THE INFLUENCE OF THE ELDERLY

ON SCHOOL SPENDING IN A

MEDIAN VOTER FRAMEWORK

Deborah Fletcher

经济系

Miami University
牛津, OH 45056-675

ﬂetchd@muohio.edu

Lawrence W. Kenny

(corresponding author)

经济系

University of Florida
Gainesville, FL 326-740

larry.kenny@cba.uﬂ.edu

抽象的
How do the elderly inﬂuence school spending if they
are a minority of the population? We estimate the deter-
minants of school spending in a median voter model,
comparing four assumptions about how the elderly in-
ﬂuence the identity of the median voter. Using a county-
level panel, we ﬁnd that elderly preferences are best
characterized by assuming all elderly or all elderly mi-
grants vote with the poor. Having more elderly results
in a median voter who is further down the community’s
income distribution. This median voter is poorer, 哪个
lowers preferred school spending, and faces a lower tax
价格, which raises preferred school spending. The evi-
dence suggests that the income effect is slightly larger
than the price effect, so the elderly on net cause a very
small drop in spending. Thus the widespread concern
about the negative impact of population aging on school
funding seems to be misplaced.

C(西德:1) 2008 American Education Finance Association

283

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INFLUENCE OF ELDERLY ON SCHOOL SPENDING

介绍

1.
Families with children beneﬁt from higher spending on public primary and
secondary schools for their children. Since the elderly do not enjoy these
direct beneﬁts, they may be less willing to support better schools. If so, 许多
observers are deeply concerned about the resulting intergenerational conﬂict
between the elderly and their children’s generation as the elderly attempt
to block the higher school spending levels that are favored by those with
children or those who anticipate having children soon. Geographical variation
in the fraction who are elderly creates inequity in school spending. 因此,
children growing up in communities that attract a lot of elderly attend inferior
学校. 此外, the ranks of the elderly nationwide soon will swell as the
baby boom cohorts’ age and life expectancy continue to rise. Many worry that
this will lead to a deterioration of school funding and ultimately an inadequate
educational system.

The literature on the effect of the elderly on school spending has tested
whether school spending falls as the elderly share in the population rises,
holding jurisdictional income and other variables constant. This literature,
which is reviewed in the next section, is inconclusive on this question.

The empirical analysis of the determinants of government spending gen-
erally is based on the median voter model.2 This model recognizes that the
school spending level preferred by the median voter beats any other spend-
ing level in a referendum. Thus referenda are expected to result in spending
preferred by the median voter. 相似地, a candidate for school board who
proposes to spend the amount preferred by the median voter defeats an oppo-
nent who proposes some other spending level. Recognizing this, all candidates
for school board promise the spending level preferred by the median voter.
Empirical studies based on the median voter model rely on measures of the
median voter’s income and the “price” of school quality faced by the median
voter to explain school spending.

Almost all jurisdictions include some elderly, but they make up a mi-
nority of the population. How do the elderly inﬂuence school spending if
they are a minority of the population? In a median voter framework, 这
elderly affect spending only if they alter the identity of the median voter.
For illustrative purposes, suppose that everyone has the same probability of

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.

External beneﬁts associated with the effects of better schools today on these school cohorts’ reduced
future participation in crime and increased Social Security contributions (see Poterba 998 and
Kemnitz 2000) appear to be very small; few elderly will live long enough to enjoy the external
beneﬁts of paying to improve education now. 此外, workforce migration will dissipate the
Social Security contribution increases from local increases in school spending.

2. The development of the median voter theorem is credited to Hotelling (929), Bowen (943),
Downs (957), 和黑色 (958). Some of the empirical literature based on the median voter model
is summarized in Mueller (2003). See also the literature referenced in section 2.

284

Deborah Fletcher and Lawrence W. Kenny

voting.3 Suppose also that within a community the preferred spending of the
non-elderly is a monotonic, positive function of the household’s income. 如果
there were no elderly in the jurisdiction, the median voter would be the house-
hold with median income in the jurisdiction. Consider a second jurisdiction
that contains some elderly, and suppose that all the elderly prefer there be no
spending on schools. Then the distribution of preferred school spending levels
has a mass point at $0 that reﬂects elderly preferences. The median of this distribution of preferred spending is the level of spending that is preferred by a household that we call the median voter household. The income of this median voter household is lower than the median household income among the non-elderly. Median voter household income is also smaller than median income in the community if some elderly make more than the community’s median household income. Under various assumptions about elderly preferences, we calculate the income of the median voter household and the tax price facing that household and use these two variables along with others to explain school spending. Our use of a median voter household income and modiﬁed tax price is ﬁrmly based in the median voter model. Our empirical analysis contrasts with prior research on the effect of the elderly on school spending, which has used median household income in the community and the percent elderly, 虽然 () the community’s median household income clearly is not the median voter household’s income and (2) the elderly share is not directly linked to the median voter’s preferences. 此外, none of the papers on generational conﬂict uses a tax price variable speciﬁed by the median voter framework. Thus the empirical speciﬁcation used in the literature to estimate the effect of the elderly on school spending is at best weakly linked to the median voter model. Our various assumptions about elderly preferences are motivated by Fletcher (2006), who hypothesized that the elderly who have lived in a com- munity for a long period of time may be more likely to support higher school spending than those who have recently moved to the area. This is because the long-term elderly may be more likely to have grandchildren in the district’s schools and may care about other children in the school system. 相似地, the elderly who moved from another county in the state may have more ties to their new community than elderly who moved from another state. Our analysis compares the explanatory powers of four assumptions about elderly preferences on school spending in a median voter model. Under the ﬁrst, elderly spending preferences are no different than those of others with 3. The large empirical literature that uses median jurisdictional income to explain government spend- ing is based on the assumption that all have the same probability of voting. Our empirical analysis allows the elderly to be weighted more, reﬂecting their higher probability of voting. l 从http下载 : / / 直接的 . 米特 . F / / e d u e d p a r t i c e – p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 压力 . . . . . f f b y g u e s t t o n 0 7 九月 2 0 2 3 285 INFLUENCE OF ELDERLY ON SCHOOL SPENDING their income; this amounts to using the community’s median income for all citizens. Under the second assumption, the elderly who moved from an- other state align themselves with the poorest households, while long-term elderly residents and recent movers from within the state have the same pref- erences as non-elderly with their incomes. In the third assumption, the elderly from a different county within the state or another state vote with the poorest households, while long-term elderly residents have the same preferences as non-elderly with their incomes. Under the fourth assumption, all elderly are aligned with the poorest families. In calculating the median voter household income under these four assumptions, we also allow the elderly to have a greater weight that reﬂects their greater propensity to vote. Additional regressions were estimated that allow the elderly to align them- selves with the richest citizens in the jurisdiction. Since these speciﬁcations did not ﬁt the data as well as the speciﬁcations in which the elderly align themselves with the poorest citizens, we report only the regressions in which the elderly are aligned with the poorest citizens. To create the median voter household income and modiﬁed tax price vari- ables that reﬂect the elderly aligning with the poor (or rich), we need the distribution of income for the elderly and non-elderly. The crucial data on income distribution by age and on elderly migration are available at the county level but are not available for individual school districts. 因此, our em- pirical analysis is at the county level. We test which of the four assumptions about elderly preferences best explains per pupil spending in 3,00 counties in 990 and 2000. In this two-year panel with county ﬁxed effects, we ﬁnd that elderly preferences are generally best characterized by assuming that all the elderly vote with the district’s poorest voters. We sometimes get a better ﬁt taking into account the higher voter turnout among the elderly when cal- culating median voter household income. Note that we are precluded from testing whether all households without children (not just the elderly) align themselves with the community’s poorest or richest households because data on the income distribution are not reported separately for households with and without children. Communities with more elderly have more households that are aligned with the community’s poorest voters, which creates a new median voter house- hold that is located farther down the community’s income distribution. The new median voter is not as afﬂuent, which reduces school spending. Working against this income effect is a price effect, in which the new median voter beneﬁts more from being subsidized through property taxes by those in the community who are more afﬂuent. We ﬁnd that the income effect is slightly larger than the price effect. Our ﬁnding that the elderly align themselves with those who prefer to spend the least on education— the poorest households—is 286 l 从http下载 : / / 直接的 . 米特 . F / / e d u e d p a r t i c e – p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 压力 . . . . F . 来宾来访 0 7 九月 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny consistent with these results. On net, having more elderly results in a statisti- cally signiﬁcant but very small drop in school spending. These results imply that the entry of the baby boom cohorts into the ranks of the elderly or the inﬂux of the elderly into locations they ﬁnd attractive will have very little impact on school spending. Thus the widespread fears that the elderly have a sizeable adverse impact on school spending appear to be misplaced. The next section provides a brief review of the literature on the impact of the elderly on school spending. Some theoretical structure is provided in section 3. 部分 4 describes the sample and develops the hypotheses to be tested and the variables that will be used to test them. The empirical results are reported in section 5. 2. LITERATURE ON THE EFFECT OF THE ELDERLY ON SCHOOL SPENDING The evidence is mixed on whether spending falls as the percent who are elderly rises. In Miller’s (996) 学习, the percent who are elderly had a signiﬁcantly negative impact on educational spending per adult in a panel of Texas counties but was insigniﬁcant in a panel of forty-eight states. Using a state panel, Poterba (997) found that per child education spending falls as the state’s fraction who are elderly rises if the percent living in urban areas is not included in the regression. Ladd and Murray (200) conducted an analysis similar to Poterba’s but at the county level with county and time ﬁxed effects and found that the proportion who are elderly does not signiﬁcantly affect per child education spending. With a panel of school district data, 哈里斯, 埃文斯, and Schwab (200) found that the elderly share had a signiﬁcant but small negative effect on revenues per pupil.4 Using survey data, Brunner and Balsdon (2004) found that the elderly were less likely than younger voters to support school bond initiatives in California. Other research suggests that the impact of the elderly depends on whether the elderly are long-term residents or can capitalize the beneﬁts of having good schools into housing prices. Similar to Fletcher (2006), Berkman and Plutzer (2004, p. 8) hypothe- size that “those who have lived in their communities for some time may . . . have developed loyalty to the community and its schools,” making them more supportive of larger school budgets. Using school district data, they ﬁnd that school spending in 994–95 was higher in counties with a larger share of the population who were long-term elderly residents. 另一方面, school spending was lower in counties with a larger share who were elderly migrants in regressions with no state ﬁxed effects; the elderly migrant variable was not 4. In a related study, Button (992) found that the share of voters aged ﬁfty-ﬁve or older had a negative impact on the success of school bond proposals in Florida. l 从http下载 : / / 直接的 . 米特 . F / / e d u e d p a r t i c e – p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 压力 . . . . F . 来宾来访 0 7 九月 2 0 2 3 287 INFLUENCE OF ELDERLY ON SCHOOL SPENDING signiﬁcant in a regression that allowed for state ﬁxed effects. 如前所述, 弗莱彻 (2006) also expected long-term elderly to be more favorably disposed to greater school spending than recent elderly migrants. Using county data for 990 and two-stage least squares (2SLS) and three-stage least squares (3SLS) procedures that take account of the endogeneity of elderly migration, she found that school spending was higher in counties with more long-term elderly and was lower in counties with a larger share who were elderly and had moved from another state. Hilber and Mayer (2004) hypothesized that there would be greater capi- talization of school quality into home prices if there was little land available for development. The opportunity to capitalize the value of better schools into home prices was expected to make the elderly more supportive of larger school budgets. Consistent with this reasoning, using a district-level cross section the authors found that the percent who were elderly had a negative impact on spending in locations where there was much land that had not been developed (IE。, little potential for capitalization) and had a positive impact on spending in communities with little available land (IE。, great potential for capitalization). The estimated effect of the elderly thus appears to be sensitive to the chosen sample or level of aggregation, the inclusion of certain variables, the potential for capital gains, and the time the elderly have spent in their current location. 此外, in the intergenerational conﬂict literature the coefﬁcient on the percent sixty-ﬁve or older variable often has been interpreted as reﬂecting elderly preferences on school spending relative to those of parents or other younger adults for school spending. The ﬁnding of some studies that the percent elderly has a positive impact on school spending thus seems to imply that the elderly want to spend more than other voters on schools, which is very difﬁcult to rationalize. The median voter framework developed later in this article will provide an explanation for this apparent anomaly: as more elderly vote with the poor, the median voter is poorer and demands better schools if the price effect overwhelms the income effect; these were described earlier. 3. THEORETICAL BACKGROUND Here we provide the theoretical underpinnings for some aspects of our em- pirical speciﬁcation. Following Lovell (975), assume that school taxes are proportional to income. This is consistent with schools being ﬁnanced by property taxes that are proportional to house values and the income elasticity for housing being . A household with income Mi and facing a tax rate of t pays t · Mi in taxes, leaving Ci units of private goods (the numeraire) to be consumed. Mi = Ci + t · Mi. () 288 l 从http下载 : / / 直接的 . 米特 . / / f e d u e d p a r t i c e – p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 压力 . . . F . . 来宾来访 0 7 九月 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny Each of N households receives G in government services (例如, school quality), which are produced at a cost of PG each. The government budget constraint requires that total taxes equal total spending, or t · ((西德:1)米) = PG · G · N. Solving equation 2 for t, t = (PG · G · N)/((西德:1)米) = (PG · G)/Mmean (2) (3) where Mmean is mean household income. Substituting equation 3 into equation  yields Mi = Ci + PG · (Mi/Mmean) · G. (4) 因此, for the household with income Mi, the price of government services equals PG · (米 / Mmean). An increase in the cost of producing each unit of G [PG], due perhaps to teachers unionizing, raises the household’s cost of acquiring one more G. Having a better school is more expensive for a relatively rich household in the community [(米 / Mmean) > ] than for a relatively poor household in the community [(米 / Mmean) < ] because this entails a larger increase in property taxes for the richer household. This effect reﬂects the redistribution from richer households to poorer households within the jurisdiction. Kenny (978) showed that the preferred level of school spending increased as household income rose within the jurisdiction if the income effect associated with the household being better off (i.e., Mi rises) dominated the substitution effect associated with the richer household facing a higher price of having a better school [i.e., (Mi / Mmean) rises]. He showed that this condition is equivalent to () the income elasticity for school quality G being greater than the elasticity of substitution between school quality G and private consumption C, or equivalently (2) the income elasticity for school quality being greater than the uncompensated price elasticity for school quality. Lovell (978), using this framework, estimated that the income elasticity for school spending was higher than the price elasticity, suggesting that a community’s richer households prefer better schools than are preferred by its poorer households. Suppose that preferences over school spending can be characterized in one of two ways. Some share of the community αe (e.g., all the elderly) are assumed in this example to align themselves with the poorest households (M = 0) regardless of their income. For the remainder of the community l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . f . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 289 INFLUENCE OF ELDERLY ON SCHOOL SPENDING ( − αe), preferred spending G∗ is a monotonic function of household income (Mi). The cumulative distribution of income for the non-elderly is given by [F(Mi)]. The median voter household is the household with income M(cid:2) for which (cid:2) αe + ( − αe) · F(M ) = 0.50. That is, if 20 percent vote with the poorest households, the median voter household is found by going up the distribution of non-elderly income until another 30 percent of the total households are added to the voting coalition of the poor. This occurs where F(M(cid:2)) = 0.375, or where 3/8 of the non-elderly have an income below M(cid:2). This illustrates how the income of the median voter household (Mmedian voter) is calculated under the various assumptions about which elderly are aligned with the poor. 4. SAMPLE, HYPOTHESES, AND VARIABLES Sample Ladd and Murray (200) argued that a county- or district-level analysis is more appropriate than a state-level analysis because less aggregate data capture important features of education ﬁnance that would be missed at the state level. In the median voter framework, because school spending decisions are made at the local level, the income of the median voter household (Mmedian voter) and its tax price (Mmedian voter / Mmean) are best measured at the county or school district level. Since the elderly migration rates and the income distribution by age data are available from the Bureau of the Census at the county level and not the school district level, the empirical analysis in this article uses county data. Data from the 990 Census of Population and Housing (U.S. Census Bureau 990) were available for 3,4 counties or county equivalents. These data were merged with public school district enrollment and ﬁnance data taken from the 992 Census of Governments (U.S. Census Bureau 992). Ninety- eight of the 5,868 school districts in the Census of Governments could not be matched with a county Federal Information Processing Standards (FIPS) code. The school district data were aggregated to the county level (total revenue/total enrollment for the county). There were school districts in 3,26 of the 3,4 counties, but student enrollments were zero in three of these counties, which were dropped from the sample. Thus the initial sample for 990 consists of 3,23 counties and county equivalents. All of the 5,383 school districts in the 2002 Census of Governments could be matched with a county FIPS code (U.S. Census Bureau 2000). Data from the 2000 Census of Population and Housing (U.S. Census Bureau 290 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . . . f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny 2000) were available for 3,4 counties or county equivalents.5 Based on the 2002 Census of Governments (U.S. Census Bureau 2002), 3,23 of these counties had school districts. Two of these counties were dropped from the sample due to zero student enrollments. Twenty-four counties and thirty-one independent cities (county equivalents) in Virginia were dropped because the migration data for the cities were merged with the data for the surrounding or adjacent counties. One county was dropped because a change in the county boundaries was reﬂected in the Census of Population and Housing but not in the Census of Governments. Thus the initial sample for 2000 consists of 3,065 counties and county equivalents. The initial pooled sample consists of 3,23 counties in 990 and 3,065 counties in 2000, for a total of 6,88 observations. The dependent variable is the county per pupil state and local revenues for public primary and secondary schools, inﬂated to 2000 dollars using the implicit government purchases deﬂator. This variable ranged from $2,486 to $28,45 in 990 and from $3,836 to $50,4 in 2000. To eliminate outliers due to data errors, a subsample was created by trimming in each year the  percent of the observations with the largest per pupil school revenues and the  percent of the observations with the smallest per pupil school revenues, resulting in 6,064 observations from 3,00 counties. Summary statistics for school revenue and the independent variables in this trimmed sample are reported in table . The range in school revenue per pupil was $3,000–$2,478 in 990 and $4,586–$5,223 in 2000. Thus the trimmed sample has a range that is 0.365 (0.230) the range in the untrimmed sample in 990 (2000). Note, however, that we get very similar results, reported in the appendix, when we use the (untrimmed) initial sample. County characteristics provide a perfect match to school district charac- teristics in the six states in which the school district is the county (FL, LA, MD, NV, VA, WV). Using county data to characterize school districts is more difﬁcult in states in which school districts often wander across county borders. To minimize this problem, a second sample is constructed that restricts the trimmed sample to the twenty-eight states in which no more than 20 percent of the school districts span two or more counties, which we call the “districts- within-county states.”6 As already noted, the match between county and school 5. There were a few differences between the 3,4 counties in 990 and the 3,4 counties in 2000. Two county equivalents in 990 did not exist in the 2000 census: Yellowstone National Park, listed as a county equivalent in 990, is legally part of Gallatin County, MT, and Park County, MT. In 995, South Boston City, VA, was absorbed into Halifax County, VA. Two new county equivalents were also created between 990 and 2000: Yakutat Borough, AK, and Broomﬁeld County, CO. 6. This is compiled from state-level data reported in the Government Organization section of the 992 Census of Governments. Note that we get very similar results using only states in which less than 0 percent of the school districts span county boundaries. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d f . . . . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 291 INFLUENCE OF ELDERLY ON SCHOOL SPENDING Table 1. Data Characteristics A. Non-median income variables Trimmed Sample (n = 6,064) Mean Std Dev Min Max STATE & LOCAL SCHOOL REVENUE 6554 1831 3000 15223 FEDERAL REVENUE FRACTION 5–17 FRACTION URBAN HOMEOWNER DUMMY SUPREME CT RULING RELATIVE STATE INC SUPREME CT RULING × RELATIVE STATE INC RACIAL MISMATCH 612 525 0 10391 .195 .383 .990 .178 .865 .230 .093 .026 .302 .097 .383 .168 .392 .095 .067 .360 0 0 0 1 1 1 .426 1.897 0 1.897 −.495 .586 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . f . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 B. Median income variables: Elderly and non-elderly equally weighted Same preferences MED HHD INCOME Trimmed Sample (n = 6,064) Mean Std Dev Min Max 35098 9095 12601 86624 MED INCOME/MEAN INCOME .794 .059 .446 .978 Elderly cross-state migrants aligned with poor MED HHD INCOME 34978 9087 12575 86466 MED INCOME/MEAN INCOME .791 .060 .446 .977 All elderly migrants aligned with poor MED HHD INCOME 34794 9081 12488 86289 MED INCOME/MEAN INCOME .787 .061 .445 .975 All elderly aligned with poor MED HHD INCOME 28235 10217 6601 85118 MED INCOME/MEAN INCOME .628 .110 .174 .959 C. Median income variables: Elderly and non-elderly weighted by voter turnout Elderly cross-state migrants aligned with poor MED HHD INCOME Trimmed Sample (n = 6,064) Mean Std Dev Min Max 34218 9006 12524 85869 MED INCOME/MEAN INCOME .773 .058 .434 .970 All elderly migrants aligned with poor MED HHD INCOME 34001 8997 12427 85653 MED INCOME/MEAN INCOME .768 .059 .433 .968 All elderly aligned with poor MED HHD INCOME 25759 10491 6147 84212 MED INCOME/MEAN INCOME .568 .125 .122 .951 Notes: SCHOOL SPENDING and FEDERAL REVENUE are deﬂated to 2000 dollars using implicit government purchases deﬂator. MEAN HHD is deﬂated to 2000 dollars using the CPI-U. 292 Deborah Fletcher and Lawrence W. Kenny district is perfect in the six states with countywide school districts. Less than 3 percent of the school districts wander across county boundaries in nine states (AK, AZ, CT, GA, KY, NJ, RI, UT, VT), and county borders are spanned for 3–9 percent of the school districts in AL, CA, IN, MA, ME, MS, MT, NH, NC, PA, SC, TN, and WY. This sample consists of 2,805 observations from ,462 counties.7 A number of states have sought to reduce the variation in educational spending across school districts in the state. These “reforms” leave school districts with much less latitude in determining school spending. To take one extreme example, the California state supreme court in its Serrano decision decreed that there be no more than $00 variation in per pupil spending across districts. In reform states, the usual demand variables are expected to have very little impact on spending. To obtain better estimates of the demand for school spending in districts that are relatively unfettered by state government, we created another subsample by removing states where the coefﬁcient of variation (CV) in state and local per pupil revenues is less than 0.. Twelve states (AR, AZ, CT, DE, HI, KY, ME, NH, NJ, NY, RI, WI) were removed in 990, and eighteen states (AL, AR, AZ, CT, DE, HI, IA, IN, KY, MA, NH, NJ, RI, SD, TN, VT, WI, WV) were stricken in 2000, leaving 4,85 observations from 2,754 counties. A fourth sample was created from the intersection of the second and third samples. It consists of states with few districts spanning county borders and states with a coefﬁcient of variation in spending that is at least 0.. It comprises 2,3 observations from ,269 counties. In these four samples there is a trade-off between having more appropriate data and having more data. The fourth sample is based on the most appropriate data, but it is much smaller than the other three samples. The regressions that we report from all four samples provide some evidence on how robust our ﬁndings are to varying the sample. Independent Variables and Hypotheses An increase in income is expected to lead, through an income effect, to higher school revenues. MED HHD INCOME equals the income of the median voter household (Mmedian voter) inﬂated to 2000 dollars using the consumer price index for all urban consumers (CPI-U). This is calculated for each of the four 7. Even if school districts are conﬁned to a single county, the median voter in a county may not have the same characteristics as the median voters in the school districts in the county. This is not a problem in 63 percent of the counties in the districts-within-county states, where there is only one uniﬁed or high school district; in these the median voter in the county is the median voter in the school district. It is our belief that in many of the remaining counties there is a dominant large-city school district that makes plausible our assumption that the median voter in the county is a reasonable approximation to the weighted school district median voter. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d f . . . . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 293 INFLUENCE OF ELDERLY ON SCHOOL SPENDING scenarios described above by aligning the appropriate group of elderly with the county’s poorest households and then moving up the income distribution of the remaining households until the median voter household is found. Inter- polation between the midpoints of adjacent income categories is used to ﬁnd the household income of this median voter household. It can be seen in table  that the calculated income of the median voter household falls as more elderly vote with the poor. As already noted, we also tried aligning the elderly with the county’s richest households. Since this assumption consistently provided a worse ﬁt than assuming that the elderly vote with the poor, the alignments with rich regressions are not reported. The ratio of the median voter household’s income to mean household in- come in the county (MED INCOME / MEAN INCOME) corresponds to the term Mmedian voter / Mmean. Due to the skewness in the income distribution, me- dian income is less than mean income in each county. The ratio of the median voter’s income to mean income falls in table  as more elderly vote with the poor. As the ratio of the median voter household’s income to mean household income falls, the median voter faces a lower price to increase school quality, which should lead to more spending. There is some support for this prediction in the literature (e.g., Lovell 978; Gemmell, Morrissey, and Pinar 2002). The variable just described captures the potential for redistribution from the community’s richer households to the median voter. Nonresidential prop- erty offers another vehicle for redistribution to the median voter through property taxation. Unfortunately there are no reliable data on the share of nonresidential property values in the total value of assessed property.8 The bias on the coefﬁcient of the tax price variable that we do use (Mmedian voter / Mmean) due to not having some measure of the importance of nonresidential property hinges on the correlation between this variable and the importance of nonresidential property, which appears to be small and of unknown sign. Note that the county ﬁxed effects included in all the regressions probably capture much of the variation across counties in nonresidential property relative to residential property. An increase in the number of students per household makes it more expensive to increase spending on each student by $00, which is expected to result in lower spending per student. This effect is captured by the fraction of the population who are aged 5–7 (FRACTION 5–7). This hypothesis has 8. Mark Schneider, commissioner of the National Center for Education Statistics (NCES), in a speech at the American Education Finance Association meetings in Baltimore in March 2007, lamented that it is impossible to get high-quality data on the property tax base that would be consistent across the ﬁfty states and could be “certiﬁed” by NCES. We also searched state blue books and state ﬁnance Web sites and were unable to ﬁnd consistent data on residential and nonresidential property for 990 and 2000 for more than a handful of states. 294 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . f . . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny been supported in Poterba (997), Ladd and Murray (200), Harris, Evans, and Schwab (200), and a number of other papers. Per pupil revenue from the federal government (FEDERAL REVENUE) has an ambiguous impact on state and local school revenues. The largest federal program for primary and secondary education, Title I, is a block grant. This has an income effect that should lead to higher total revenues for schooling but lower state and local funds, as some of these are diverted to fund increases in noneducational programs. Gordon (2004) studied the effect of discrete census- induced changes in Title I funding and concluded that greater funds from this program led to no change in state revenues and to smaller local revenues. But other federal programs, such as the free/reduced lunch and technology funds programs, require some local matching. Matching provisions could lead to greater state and local spending. Ladd and Murray (200) reported that aggregate federal aid had a signiﬁcantly positive impact on state and local revenues in the urban sample of counties but was unrelated to spending in the complete sample. Harris, Evans, and Schwab (200) found that aggregate federal revenues had a positive effect on school district local revenues. There is some evidence in the intergenerational conﬂict literature that school spending is lower in communities in which the elderly are of a different race than the students, suggesting that the elderly care more about educating children of their race than about educating children of a different race. This is tested here with RACIAL MISMATCH, which equals the fraction of those aged 5–7 who are nonwhite less the fraction of those sixty-ﬁve or older who are nonwhite. An increase in the fraction of a county’s population living in an urban area (FRACTION URBAN) makes it easier to take advantage of economies of scale in schooling, which leads to lower expenditure (see Kenny 982). There is also generally more competition among school districts in urban areas, which should make public schools more efﬁcient and thus lower spending. On the other hand, teacher salaries are higher in urban areas due to the higher cost of living (see Kenny and Denslow 980), making the net effect ambiguous. Fischel (200) argued that the ability to capitalize good schools into home values makes homeowners more willing than renters to support higher spend- ing on schools. But Denzau and Grier (984) rationalized the negative coef- ﬁcient often found on the fraction of housing units that are owner occupied with “renter illusion,” in which renters favor higher taxes because they do not expect the higher taxes to result in higher rents. The fraction of housing units that are owner occupied is commonly used in spending studies and is another variable that does not ﬁt into a median voter framework. To overcome this problem, we use a HOMEOWNER DUMMY, which equals  if a majority of housing units are owner occupied and 0 if a majority are rentals. A value l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . f . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 295 INFLUENCE OF ELDERLY ON SCHOOL SPENDING of  suggests that the median voter is a homeowner. Only 40 of the 3,06 counties in the full trimmed sample for 990 did not have a majority living in owner-occupied housing; in 2000 there were only 8 “renter” counties. State governments engage in redistribution from a state’s richer school districts to a state’s poorer school districts, which results in relatively afﬂuent districts spending less and relatively poor districts spending more. A number of state supreme courts have ruled that the state’s educational ﬁnance system was unconstitutional because of the disparity in school resources or spending across districts. This court-mandated redistribution is expected to be more sub- stantial than the redistribution by the state that took place without a court rul- ing. There is some support in the literature for this prediction. Harris, Evans, and Schwab (200) interacted dummies capturing a school district’s position in the state income distribution with a dummy indicating whether the state supreme court had overturned the state’s school ﬁnance system. Overturning the educational ﬁnance structure resulted in a shift in total revenues from richer districts to poorer districts. Card and Payne (2002) similarly showed that rulings that the school ﬁnancing system was unconstitutional caused the slopes describing the effect of district income on state revenues and on total spending to be ﬂatter. The county’s position on the state’s income distribution is measured here by the ratio of mean income in the county to mean income in the state (REL- ATIVE STATE INC). SUPREME CT RULING equals  for 990 in the seven states in which the state supreme court had overturned the state’s educational ﬁnance system prior to 987 (NJ 973, CA 976, CT 977, WA 978, WV 979, WY 980, and AR 983); another six states (KY 989, MT 989, TX 989, MA 993, TN 993, and AZ 994) were added for 2000 based on a similar criterion.9 This treatment allows some time for the court ruling to affect the distribution of spending within the state. The interaction between these two variables (SUPREME CT RULING × RELATIVE STATE INC) provides a test for the hypothesis described above. County ﬁxed effects control for variation in local amenities, the timing of school board elections, state education policies, and so on. A year dummy allows for spending to change over the decade in response to factors that have not been taken into account by other variables. 5. EMPIRICAL RESULTS Results for county ﬁxed effects regressions under the four scenarios describing elderly preferences are reported in () tables 2 and 3 for the full trimmed sample, (2) tables 4 and 5 for the trimmed sample limited to the twenty-eight 9. This classiﬁcation is based on Figlio, Husted, and Kenny (200). 296 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . f . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny Table 2. Spending Regressions: Full Trimmed Sample, 6,064 Observations from 3,100 Counties. Elderly and Non-elderly Equally Weighted Elderly Aligned with Poor Same Preferences Cross-State Migrants All Migrants All Elderly MED HHD INCOME MED INCOME/ MEAN INCOME FEDERAL REVENUE FRACTION 5–17 FRACTION URBAN HOMEOWNER DUMMY RELATIVE STATE INC SUPREME CT RULING SUPREME CT RULING × RELATIVE STATE INC RACIAL MISMATCH 2000 DUMMY R2: Within Between Overall F-statistic: Overall F-statistic: Fixed effects = 0 σ (error) .043 (3.20) −1694 (2.26) .351 (5.53) −6553 (4.88) 42.8 (0.23) −389 (1.32) −923 (1.47) −219 (4.11) −1332 (2.26) −1003 (2.53) 1433 (21.0) .7161 .0785 .2421 677.22 6.02 743.7 .045 (3.30) −1845 (2.46) .352 (5.55) −6528 (4.86) 41.2 (0.22) −388 (1.32) −995 (1.59) −219 (4.10) −1330 (2.25) −1006 (2.54) 1425 (20.9) .7162 .0798 .2433 677.40 6.03 743.7 .045 (3.32) −1831 (2.44) .352 (5.55) −6520 (4.85) 40.9 (0.22) −389 (1.32) −992 (1.59) −219 (4.10) −1325 (2.25) −1002 (2.53) 1425 (20.9) .7162 .0807 .2443 .058 (4.56) −2503 (4.12) .363 (5.77) −6432 (4.80) −27.6 (0.15) −417 (1.42) −1060 (2.08) −212 (3.98) −1243 (2.11) −1006 (2.53) 1421 (26.4) .7172 .0924 .2563 677.45 680.65 6.02 743.6 6.14 742.4 Note: Absolute t-statistics are in parentheses. districts-within-county states, (3) tables 6 and 7 for the trimmed sample in which the low-spending inequality states were removed, and (4) tables 8 and 9 for the trimmed sample with the low-spending inequality states removed and limited to the districts-within-county states. In tables 2, 4, 6, and 8, the elderly and non-elderly receive equal weights; in tables 3, 5, 7, and 9, the elderly receive more weight to reﬂect their higher voter turnout rate.0 The regressions 0. The voter turnout rates pertain to the 2000 presidential election and were obtained from the U.S. Bureau of the Census (2002). l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d f . . . . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 297 INFLUENCE OF ELDERLY ON SCHOOL SPENDING Table 3. Spending Regressions: Full Trimmed Sample, 6,064 Observations from 3,100 Counties. Elderly and Non-elderly Weighted by Voter Turnout Elderly Aligned with Poor Same Preferences Cross-State Migrants All Migrants All Elderly MED HHD INCOME MED INCOME/ MEAN INCOME FEDERAL REVENUE FRACTION 5–17 FRACTION URBAN HOMEOWNER DUMMY RELATIVE STATE INC SUPREME CT RULING SUPREME CT RULING × RELATIVE STATE INC RACIAL MISMATCH 2000 DUMMY R2: Within Between Overall .043 (3.20) −1694 (2.26) .351 (5.53) −6553 (4.88) 42.8 (0.23) −389 (1.32) −923 (1.47) −219 (4.11) −1332 (2.26) −1003 (2.53) 1433 (21.0) .7161 .0785 .2421 .045 (3.30) −1846 (2.46) .351 (5.54) −6566 (4.89) 36.8 (0.20) −391 (1.33) −973 (1.57) −218 (4.09) −1329 (2.25) −1014 (2.56) 1428 (21.4) .7162 .0791 .2428 .046 (3.32) −1836 (2.44) .352 (5.55) −6556 (4.88) 36.5 (0.20) −391 (1.33) −970 (1.57) −218 (4.09) −1324 (2.24) −1010 (2.55) 1428 (21.4) .7162 .0801 .2438 .057 (4.67) −2514 (4.45) .359 (5.73) −6522 (4.88) −46.9 (0.25) −429 (1.46) −889 (1.86) −211 (3.95) −1249 (2.12) −1031 (2.60) 1443 (29.3) .7173 .0864 .2512 F-statistic: Overall 677.22 677.41 677.45 681.20 F-statistic: Fixed effects = 0 σ (error) 6.02 743.7 6.04 743.7 6.04 743.6 6.23 742.2 Note: Absolute t-statistics are in parentheses. are highly signiﬁcant. With ﬁxed effects, the ordinary R2 is maximized and is reported as the R2 within. This ranges from 0.63 to 0.72. The hypothesis that the set of county ﬁxed effects adds nothing to the regressions is soundly rejected. The standard deviation in estimated county ﬁxed effects is quite large, falling between 393 and 554. 298 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . f . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny Table 4. Spending Regressions: Trimmed Sample, Districts-within-County States, 2,805 Observations from 1,462 Counties. Elderly and Non-elderly Equally Weighted Elderly Aligned with Poor Same Preferences Cross-State Migrants All Migrants All Elderly MED HHD INCOME MED INCOME/ MEAN INCOME FEDERAL REVENUE FRACTION 5–17 FRACTION URBAN HOMEOWNER DUMMY RELATIVE STATE INC SUPREME CT RULING SUPREME CT RULING × RELATIVE STATE INC RACIAL MISMATCH 2000 DUMMY R2: Within Between Overall .163 (8.16) −7048 (6.50) .294 (2.94) −3676 (1.98) −503 (2.01) −264 (0.67) −4957 (5.50) −449 (6.29) −525 (0.65) −1392 (2.02) 979 (10.4) .7025 .2835 .3695 .165 (8.27) −7351 (6.78) .294 (2.95) −3625 (1.95) −500 (2.01) −260 (0.66) −5081 (5.66) −448 (6.29) −520 (0.65) −1398 (2.03) 965 (10.3) .7030 .2823 .3685 .168 (8.35) −7359 (6.78) .297 (2.98) −3557 (1.91) −503 (2.02) −259 (0.66) −5106 (5.69) −450 (6.32) −507 (0.63) −1381 (2.01) 963 (10.3) .7032 .2849 .3705 .165 (8.76) −6850 (7.14) .283 (2.87) −4550 (2.48) −534 (2.15) −315 (0.81) −4081 (5.30) −448 (6.27) −264 (0.33) −1303 (1.88) 1108 (14.2) .7046 .2882 .3769 F-statistic: Overall 285.95 286.61 286.96 288.85 F-statistic: Fixed effects = 0 σ (error) 6.01 722.4 6.03 721.8 6.04 721.5 6.31 719.8 Note: Absolute t-statistics are in parentheses. Speciﬁcation Tests The results of various speciﬁcation tests comparing the seven regressions esti- mated for each of the four samples are summarized in table 0. Akaike’s ACI . The relative weighting of the elderly and younger households has no impact on the regression if elderly and younger households have the same preferences about school spending. Thus for each sample, the ﬁrst regression in the sample’s second table duplicates the ﬁrst regression in the sample’s ﬁrst table. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . f . . . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 299 INFLUENCE OF ELDERLY ON SCHOOL SPENDING Table 5. Spending Regressions: Trimmed Sample, Districts-within-County States, 2,805 Observations from 1,462 Counties. Elderly and Non-elderly Weighted by Voter Turnout Elderly Aligned with Poor Same Preferences Cross-State Migrants All Migrants All Elderly MED HHD INCOME MED INCOME/ MEAN INCOME FEDERAL REVENUE FRACTION 5–17 FRACTION URBAN HOMEOWNER DUMMY RELATIVE STATE INC SUPREME CT RULING SUPREME CT RULING × RELATIVE STATE INC RACIAL MISMATCH 2000 DUMMY R2: Within Between Overall .163 (8.16) −7048 (6.50) .294 (2.94) −3676 (1.98) −503 (2.01) −264 (0.67) −4957 (5.50) −449 (6.29) −525 (0.65) −1392 (2.02) 979 (10.4) .7025 .2835 .3695 .167 (8.28) −7398 (6.75) .292 (2.93) −3853 (2.08) −515 (2.07) −266 (0.68) −5034 (5.62) −447 (6.27) −510 (0.63) −1441 (2.10) 978 (10.6) .7030 .2811 .3677 .170 (8.36) −7423 (6.75) .295 (2.96) −3774 (2.04) −517 (2.07) −265 (0.68) −5061 (5.67) −448 (6.30) −495 (0.62) −1423 (2.07) 975 (10.6) .7033 .2838 .3700 .159 (8.61) −6490 (7.06) .266 (2.70) −5132 (2.81) −540 (2.17) −341 (0.87) −3575 (4.89) −445 (6.22) −253 (0.31) −1338 (1.93) 1174 (16.2) .7041 .2750 .3669 F-statistic: Overall 285.95 286.59 286.98 288.13 F-statistic: Fixed effects = 0 σ (error) 6.01 722.4 6.06 721.8 6.06 721.5 6.39 720.5 Note: Absolute t-statistics are in parentheses. criterion, Amemiya’s PC R2 criterion, Hocking’s Sp criterion, the Davidson- McKinnon J test and the prediction sum of squares (PRESS) criterion are described in Maddala (992), and the Schwartz’s SBC criterion is described in Greene (2003). Table 0 reports which of the seven speciﬁcations provided the best ﬁt and which provided the second best ﬁt. In the three largest samples, all the tests indicate that the best ﬁt is obtained assuming all the elderly are aligned with the county’s poorest households. The 300 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . f . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny Table 6. Spending Regressions: Trimmed Sample, Low-CV States Removed, 4,851 Observations from 2,754 Counties. Elderly and Non-elderly Equally Weighted Elderly Aligned with Poor Same Preferences Cross-State Migrants All Migrants All Elderly MED HHD INCOME MED INCOME/ MEAN INCOME FEDERAL REVENUE FRACTION 5–17 FRACTION URBAN HOMEOWNER DUMMY RELATIVE STATE INC RACIAL MISMATCH 2000 DUMMY R2: Within Between Overall .087 (5.07) −3022 (3.25) .477 (5.70) −8692 (5.11) 145 (0.61) −277 (0.79) −2705 (3.71) −1262 (2.71) 1195 (13.5) .6768 .3016 .3531 .089 (5.16) −3216 (3.46) .478 (5.71) −8667 (5.09) 143 (0.60) −277 (0.78) −2788 (3.83) −1260 (2.70) 1186 (13.4) .6769 .3006 .3528 .090 (5.19) −3196 (3.43) .478 (5.72) −8662 (5.09) 142 (0.60) −277 (0.79) −2782 (3.84) −1254 (2.69) 1186 (13.4) .6769 .3012 .3533 .087 (5.47) −3186 (4.30) .465 (5.63) −8803 (5.17) 84.6 (0.35) −320 (0.91) −2159 (3.80) −1221 (2.62) 1275 (18.5) .6773 .2976 .3491 F-statistic: Overall 485.80 486.00 486.15 487.04 F-statistic: Fixed effects = 0 σ (error) 4.39 818.3 4.40 818.2 4.40 818.1 4.36 817.6 Note: Absolute t-statistics are in parentheses. only difference is whether the best ﬁt is found by weighting the elderly and younger households according to their voter turnout rates or by equally weight- ing elderly and younger households. In the full trimmed sample, weighting according to voter turnout yields the best ﬁt. In the other two samples, the best ﬁt is obtained in nearly two-thirds of the tests by weighting the two age groups equally and in the remainder of the tests by using voter turnout weights. States with low coefﬁcients of variation and states in which school districts often spilled across county boundaries are not included in the smallest sample. In this sample, the Hocking’s Sp and the PRESS criterion tests conclude that the best ﬁt is found assuming that all (i.e., recent migrants and long-term residents) elderly are aligned with the jurisdiction’s poorest voters. But in the l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . f . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 301 INFLUENCE OF ELDERLY ON SCHOOL SPENDING Table 7. Spending Regressions: Trimmed Sample, Low-CV States Removed, 4,851 Observations from 2,754 Counties. Elderly and Non-elderly Weighted by Voter Turnout Elderly Aligned with Poor Same Preferences Cross-State Migrants All Migrants All Elderly MED HHD INCOME MED INCOME/ MEAN INCOME FEDERAL REVENUE FRACTION 5–17 FRACTION URBAN HOMEOWNER DUMMY RELATIVE STATE INC RACIAL MISMATCH 2000 DUMMY R2: Within Between Overall .087 (5.07) −3022 (3.25) .477 (5.70) −8692 (5.11) 145 (0.61) −277 (0.79) −2705 (3.71) −1262 (2.71) 1195 (13.5) .6768 .3016 .3531 .089 (5.10) −3139 (3.37) .476 (5.69) −8737 (5.14) 140 (0.59) −280 (0.79) −2701 (3.75) −1274 (2.73) 1196 (13.8) .6768 .3011 .3529 .090 (5.14) −3123 (3.35) .476 (5.70) −8730 (5.13) 138 (0.58) −281 (0.80) −2696 (3.77) −1267 (2.72) 1296 (13.8) .6769 .3018 .3534 .081 (5.27) −2960 (4.29) .451 (5.49) −8934 (5.25) 78.4 (0.33) −332 (0.94) −1809 (3.43) −1250 (2.67) 1321 (20.8) .6770 .2946 .3453 F-statistic: Overall 485.80 485.81 485.97 486.26 F-statistic: Fixed effects = 0 σ (error) 4.39 818.3 4.40 818.3 4.40 818.2 4.39 818.0 Note: Absolute t-statistics are in parentheses. other four tests, assuming that all elderly migrants (from another county in the state or a different state) are clumped with the poorest households and that long-term elderly residents have the same preferences as younger households provides the best ﬁt. In summary, almost all of the speciﬁcation tests indicate that all elderly are aligned with the poorest households. But there is some evidence in the smallest sample that elderly alignment with the poorest households is conﬁned to those who have migrated recently from another county in the state or a different state. This evidence based on the smallest sample suggests that long-term elderly residents, who may be more likely to have grandchildren in the school 302 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . . . f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny Table 8. Spending Regressions: Trimmed Sample, Low-CV States Removed, Districts-within-County States, 2,113 Observations from 1,269 Counties. Elderly and Non-elderly Equally Weighted Elderly Aligned with Poor Same Preferences Cross-State Migrants All Migrants All Elderly MED HHD INCOME MED INCOME/MEAN INCOME FEDERAL REVENUE FRACTION 5–17 FRACTION URBAN HOMEOWNER DUMMY RELATIVE STATE INC RACIAL MISMATCH 2000 DUMMY R2: Within Between Overall .205 (8.06) −7973 (5.67) .288 (2.35) −6281 (2.55) −288 (0.83) 195 (0.41) −5757 (5.50) 351 (0.40) 552 (4.41) .6280 .2997 .3345 .207 (8.16) −8364 (5.96) .289 (2.36) −6246 (2.53) −278 (0.80) 203 (0.43) −5904 (5.66) 347 (0.39) 534 (4.28) .6286 .2967 .3320 .209 (8.21) −8321 (5.93) .291 (2.37) −6195 (2.51) −283 (0.82) 203 (0.43) −5894 (5.67) 362 (0.41) 537 (4.31) .6290 .2972 .3321 .194 (7.98) −7665 (6.06) .249 (2.05) −7498 (3.07) −288 (0.83) 123 (0.26) −4425 (4.99) 344 (0.39) 753 (7.17) .6275 .2971 .3378 F-statistic: Overall 156.62 157.06 157.29 156.32 F-statistic: Fixed effects = 0 σ (error) 3.84 808.7 3.86 807.9 3.86 807.6 3.91 809.2 Note: Absolute t-statistics are in parentheses. system and who may care about others in the public schools, have the same preferences as younger households about school spending. Individual Variable Effects Our summary of the empirical results will be based on the speciﬁcation in each of the four samples that best ﬁt the data according to the speciﬁcation tests described above. Estimates of the impact of a variable will be taken from the two samples that do not include states in which the school districts appear to be given little latitude in determining school spending. Removing states with little variation in school spending across counties should result in a sample that is comprised mostly of states that interfere little l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . f . . . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 303 INFLUENCE OF ELDERLY ON SCHOOL SPENDING Table 9. Spending Regressions: Trimmed Sample, Low-CV States Removed, Districts-within-County States, 2,113 Observations from 1,269 Counties. Elderly and Non-elderly Weighted by Voter Turnout Elderly Aligned with Poor Same Preferences Cross-State Migrants All Migrants All Elderly MED HHD INCOME MED INCOME/ MEAN INCOME FEDERAL REVENUE FRACTION 5–17 FRACTION URBAN HOMEOWNER DUMMY RELATIVE STATE INC RACIAL MISMATCH 2000 DUMMY R2: Within Between Overall .205 (8.06) −7973 (5.67) .288 (2.35) −6281 (2.55) −278 (0.83) 195 (0.41) −5757 (5.50) 351 (0.40) 552 (4.41) .6280 .2997 .3345 .208 (8.13) −8209 (5.76) .288 (2.35) −6521 (2.65) −288 (0.83) 193 (0.41) −5773 (5.54) 315 (0.36) 553 (4.50) .6284 .2981 .3335 .210 (8.18) −8176 (5.73) .289 (2.36) −6462 (2.63) −294 (0.85) 194 (0.41) −5762 (5.55) 329 (0.38) 556 (4.54) .6288 .2986 .3336 .183 (7.64) −7127 (5.85) .222 (1.83) −8212 (3.37) −285 (0.82) 87.3 (0.18) −3761 (4.49) 258 (0.29) 843 (8.65) .6254 .2971 .3396 F-statistic: Overall 156.62 156.90 157.15 154.88 F-statistic: Fixed effects = 0 σ (error) 3.84 808.7 3.86 808.2 3.87 807.8 3.91 811.5 Note: Absolute t-statistics are in parentheses. in the local determination of school spending. Consider education “reform,” which is designed to reduce the impact of income on school revenues. Remov- ing states that had undertaken education reform to equalize spending should result in larger coefﬁcients for the income variables. This is indeed the case. The coefﬁcient on MED HHD INCOME is 53 percent larger in table 6 than in table 3, and the coefﬁcient on MED INCOME / MEAN INCOME is 27 percent larger when the low-CV states are removed. Note also that the FEDERAL REV- ENUE and FRACTION 5–7 coefﬁcients are 30 percent and 35 percent greater, respectively, in table 6 than in table 3. Let us now turn to the results for the individual variables. Income has the anticipated positive impact on school revenues. In the fourth regression in table 6, a one standard deviation rise in median household 304 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d f . . . . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny s e t a t S V C w o L s s e L - o C s s o r C s s e L s e t a t S s e t a t S - V C w o L s s e L - o C s s o r C s s e L s e t a t S l l u F n o i t a c ﬁ c e p S i n o i t a c ﬁ c e p S i n o i t a c ﬁ c e p S i n o i t a c ﬁ c e p S i y l r e d e l l l A E s t n a r g m i l l A T s t n a r g m i l l A T y l r e d e l l l A E s s o r C T i s t n a r g m e t a t s e m a S s ’ f e r p y l r e d e l l l A T s t n a r g m i l l A E s t n a r g m i l l A E y l r e d e l l l A T s t n a r g m i l l A E s t n a r g m i l l A T s t n a r g m i s t n a r g m i d n 2 l l A T t s e B l l A E d n 2 l l A T y l r e d e l y l r e d e l l l A E y l r e d e l l l A T y l r e d e l l l A T y l r e d e l l l A E ∗ s ’ c e p s 3 t s e B l l A E y l r e d e l y l r e d e l l l A T y l r e d e l l l A E y l r e d e l l l A E y l r e d e l l l A T y l r e d e l l l A E s n o i t a c ﬁ i c e p s o w T . s e m e h c s i g n i t h g e w o w t e h t n e e w t e b e c n e r e f f i d s t n a r g m i d n 2 l l A T y l r e d e l l l A E y l r e d e l l l A T y l r e d e l l l A T y l r e d e l l l A E l l - a n o N y l r e d e l t s e B l l A E y l r e d e l y l r e d e l l l A T y l r e d e l l l A E y l r e d e l l l A E y l r e d e l l l A T y l r e d e l l l A d n 2 l l A E y l r e d e l y l r e d e l l l A E y l r e d e l l l A E y l r e d e l l l A E i i g n n a m e R s ’ c e p s l l - a n o N y l r e d e l t s e B l l A T y l r e d e l y l r e d e l l l A T y l r e d e l l l A T y l r e d e l l l A T y l r e d e l y l r e d e l l l A T l l A 2 R C P a y i m e m A n o i r e t i r c p S s ’ g n k c o H i n o i r e t i r c I C A s ’ e k a k A i n o i r e t i r c n o i r e t i r c s e r a u q s f o m u s n o i t c d e r P i e v i s u c n o c l t s e t J C B S s ’ z t r a w h c S n o i r e t i r c s ’ c e p s p o t f o s n o s i r a p m o c t n a c ﬁ n g s i i o n s a w e r e h t t a h t s e t a c d n i i T r o E o N . s t h g e w i t u o n r u t r e t o v = T ; s t h g e w i l a u q e = E : s e t o N y l t n a c ﬁ n g s i i e r a s n o i t a c ﬁ i c e p S . s n o i t a c ﬁ c e p s i r e h t o n a h t r e t t e b e r e w t u b , r e h t o n a e n o m o r f t n e r e f f i d y l t n a c ﬁ n g s i i t o n e r e w s n o i t a c ﬁ i c e p s e h t t a h t n a e m d n 2 r o t s e B r o f l s e p m a S d e m m i r T r o o P e h t h t i w n g i l A s p u o r G y l r e d E l h c i h W r o f s t s e T n o i t a c ﬁ c e p S i . 0 1 e b a T l . y l r e d e l l l a d e t h g e w i - t u o n r u t d n a i , s t n a r g m e t a t s s s o r c - d e t h g e w i - t u o n r u t , s e c n e r e f e r p e m a S . l e v e l % 5 e h t t a t n e r e f f i d ∗ l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . . . f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 305 INFLUENCE OF ELDERLY ON SCHOOL SPENDING income ($0,39) is estimated to raise spending per pupil by $879. The esti- mated income elasticity, evaluated at mean values for spending and income, is 0.37 in table 6 and .8 in table 8. Communities in which the median voter is less able to take advantage of redistribution within the jurisdiction spend less on schools. In the fourth regression in table 6, a one standard deviation rise in MED INCOME / MEAN INCOME (0.2) leads to a $356 fall in school revenues. The price elastic- ity, evaluated at mean values, equals −0.3 in table 6 and −.05 in table 8. Our ﬁnding that the Mmedian voter / Mmean variable has the predicted effect on school spending suggests that this variable is capturing at least an important component of the tax price facing the median voter. It also is costlier to increase school quality if school-age children represent a larger share of the population. The coefﬁcients on FRACTION 5–7 have the predicted negative sign and are statistically signiﬁcant. In table 6, a one standard deviation rise in the fraction of those of school age results in a small $232 fall in school revenue per pupil. Unlike some other studies, we ﬁnd that state and local school revenue increases when the federal government provides more revenue for primary and secondary schools. In the fourth regression in table 6, a typical rise in FEDERAL results in a modest $234 rise in state and local revenues. Part of the generational conﬂict over school funding may reﬂect racial preferences. That is, older whites may be more likely to support higher school spending if the students are mostly white than if the students are mostly black. This is captured by RACIAL MISMATCH, which equals the fraction of school- age children who are nonwhite less the fraction of elderly who are nonwhite. The negative coefﬁcients support this hypothesis and are statistically signiﬁ- cant in the three largest samples. A typical rise in this variable is estimated to result in a very small $8 fall in school spending. With two-tailed tests, the HOMEOWNER DUMMY is never statisti- cally signiﬁcant and FRACTION URBAN is statistically signiﬁcant only in tables 4 and 5. The latter ﬁnding suggests that the effects associated with economies of scale and the greater competition among districts typically found in urban areas are dominating the higher teacher salaries paid in urban areas. The signiﬁcantly negative coefﬁcients on RELATIVE STATE INC in tables 6–9 provide evidence of redistribution from a state’s richer counties to its poorer counties even when states with little variation in spending have been removed. Counties with higher values of the ratio of mean county income to mean state income are higher up the state’s income distribution. Holding median income constant, a one standard deviation increase in this ratio is associated with $366 lower spending in table 6. 306 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d f . . . . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny The regressions in tables 2–5 utilize states with a low coefﬁcient of variation in school spending as well as states with medium and high CVs. Estimates of the effects of state supreme court rulings that overturned the state’s education ﬁnance system are found in these regressions. Tables 2 and 3 are based on the full trimmed sample. The coefﬁcients imply that after a school ﬁnancing system was ruled unconstitutional, revenues fell in all the state’s counties, particularly in the richer counties. A court mandate to equalize spending led to a $,29 fall in revenues evaluated at the mean value for RELATIVE STATE INC and to a $,50 fall in revenues evaluated at one standard deviation above the mean of RELATIVE STATE INC. There is also evidence, based on the signiﬁcantly negative coefﬁcient of RELATIVE STATE INC, of redistribution within the state even with no court mandate to equalize spending. Tables 4 and 5 utilize the twenty-eight states with little school district spillover across county borders. Once again, there is evidence of redistribution within the state with no supreme court mandate and evidence that a state supreme court ruling resulted in lower school spending. But the surprising lack of statistical signiﬁcance for the interaction variable SUPREME CT RULING × RELATIVE STATE INC suggests that the fall in spending due to a court ruling was no greater in the state’s richer counties than in the state’s poorer counties. Finally, note that real spending was $537–,443 higher in 2000 than in 990, holding our other variables constant. Estimating the Effect of the Elderly on Spending The estimated income elasticity is slightly (0.06–0.3) greater, although not statistically signiﬁcantly greater, than the estimated price elasticity. As noted earlier, this difference implies that a district’s poorer citizens prefer to spend less money on schools than do the district’s richer citizens. Since the elderly beneﬁt less from better schools than do parents, the elderly are expected to align themselves with others who prefer lower school revenues. And, as expected, we get a better ﬁt by assuming that the elderly vote with the community’s poorest households than by assuming that the elderly vote with the richest households. The regressions provide no direct evidence on how much the elderly affect spending. In the median voter model used in this article, the elderly affect spending through a change in the identity of the median voter household and, through a reduction in the number of school-age children, make it less expensive to raise school expenditure per child. Let us begin by examining the effect on the identity of the median voter. Median Voter Effects of the Elderly on Spending The alignment of the elderly with the poor results in a median voter household that is further down the community’s income distribution. The median voter l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . f . . . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 307 INFLUENCE OF ELDERLY ON SCHOOL SPENDING household is poorer than would have been the case if the elderly did not clump with the poor. In table 6, the change in a community’s median voter household’s income due to its elderly equals the community’s median voter household income calculated under the assumption that all the elderly are aligned with the poor (used in regression 4) less median income calculated under the assumption that age does not matter, which is median household income in the community (used in regression ): MED HHD INCOMEall elderly − MED HHD INCOMEsame preferences. The estimated effect of the change in median voter household income on spending will be calculated using the regression coefﬁcient in the fourth re- gression in table 6. 0.0867 × (MED HHD INCOMEall elderly − MED HHD INCOMEsame preferences) The median voter household also faces a lower tax price due to there being some elderly in the community. The effect of the elderly on the median voter household’s tax price is given by MED INCOME/MEAN INCOMEall elderly − MED INCOME/MEAN INCOMEsame preferences. In turn, the effect of the elderly on spending through a change in the tax price equals −385.545 × (MED INCOME/MEAN INCOMEall elderly − MED INCOME/MEAN INCOMEsame preferences). The net effect of the elderly on school spending, working through a change in the identity of the median voter, is given by summing the above income and price effects: 0.0867 × (MED HHD INCOMEall elderly − MED HHD INCOMEsame preferences) − 385.545 × (MED INCOME/MEAN INCOMEall elderly − MED INCOME/MEAN INCOMEsame preferences). 308 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . f . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny Table 11. Distribution of Estimated Net Median Voter Effect of Elderly on Spending. Elderly and Non-elderly Equally Weighted Trimmed Samples Less Low-CV States Less Low-CV States Less Cross-County States Table 6: 4th regression Table 8: 3rd regression Mean Standard deviation 5th percentile 10th percentile 25th percentile 50th percentile 75th percentile 90th percentile 95th percentile −65∗ 116 −230 −180 −123 −66 −7 65 117 ∗ Mean is signiﬁcantly different from 0. −8∗ 23 −46 −28 −11 3 8 12 23 This estimate of the net effect of the elderly on school revenues was calculated for each of the 4,85 observations in the trimmed sample where the low- spending CV states were removed. The distribution of estimated net median voter effects based on table 6 is reported in the ﬁrst column of table . The presence of the elderly is estimated to lower per pupil school revenues by $66 in the median county. In over three-quarters of the counties, the elderly have resulted in lower school spending. This negative impact is consistent with the income elasticity being larger than the price elasticity and with the elderly aligning with the poor. The mean effect (−$65) is signiﬁcantly negative, but the effect is tiny in comparison with mean per pupil revenues ($6,50) and the effects estimated for other variables. A similar calculation of the effect of the elderly is based on the third regression in table 8, which uses only states in which few school districts spill over into two or more counties and which excludes states with little variation in spending. In this sample, the best ﬁt was found assuming that all elderly migrants were aligned with the jurisdiction’s poorest households. The estimated effect of the elderly, working through changes in the identity of the median voter, based on this regression is 0.2090 × (MED HHD INCOMEall migrants − MED HHD INCOMEsame preferences) − 832 × (MED INCOME/MEAN INCOMEall migrants − MED INCOME/MEAN INCOMEsame preferences). l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . . f . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 309 INFLUENCE OF ELDERLY ON SCHOOL SPENDING The distribution of estimated net median voter effects is described in the second column of table . The elderly are estimated to have a much smaller impact in this sample than in the larger sample that is not limited to states with few districts crossing county boundaries. The mean estimated net median voter effect based on the regression in table 8, although signiﬁcant, is only −$8. Estimated Effect of Elderly through Fewer School-Age Children In communities with more elderly, there are fewer households with school- age children, which makes it cheaper for the median voter to increase school spending per pupil. There is strong evidence in this and other studies that spending per pupil is higher in communities with few school-age children. To gauge the magnitude of this effect, we ﬁrst estimated a simple bivariate regression using the full trimmed sample, in which the fraction who are of school age is explained by the fraction who are aged sixty-ﬁve or older. The coefﬁcient on the elderly variable (−0.73) is negative, as predicted, and is highly signiﬁcant (t = 23.7). A one standard deviation rise in the fraction sixty- ﬁve and older (0.0429) is estimated to lead to a reduction in FRACTION 5–7 by 0.00742. This estimated drop in the fraction of school age then is multiplied by the relevant FRACTION 5–7 coefﬁcients. The coefﬁcient in the fourth regression in table 6 (−8803), corresponding to the sample with low-CV states removed, implies a $65 rise in per pupil spending. Similarly, a $46 rise in school spending is implied by the third regression in table 8; this sample in addition is conﬁned to states in which few districts wander across county lines. 6. CONCLUSION The literature on the effect of the elderly on primary and secondary school spending has not taken advantage of the structure provided by the median voter model. As a result, the speciﬁcation used in this literature offers little insight into how the elderly affect school spending. We have used the median voter model to estimate the demand for school spending under four assumptions about elderly preferences and under two assumptions about how the elderly and non-elderly populations should be weighted in determining the median voter household income. There is strong evidence that median income and tax price measures that are constructed based on the assumptions that all the elderly or all elderly migrants align themselves with the county’s poorest households better explain school spending than unadjusted county median income and tax price variables, which are based on no differences in preferences between elderly and non-elderly households. The alignment of the elderly with the group that favors the least school spending (the poor) provides evidence of intergenerational conﬂict and correspondingly 310 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / / f e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . f . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny that the elderly alter the identity of the median voter. Furthermore, elderly preferences are best described by assuming that all the elderly or all elderly migrants vote with the poor. Elderly opposition to higher school spending comes from more than elderly migrants from other states. In jurisdictions with more elderly, the median voter household is further down the jurisdiction’s income distribution. Due to lower income, this house- hold would spend less on schools. But this household also faces a lower price to improve schools because its income is lower relative to mean income in the county. Several bits of evidence suggest that the income effect is slightly larger than the price effect, implying that spending is lower in communities with more elderly. First, the income elasticity is 0.06–0.3 greater than the price elasticity. Second, the elderly vote with the poor, who, based on these numbers, support lower spending on schools. Third, the typical estimated ef- fect of the shift in the median voter on spending due to the elderly, working through these income and tax price effects, is negative, although small (−$8 to −$65). An increase in the elderly population is also associated with a drop in the school-age population. This reduces each voter’s cost of raising per pupil spending, leading to higher spending. We estimate that a typical rise in the elderly share leads, through a fall in the school-age population, to a $46–$65 rise in spending per pupil. To summarize, an inﬂux of the elderly leads to a small fall in spending due to a shift in the identity of the median voter and leads to a small rise in spending due to there being fewer children to educate. On net, a rise in the fraction who are elderly is associated with a very small, if any, rise in spending per pupil. The lack of consistent evidence in the literature on the impact of the elderly on spending may be due to the net effect being close to zero. These results suggest that there is little reason to be concerned about the inﬂuence of a graying population on support for better schools. School districts experiencing a growth in the fraction aged sixty-ﬁve and older have no need to prepare for a sizeable ensuing drop in school spending because the elderly have an almost imperceptible impact on school spending. Similarly, there is no reason to be concerned about children in elderly havens receiving an inferior education. We thank Steve Slutsky for stimulating discussions that led to this article. We have also beneﬁted from valuable comments from Burton Abrams, Eric Brunner, David Figlio, David Monk, Randy Reback, Kim Rueben, panel participants at the American Education Finance Association meetings and the Public Choice Society meetings, seminar participants at the University of Northern Illinois, and three anonymous referees. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . . f . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 311 INFLUENCE OF ELDERLY ON SCHOOL SPENDING REFERENCES Berkman, Michael B., and Eric Plutzer. 2004. Gray peril or loyal support? The effects of the elderly on education expenditures. Social Science Quarterly 85: 78–92. Black, Duncan. 958. The theory of committees and elections. Cambridge, UK: Cambridge University Press. Bowen, Howard R. 943. The interpretation of voting in the allocation of economic resources. 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American Economic Review 88: 35–20. U.S. Bureau of the Census. 2002. Current population reports, Series P-20, No. 542. Washington, DC: U.S. Government Printing Ofﬁce. U.S. Census Bureau. 990. Census of population and housing, summary tape ﬁles  and 3. Available factﬁnder.census.gov/servlet/BasicFactsServlet. Accessed 0 May 2006. U.S. Census Bureau. 992. Federal, state, and local governments: 992 public elementary- secondary education ﬁnance data. Available www.census.gov/govs/www/school92.html. Accessed  March 2006. U.S. Census Bureau. 2000. Census of population and housing, summary tape ﬁles  and 3. Available factﬁnder.census.gov/servlet/BasicFactsServlet. Accessed 0 May 2006. U.S. Census Bureau. 2002. Federal, state, and local governments: 2002 public elementary- secondary education ﬁnance data. Available www.census.gov/govs/www/school02.html. Accessed  March 2006. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . / f / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d . . . . . f f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 313 INFLUENCE OF ELDERLY ON SCHOOL SPENDING APPENDIX Table A.1. Spending regressions: Untrimmed Sample, 6,188 Observations from 3,124 Counties. Elderly and Non-elderly Equally Weighted Elderly Aligned with Poor Same Preferences Cross-State Migrants All Migrants MED HHD INCOME MED INCOME/MEAN INCOME FEDERAL REVENUE FRACTION 5–17 FRACTION URBAN HOMEOWNER DUMMY RELATIVE STATE INC SUPREME CT RULING SUPREME CT RULING × RELATIVE STATE INC 2000 DUMMY R2: Within Between Overall .075 (4.44) −3701 (3.87) .577 (7.74) −10639 (6.24) 93.3 (0.38) −366 (0.87) −2396 (3.02) −16.7 (0.24) −2307 (3.07) 1154 (14.0) .5924 .0431 .1404 .077 (4.52) −3823 (4.00) .577 (7.75) −10598 (6.22) 92.6 (0.38) −335 (0.87) −2455 (3.10) −16.6 (0.24) −2304 (3.07) 1147 (13.9) .5925 .0437 .1411 .077 (4.54) −3930 (4.10) .577 (7.75) −10551 (6.18) 91.9 (0.37) −335 (0.87) −2481 (3.13) −16.0 (0.23) −2293 (3.05) 1144 (13.9) .5925 .0438 .1415 All Elderly .090 (5.65) −4388 (5.62) .587 (7.93) −10432 (6.14) −20.4 (0.08) −367 (0.95) −2172 (3.32) −5.76 (0.08) −2227 (2.97) 1178 (18.3) .5942 .0485 .1489 F-statistic: Overall 443.80 444.01 444.11 447.28 F-statistic: Fixed effects = 0 σ (error) 5.80 1006.1 5.81 1005.9 5.81 5.93 1005.9 1003.8 Note: Absolute t-statistics are in parentheses. 314 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d f . . . . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 Deborah Fletcher and Lawrence W. Kenny Table A.2. Spending regressions: Untrimmed Sample, 6,188 Observations from 3,124 Counties. Elderly and Non-elderly Weighted by Voter Turnout Elderly Aligned with Poor Same Preferences Cross-State Migrants All Migrants MED HHD INCOME MED INCOME/MEAN INCOME FEDERAL REVENUE FRACTION 5–17 FRACTION URBAN HOMEOWNER DUMMY RELATIVE STATE INC SUPREME CT RULING SUPREME CT RULING × RELATIVE STATE INC 2000 DUMMY R2: Within Between Overall .075 (4.44) −3701 (3.87) .577 (7.74) −10639 (6.24) 93.3 (0.38) −366 (0.87) −2396 (3.02) −16.7 (0.24) −2307 (3.07) 1154 (14.0) .5924 .0431 .1404 .078 (4.53) −3999 (4.17) .576 (7.73) −10677 (6.28) 79.9 (0.32) −339 (0.88) −2465 (3.14) −15.2 (0.22) −2304 (3.07) 1150 (14.2) .5926 .0427 .1401 .078 (4.55) −4148 (4.32) .575 (7.72) −10623 (6.24) 78.7 (0.32) −339 (0.88) −2499 (3.19) −14.4 (0.21) −2291 (3.05) 1146 (14.2) .5926 .0427 .1405 All Elderly .088 (5.64) −4127 (5.65) .581 (7.88) −10698 (6.32) −39.1 (0.16) −384 (1.00) −1830 (2.96) −6.51 (0.09) −2253 (3.00) 1224 (21.0) .5943 .0440 .1435 F-statistic: Overall 443.80 444.17 444.32 447.29 F-statistic: Fixed effects = 0 σ (error) 5.80 1006.1 5.82 1005.8 5.82 6.00 1005.7 1003.7 Note: Absolute t-statistics are in parentheses. l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . f / / e d u e d p a r t i c e - p d l f / / / / / 3 3 2 8 3 1 6 8 9 0 8 7 e d p 2 0 0 8 3 3 2 8 3 p d f . . . . . f b y g u e s t t o n 0 7 S e p e m b e r 2 0 2 3 315 THE INFLUENCE OF THE ELDERLY image

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