of working a<br>rural areas an|icient estimates (P<br>cient of mother’s y<br>standard errors<br>ude: the child gen<br>ency ratios (ratio<br>ge members 15-64<br>d a set of binaryva|-value < 0.0<br>ears of edu<br>der, child ag<br>of househol<br>years old),<br>riables for r|5)<br>cation<br>e in mont<br>d members<br>binary vari<br>egion of re|hs and age in mont<br>younger than 15 y<br>ables for the house<br>sidence.|hs<br>ears old<br>hold’s|

A different picture emerges from the same analysis with data from São Tomé and Príncipe. The estimates based on the ad-hoc choice of controls (column 1 Table 4) suggest that HAZ, stunting, and maternal education are mostly significantly associated with early childhood development. Only stunting status is not correlated with the measure of a child being on track in ECD.

17
**Table 4: São Tomé and Príncipe: Effects on Early Childhood Development (children 36-59 months)**

|||**(1)**<br>**Ad-hoc**<br>|||**(2)**<br>**DML approach**<br>||
|---|---|---|---|---|---|---|
|**Dependent variable: ECD Index**<br>**(standardized)**|**Coeff**|**95% CI**|**P-value**|**Coeff**|**95% CI**|**P-value**|
|**Specification A**|||||||
|Child HAZ score|0.118|[0.051,0.186]|0.001|0.108|[0.034,0.183]|0.004|
|Mother’syears of education|0.0429|[0.024,0.059]|0.000|0.034|[0.0160,0.053]|0.000|
|**Specification B**|||||||
|Whether child is stunted|-0.205|[-0.404,-0.006]|0.044|-0.145|[-0.349,0.060]|0.166|
|Mother’syears of education|0.042|[0.025,0.059]|0.000|0.036|[0.018,0.054]|0.000|
|**Dependent variable: Binary (0,1)**<br>**variable on whether child is on track**<br>**in ECD**|**OR**|**95% CI**|**P-value**|**OR**|**95% CI**|**P-value**|
|**Specification A**|||||||
|Child HAZ score|1.188|[1.027,1.374]|0.020|1.090|[0.920,1.292]|0.318|
|Mother’syears of education|1.069|[1.025,1.115]|0.002|1.058|[1.004,1.115]|0.036|
|**Specification B**|||||||
|Whether child is stunted|0.895|[0.561,1.427]|0.640|0.984|[0.563,1.723]|0.956|
|Mother’syears of education|1.070|[1.027,1.116]|0.001|1.071|[1.017,1.127]|0.009|
|Shaded cells denote variables with sign<br>Confidence intervals reported are base<br>The control variables used in the ad-ho<br>squared, household size, the dependen<br>set of binaryvariables for region of resi|ificant coeff<br>d on robust<br>c model inc<br>cy ratio, the<br>dence.|icient estimates (P<br>standard errors<br>lude: the child gen<br>household’s weal|-value < 0.05<br>der, child ag<br>th quintile, a|)<br>e in month<br>binary var|s and age in mont<br>iable for rural are|hs<br>as and a|

The DML estimates, on the other hand, reveal that only maternal education has a consistent and statistically significant effect irrespective of the dependent variable used to measure ECD (standardized EDC index, vs. dichotomous indicator for being on track in ECD) and the specification for child undernutrition (HAZ vs. stunting) (see column 2 Table 4). A child being stunted does not appear to have a statistically significant effect on the ECD index or on the odds ratio of being on track in development (see specification B in column 2 Table 4). Moreover, the absence of any relationship between stunting and being on track in development appears to hold irrespective of the method used (ad-hoc vs. DML) (compare columns 1 and 2 in specification B of Table 4).

As for the Republic of Congo, the relationship between HAZ and stunting and maternal education controlling for covariates using the alternative approaches (ad-hoc vs. DLM) was also carried out for São Tomé and Príncipe. Table 5 presents estimates of the relation between years of maternal education and different child anthropometric measures for the sample of all children less than 5 years of age (0-59 months) commonly used in the empirical literature as well as separately for the sample of children less than 36 months and the sample of children 36-59 months of age for which ECD indicators are also 18
available. Contrary to expectations, maternal education does not appear to have no statistically significant relationship (causal or not) with child HAZ or stunting.

**Table 5: São Tomé & Príncipe: The effect of a mother’s years of schooling on**

|||**(1)**<br>**Ad-hoc model**|||**(2)**<br>**DML approach**||
|---|---|---|---|---|---|---|
||**Odds**<br>**Ratio**<br>**(OR)**|**95% CI**|**P-value**|**OR**|**95% CI**|**P-value**|
|**Sample: Children 0-59 months**|||||||
|Child HAZ score|0.009<sup>a</sup>|[-0.004,0.022]|0.161|0.008<sup>a</sup>|[-0.007,0.023]|0.287|
|Whether child is stunted|0.992|[0.962,1.023]|0.608|0.000|[-0.004,0.004]|0.903|
|Whether child underweight|0.987|[0.950,1.025]|0.502|-0.001|[-0.004,0.002]|0.689|
|Whether child is wasted|1.008|[0.951,1.068]|0.783|0.000|[-0.003,0.003]|0.926|
|**Sample: Children < 36 months**|||||||
|Child HAZ score|0.015<sup>a</sup>|[-0.002,0.032]|0.091|0.014<sup>a</sup>|[-0.006,0.034]|0.166|
|Whether child is stunted|0.991|[0.955,1.028]|0.638|-0.000|[-0.006,0.005]|0.976|
|Whether child underweight|0.965|[0.924,1.007]|0.106|-0.001|[-0.005,0.002]|0.493|
|Whether child is wasted|0.947|[0.879,1.019]|0.146|-0.002|[-0.005,0.002]|0.408|
|**Sample: Children 36-59 months**|||||||
|Child HAZ score|-0.002<sup>a</sup>|[-0.022,0.018]|0.849|-0.003<sup>a</sup>|[-0.024,0.017]|0.746|
|Whether child is stunted|0.991|[0.936,1.049]|0.754|-0.000|[-0.007,0.006]|0.880|
|Whether child underweight|1.046|[0.964,1.134]|0.279|0.001|[-0.004,0.006]|0.774|
|Whether child is wasted|1.140|[1.033,1.258]|0.009|0.003|[-0.001,0.007]|0.105|
|Shaded cells denote variables with sig<br>a: regression coefficient of mother’s y<br>Confidence intervals reported are bas<br>The control variables used in the ad-h<br>squared, household size, the young a<br>or older than 64 and the total numbe<br>wealthquintile,a binaryvariable for r|nificant coeff<br>ears of educa<br>ed on robust<br>oc model incl<br>nd old depend<br>r of working a<br>ural areas an|icient estimates (P<br>tion on child HAZ-<br>standard errors<br>ude: the child gen<br>ency ratios (ratio<br>ge members 15-64<br>d a set of binaryva|-value < 0.0<br>score<br>der, child ag<br>of househol<br>years old),<br>riables for r|5)<br>e in month<br>d members<br>binary vari<br>egion of re|s and age in month<br>younger than 15 y<br>ables for the house<br>sidence.|s<br>ears old<br>hold’s|

# **Discussion**

Estimates of the relationship between a mother’s education and child stature measures with early childhood development are contrasted between two empirical approaches: the conventional approach whereby control variables are selected in an ad-hoc manner and the double machine-learning (DML) approach that employs data-driven methods to select controls from a much wider set of variables available in the survey along with statistical learning methods that yield information that would not be available from fitting the model only once using the original sample.

It is hoped that the analysis and comparisons carried out in this paper have made it clear that there is much to be gained by moving away from the customary approach of controlling for a few selected confounding factors in the regression analysis that is primarily equipped to establish partial correlations 19
and not necessarily causal inferences. The DML estimates are preferred because they are estimates of the causal effect with a more reasonable set of assumptions, they minimize potential omitted variable bias, and they allow for the inclusion of different confounding factors influencing the outcome variable (ECD measure) and the variables for which inferences are desired (child HAZ or stunting) and maternal education, in this study.

The comparison between the conventional OLS estimates and the preferred DML estimates within each of the two countries analyzed reveals that frequently the customary approach tends to suggest significant associations when in fact there is no causal relation (based on the DML). One might say that this simply confirms the old dictum “correlation is not causation” but then one cannot help but wonder why one would bother to include confounding factors in the regression analysis if the underlying (or unstated) objective is not causation. Omitted variables are likely to result in biased coefficients (or partial correlations) of variables of interest in a regression equation with a few selected control variables. For example, in the Republic of Congo, the conventional OLS approach suggests that maternal education has a direct and significant association with the standardized ECD index. The preferred DML approach reveals that after controlling for omitted variable bias there is no such association between maternal education and ECD. Another example, of such a discordance between the conventional OLS and DML estimates in the Republic of Congo, concerns the relationship between child HAZ and a child being on track in development. The conventional OLS estimates suggest that children experiencing a lower HAZ (or mild forms of growth faltering), not just those classified as stunted, are more likely to be off track in their development. The DML estimates, in contrast, make it apparent that in the Republic of Congo it is only stunted children that experience lower child development outcomes.

The same pattern between HAZ and a child being on track in development appears in São Tomé and Príncipe. The conventional OLS estimates suggest that mild forms of growth faltering (lower HAZ) in general are associated a lower likelihood of being on track in child development outcomes. The DML estimates, in contrast, reveal that in São Tomé and Príncipe there is no relationship at all between HAZ or even stunting and child development outcomes (measured either in terms of the standardized ECD or being on track in ECD).

Overall, the findings based on the preferable DML approach differ across the two countries depending on the measure of ECD and child stature (HAZ vs stunting) used in the analysis (a summary is provided in Table 6). Clearly country-specific context matters a lot in the relationship among child stature, maternal education and early childhood development. This finding also suggests that country-specific policy 20
advice based on relationships observed from data in other countries may be quite risky, if not misleading, unless the same relationship is also validated with country-specific data. DML estimates from the Republic of Congo suggest that HAZ and stunting have a direct causal effect on early childhood development. In contrast, in São Tomé and Príncipe only HAZ has a positive effect on the ECD index, but otherwise the growth measures do not have a relationship with child development outcomes. This is very much in line with the conclusion of Tran et al (2019) that “...overall, growth is not a sensitive and therefore suitable indicator of child development.” The reasons for the absence of a relationship (causal or not) between stunting and child development outcomes in São Tomé and Príncipe are not clear, but certainly deserving of more investigation.

**Table 6: Summary of the effects of a child stature and maternal education on early childhood development based on the DML approach**

||**Dependent variable: ECD**<br>|**Index(standardized)**<br>|
|---|---|---|
||**Republic of Congo **|**São Tomé & Príncipe **|
|**Specification A**|||
|Child HAZ score|Positive effect|Positive effect|
|Mother’s years of education|No direct effect,<br>(but indirect effect through improved<br>child stature)|Positive effect<br>(no effect on child stature)|
|**Specification B**|||
|Whether child is stunted|Negative effect|No effect|
|Mother’s years of education|No direct effect,<br>(but indirect effect through improved<br>child stature)|Positive effect<br>(no effect on child stature)|
||**Dependent variable: Binary variable(0,1)**|**on whether child is on track in ECD**|
||**Republic of Congo**|**São Tomé & Príncipe**|
|**Specification A**|||
|Child HAZ score|No effect|No effect|
|Mother’s years of education|No direct effect,<br>(indirect through better child stature)|Positive effect<br>(no effect on child stature)|
|**Specification B**|||
|Whether child is stunted|Negative effect|No effect|
|Mother’s years of education|No direct effect,<br>(indirect through better child stature)|Positive effect<br>(no effect on child stature)|

In the Republic of Congo, maternal education does not have any direct effect on early childhood development and the main effect of maternal education on ECD is an indirect one through improved child HAZ or reduced incidence of stunting in the first two years of a child’s life. In contrast, in São Tomé and Príncipe maternal education has a direct effect on child ECD. One important caveat is that all of the 10 questions on the developmental status of children 36-59 months used to construct the ECDI are addressed to and responded by the caregiver of the child, usually the mother. This suggests that socio21
economic characteristics of the mother and especially the education of the mother are likely to play a very important role. While these features imply that it is imperative to take into account the potential influences of these confounding factors in determining the impact of maternal education on ECD, the DML approach that addresses these issues explicitly reveals that in São Tomé and Príncipe at least, maternal education has a direct effect on ECD. Yet, one more intriguing result from the analysis in São Tomé and Príncipe is that maternal education has no relationship at all with child stature. This result appears to contradict much of the conventional wisdom derived from other countries regarding the effect of maternal education on child nutrition. However, it is important to bear in mind that the conventional wisdom is based more on correlations as opposed to established causal relations (Desai and Alva, 1998). A more recent study by Alderman and Heady (2017), addressing explicitly the problem of omitted variable bias in the relationship between parental education and child nutrition, finds that the nutritional returns to parental education are reduced substantially in models that include cluster fixed effects, which are typically omitted from conventional regression models, thus resulting in omitted variable bias in the estimated coefficients.

In conclusion, country-specific policy advice based on relationships observed from data in other countries may be quite risky, if not misleading. DML offers the opportunity to identify and validate causal relationships with country-specific observational data. Given the constraints faced by randomized control trials to address every possible question, DML provides a practical and feasible approach to reducing threats to internal validity to derive robust inferences based on observational data for evidence-based policy advice. The extent to which the DML estimates are close to the true causal or impact estimates has yet to be established and this can only be ascertained by comparing with causal estimates derived from an RCT. Nevertheless, there is promising evidence that estimates based on the DML represent an improvement over the usual OLS in the sense that they are closer (and sometimes quite close) to the impact estimates from the preferred instrumental variable method (Duflo, 2018).

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