The Gap Within the Gap - Katherine Michelmore; Susan Dynarski (SAGE Publishing, 2017)
Gaps in educational achievement between high- and low-income children are growing. Administrative data sets maintained by states and districts lack information about income but do indicate whether a student is eligible for subsidized school meals. We leverage the longitudinal structure of these data sets to develop a new measure of economic disadvantage. Half of eighth graders in Michigan are eligible for a subsidized meal, but just 14% have been eligible for subsidized meals in every grade since kindergarten. These children score 0.94 standard deviations below those who are never eligible for meal subsidies and 0.23 below those who are occasionally eligible. There is a negative, linear relationship between grades spent in economic disadvantage and eighth-grade test scores. This is not an exposure effect; the relationship is almost identical in third-grade, before children have been exposed to varying years of economic disadvantage. Survey data show that the number of years that a child will spend eligible for subsidized lunch is negatively correlated with her or his current household income. Years eligible for subsidized meals can therefore be used as a reasonable proxy for income. Our proposed measure can be used to estimate heterogeneous effects in program evaluations, to improve value-added calculations, and to better target resources.