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In equation [2], $dst is spending in district d in state s in year t, Qd is an indicator for the percentile of the district’s median income in the state distribution in 1962 (this is fixed within a district over time), θd is a district fixed effect (which subsumes a state fixed effect), θt is a year fixed effect, and εdt is a district-by-year level error term. Because some states had multiple reforms, we estimate treatment effects for the first reform of each type. The main treatment court legislate variables for the first reforms are I y   and  I y. These are indicator variables equal to 1 if state s will implement its first court-mandated reform or legislative reform in y years, and 0 otherwise. These indicator variables map out the dynamic treatment of the two broad types of

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of the first court-mandated reform on per-pupil spending for districts in quartile q. Similarly, the coefficients  q, y  map out the dynamic treatment effect of the first legislative reform on perlegislate

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income quartile district of implementing the first legislative reform 10 years in the future, and  1,5 legislate is the effect today in a bottom quartile district of having implemented the first legislative reform in the bottom quartile five years ago. We plot the estimated treatment effects to illustrate how per-pupil spending evolves in the years before, during, and after the first legislative and court-mandated reforms. A visual inspection of this event-study plot should reveal any prereform trends in spending and any structural break in outcomes.

Because different kinds of reforms may have different effects, we also estimate dynamic treatment effects for different aspects of each reform by coding the first year that a district uses a formula with a (a) spending limit, (b) local equalization, (c) foundation plan, or (d) equalization plan. To estimate the dynamic treatment effect for particular types of funding formulae, we can limit localeq, I yfoundation, and use equation [2] while replacing the reform-type indicators with I y, I y equalization Iy.  These are indicator variables equal to 1 if state s will implement its first spending limit, local equalization, foundation plan, or equalization plan in y years, and 0 otherwise. One can then plot the coefficients on these indicators interacted with the district quartile to observe how district per-pupil spending evolved before, during, and after the changing of the school finance formulas in these specific ways.

To quantify the effect of these reforms on per-pupil spending, we form linear combinations of the estimated treatment effects for different years. For example, the effect of court-ordered reforms on the spending for the bottom 10 percent of income districts can be estimated by the average of the 5 years after reforms minus the average of the 5 years prior to reforms. This estimate is obtained by computing the following linear combination of coefficient ( q,5   q,4   q,3   q,2   q,1 ) / 5  ( q,5   q,4   q,3   q,2   q,1 ) / 5.

court court court court court court court court court court


Whether this computed difference is statistically significant is determined by testing the statistical significance of the linear combination of the estimated coefficients. We present the results of such tests to accompany the event-study graphs. Note that the standard errors for all the


estimates are clustered at the state level.

a. Event-Study Analysis for Court-Mandated Reforms Much of the empirical literature of SFR has focused on court-mandated reforms. Figure 5 presents the event-study graph for court-mandated reforms for school districts in different percentiles of the income distribution in 1962 (a year before any reforms were implemented).

The figure depicts how district-level per-pupil spending evolved annually from nine years prior to the first court-mandated reforms through 20 years after the reforms. The evolution of spending is presented separately for districts in the bottom 10 percent of median incomes, those in the 11th to 25th percentile, those in the 26th to 50th percentile, those in the 51th to 75th percentile, those in the 76th to 90th percentile, and those in the top 10 percent. The series for the bottom 10 percent depicts how per-pupil spending evolved for districts in the bottom 10 percent of the state income distribution over time in states with a court-mandated reform, relative to such districts in states without a court-mandated reform over the same time period. To show how per-pupil spending was affected for all districts on the same scale, each series is re-centered around the average for the 10 years prior to reforms. This means that a value of 0 in a given year would indicate that spending in that year was the same as the 10-year average prior to reforms. Also, note that year 0 is the year of the reform. As such, if reforms increase spending relative to pre-reform years, we should see positive values for years 1 through 20, and if reforms decrease spending, we should see negative values for these years.

In Figure 5, all the series are centered on 0 during the pre-reform years. During the 10 years prior to reforms (years -10 through -1), districts in reform states saw similar changes in per-pupil spending as districts in non-reform states of the same income level. Within the first five post-reform years however, districts in the bottom quartile (solid black lines) saw increases in per-pupil spending above and beyond comparison districts in non-reform states. Districts between the 25th and 75th percentiles experienced modest increases after reforms (as evidenced by most post-reform data points for these districts being above the pre-reform mean). In contrast, districts in the top 25 percent of incomes in 1962 saw little change in spending within the first 14 years after reforms, and there is evidence of a slight decrease 15 years after reforms for the very highest income districts. Note that the sharp decline in spending at year 8 is due to a compositional change. The lower panel of Figure 5 plots the same dynamic treatment effects, but only using districts that were observed for more than 10 post-reform years. Using this more balanced panel, there is no sudden drop in year 9, but the basic patterns are similar (increased 15     school spending for the lowest-income districts and decreases for the highest-spending districts).

Because the more balanced panel includes only older cases, it includes relatively few adequacy cases. We will show that the difference between the top and bottom panels of Figure 5 is due to the fact that the first seven years presented in the top panel include many recent adequacy cases, and these generate somewhat different patterns from the older equity cases.

To better quantify the patterns in Figure 5, we estimate the effect of court-mandated reform as the difference between the average effect in the 10 years prior to reforms and the 10 years after reforms. Based on the linear combination of coefficient estimates, these reforms increased per-pupil spending for the bottom 10 percent income districts over the first 10 years by $582.81 in 2010 dollars (p-value=0.07). Between 1980 and 1990, the average per-pupil spending for these low-income districts was $6,590.66, representing a relative spending increase of about nine percent. To get a better sense of the longer run effects of spending for these districts, we compute the average effect for years 5 through 10 relative to the 10 years prior to reforms. This calculation indicates that after five years these reforms increased per-pupil spending for the bottom 10 percent income districts by $651.12 (p-value=0.02), an increase in spending for lowincome districts of about 11 percent. Similar calculations for the top 10 percent income districts show little effect. The estimated effects suggest that these reforms reduced spending during the first 10 years by $110.41 (p-value=0.27) and in years 5 through 10 by $191.12 (p-value=0.56).

In sum, court-mandated reforms increased spending in the lowest-income districts by about 10 percent and had little effect for the highest-income districts. Using the estimates, after 10 years court-mandated reforms reduced the spending gap between the top-income districts and the bottom-income districts by $842.01 (p-value0.01). The spending gap between these two groups of districts between 1980 and 1990 was $1,197.33, so that court-mandated reforms reduced this spending gap by about 70 percent on average. The magnitude of these effects, coupled with the rapid increase in the number of court-mandated reforms during the early 1990s, can account for a sizable portion of the spending “catch-up” documented in Figure 4 between the lowest- and highest-income districts.

There are two types of court-mandated reforms: those argued on equity grounds and those argued on adequacy grounds. One might wonder if these different kinds of cases lead to different kinds of reforms that have different effects. This question was investigated empirically by Springer, Liu, and Guthrie (2009) and Berry (2007), who found no difference between these two kinds of cases in simple regression settings. We investigate this question using the more 16     flexible event-study approach.

The top panel of Figure 6 presents the dynamic effects of equity-based court-mandated reforms on the level of per-pupil spending. The effects are relative to non-reform states. There is a dip in spending (of about $500) in all districts two years prior to reforms for those states that had their first court-mandated case based on equity grounds relative to similarly affluent districts in non-reform states. While this pre-reform dip makes the effect of such cases on the overall level of spending unclear (because it is unclear what the trajectory of school spending would have looked like absent reforms), it is apparent that equity cases do lead to greater equity in spending: while the top-income and bottom-income districts are on very similar trajectories prior to reforms, such that the spending gap was stable in the pre-treatment years, the spending gap narrowed by $807.54 (p-value=0.01) after five years post-reform. The aim of these cases was to increase spending equity. Reforms induced by these equity based cases achieved this objective.

The bottom panel of Figure 6 presents the event-study graph for adequacy cases (primarily the second wave of cases). The objective of these cases was not to explicitly reduce inequality in education spending, but rather to ensure that spending permitted all children (especially those in low-income districts) to receive adequate resources for a quality education.

Because these cases are more recent, we present the dynamic treatment for the first seven years of the reform. As one can see, spending in all districts in states with adequacy cases was fairly stable (relative to non-reform districts) prior to reforms. The trajectory of spending was quite flat four years prior to reforms. After reforms, there is evidence of an increase in school spending that is most pronounced for the poorest 10 percent of districts. While all districts experience an increase in spending of about $430 within the first five years of reforms, the poorest 10 percent of districts break from the other districts with an increase in spending of over $1,000 within the first five years. Because all districts experienced spending increases, adequacy cases are associated with a smaller reduction in spending gaps than equity cases. Five years after an adequacy case, the gap in spending between the highest- and lowest-income districts is narrowed by $377.25 (p-value=0.02). In sum, consistent with the aims articulated by the courts, equity cases led to greater equity in school spending, while adequacy cases led to increased school spending overall, with particularly large increases for low-income districts.

b. Event-Study Analysis for Legislative Reforms Legislative reforms have received much less attention in the literature than courtmandated reforms, and the consensus seems to be that legislative reforms were largely 17     ineffective at increasing school spending for low-income districts or reducing spending inequality. To investigate this conclusion further, Figure 7 plots the change in district per-pupil spending over time for states that experienced legislative reforms relative to similarly affluent districts in non-reform states. As in Figure 5, the series are presented for districts that were at different points in the distribution of median income in 1962, and they are re-centered around the mean for the 10 years prior to reforms. Similar to states that passed court-mandated reforms, those states that passed legislative reforms were on a trajectory of per-pupil spending similar to that of non-reform states during the few years preceding the reforms. However, in the postreform years, there is a clear downward trend in spending for all districts in legislative reform states.

Figure 7 also provides visual evidence that legislative reforms reduce spending inequality. The three series in black are districts above the median and those in grey are districts below the median. Prior to reforms, the black and grey series move together, and no single series is systematically above the other. In contrast, in the post-reform years, districts below the median income (black series) are on top and those above the median income (gray series) are on the bottom. This suggests that legislative reforms induced slower spending growth but also reduced spending inequality between low- and high-income districts.

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