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Card and Payne (2002) codify formulas into three broad categories: flat grant plans, which give the same dollar amount per student to all districts in a state; minimum foundation plans, which set a floor on per-pupil spending (the state provides the difference between the minimum amount per pupil and an estimate of how much local revenue a given district can raise); and variable grant plans, which provide different amounts of state aid to districts based on local property values, income levels, and how much local revenues are actually raised.

8     Hoxby (2001) argues that these labels may not fully capture the economic incentives associated with the formulas. For example, some plans that would be in the same category in Card and Payne (2002) induce more spending by providing more state funding for districts that raise more local funds, while others induce less spending on the margin by providing more state funds to districts that raise fewer local funds. Accordingly, Hoxby (2001) advocates classifying reforms based on inverted tax prices. The inverted tax price is the amount of additional funding the district has to spend if it raises tax revenue by one dollar.

An inverted tax price of zero means that a district cannot raise education spending no matter how much it increases its tax revenue (a clear disincentive to raise local funds). This occurs in states that impose spending limits on districts (Downes and Figlio, 1998). An inverted tax price greater than one means that a district can raise education spending by more than one dollar by raising tax revenue by one dollar (a clear inducement to raise local funds). To capture this important feature, Hightower, Mitani, and Swanson (2010) disaggregate variable grant plans into two groups to make a distinction between those plans that focus on school districts’ inverted tax prices (local effort equalization plans) and those that do not (equalization plans).

Augenblick, Meyers, and Anderson (1997) aptly refer to these local effort equalization plans as “reward for effort” policies. We also use this intuitive label.

We combine these approaches to create the following five categories. Note that many state funding plans fall into more than one category. While any approach to summarize numerous different reforms into a manageable number of variables will be imperfect, we believe that our classification captures the key elements highlighted in the literature.

 Foundation Plans: These plans ensure a basic floor to spending. These include foundation plans, foundation grants, and guaranteed minimum tax base plans. These plans establish a foundation level of per-pupil spending, estimate a district’s required local contribution to fund this foundation level based on income and wealth levels in the district, and provide the difference between the expected contribution and the foundation level.

These plans do not affect tax prices. They provide extra funding to low-income/lowo wealth districts while leaving high-income/wealthy districts largely unchanged.

 Flat Grants: These plans give aid on a per-pupil basis to all districts.

Flat grants do not affect tax prices. They provide similar state funds for all districts and o should have little effect on spending inequality, all else equal.


 Equalization Plans: These plans provide aid to districts based on property values and income levels. They include power equalization plans (which give more money to low-wealth districts), categorical aid strategies (which give money to low-income districts), and other equalization plans that distribute state funds to districts based on wealth or income levels.

o Because funds are distributed based on wealth and income levels, these plans do not affect tax prices directly (although they may provide incentives to alter the tax base).

These plans tend to provide extra funding to low-income/low-wealth districts while possibly taking money away from high-income/wealthy districts.

 Reward for Effort Plans (inverted tax prices greater than one): These plans seek to promote local efforts to raise school spending by increasing state aid to low-wealth districts that have high tax rates. The key feature of these plans is that districts receive more state aid when they raise more local taxes.10 o Reward for effort plans promote local efforts to raise education spending by targeting the inverted tax price directly. Such plans typically provide greater incentives for lower-income/low-wealth districts to increase taxes by allowing some districts to have more than one dollar in spending for each dollar raised in taxes. Such policies should increase spending overall, with larger spending increases for low-income districts.

 Spending Limits (inverted tax price equal to zero): Under such plans, the state imposes a limit on how much a district may spend on education. In addition, some equalization plans take away all tax revenues raised above a certain amount (i.e., if there is a recapture provision). The key feature of such plans is that districts are unable to increase school spending above some limit—that is, around the limit districts face a zero inverted tax price.

o Spending limits are designed to limit education spending at the local level for highspending districts. Because high-income districts also tend to have more spending, one would expect such policies to reduce spending for all districts, with a more pronounced effect for high-income districts. Such policies likely do reduce inequality, but at the expense of lower overall education spending. Because education spending tends to increase over time as spending levels rise to that of the limit, spending limits may reduce spending for all school districts.


10 For example, in Georgia, school districts at or below 75 percent of the state average property tax wealth level receive equalization funding in proportion to the number of mills they raise above the required five mill.


b. Changes in School Finance Formulae Over Time Since 1970, virtually every state has enacted at least one aid formula from among the categories listed above. To provide an overview of the evolution of school finance formulas, Figure 3 plots the number of states that have employed each kind of funding formula in each year. The first notable pattern is that the use of foundation plans was quite high in 1970 and increased slightly during the entire period (from 27 states in 1970 to 36 states in 2010). As more states implemented SFRs, the use of flat grants declined (from 26 states in 1970 to 5 states in 2020), while the use of equalizing plans increased (from 9 states in 1970 to 30 states in 2010).

The reward for effort approach was unpopular in 1970, but the number of states employing reward for effort has increased over time (from 0 states in 1970 to 21 states in 2010), as has the number of states imposing spending limits (from 0 states in 1970 to 12 states in 2010). In Section III we investigate the effects of these different kinds of reforms on the level and distribution of school spending.

c. Changes in School Spending Over Time Data on district and state funding come from the Census of Governments, the Historical Database on Individual Government Finances (INDFIN),11 and the Common Core of Data (CCD) School District Finance Survey (F-33). The Census of Governments has been conducted every five years since 1967 and records administrative data on school spending for every school district in the United States. This is the data source used in most existing national studies of school finance reforms. We augment this data with annual data from other sources. The INDFIN contains school district finance data annually for a sub-sample of large school districts from 1967 through 1991.12 After 1992, the CCD School District Finance Survey (F-33) consists of data submitted annually to the National Center for Education Statistics (NCES) and includes data on school spending for every school district in the United States.13 We combine these data sources


11  The Historical Database on Individual Government Finances (INDFIN) represents the Census Bureau’s first effort to provide a time series of historically consistent data on the finances of individual governments. This database combines data from the Census of Governments Survey of Government Finances (F-33), the National Archives, and the Individual Government Finances Survey.  12 Per-pupil spending data from before 1992 is missing for Alaska, Hawaii, Maryland, North Carolina, Virginia, and Washington, D.C. Per-pupil spending data from 1968 and 1969 is missing for all states. Spending data for certain years is also missing for the following states: Florida (1975, 1983, 1985–1987, and 1991); Kansas (1977 and 1986);

Mississippi (1985 and 1988); Montana (1976); Nebraska (1977); Texas (1991); and Wyoming (1979 and 1984).

Where data for only a year or two was missing, it was filled in using linear interpolation.

13  Both NCES and the Governments Division of the U.S. Census Bureau collect public school system finance data, and they collaborate in their efforts to gather these data. 


to construct a long panel of annual per-pupil spending for school districts in the United States between 1967 and 2010.

This paper focuses on how SFRs affected school spending levels in different local communities, rather than aggregate state-level measures of spending inequality over time. As such, we classify school districts based on their median income levels in 1962. To show how perpupil spending has changed for neighborhoods that were low and high income in 1962, Figure 4 plots the mean per-pupil spending each year between 1976 and 2010 for district by their quartile in the state income distribution in 1962. This figure depicts the evolution of per-pupil spending over time for districts with different income levels in 1962 (before any SFRs). Note that because quartiles are defined within a state, this plots within-state changes in inequality.

There are a few notable patterns. First, per-pupil spending has been increasing over time in all districts. In 2012 dollars, the average district spent about $4,612 per student in 1967 and about $12,772 per student in 2010. This represents a 175 percent increase (in real terms) over 43 years. This increase of about 4 percent annual growth was experienced in both low- and highincome districts. A second notable pattern is that the difference between low- and high-income districts was wide in the early 1970s, narrowed during the late 1970s (corresponding to the first wave of reforms), was stable during the 1980s, and then narrowed again in the mid-1990s (corresponding to the second wave of reforms). One unexpected pattern is that per-pupil spending in the lowest income districts (in 1962) was always below that of other districts until the mid-1990s, when spending in the poorest districts rose to levels above that of the middleincome districts. While districts in the lowest income group spent about 8 percent less than the median income district in 1967, by 2010, the districts that were in the lowest-income group spent seven percent more than those in the middle income groups in 1962.

A comparison of Figures 2 through 4 suggests why this reversal may have taken place during the late 1990s. The timing of the increases in education spending for the low-income districts are very much in line with the timing of the second wave of court-mandated reforms that emphasized adequate spending for low-income districts and relatively rapid increases in the use of reward for effort plans. The timing of the reversal coincides with the increased use of reforms that one might expect to lead to a disproportionate increase in school spending in these lowincome areas. Of course, the extent to which these reforms actually had the expected effects is an empirical question, which we investigate in the following section.


III. Event-Study Analysis of Effects on School Spending Our empirical approach to estimating the effect of SFR on the distribution of per-pupil spending across district income levels is to analyze data using a Difference-in-Differences (DiD) methodology. Using the district-by-year data as described in Section II, we can compare the spending in low- or high-income districts (districts with low or high median incomes in 1962) before implementation of a SFR to the spending in the same district after implementation.

Because there may be a tendency for spending to increase over time, we use the difference in spending for low- or high-income districts across the same years in states that did not implement any reforms over that time period as a basis for comparison.

To give an example, Illinois implemented its first SFR in 1973, while Missouri implemented its first SFR in 1977. One can compare spending for low-income districts in Illinois in 1972 (the year before the reform) to that in 1976 (four years post-reform). Because there may have been some national and region-specific changes that affected spending in all districts between 1972 and 1976, one can use the difference in spending for low-income districts between 1972 and 1976 in Missouri (both pre-reform years in MO) as an estimate of what the change in spending would have been for low-income districts in Illinois absent reforms. If reforms increase spending for low-income districts, we should see that the difference in spending for low-income districts between 1972 and 1976 in Illinois is greater than the difference in spending for lowincome districts between 1972 and 1976 in Missouri. The same logic can be applied to spending in medium- and high-income districts. This is the logic of the DiD estimator. One can implement this DiD strategy within a regression framework by estimating equation [2], below.

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