Linear decompositions of cognitive achievement gaps: a cautionary note and an illustration using Peruvian data

Developmental gaps between children of different socioeconomic backgrounds emerge early and persist over time. Cognitive skill formation is a cumulative process and, thus, all relevant influences that took place until the time skill is measured can play role in shaping these gaps. Linear decompositions based on the Oaxaca-Blinder technique are a fairly common way of estimating the contribution of two or more categories of variables to these differences in cognitive achievement. Two prominent examples of these categories are family and school influences. In this regard, the literature exhibits no consensus in terms of decomposition strategy and interpretation of its components, as well as a tendency to separate home and school influences by assigning all observed household, family and child characteristics to the first category. I argue this can lead to misleading policy implications and to biases in the estimated contributions of the categories. This analysis seeks to contribute to the literature in two ways. First, it formally explores the potential for biases in the decomposition exercises attempted so far. Second, it offers an alternative decomposition strategy consistent with explicit behavioral assumptions regarding the determination of skill inputs. This prevents arbitrary choices in terms of decomposition technique, its components and interpretation, and also makes the analysis less prone to biases. I illustrate empirically the main points of the analysis employing a rich dataset that contains longitudinal information on cognitive test scores, family and school characteristics, to decompose the cognitive skill gap observed, at age 8, between urban and rural children in Peru.