School Finance Reform and the Distribution of Student Achievement

May combine two claims.

SFRs have effects on teachers per pupil and total teacher salaries but not on average teacher pay.

“We also see effects on teachers per pupil and total teacher salaries but not on average teacher pay”

May combine two claims.

Little of the increase in relative funding goes to instructional expenditures, while roughly half goes to capital spending.

“Little of the increase in relative funding goes to instructional expenditures, while roughly half goes to capital spending.”

May combine two claims.

Using each measure, there are sharp increases in relative state funding for low-income districts following events that show no sign of eroding thereafter.

“Using each measure, we see sharp increases in relative state funding for low-income districts following events that show no sign of eroding thereafter.”

May combine two claims.

Following reforms, state revenues increase sharply, with larger increases in low-income districts and smaller but still positive increases in high-income districts.

“Following reforms, we document sharp increases in state revenues, with larger increases in low-income districts and smaller but still positive increases in high-income districts.”

• AssumptionThe authors state this as an assumption: The exact timing of school finance reform events is as good as random.

May combine two claims.

SFRs have substantial impacts on average instructional spending, both overall and in Q1 districts.

“We see substantial impacts of SFRs on average instructional spending, both overall and in Q1 districts (columns 2 and 3).”

May combine two claims.

Average state funding rises by $1,225 following events in first quintile districts and by $527 (not significant) in fifth quintile districts.

“The former indicates that average state funding rises by $1,225 following events in first quintile districts and by $527 (not significant) in fifth quintile districts.”

May combine two claims.

In the student achievement analysis, the post-event jump is never distinguishable from zero, and all of the estimated effect operates through the phase-in coefficient.

“By contrast, in our student achievement analysis, the”

May combine two claims.

In the parametric event-study model for the test-score slope, the hypothesis that the pre-event trend is zero has p=0.80, and the test that the post-event jump and change in trend is zero has p=0.02.

“In the parametric model, the p-value for the hypothesis that the pre-event trend is zero is 0.80; for the test that the post-event jump and change in trend is zero is 0.02.”

May combine two claims.

There is no indication that growth in educational spending following events crowds out state spending on other programs; rather, SFRs are associated with increases in state tax collections large enough to fully fund the increase in state transfers to districts.

“we have found no indication that growth in educational spending following events crowds out state spending on other programs; rather, SFRs are associated with increases in state tax collections large enough to fully fund the increase in state transfers to districts.”

May combine two claims.

Reforms are associated with sharp increases in total state education expenditures and tax collections.

“Reforms are associated with sharp increases in total state education expenditures and tax collections.”

May combine two claims.

In the three-parameter parametric model, the post-event change in trend is large and statistically significant.

“the post-event change in trend is large and statistically significant.”

May combine two claims.

In the nonparametric event-study model for the test-score slope, the omnibus test of zero pre-event effects has p=0.43, and the test of zero post-event effect has p<0.001.

“The p-value for the omnibus hypothesis test of zero pre-event effects in the nonparametric model is 0.43; the p-value for zero post-event effect is <0.001.”

May combine two claims.

The impact of events on the test score gap between bottom- and top-quintile districts is 0.008 SDs per year, or 0.013 SDs in the more flexible model (column 6).

“column 5 shows that the impact of events on the test score gap between bottom-and top-quintile districts is 0.008 SDs per year, or 0.013 SDs in the more flexible model (column 6).”

• AssumptionRests on an assumption: Absent school finance reforms, the differential trend in student achievement between low- and high-income districts in reform states would have continued as before (parallel trends assumption).

May combine two claims.

Impacts on state revenues appear to persist through the end of the sample, though out-year estimates are noisy.

“Though out-year estimates are noisy, impacts appear to persist through the end of our sample.”

May combine two claims.

Estimated changes in funding following reforms are much smaller in high-income districts; nonparametric post-event effects are jointly significant, but parametric estimates are not and magnitudes are quite small.

“Estimated changes in funding following reforms are much smaller here; while the nonparametric post-event effects are jointly significant, the parametric estimates are not and in any event the magnitudes are quite small.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Earlier finance analyses also indicated larger effects for quintile gaps than for slopes.

“Our earlier finance analyses also indicated larger effects for quintile gaps than for slopes.”

May combine two claims.

There is no indication that declines in local revenues offset increases in state funding in low-income districts, nor of pre-trends or erosion of initial impacts.

“There is no indication that declines in local revenues offset increases in state funding in low income districts, nor in (panel D) of pre-trends or erosion of initial impacts.”

May combine two claims.

The average low-income student does not live in a particularly low-income district, so is not well targeted by a transfer of resources to low-income districts.

“the average low-income student does not live in a particularly low-income district, so is not well targeted by a transfer of resources to the latter.”

May combine two claims.

Results from alternative approaches to event multiplicity are similar to main specifications, though the initial court order approach yields less precise, insignificant estimates of finance effects in panel B.

“Results are similar to those from our main specifications, though the initial court order approach yields less precise, insignificant estimates of finance effects in panel B.”

May combine two claims.

Schools used additional funds to increase instructional spending, reduce class size, and for capital outlays.

“Schools used these additional funds to increase instructional spending, reduce class size, and for capital outlays.”

May combine two claims.

Using nationally representative data on student achievement, the reforms were productive: they increased the absolute and relative achievement of students in low-income districts.

“Using nationally representative data on student achievement, we find that these reforms were productive: Reforms increased the absolute and relative achievement of students in low-income districts.”

• AssumptionRests on an assumption: Absent school finance reforms, the differential trend in student achievement between low- and high-income districts in reform states would have continued as before (parallel trends assumption).

May combine two claims.

The SFR effect on achievement is not sensitive to including controls for the presence of a school accountability policy in a state, and does not vary with school accountability.

“We found evidence for neither.”

May combine two claims.

Finance reforms reduced achievement gaps between high- and low-income school districts but did not have detectable effects on resource or achievement gaps between high- and low-income (or white and black) students.

“Thus, we find that finance reforms reduced achievement gaps between high-and low-income school districts but did not have detectable effects on resource or achievement gaps between highand low-income (or white and black) students.”

• AssumptionRests on an assumption: Absent school finance reforms, the differential trend in student achievement between low- and high-income districts in reform states would have continued as before (parallel trends assumption).

May combine two claims.

There is no discernible effect on achievement gaps by race or income or on the overall dispersion of test scores.

“There is no discernible effect on achievement gaps by race or income or on the overall dispersion of test scores.”

May combine two claims.

Roughly one-quarter of nonwhite and low-scoring students, and one-third of low-income students, live in first-quintile districts, while about 10 percent of each live in fifth-quintile districts.

“Roughly one-quarter of nonwhite and low-scoring students, and one-third of low-income students, live in first-quintile districts, while about 10 percent of each live in fifth-quintile districts (online Appendix Table A5).”

May combine two claims.

This district saw an increase in relative state aid of $622 per pupil for each of those ten years, and an increase in total revenues of $424 per pupil.

“Our finance estimates indicate that this district saw an increase in relative state aid of $622 per pupil for each of those ten years, and an increase in total revenues of $424 per pupil.”

May combine two claims.

Each year after an event, a district with log mean income one unit (about two-thirds) below the state average sees its scores rise relative to the state average by 0.010 standard deviations, accumulating to 0.10 SDs over ten years.

“This implies that each year after an event, a district with log mean income one unit (about two-thirds) below the state average sees its scores rise relative to the state average by 0.010 standard deviations, accumulating to 0.10 SDs over ten years.”

• AssumptionRests on an assumption: Absent school finance reforms, the differential trend in student achievement between low- and high-income districts in reform states would have continued as before (parallel trends assumption).

May combine two claims.

There is a small upward trend in state revenues prior to finance reform events, but it is not statistically significant in either the parametric or nonparametric specification.

“There is a small upward trend in state revenues prior to the finance reform events, but this is not statistically significant in either the parametric or the nonparametric specification.”

• AssumptionThe authors state this as an assumption: The exact timing of school finance reform events is as good as random.

May combine two claims.

There is no sign of a pre-event trend that would suggest a violation of the quasi-random timing assumption, nor any sign that increased progressivity of state aid is offset by local revenues.

“In no case is there any sign of a pre-event trend that would suggest a violation of our quasi-random timing assumption, nor is there any sign that increased progressivity of state aid is offset by local revenues.”

• AssumptionThe authors state this as an assumption: The exact timing of school finance reform events is as good as random.

Probably not a substantial claim: may not pass S4 (based).

Sharp, permanent changes in funding, if used productively, should increase the flow of educational services.

“Sharp, permanent changes in funding, if used productively, should increase the flow of educational services.”

May combine two claims.

The gap in mean log incomes between the top and bottom quintiles averages 0.65, so the quintile point estimate is a bit larger than what is obtained for the income slope measure in columns 1-2.

“The gap in mean log incomes between the top and bottom quintiles averages 0.65, so the quintile point estimate is a bit larger than what we obtain for our income slope measure in columns 1-2.”

Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

The literature regarding whether money matters in education is contentious and does not offer clear guidance.

“The literature regarding whether”

• cites Hanushek 1986, 2003, 2006Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Card and Krueger 1992aNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Burtless 1996Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

In only one of the specifications estimated do the authors reject the null hypothesis that the pre-event coefficients are all zero, and in this case it appears to be an idiosyncratic blip in a single β -r coefficient.

“In only one of the specifications that we estimate do we reject the null hypothesis that the pre-event coefficients ( β trend in (2) and { β -k , … , β -1 } in (3)) are all zero, and in this case it appears to be an idiosyncratic blip in a single β -r coefficient”

• AssumptionThe authors state this as an assumption: The exact timing of school finance reform events is as good as random.

May combine two claims.

There is no sign of systematic changes in either funding or test scores in the period leading up to a reform, supporting the assumption that reform timing is exogenous.

“We find no sign of systematic changes in either funding or test scores in the period leading up to a reform, supporting our assumption that reform timing is exogenous.”

• AssumptionThe authors state this as an assumption: The exact timing of school finance reform events is as good as random.

May combine two claims.

On average in the sample, the slope of test scores with respect to log income is 0.96, so SFRs reduce this gradient by approximately one-tenth within ten years.

“This is quantitatively meaningful-on average in our sample the slope of test scores with respect to log income is 0.96 so SFRs reduce this gradient by approximately one-tenth within ten years.”

• AssumptionRests on an assumption: Absent school finance reforms, the differential trend in student achievement between low- and high-income districts in reform states would have continued as before (parallel trends assumption).

May combine two claims.

Current spending per pupil in Tennessee is around $9,000, so comparable proportional class size reductions would cost around $2,700 per pupil per year.

“Current spending per pupil in Tennessee is around $9,000, so comparable proportional class size reductions would cost around $2,700 per pupil per year.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

STAR raised costs by about 30 percent in K-3, and raised early grade test scores by 0.17 SDs.

“STAR raised costs by about 30 percent in K-3, and raised early grade test scores by 0.17 SDs”

• cites Krueger 1999, 2003; Krueger and Whitmore 2001Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

Achievement is cumulative, so educational services are unlikely to have immediate impacts on test scores, but should raise scores gradually as students are exposed for longer.

“Achievement is cumulative, so these services are unlikely to have immediate impacts on test scores, but should raise scores gradually as students are exposed for longer.”

May combine two claims.

For both finance and achievement outcomes, the slope and quintile gaps are highly negatively correlated, and all results are robust to the choice of relative outcome measure.

“For both finance and achievement outcomes, the slope and quintile gaps are highly (negatively) correlated, and all of our results are robust to the choice of relative outcome measure.”

Probably not a substantial claim: may not pass S2 (checkable), S4 (based). May combine two claims.

State funding formulas are the main policy tool available to address inequities in academic outcomes, so funding shifts deriving from changes in these formulas are the most policy-relevant variation in school resources.

“State funding formulas are the main policy tool available to address inequities in academic outcomes, so funding shifts deriving from changes in these formulas are the most policy-relevant variation in school resources.”

May combine two claims.

In Monte Carlo simulations, the method of stacking copies works well to identify the average effect of events both when each event has the same effect and when only one event in a state has a nonzero effect.

“In Monte Carlo simulations (see online Appendix), this method works well to identify the average effect of events both when each event has the same effect and when only one event in a state has a nonzero effect.”

Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

The focus on the r = 10 estimate is arbitrary.

“Nevertheless, the focus on the r = 10 estimate is arbitrary.”

Classified as probably not a substantial claim. May combine two claims.

Attacking these gaps would require policies aimed at the distribution of achievement within school districts, something that was generally not a focus of the reforms studied.

“Attacking these gaps would require policies aimed at the distribution of achievement within school districts, something that was generally not a focus of the reforms that we study.”

• AssumptionRests on an assumption: Absent school finance reforms, the differential trend in student achievement between low- and high-income districts in reform states would have continued as before (parallel trends assumption).

May combine two claims.

The research design is more credible for outcome disparities than for the level of outcomes, because the latter would be confounded by unobserved shocks to average outcomes in a state correlated with the timing of school finance reforms.

“our research design is more credible for outcome disparities than for the level of outcomes, as the latter would be confounded by unobserved shocks to average outcomes in a state that are correlated with the timing of school finance reforms”

• cites Hanushek, Rivkin, and Taylor 1996a,bNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The results show that money can and does matter in education, and complement similar results for the long-run impacts of school finance reforms from Jackson, Johnson, and Persico (2016).

“Our results thus show that money can and does matter in education, and complement similar results for the long-run impacts of school finance reforms from Jackson, Johnson, and Persico (2016).”

• cites Jackson, Johnson, and Persico (2016) sourceNot checked — no full text of the source

• AssumptionRests on an assumption: Absent school finance reforms, the differential trend in student achievement between low- and high-income districts in reform states would have continued as before (parallel trends assumption).

Classified as probably not a substantial claim. May combine two claims.

Both event study regressions include state and subject-grade-year fixed effects.

“Both event study regressions include state and subject-grade-year fixed effects.”

May combine two claims.

The results do not support claims that school finance reforms will be offset by changes in district or voter choices over tax rates or that funds will be spent so inefficiently as to be wasted.

“Our results do not support these claims.”

May combine two claims.

While reforms aimed at low-income districts appear to have been successful at raising resources and outcomes in these districts, within-district changes-in the distribution of funding or in other policies that reduce achievement gaps-would be necessary to have dramatic impacts on the average low-income, minority, or low-scoring student.

“Thus, while reforms aimed at low-income districts appear to have been successful at raising resources and outcomes in these districts, we conclude that within-district changes-in the distribution of funding or in other policies that reduce achievement gaps-would be necessary to have dramatic impacts on the average low-income, minority, or low-scoring student.”

• AssumptionRests on an assumption: Absent school finance reforms, the differential trend in student achievement between low- and high-income districts in reform states would have continued as before (parallel trends assumption).

May combine two claims.

The estimates are interpreted as reflecting the productivity of additional resources, though other interpretations cannot be ruled out.

“We thus interpret our estimates as reflecting the productivity of additional resources, though other interpretations cannot be ruled out.”

• AssumptionRests on an assumption: Absent school finance reforms, the differential trend in student achievement between low- and high-income districts in reform states would have continued as before (parallel trends assumption).
• AssumptionRests on an assumption: For the typical school finance reform, the main policy change was in funding rather than other accompanying policies.
• AssumptionRests on an assumption: The average finance reform involved roughly unconstrained increases in resources.

Classified as probably not a substantial claim.

Standard errors are clustered at the state level.

“Standard errors are clustered at the state level.”

Classified as probably not a substantial claim. May combine two claims.

All event study specifications include state and subject-grade-year fixed effects, and are weighted by the inverse squared standard error of the dependent variable.

“All event study specifications include state and subject-grade-year fixed effects, and are weighted by the inverse squared standard error of the dependent variable.”

May combine two claims.

The benefit-cost ratio is not wholly robust: the quintile analysis shows larger revenue effects, implying a benefit-cost ratio below one, while Jackson, Johnson, and Persico (2016) implies much larger benefits per dollar.

“Our quintile analysis shows larger revenue effects, implying a benefit-cost ratio below one, while Jackson, Johnson, and Persico (2016) study of the effects of earlier finance reforms on students' adult outcomes implies much larger benefits per dollar than does our calculation.”

• cites Jackson, Johnson, and Persico (2016) sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

The event study specification includes state-by-event (-by-grade-by-subject) fixed effects in the stacked all-events approach.

“Event study specification is modified to include state-by-event (-by-grade-by-subject) fixed effects.”

May combine two claims.

The DD estimate of the effect on mean pooled test scores is not significant and implies a smaller impact per dollar than the between-district contrasts, though comparable effect sizes cannot be ruled out.

“The point estimate (not significant) implies a smaller impact per dollar than do our between-district contrasts, though we cannot rule out comparable effect sizes.”

• AssumptionRests on an assumption: Absent school finance reforms, the differential trend in student achievement between low- and high-income districts in reform states would have continued as before (parallel trends assumption).