Is it just noise? Measuring unobservable cognitive abilities in early childhood

Evidence suggests that children from disadvantaged backgrounds have lower cognitive abilities than their socioeconomically advantaged peers. However, two characteristics of the measurement of cognitive constructs make it difficult to quantify these inequalities. First, items on a test may provide ordinal information, but they do not conform to the properties of an interval scale. Second, a causal understanding of validity is incompatible with the standard validation framework, complicating what it means to measure unobservable constructs and the estimation of causal effects on such variables. Measurement invariance generates endogeneity bias in causal inference for effects variables on test scores and may make comparison across groups invalid. This paper analyzes these data problems using three standardized assessments taken by German children. It explores the limits of these assessments based on nonparametric psychometric models and the representational theory of measurement. This alternative framework may help to determine whether data fit the assumptions of a measurement model, and to overcome some limitations. A comparison of competing statistical modeling alternatives reveals substantial differences in the quantification of social inequalities. Although measurement error is not random noise, after accounting for it, an unsettling reduction in estimated effect sizes associated with the variables studied is found.