Permanent Income and the Black-White Test Score Gap

TL;DR

The paper argues that prior estimates of the black-white test score gap conditional on income are overstated because they control for current rather than permanent family income. Using CNLSY and ECLS data, it finds that permanent income explains about twice as much of the gap as current income, leaving conditional math gaps of roughly 0.2–0.3 SD in the two data sets.

Key findings

• Current income explains only about half as much of the black-white test score gap as permanent income; the remaining math gap among families with the same permanent income is only 0.2 to 0.3 standard deviations in two commonly used data sets.
• In the CNLSY PIAT math sample, the raw black-white gap is 0.77 SD; demographic controls reduce it to 0.56, current income to 0.43, permanent income OLS to 0.36, and 2SLS to 0.32.
• In the ECLS 5th grade math sample, the raw gap is 0.85 SD (0.78 in the restricted sample); current income reduces it to 0.38, short-run average income to 0.34, and the TS2SLS permanent-income estimate to 0.18.
• Adding permanent income to Fryer and Levitt’s (2006) 3rd grade controls reduces the unexplained black-white math gap from 0.34 to 0.15 SD; overall, family financial circumstances can explain 40 to 75% of the raw gap at age 10 or 11.

Methods

• The analysis uses two nationally representative samples: the CNLSY, with PIAT math, PIAT reading, and PPVT scores at ages 10–11 and permanent income measured as average real family income when the mother was aged 25–39; and the ECLS Kindergarten Cohort, focusing on 5th grade math scores and, for comparison, 3rd grade math scores.
• The paper develops an errors-in-variables model showing that controlling for annual income attenuates the income coefficient and biases the black coefficient toward the unconditional gap; it proposes IV and two-sample two-stage least squares (TS2SLS) estimators that use current income as an instrument for permanent income, with an auxiliary sample to estimate the first stage.
• Main estimates are OLS and 2SLS/TS2SLS regressions of standardized test scores on a black indicator and income controls, with demographic controls such as child age, gender, mother’s age at birth, parity, and calendar year; the analysis is descriptive, not causal.

Limitations

• The paper states that the analysis is purely descriptive and does not distinguish the causal effect of family income from other characteristics correlated with income, such as IQ or culture; results are only suggestive about income-focused interventions.
• The IV strategy relies on the assumption that transitory annual income is unrelated to outcomes conditional on permanent income, which could be violated by credit constraints or other PIH failures; the authors probe this with future-income instruments and timing specifications.
• The permanent income proxy is a 15-year average with reliability about 0.8, and the ECLS income measure is much lower quality than the NLSY measure, so the authors state their estimates almost certainly undercorrect for true permanent income; the CNLSY subsample is also not representative of all 10–11 year olds, with children of older mothers underrepresented.