A major strength of our study is the use of a common measure of child cognitive development: performance on the widely-used _Test de Vocabulario en Imágenes Peabody_ (TVIP), the Spanish version of the Peabody Picture Vocabulary Test (PPVT) (Dunn et al. 1986). Children are shown slides, each of which has four pictures, and are asked to identify the picture that corresponds to the object (for example, “boat”) or action (for example, “to measure”) named by the test administrator. The test continues until the child has made six mistakes in the last eight slides. The test is a measure of receptive vocabulary because children do not have to name the objects themselves and because children need not be able to read or write. Performance on the PPVT and TVIP at early ages has been shown to be predictive of important outcomes in a variety of settings.<sup>3</sup> To analyze socioeconomic gradients in TVIP scores, we construct country-specific, agespecific z-scores by subtracting the month-of-age-specific mean of the raw score and dividing by the month-of-age-specific standard deviation, separately by country and by urban-rural place of residence (as in Cunha and Heckman 2007 and many others).<sup>4</sup> As a robustness test, we also report results that use the tables given by the test developers to standardize the test (as done by Paxson and Schady 2007).

A fraction of children in every survey, ranging from 2 percent in Colombia to 18 percent in Nicaragua, did not take the TVIP. Although we do not have data that are comparable across all 5 countries on the reasons why these children did not take the test, it appears that most of them had difficulty understanding the instructions and making it past the practice items that are applied at the outset. Consistent with this, there are more children with missing test data at younger ages, and more in the poorest country, Nicaragua. Earlier work on Ecuador has shown that children who miss a given test do worse on other tests, or on the same test in different survey waves, than other children with comparable wealth and parental schooling levels (Paxson and Schady 2010; Schady 2011). Because children who miss tests are likely to be “low performers”, we assign these children a test score of zero. We test the robustness of our results to this approach to handling missing data.

> 3 Some examples include Schady (2011), who shows that children with low levels of TVIP scores before they enter school are more likely to repeat school grades and have lower scores on tests of math and reading in primary school in Ecuador; Case and Paxson (2008), who show that low performance on the PPVT at early ages predicts wages in adulthood in the United States; and Cunha and Heckman (2007) who use the National Longitudinal Survey of Youth (NLSY) to show that, by age 3 years, there is a difference of approximately 1.2 standard deviations in PPVT scores between children in the top and bottom quartiles of the distribution of permanent income in the United States, and that this difference is largely unchanged until at least 14 years of age. More generally, there is a large literature that shows that vocabulary size in kindergarten and earlier predicts reading comprehension throughout school and into early adulthood (see the discussion in Powell and Diamond 2012, and the references therein).

> 4 These calculations give equal weight to each month of age, thereby standardizing for possible differences across samples in the age distributions of children. The t-statistics adjust for the possible correlation of errors at the level of communities or census tract in Colombia, Ecuador, Nicaragua, and Peru, and at the state level in Chile.

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