Studies of pre-k in Tulsa, by William Gormley and his colleagues at Georgetown, provide good direct evidence on the relative effects of a state pre-school program on kindergarten readiness for different income groups. Tulsa participates in Oklahoma’s universal pre-k program, which enrolls over 70% of the state’s 4 year-olds.

Gormley’s studies, like many studies of preschool’s effects on kindergarten readiness, rely on what economists call “regression discontinuity” analysis. This method is well-respected by econometricians and other statisticians. Regression discontinuity analysis is regarded as a rigorous approach to evaluation with a good comparison group. It is not as precise as random assignment experimentation, but is usually unlikely to be biased if correctly applied. The intuitive idea of regression discontinuity analysis in the case of pre-k is that we are comparing entering kindergarten test scores and entering pre-k test scores, on the same test, of children who are of almost the same age, but some of whom just made the age cutoff for attending pre-k the previous year, and others who had to wait a year because they just missed the age cutoff.

Gormley analyses the effects of Tulsa’s pre-k program on three income groups: those children eligible for a free lunch, those children eligible for a reduced price lunch, and those children ineligible for any lunch subsidy. “Free lunch eligibility” means that family income is below 130% of the federal poverty line for a family of that size. “Reduced price lunch eligibility” corresponds to family income between 130% and 185% of the federal poverty line. The most advantaged income group has income above 185% of the federal poverty line.

Gormley finds that Tulsa’s pre-k program has significant effects on test scores at kindergarten readiness for all three groups. In one study, he reports that the absolute test score increase in points tends to be similar for the free lunch and full-price lunch students, but higher for the reduced-price lunch students. In another study, he finds that percentage effects of test scores tend to be somewhat greater for the lower income students. These findings are consistent because the baseline levels of test scores tend to be lower for the lower income students, so a similar absolute test score effect can be a greater percentage effect.

But how would we expect these test score effects to be reflected in later effects on adult earnings? This has been studied by Harvard economist Chetty and his colleagues. Their focus is on the relationship between end of kindergarten test scores and adult earnings, but it is reasonable to assume that similar relationships would hold between beginning of kindergarten test scores and adult earnings.

If we use Chetty’s results, we find that the absolute test score effects give us a better predictor of dollar effects on adult earnings. Using information from Chetty et al’s results and Gormley et al’s results, I calculate that in Tulsa, the predicted effect of pre-k on adult earnings would be about one-fifth greater in dollars for reduced price lunch students than for free lunch students, and the predicted effect on adult earnings would be about one-fifth less in dollars for full price lunch students than for free lunch students.

The bottom line is this: Gormley’s results imply roughly similar dollar effects on adult earnings for all three income groups. The variance of effects across income groups imply that the “near poor” (the reduced price lunch students) have somewhat greater effects from pre-k than the “poor”, but the non-poor (the full price lunch students) have somewhat smaller effects from pre-k than the poor. So there is no simple regularity that the poor always benefit more from pre-k than all other groups, rather some middle group may benefit the most.

Of course, Gormley’s results don’t tell us how effects vary within the full price lunch group. Perhaps effects are quite large for students above 185% but below some higher x% of poverty, but then tail off towards zero beyond some income bracket.

Although regression discontinuity estimates are unbiased, we might also want to see effects of random assignment experimental evaluations of preschool for children from advantaged groups. I will consider that topic in a future blog post.

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