2.1.1. Description

To measure the effects of MMH on child development, we used the first 3 rounds of the Young Lives Peru Survey (YL), conducted by the University of Oxford and core-funded by the UK Department for International Development. The YL survey was also being conducted in Vietnam, Ethiopia, and India (Andra Pradesh region). As of now, 5 rounds of data have been collected, which can be publicly accessible through the Young Lives website (https://www.younglives.org.uk/content/data-research). This was a rich longitudinal survey that included a complete set of individual, parental, household, and community characteristics, including early developmental, economic and demographic indicators,

as well as information about social assistance programs in every community. The baseline sample of YL was cluster stratified, with 20 districts randomly selected across the country. Because the YL project was particularly interested in children living in poorer households, the sampling frame excluded the top 5 percent of districts as measured by a district poverty ranking. Despite excluding the least poor, it has been documented that the data reflects the Peruvian population in a broad range of indicators. Within each of the selected districts, 100 households with at least one child born between 2001 and 2002 (index child) were chosen randomly to participate in the project. Within each household, YL surveyed an index child who was born in 2000–2001 and was followed from infancy until they reached their mid-teens. The baseline round was conducted in 2002 when the index children were aged 6–20 months, the first follow-up conducted in 2006/2007, when they were between 4 and 6 years old, and the last round in 2009/2010, when they were between 7 and 8 years of age. The attrition rate between the 3 rounds of data collection was approximately 4 percent, which was low by international standards [14].

Of the 2000 index children in the baseline round, we focused our analysis on the sample of 1095 of them that were present in the first 3 waves for whom data on maternal mental health and Peabody Picture Vocabulary Test (PPVT) scores were available. We presented below tests for differences in some characteristics between the included and excluded samples.

#### 2.1.2. Measures of a Dimension of Child Development

We use PPVT scores [15] as the measure of early vocabulary skills, a strong predictor of later cognitive ability, including writing and reading skills, schooling, and labor market outcomes later in life [13,16–18]. In the YL survey, this outcome was measured using the Spanish version of the PPVT instrument. The PPVT measures receptive vocabulary; children are shown slides, each of which has 4 pictures, and were asked to identify the picture that corresponded to objects or actions named by the test administrator. Children did not need to name the objects or actions or be able to read or write them. It was just an object identification or association process. The test continued until the child had made 6 mistakes in the last 8 slides. The number and the level of difficulty of questions differed according to children's age (see [19]). We, therefore, constructed age-specific z-scores by subtracting the month-of-age-specific mean of the raw score and dividing by the month-of-age-specific standard deviation. PPVT scores were available in the 2nd and 3rd rounds of the YL survey, i.e., when children were 4–6 and 7–8 years.

#### 2.1.3. Measures of Maternal Mental Health

The explanatory variable was constructed using the information on maternal common mental disorders from the Self Reporting Questionnaire 20 items (SRQ20), a screening (case-finding) tool included in the YL survey. The SRQ20 consisted of 20 yes/no questions with a reference period of the previous 30 days. The tool had a number of limitations, including the small number of items, the fact that it was not diagnostic, and could not separate out anxiety from depression. Still, the tool had been recommended by the World Health Organization and has acceptable levels of reliability and validity in developing countries. To the extent that depression and anxiety are closely related, and both of them can undermine the quality of care mothers provide to their children, the information gathered from the questionnaire was very valuable. Henceforth, we will use the term mental health to refer to both cases of depression and/or anxiety.

Using the responses to the questionnaire, we estimated 3 mental health indexes: The simple average of all items and 2 standardized items using factor analysis and principal components analysis. As we explain below, we used the information on maternal mental health from the first round of the YL survey.

#### 2.1.4. External Shocks

We exploited the availability of data on exposure to external shocks in the first round of the Peruvian YL. Caregivers were asked about events or changes that negatively affected the household welfare, and that occurred since the mother of the index child was pregnant until the day of the interview. The survey respondents described the event, and the enumerator classified it among the 14 categories. We grouped these categories into 6 groups of shocks, including natural disaster, crop or livestock loss, decrease in food availability, job or income loss, death or severe illness, and birth/new household member.
