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As discussed previously, using all sources of differences in school spending to identify effects might introduce endogeneity bias, so we isolate exogenous variation in school spending due to reforms. Changes in this measure across cohorts from the same district are sensitive to both the years of exposure to reforms and the amount of the district’s change in spending due to reforms. Accordingly, in order to identify impacts solely from the variation in school spending 32     caused by reforms, we use the number of school-age years of exposure interacted with the district-specific change in spending as our instrument for school spending. Specifically, we estimate the following system of equations by two-stage least squares (2SLS).

 PPE 517   1 (ticb  Tc* )  SPENDc  X icb 2  Z cb 3  (W1960 c  b) 4  c1  br1  gr1 * b [4]  Yicb    PPE 517  X icb   Z cb  (W1960 c  b)  c  br  gr * b   icb All variables are defined as in [3], and include the same full set of controls. The difference between [3] and [4] is that we replace the event time indicator variables interacted with the district-specific spending change with a single measure of per-pupil spending, PPE5-17, in the second stage regression. In the first stage regression, we instrument for PPE5-17, with a parameterized version of the event time indicators (i.e., linear in years of exposure) interacted with the district-specific reform-induced spending change, (ticb  Tc* )  SPENDc. Standard errors are clustered at the school district level.

The instrumental variables models exploit both the variation in timing and intensity of school spending changes due to court-mandated reforms to obtain clean causal estimates of the effects of school spending on adult outcomes. The coefficient δ from the instrumental variables regressions should uncover the causal effect of school spending on adult outcomes so long as the timing of court mandated SFRs is exogenous to changes in outcomes across birth cohorts within districts that saw larger versus smaller increases in school spending due to the reforms. Both the event study analysis and additional placebo tests provide strong supportive evidence that this is the case. For comparison purposes, we also present results from a naïve ordinary least squares specification that does not instrument for per-pupil spending.

VI. Estimated Effects on Longer-Run Outcomes Educational Attainment. Figure 12 presents the semi-parametric event-study model results of the effects of reform-induced changes in per-pupil spending on the probability of graduating from high school. These are shown separately for poor (left) and non-poor (right) children. We obtained the coefficients on the individual event time indicator variables interacted with the district-specific change in spending and plot the estimated event time graph for a 10 percent, 20 percent, and 25 percent spending increase (these roughly correspond to $500, $1,000, and $1,250 increases in per-pupil spending). All estimates use as the reference comparison the outcome for an individual who was 17 years old when the court order was first enacted.


Additionally, to conserve space, event study figures with confidence intervals for impacts of 20 percent increases in school spending across the various outcomes are shown in the Appendix. As detailed in Section V, all models include school district fixed effects, race-specific region and year of birth effects; controls for linear cohort trends in 1960 county characteristics; controls at the county level for the timing of school desegregation and hospital desegregation, roll-out of the "War on Poverty," and related safety-net programs; and childhood family characteristics.

Looking first at children from poor families, the event-study plots for the effects of a 10, 20, and 25 percent school spending increase all follow a similar broad pattern. Districts that saw increases in school spending exhibit no discernible trending in high school graduation rates for the pre-treatment cohorts (those that were 18 or older at the time of the reforms). Importantly, the pre-reform year effects are very similar for districts that experienced a 10, 20, and 25 percent spending increase. That is, districts that had large spending increases after reforms were on the same trajectory as districts that saw small increases or reductions in school spending after reforms. This indicates that the timing of the reforms was exogenous to changes in high school graduation rates in a given district and that the size of the eventual spending increase was unrelated to the pre-reform trends in outcomes. This lends credibility to our empirical design and the resulting instrumental variables estimates.

Looking at partially exposed cohorts, the results are consistent with significant causal effects on exposed cohorts from poor families. That is, cohorts with more years of exposure to spending increases have higher high school graduation rates than unexposed cohorts and cohorts with fewer years of exposure. Also, the increases associated with exposure are larger in districts that experienced the largest increases in spending. Both the patterns in timing and intensity support the hypothesis that policy-induced increases in school spending led to significant increases in the likelihood of high school graduation. Looking to the fully treated cohorts, the results are somewhat noisier, but there is a clear pattern of better outcomes for those fully treated cohorts (than untreated cohorts) in districts that saw larger increases in school spending.

The estimates for non-poor children reveal a very different pattern from those of poor children. To allow for an easy direct comparison, the event study plots for poor and non-poor children are presented on the same scale. For non-poor children, there is suggestive evidence of a rather slight increase in high school graduation after the passage of reforms. Exposed cohorts do appear to have slightly higher high school graduation rates than the pre-reform cohorts, and districts that experienced larger spending increases do seem to have somewhat better high school 34     graduation rates than those with smaller spending increases for the exposed cohorts. While the pattern of results might indicate small effects for children from non-poor families, the magnitudes of these effects are much smaller than those for children from poor families.

Looking beyond high school graduation to overall years of education reveals very similar patterns to those for high school completion. Figure 13 presents the event study plots for a 10, 20, and 25 percent spending increase on years of educational attainment. As with high school graduation, there is no trending in outcomes for the pre-reform cohorts. For children from poor families (left), years of education is increasing in years of exposure and the increases are larger for those districts that experienced the largest spending increases. As with high school graduation, for non-poor families there is very weak evidence of somewhat positive effects.

We conclude based on the consistent pattern of these results that these impacts indeed reflect the causal effect of school spending in that spending increases only improve educational outcomes for those who are exposed during their school-age years, and that the benefits associated with improved spending are concentrated among children from poor families. That is, while outcomes are largely similar across exposed and unexposed cohorts for children from nonpoor families, for children from poor families we see that (a) increases in educational outcomes occur only for exposed children during school-age years, (b) improvements are monotonically increasing in years of exposure, (c) improvements are larger with larger spending increases, (d) the timing of improvements in outcomes track the timing of the increases in spending, and (e) there are no differential pre-reform trends in outcomes for districts that experience increases or decreases in spending.

Having established that there are significant policy-induced improvements in long-run educational attainment associated with larger school spending increases for exposed cohorts, we now quantify the relationship between school spending and longer-run educational attainment.

For this we turn to the instrumental variable regression results that use the event study patterns to predict changes in childhood exposure to per-pupil spending. Putting all the variation together, the 2SLS/IV models provide a direct estimate of the effect of school spending on adult outcomes and allow for tests of statistical significance.

The regression estimates are presented in Table 2. The main outcomes are the educational attainment measures and the variable of interest is the natural log of average per-pupil spending during an individual’s school-age years divided by 0.2. The interpretation of a unit change in this variable is the effect of increasing school spending by 20 percent throughout all 12 of an 35     individual’s school age years. The excluded instrument for this spending variable is the number of school-age-years of exposure to reforms interacted with the respective school district’s reform-induced change in school spending. The first stage F-statistic is greater than 50 in all models. For comparison purposes, we also show estimates from ordinary least squares (OLS) regression models that do not account for the possible endogeneity of school spending.

Column 4 in the top panel of Table 2 presents the 2SLS/IV regression results based on variation presented in Figures 12 for children from poor families. The 2SLS estimates indicate that for children from poor families, increasing per-pupil spending by 20 percent in all 12 schoolage years increases the likelihood of graduating high school by 23 percentage points. This estimate is statistically significant at the one percent level and the 95 percent confidence interval is between 8.7 and 37 percentage points. To put these high school graduation estimates in perspective, the high school graduation rates for non-poor and poor children were 79 and 92 percent, respectively. Increasing per-pupil school spending by 20 percent over the entire schooling career of a cohort of low-income children will increase the high school graduation rate for those children by between 11 and 46 percent. In fact, the effects are large enough to completely eliminate the high school graduation gap between children from poor and non-poor families. Consistent with Figure 12, there is a small statistically insignificant effect for children from non-poor families (top panel column 6, 2SLS estimate: 0.0647 (se=0.0526)).

The lower panel presents the regression estimates for completed years of education. For children from poor families (lower panel column 4), the 2SLS estimate indicates that increasing per-pupil spending by 20 percent in all 12 school-age years increases educational attainment by

0.93 years. This estimate is statistically significantly at the one percent level and the 95 percent confidence interval is between 0.36 and 1.49 years. The education gap between children from poor and non-poor families is one full year. Thus, the estimated effect for poor children is large enough to almost completely eliminate the education gap between children from poor and nonpoor families. Looking to children from non-poor families, there is a small statistically

insignificant effect for children from non-poor families (top panel column 6, 2SLS estimate:

0.2959 (se=0.3259)).

In sum, both the event study and 2SLS/IV models reveal that increases in school spending (caused by school finance reforms) led to substantial improvements in educational outcomes of affected children from poor families. Both analyses suggest that there is little to no effect for children from non-poor families. The magnitude of these effects for children from poor 36     families are large enough to eliminate the high-school completion gap and years of educational attainment gap between children from poor and non-poor families. We present tests for robustness in section VI.2.

Labor Market Outcomes, Adult Family Income, and Poverty Status. The next series of results reveals large, significant effects of school spending on poor children’s subsequent adult economic status and labor market outcomes, using the same model specifications. Figures 14, 15, and 16 present school spending effects by childhood poverty status on adult economic outcomes (ages 25–45), including wages (Figure 14), annual family income (Figure 15), and the annual incidence of poverty (Figure 16). In light of the parallel set of findings across all of these longrun economic outcomes, the results are discussed in succession below.

As with the educational outcomes, the economic outcome patterns are similar to those hypothesized in Figure 11 for poor children and are indicative of the causal effects of increases in school spending induced by court-mandated reforms. We first discuss the earnings outcomes.

For both the log of earnings and family income (Figures 14 and 15), there is no evidence of trend differences prior to reforms between districts that saw larger or smaller increases in school spending after reforms. In contrast, for children from poor families, both earnings outcomes exhibit substantial improvements across cohorts associated with more years of exposure to a spending increase. For children from poor families the increases are only associated with the school-age years, and there is no systematic difference in outcomes across cohorts born at different times but with the same number of years of exposure – consistent with a causal effect of spending increases. The results by treatment intensity strongly reinforce the evidence of long-run causal effects of spending. For both adult earnings and family income, the increases for exposed cohorts are larger for those in districts that experience larger increases in spending. The differences by spending increase are more pronounced for family income (Figure 15) than for earnings (Figure 14), but for both outcomes, the event study for a 10 percent increase (dashed line) lies below that of a 25 percent increase (sold grey line) for the exposed cohorts.

The figures for children from non-poor families tell a different story than that for children from poor families. For children from non-poor families, we find small, statistically insignificant effects of school spending on adult earnings and family income, and the point estimates are not even consistently positive.

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