This paper develops a general method for assessing the robustness of standard empirical methods measuring group differences in achievement to violations in the cardinal comparability of achievement test scores. The paper defines a distance measure over possible test scales and then constructs...

This article reviews recent developments in the econometrics of early childhood human capital and investments. We start with a discussion about the lack of cardinality in test scores, the reasons it matters for empirical research on human capital, and the approaches researchers have used to...