Harris Evans Schwab 2001

Journal of Public Economics 81 (2001) 449–472www.elsevier.nl / locate /econbase

Education spending in an aging Americaa,b , b b*Amy Rehder Harris , William N. Evans , Robert M. Schwab

aCongressional Budget Office, 2nd and D Streets, S.W., Washington, DC 20515, USAbUniversity of Maryland, College Park, MD, USA

Received 30 December 1999; accepted 31 July 2000

Abstract

In this paper we use a national panel of public school districts to study the impact of anaging population on public education spending. In contrast to previous analyses that usestate-level data, we find that the elderly have only a modest overall negative effect oneducation spending at the district level. Our results confirm, however, that a growing shareof elderly at the state level tends to depress state spending on education. These results areconsistent with the hypothesis that the elderly believe only higher local spending iscapitalized into house values. 2001 Elsevier Science B.V. All rights reserved.

Keywords: Public education financing; Aging

JEL classification: I22; J14

1. Introduction

A number of important demographic trends — the post-war baby boom, thesubsequent baby bust, rising life expectancy — will have dramatic effects on theage distribution of the U.S. population well into the next century. In particular,America is growing much older. Today, less than 13 percent of the population isage 65 or older; by 2030, this number will increase to over 20 percent.

This graying of America will have significant consequences for the federal

*Corresponding author. Congressional Budget Office, 2nd and D Streets, S.W., Washington, DC20515, USA. Tel.: 11-202-226-5669; fax: 11-202-755-1085.

E-mail address: [email protected] (A.R. Harris).

0047-2727/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved.PI I : S0047-2727( 00 )00133-X

450 A.R. Harris et al. / Journal of Public Economics 81 (2001) 449 –472

government’s budget. The Social Security Board of Trustees predicts the OASDITrust Fund, with assets near $900 billion today, will be depleted by 2037;Medicare’s Hospital Insurance Trust Fund will run dry by 2025. The growingelderly population will strain state budgets as well. Many elderly, for example, areeligible for Medicaid, and the states are responsible for meeting roughly half thecost of this program.

Local governments may confront a different set of challenges. They face thevery real possibility that as the population grows older there will be less supportfor spending on public education, the major public program funded by localgovernments. The elderly may believe that families with school-age childrenreceive nearly all of the benefits from spending on public schools. As aconsequence, an aging population may push for a shift of public resources awayfrom education.

On the other hand, as Poterba (1998) argues, there are a number of reasons whythe elderly might continue to support public education. First, the elderly may hopeto improve the skills and productivity of younger workers in order to increasewages; these higher wages can then be taxed to help fund Social Security andMedicare. Second, the elderly may be altruistic. Third, elderly homeowners maybelieve that higher spending on education will be capitalized into the value of theirhomes. Fourth, even if an aging population’s demand for public education falls,Tiebout sorting by the elderly could leave education spending unchanged, simplyconcentrating the elderly in districts with low education spending. Finally, theelderly might believe that public schools socialize children, giving them anunderstanding of civic duties, social norms, and regular work habits that may

1reduce crime rates and increase economic activity.Most of the empirical work on this issue suggests that support for public

education spending among the elderly is weak. In a recent survey, respondentswere first presented with various public policies to improve schools, such assmaller class sizes or higher teacher salaries, and then the respondents were askedwhat amount of additional taxes they would support to fund such policies: $500,$200, $100, less than $100, or none. Among all respondents, 55 percent werewilling to pay an additional $500; among those 65 or older, only 36 percent were

2willing to pay an additional $500. Using survey data from Massachusetts, Ladd

1Field (1979) argues that the socialization view of public education existed during the mid-nineteenth century development of the modern American public education system in Massachusetts. Heshows it was the elite members of society who supported longer school years during the early stages ofthe Industrial Revolution. He claims the elite class believed public schools would socialize childrenfrom the lower classes to obey the law and would teach these children punctuality and discipline inpreparation for their lives as factory workers.

2We thank John Benson, Deputy Director for Public Opinion and Health /Social Policy at theHarvard School of Public Health, for providing us with the numbers for elderly respondents to theNPR/Kaiser /Kennedy School Education Survey. Numbers for all respondents were taken from theNational Public Radio web page (1999). The random telephone survey of 1422 adults nationwide wasconducted between June 25 and July 19, 1999.

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and Wilson (1983) found that households where the head was at least 60 years oldwere more likely to have supported the property tax limitation proposition passedin 1980. Button (1992) looked at voting in school bond elections in six Floridacounties during the 1987–1989 period. He found that the share of voters 55 orolder had a negative effect on the school bonds’ success rates. Miller (1996)studied education expenditures for a panel of 48 states in 1960, 1970, 1980 and1990, along with a panel of Texas counties in 1970 and 1980. Regressing per-adulteducation expenditures on the share of the voting-age population aged 65 and over,she found negative coefficients on the elderly share for both sets of data, althoughthese coefficients were statistically insignificant in most specifications.

Poterba (1997) presents some recent evidence on this question. Using a panel ofstate-level data from 1961, 1971, 1981 and 1991, Poterba regressed per-childeducation spending on the percent of the population aged 65 and over. Aftercontrolling for other basic demographic characteristics plus state and year effects,Poterba found that a growing elderly population lowered education spending. Heestimated that the elasticity of per-child education spending with respect to thepopulation share aged 65 and over was approximately 2 0.25. In another equation,he used non-education spending per capita as the dependent variable and found apositive and statistically significant coefficient on the elderly share, showing thatthe elderly do not want lower public spending in general, only lower publicspending on education.

Ladd and Murray (1999), however, come to a very different conclusion. Theypresent results which suggest that state-level data may overstate the effect of theelderly on reducing support for public education. Using a national panel ofcounty-level data for 1972, 1982 and 1992, they run a county-fixed effects modelwhich closely parallels Poterba’s (1997) state-level model and find no statisticallysignificant effects of the population share aged 65 and older.

Our goal in this paper is to try to reconcile the Poterba and Ladd and Murrayresults about the effects of an aging population on public education spending. Wehave matched school district finance data for 1972, 1982 and 1992 to demographicdata, including the age distribution, collected in 1970, 1980 and 1990. Using thispanel data set, we are able to address this research question at the school districtlevel. We regress total revenues per pupil on the share of the school districtpopulation aged 65 and older in a model with district fixed effects and year-specific state effects. Our district-level data show that the elderly do have anegative effect on education spending. The estimated impact, however, is muchsmaller than earlier state-level estimates. Our single-equation estimates suggestthat the elasticity of total revenues per pupil with respect to a district’s populationshare aged 65 and older is 2 0.096, about 40 percent of Poterba’s estimate.

We also find evidence that the elderly are much less willing to support statespending on schools than local spending, and that it is this distinction thataccounts for the differences between Poterba (1997) on the one hand and Ladd andMurray (1999) and this paper on the other. This pattern is consistent with thehypothesis that the elderly believe higher local spending on schools will be


capitalized into higher property values. In studies based on district-level data,variation in education spending is dominated by variation in local spending(assuming that state fixed effects have eliminated between-state differences ineducation expenditures). The elderly’s support for local spending then leads tosmaller estimated effects of the elderly in studies based on district-level data thanstudies based on state-level data.

The remainder of the paper has the following organization. Section 2 discussesthe potential benefits and costs of moving to district-level data to address ourquestion. Section 3 discusses the data and econometric specification used in ourstudy. We present our results in Section 4, starting with a comparison of ourstate-level results to Poterba’s, and then turning to the district-level results. Wepresent both OLS and instrumental variables models and then attempt to explainthe large differences between the observed effects from the elderly at the state anddistrict level. Summary and conclusions are presented in the final section.

2. The consequences of using district-level data

There is a strong case to be made that states are not the appropriate level ofanalysis to study the impact of the elderly on education. There are roughly 15,000local school districts in the U.S. These local districts and the state governmentseach provide a little less than half of the funding for public education. Thus ananalysis such as Poterba (1997) that focuses on the sum of state spending and localspending aggregated to the state level cannot fully capture the way educationspending decisions in the U.S. are made.

Implicitly, the argument in favor of using district-level data assumes that thereis significant within-state variation in school spending and in the age distributionof the population. If this were not the case, then little would be gained fromlooking at districts rather than states. In this section we offer some evidence thatthis within-state variation is in fact large.

2.1. The good news

Table 1 demonstrates the variation in total revenues per pupil between districtswithin states across all levels of state support. In this table, we present information

3for four states: New Hampshire, Iowa, Georgia, and New Mexico. For the1991–92 school year, New Hampshire had the lowest level of state support, NewMexico the highest. Iowa and Georgia received state support at levels just abovethe national average of 46.4 percent. Comparing columns (4) and (5) we see that

3Concerned about errors in the data, we removed about 2 percent of observations with revenues perpupil greater than 150 percent of the 95th revenue percentile for each state in each data year, or lessthan 50 percent of the 5th revenue percentile for each state /year.

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Table 1aVariation in total revenues per pupil at the district level for various states

Percent of total revenues raised locally

(1) (2) (3) District-level: 1992

State funding State-level: Number of total revenues per pupil (6) (7)

percent for 1992 total districts in Districts in top 10 Districts in bottom

1991–92 revenues the balanced (4) (5) percent of total 10 percent of total

State school year per pupil panel Maximum Minimum revenues per pupil revenues per pupil

New Hampshire 8.5 $6038 83 $9988 $4151 96 77

Iowa 47.3 $5052 406 $10,599 $2981 58 47

Georgia 47.7 $4513 178 $7197 $2999 51 21

New Mexico 73.8 $4267 66 $7948 $3427 15 11

a State funding percents for the 1991–92 school year are taken from Table 156, Digest of Education Statistics, 1995, p. 153. All other information is based onauthors’ calculations.


each state’s highest-spending district collects over twice the revenues per pupil asthe lowest-spending district. The high-spending districts appear to rely on localsources for the additional dollars as shown in columns (6) and (7), a demonstra-tion of how local decisions can influence education spending.

State-level data also conceal within-state variation in the distribution of theelderly. In Fig. 1, we report the county-level change between 1970 and 1990 in theshare of the population aged 65 and over for three states: Texas, Florida and

4Washington. We focus on changes in the elderly share because, like Poterba(1997), we will use fixed-effect models that examine the time-path of spending ina district as the elderly population changes. We picked these three states because ofthe wide differences in state-level aging: Texas experienced only a 1 percentagepoint increase in the number of people age 65 and older over the two decades,Washington had a 2.4 percentage point increase, and Florida, the state most oftenthought of in connection with a rising elderly population, had a 3.8 percentage

5point increase. In the figure, we indicate where each county’s growth falls within6the national distribution of counties.

Fig. 1 demonstrates the considerable heterogeneity in the county-level growth inthe elderly population share. The maps show that all states have counties in eachquartile of the county distribution of changes in elderly concentration. The figurealso demonstrates how state-level data can conceal aging; while Texas was agingslowly in the aggregate many Texas counties experienced increases in elderlyconcentration over four times the state-wide average.

2.2. . . . and the bad news

Using district-level data also has drawbacks. The Tiebout (1956) hypothesissuggests that given a full spectrum of local communities offering differenttax-expenditure bundles, individuals choose to live in the community best suited totheir tastes and budgets. As Poterba (1998) explains, if the elderly ‘‘vote with theirfeet’’ in the manner Tiebout describes, then we might expect the elderly to movefrom high- to low-spending school districts. This type of migration suggests thatthe age distribution of a school district is itself a function of a district’s spending.Because a particular characteristic — the size of the elderly population — is

4For the state of Florida, school districts boundaries coincide with the counties. For Washington andTexas, school districts are much smaller than counties; Washington had 39 counties and 293 schooldistricts in 1990, Texas had 254 counties and 1052 school districts.

5During the 1970–1990 period, the average percentage point increase in elderly share at the statelevel was 2.8, with changes ranging from 0.7 to 4.7. These three states also differ in the level of thepopulation share of elderly. In 1990 these shares for Texas, Washington and Florida were 10.1, 11.8 and18.2 percent, respectively.

6To provide a frame of reference, at the national level, counties with the 25th, 50th and 75thpercentile largest change in the share of elderly between 1970 and 1990 saw their elderly populationshares grow by 1.6, 3.0 and 4.4 percentage points, respectively.


Fig. 1. Change in elderly concentrations by county for selected states 1970 to 1990.


correlated with the unobservable determinants of the dependent variable —education spending — ordinary least-squares results are likely to overstate the

7negative effect of the elderly on public education.We address this potential bias from Tiebout sorting by estimating an instrumen-

tal variables model. As we discuss below, we instrument for the districts’population share aged 65 and older with an historical measure of the elderly, theshare aged 55 to 64 ten years earlier in the school district’s county.

3. Data and econometric specification

The goal of this paper is to estimate a model similar to Poterba’s but withdistrict-level data. In our case, data will vary across districts and over time and theestimation procedure is designed to exploit the panel nature of the data. Thedependent variable in our district-level models is the log of total revenues perpupil for district i in state j at time t. The basic model is

Log(Total Revenues Per Pupil ) 5 X b 1 (P651 )u 1 d 1 S 1 ´ ,ijt ijt ijt ij jt ijt

where the key independent variable P651 is the share of the population in adistrict that is 65 and older. We want to control for other observed characteristicsthat are correlated with expenditures. We include three types of control variables.First, in the vector X , we include basic demographic, economic and financialijt

variables that vary within a district over time. The vector X includes variablesijt

such as the racial and ethnic composition of a district, measures of householdincome and poverty, and constraints on revenues generated by recent state courtcases. Second, d are district fixed effects that are meant to capture those factorsij

that vary across districts but are permanent over time. Third, since half of schoolrevenues come from state governments, we want to control for state-specificshocks that can alter spending. We therefore include year-specific state effects S .jt

The final term in the equation, ´ , is a zero mean, constant variance, error term.ijt

The inclusion of district fixed-effects means that we are using a within-groupmodel to estimate the parameter u. Specifically, we examine how revenues perpupil change as the distribution of elderly in a district changes over time, absentthe natural trends in these variables within a state. In theory, this model can beestimated with only two observations per district. In practice, the elderly sharedoes not change much from year to year, so in order to guarantee enough samplevariation in the covariate of interest, we need observations that span a number ofyears. Thus we need a district-level panel data set that covers a long time period

7The same type of migration among families with young children could also bias the coefficient onthe elderly population share. If parents with young children move to high-spending school districts, butthe elderly are not mobile, this will by construction dilute the elderly concentration. If the higherfraction of families with children can sustain high spending levels, then the elderly share and educationspending would again be negatively correlated.


and has detailed information about education finance and the characteristics ofpeople who live within school district boundaries.

There is no readily available source of information that meets all of thesecriteria. We did, however, construct just such a data set by merging six nationalschool districts data sets: the 1970 Census of Population and Housing SpecialFifth-Count Tallies, the 1980 Census of Population and Housing Summary TapeFile 3F, the 1990 Census School District Special Tabulation, School District Data

8Book, and the 1972, 1982, and 1992 Census of Governments: School Districts.The first three data sets provide detailed information about the demographiccharacteristics of school districts, while the Census of Governments is the primaryhistorical source of school-finance data. By merging these sources, we construct a

9national panel of public school districts for 1972, 1982 and 1992.Constructing the analysis file required us to merge district-level demographic

and finance data and then link districts over time. Merges were complicated by thefact that the data sets containing demographic information used the NationalCenter of Education Statistics (NCES) code to identify school districts, whereasthe Census of Governments used a different identification code. Fortunately, in1982 and 1992 the Census of Governments also reports the NCES codes whichallowed most observations to be linked within a year and across time. Linkingobservations across time was complicated by a small number of district mergersand changes in NCES codes. When districts merged, we constructed ‘synthetic’observations by combining information from the individual districts before themerger. When codes changed over time, we matched observations by school namesand addresses.

Our final sample is a ‘balanced panel’ that contains all districts for which wehave demographic and financial data for all 3 years. This sample consists of10,753 of the roughly 15,000 elementary, secondary and unified (K-12) schooldistricts in the 48 continental states and the District of Columbia. We lose districtobservations from the panel for three reasons. First, the 1972 demographic dataprovides individual school district records only for districts with populationsgreater than 1000. We estimate that there are roughly 3800 districts in 1972 that

10are eliminated because of this sample restriction. We lost approximately 780

8Caroline Hoxby (1996) was the first to merge these data sets together to create a national panel ofpublic school districts.

9For a complete discussion of the construction of the data used in this research please refer to AmyRehder Harris, ‘Data Chapter: The Construction of a National Public School District Panel’, Universityof Maryland, College Park, November 1999, which is accessible online at www.bsos.umd.edu/econ/evans /wrkpap.htm.

10Out of concern that the loss of the small, rural districts may change the results, we created a panelusing just the 1982 and 1992 data which allowed us to keep an additional 3085 districts. Theseadditional districts had mean enrollments in 1982 of 280 students, and mean enrollments in 1992 of 322students. The OLS coefficient on the elderly variable for this panel is of smaller magnitude than theresults presented below for the 3 year panel of 10,753 districts. We found this drop mostly reflects theloss of the 1972 data year, however, rather than the addition of the small districts.


districts because we were unable to match districts to financial data in a particularyear and we lost approximately 200 districts when we eliminated observationswith implausibly high or low values for a financial or demographic variable.Despite having only two-thirds of all districts in our balanced panel, we have datafor roughly 94 percent of all public school students in the nation.

Some of the demographic variables we use in our analysis are the district-levelequivalents of the state-level variables in Poterba (1997). In those cases, we usedefinitions that parallel Poterba’s as closely as possible. Some differences,however, were unavoidable. For example, a number of the demographic charac-teristics at the district level that are measured as percents (such as the fraction pooror the fraction nonwhite) have a value of zero in some districts. As a result, all ofour models are linear in variables that are measured as percents. Thus while thekey independent variable in Poterba’s work is the log of the population share aged65 and over, in our district-level models it is the level of the population share aged65 and over. Our data set includes median household income and the percent ofhousing units that are owner-occupied; Poterba’s data set includes per capitaincome and the percent of the population that own homes. He uses spending perchild as his dependent variable rather than spending per pupil because he isconcerned that private school enrollment is a function of public school spending.Although this concern remains at the district level, we use a per-pupil measure ofeducation resources because of data restrictions. Recall that our data come fromtwo separate sources: the decennial censuses and the Census of Governments.Both sources contain public school enrollment numbers, but only the demographicdata contain population counts. To construct total revenues per child, it isnecessary to take the denominator from the former data set and the numerator fromthe latter. We prefer not to use two different data sources to construct ourdependent variable, and so we use the enrollment variable in the financial data toconstruct total revenues per pupil.

Poterba includes the share of the population 5 to 17 years old as an independentvariable. This variable is available in the first 2 years of our panel, but it is notavailable in the 1990 demographic data. Consequently, for all years, we use the

11fraction of children aged 0 to 19. It is important to include some measure of thenumber of students in these models. Hanushek and Rivkin (1997) note thatbetween 1970 and 1990 — the period covered by our data — the studentpopulation dropped by five million and per-pupil education spending rose.Hanushek and Rivkin note this was also a period of tight public budgets and claimper-pupil spending rose only because of the drop in the number of students.

We have also included several control variables that were not included inPoterba’s state-level model. We include measures of human capital: the percent ofthe district population aged 25 and older who are high school dropouts, high

11Both the 0 to 19 and 5 to 17 population shares are available in the first 2 years of our sample; thecorrelation between them at the district level is 0.87 in 1970 and 0.86 in 1980.


school graduates, or have some college education (with college graduates theomitted category). These variables, along with the log of district population,capture some of the heterogeneity among districts which may explain preferencesfor school spending. The panel does not contain any measure of a tax price for thedistricts.

The landmark 1971 Serrano case in California was the first successful courtcase to challenge the constitutionality of state school finance systems. By 1998,supreme courts in 43 states had heard similar cases. These court cases are based inpart on the argument that local funding for education is unconstitutional since itrelies on local property values and the resulting property tax revenues. Schoolfinance systems in 10 states were ruled unconstitutional between 1971 and 1992 onthe grounds that students living in districts with low property wealth do not receiveequal or adequate funding for their education as guaranteed by most state

12constitutions. Each of these states was forced to revamp their school financesystem. Evans et al. (1997) show that court-ordered school finance reform hadvery different effects on poor and wealthy school districts. To account for thedifferential effect of the court-ordered reforms we interact an indicator for acourt-ordered reform with the within-state quintile ranking of district real median

13household income for 1970. We expect a successful court challenge to raisespending more in poor districts than in wealthy districts.

Table 2 presents weighted summary statistics for the balanced panel of schooldistricts. In all of our district-level models, we weight observations by publicschool district enrollment. In essence, this means that we are focusing on theimpact of the growing elderly population on an individual student rather than theimpact of the elderly on average district spending. Throughout the paper, allmonetary variables are given in constant 1992 dollars. Over this 20-year period,the average student attended a school in a district that received $4174 per pupil inrevenues from all levels of government. State governments and local governmentseach contributed roughly one-half of those funds.

As we noted above, we have included district fixed effects and year-specificstate effects in our econometric model. By including the year-specific state effects,

12The 10 states and years of their successful court cases are California, 1971; New Jersey, 1973;Connecticut, 1977; Washington, 1978; West Virginia, 1979; Wyoming, 1980; Arkansas, 1983;Kentucky, Montana, and Texas, 1989 (Minorini and Sugarman, 1999). Table 1 in Murray et al. (1998)lists these 10 cases along with two 1976 cases in Kansas and Wisconsin. Running the model with theadditional two states slightly increased the magnitude of the coefficient on the elderly share. We alsoran the model with the effective date of court reform for California changed to 1976, the date of thesecond, more binding Serrano decision; the magnitude of the elderly coefficient decreased slightly.

13We chose to use real median household income in 1970 rather than local revenues per pupil in1972 as the measure of pre-reform district wealth since the latter is one component of the left-hand sidevariable, total revenues per pupil. The correlation between the two wealth measures is 0.56.


Table 2aSummary statistics for the national public school district panel

Variable Mean Standard deviation

Total revenues per pupil $4174 1511Local revenues per pupil $2135 1401State revenues per pupil $1994 1017Median household income $35,468 10,645Population share aged 651 0.108 0.043Population share aged 0 to 19 0.338 0.059Percent of housing units owner-occupied 0.661 0.147Percent of population nonwhite 0.197 0.205Percent of population below the poverty line 0.130 0.082Population share aged 251 dropouts 0.359 0.154Population share aged 251 high school graduates 0.322 0.074Population share aged 251 with some college 0.169 0.079Population share aged 251 college graduates 0.151 0.093Percent of population in urban areas 0.718 0.353

a All dollar values are in real 1992 dollars. The sample consists of 10,753 districts for a total of32,259 observations. District enrollments were used as weights in all district-level calculations.

we focus solely on within-state variation in our dependent and independentvariables. This has some important implications for the estimation. Within-statevariation in local spending is much larger than within-state variation in statespending. Consider, for example, the middle year of our sample period, 1982. Wecalculated the ratio of within-state variation in district local revenues per pupil todistrict state revenues per pupil for each of the 50 states. The median of this ratiowas 2.6 and the mean was 3.6. In some states the ratio was very large: 8.7 in NewYork, 8.8 in Tennessee, 11.2 in Nebraska, 16.4 in New Hampshire, and 16.9 inVirginia. As a consequence, in our model, variation in total revenues per pupil to afirst approximation represents variation in local revenues. We consider theimplications of this result below.

4. The elderly and education spending

4.1. State-level results

Our data sources and sample period are different from Poterba’s, and so it isimportant to know if we can replicate his results with our data set. We begin byaggregating our district-level data to the state level and then estimating modelscomparable to those in Poterba (1997). In our state-level data set we include all


14district /year observations that were matched with revenue data. We have tried to15follow Poterba’s model as closely as possible. Because the district data contain

only median household income, we augmented the data with state per capita16income in the relevant 3 years. Our data contain two measures of education

resources, revenues and expenditures, where the main difference is the exclusionof capital outlays from the latter. We chose to use total government revenues in thecalculation of our dependent variable since we believe it more closely approxi-

17mates Poterba’s spending measure, which also includes capital outlays. Themeans of most of the variables in our state-level data and Poterba’s data are quiteclose; the means of per capita income and per-child education resources in our

18data are higher, reflecting Poterba’s inclusion of 1961.Poterba regressed the log of total spending per child on a set of demographic

covariates, state effects, and year fixed effects. Column (1) of Table 3 presents

14Recall that the 1970 demographic data does not provide individual observations for small schooldistricts with populations less than 1000. Thirty-nine states report small districts, where thedemographic data for these districts is aggregated into one observation per state. The documentationsuggests all the small districts had enrollments of less than 300 students in 1970. We include the smalldistricts into the state-level analysis by first aggregating, by state, financial data for previouslyunmatched small school districts in the 1972 Census of Governments, those with enrollments less than325. Second we matched the small district financial data to the aggregated demographic data for the 39states. Finally, the small district demographic and financial data were included with the rest of thedistrict data in aggregating the panel to the state level.

15As noted above, the 1990 data does not contain a count of children aged 5 to 17, it contains only5-year age groupings. For our state-level data, we estimated the count of children aged 5 to 17 for thatyear by adding the count aged 5 to 14 to three-fifths of the count aged 15 to 19. To calculate the statepercent of population owning homes, we multiplied the district percent of housing units owner-occupied by the district population to get a proxy of the number in the district who owned homes,summed the district numbers by state, then divided by the state population. Since the district-level datareports federal aid funneled through the state as state revenues, our measure of federal revenues percapita is not directly comparable to Poterba’s federal aid per capita variable.

16The income data were taken from various years of the Statistical Abstract of the United States.17Poterba’s finance data comes from various issues of the U.S. Census Bureau’s Government

Finances. Education expenditures on elementary and secondary education, as reported in thispublication, include all expenditures of school systems other than for interest, duplicative inter-governmental payments, and retirement benefits paid to former education employees. Results for ouraggregated state data on total expenditures per pupil, which include expenditures of the school systemsother than for interest, capital outlays, and payments to other school systems, were not significantlydifferent from zero.

18Mean per-child spending in Poterba’s data is $3058. Mean per-child revenues in our stateaggregated data are $3430 (mean per-pupil revenues are logically higher at $4096). Revenues per childin 1961 were 55 percent of revenues per child in 1971. If we proxy mean state per-child revenues forour missing decade with 55 percent of the 1972 per-child revenues reported in our aggregated data, theaverage of the 1972, 1982 and 1992 numbers along with the 1962 proxy drops to $2933, closer toPoterba’s mean for the same four decade span. Ladd and Murray (1999) used Poterba’s data to run hisstate model using only the last three decades 1971, 1981 and 1991. They find that his results areunchanged, suggesting that our missing the first decade of data does not drive the different results wefind at the local level.


Table 3aEstimates of state-level models, Poterba (1997) and the current sample

parameter estimates (standard errors) [elasticities]

Poterba (1997) Current sample aggregated to state-level, 1972/82/92log–log model semi-log model

(1) (2) (3) (4)Log(Total Log(Total Log(State Log(Local

Independent variable spending/child) revenues /pupil) revenues /pupil) revenues /pupil)

Log(Population share aged 20.264 – – –651) (0.121)

Log(Population share aged 20.986 – – –5 to 17) (0.212)

Log(Percent of population 0.646 – – –owning homes) (0.240)

Log(Percent of population 0.033 – – –nonwhite) (0.038)

Log(Percent of population 20.094 – – –below the poverty line) (0.080)

Population share aged 651 – 22.333 24.576 0.184(1.628) (3.417) (2.994)

[20.261] [20.513] [20.021]Population share aged – 24.431 23.201 25.4375 to 17 (1.325) (2.781) (2.436)

[20.988] [20.714] [21.212]Percent of population – 0.469 20.758 0.972owning homes (0.680) (1.427) (1.250)

[0.314] [20.508] [0.651]Percent of population – 20.676 20.390 21.792nonwhite (0.489) (1.026) (0.899)

[20.103] [20.060] [20.274]Percent of population – 20.357 0.975 20.013below the poverty line (0.689) (1.447) (1.268)

[20.048] [0.131] [20.002]Log(Per capita income) 0.528 0.788 1.015 1.250

(0.192) (0.296) (0.622) (0.545)Log(Federal revenues 0.037 20.011 20.031 20.013per capita) (0.023) (0.014) (0.028) (0.025)

2Adjusted R 0.954 0.928 0.917 0.949a Both samples consist of the 48 continental United States. All models include state and year effects.

Poterba’s results are taken from the fourth column of his Table 3 on p. 57 (1997).

results from his analysis. In this model, all covariates are in log form socoefficients can be interpreted as elasticities. The key result is the large negativeeffect of the elderly on education spending. Poterba’s estimated elasticity ofspending with respect to the proportion of the population 65 and older is 20.264and is statistically significant. In column (2) we present a semi-log version ofPoterba’s model estimated on our district-level data aggregated to the state level.


At sample means, our estimate of the elasticity of school spending with respect tothe proportion of the population 65 and older is 20.261, nearly identical toPoterba’s estimate. Our estimate, however, is statistically significant only at the 10percent level. Our standard error is larger in part because we have one less year ofdata and thus 48 fewer observations. In all, when our data is aggregated to thestate level, we can produce estimates that are qualitatively similar to those inPoterba’s work.

We found that the elderly have very different effects on state revenues and localrevenues. The dependent variable in column (3) is the log of state revenues perpupil and the dependent variable in column (4) is the log of local revenues perpupil; in all other respects these models are the same as the model in column (2).We have estimated that the elasticity of state revenues with respect to the elderly is20.513, but that the elasticity of local revenues with respect to the elderly isessentially zero, though estimates are imprecise. Apparently, the elderly have verydifferent concerns about state support for schools as opposed to local support forschools. We will return to these estimates when we interpret our district-levelresults.

4.2. District-level models

We begin the analysis of our district-level data by estimating a model thatclosely parallels the specification of Poterba’s state-level model. In model (1) weinclude at the district level the covariates employed by Poterba, plus district andyear effects. The results for this exercise are reported in the first column of Table4. The estimate (standard error) of the coefficient on the population share aged 65and older is 20.366 (0.084). The implied elasticity, estimated at sample meansand reported in brackets, is just 20.04, one-sixth the value of the elasticityreported by Poterba. In this case, changing the level of aggregation appears to haveimportant consequences.

We then estimate the model outlined in Section 3. Model (2) includes additionalcovariates plus year-specific state effects in place of the year effects. The estimatesof this model are presented in the second column of Table 4. Here again, we findthat an increase in the population share aged 65 and over has a negative andstatistically significant impact on school spending, but the magnitude of that effectis much smaller than in Poterba’s work. The estimated coefficient (standard error)of 20.886 (0.082) produces an implied elasticity of 20.096, a value 40 percent ofthe size of Poterba’s estimate of 20.264.

The estimates from this expanded model also suggest that court-ordered schoolfinance reform has achieved its intended goals. Successful litigation raisesspending in the lowest income district by 14.4 percent, raises spending inlower-middle and middle income districts (districts in the second and thirdquintiles) by 11.3 to 11.8 percent and raises spending in the upper-middle incomedistricts by 7.3 percent. These results are consistent with Murray et al. (1998), who


Table 4aEstimates of district-level models, parameter estimates (standard errors) [elasticities]

Dependent variable

Log(Total Log(Total Log(Localrevenues /pupil) revenues /pupil) revenues /pupil)

Independent variable Model (1) Model (2) Model (3)

Population share aged 651 20.366 20.886 20.635(0.084) (0.077) (0.138)

[20.040] [20.096] [20.069]Population share aged 0 to 19 20.848 20.907 22.831

(0.064) (0.060) (0.108)[20.286] [20.307] [20.957]

Percent of housing units 0.043 20.023 20.375owner-occupied (0.029) (0.028) (0.051)

[0.028] [20.015] [20.248]Percent of population nonwhite 0.105 20.009 20.420

(0.021) (0.021) (0.039)[0.021] [20.002] [20.083]

Percent of population below 20.433 0.172 20.247the poverty line (0.046) (0.047) (0.084)

[20.056] [0.022] [20.032]Log(Median household income) 0.003 0.007 0.364

(0.014) (0.016) (0.028)Log(Federal revenues per capita) 0.017 0.023 0.015

(0.001) (0.001) (0.002)Population share aged 251, – 0.099 20.745dropouts (0.047) (0.084)

Population share aged 251, – 20.082 20.991high school graduates (0.037) (0.067)

Population share aged 251, – 20.154 20.791some college (0.058) (0.104)

Log(State revenues /pupil) – – 20.118(0.005)

Log(District population) – 20.049 20.054(0.006) (0.010)

Overturned*Lowest quintile in 1970 – 0.144 20.069median family income (0.011) (0.020)

Overturned*Second quintile in 1970 – 0.118 0.000median family income (0.012) (0.022)

Overturned*Third quintile in 1970 – 0.113 0.063median family income (0.011) (0.019)

Overturned*Fourth quintile in 1970 – 0.073 0.051median family income (0.009) (0.017)

Includes year-specific state effects? No Yes Yes2Adjusted R 0.825 0.878 0.881

a The sample consists of a balanced panel of 10,753 school districts located in the 48 continentalUnited States and the District of Columbia for the years 1972, 1982 and 1992. Model (1) includesdistrict and year effects. Models (2) and (3) include district fixed effects but replace year effects withyear-specific state effects. Observations are weighted by district enrollments.


found that court-ordered reform reduces inequality by raising spending in mostdistricts, but raising spending much more in the poorest districts.

We have looked at a number of alternative specifications of this model. Theresults are similar to the results in Table 4. In one version we included aninteraction of the elderly share and the percent of housing units owner-occupied.As noted in the Introduction, elderly homeowners might support higher schoolspending if they believe improved school quality will be capitalized into housevalues. Again, we found that increases in the elderly population lower schoolspending, with a coefficient on the elderly share of 21.761 (0.248). However, thecoefficient on the interaction of the elderly and home ownership variables is 1.221(0.328), offering support for the view that capitalization moderates the elderly’sdislike for public education spending.

We have also used a variant of our model to explain local revenues per pupil, asopposed to total revenues per pupil. Local spending for education depends in parton state spending. It is well understood in the fiscal federalism literature, however,that it is incorrect to treat state spending as an exogenous variable in a model thatestimates the determinants of local spending. State spending is an endogenousvariable for at least two reasons. First, many states use matching grants, such aspower equalization grants, and so higher local spending can lead to higher statespending. Second, state spending is often redistributive (see Evans et al., 1997)and so lower local spending can lead to higher state spending. A proper treatmentof this endogeneity problem would require detailed information about the structureof state aid. We do not have that information and so in model (3) we treat the logof state revenues per pupil as exogenous. As a consequence, our estimates of thedeterminants of local spending should be interpreted cautiously.

We present our local spending model in the final column of Table 4. We findthat local education spending is less sensitive to the number of elderly in a schooldistrict than is total spending. Our estimate of the elasticity of local revenues perpupil with respect to the share of the population 65 and older is 20.069, nearly 30percent smaller than our estimate of the elasticity of total revenues. We considerthe implications of this result below.

Table 5 reports the elderly coefficient of model (2) from Table 4 and the elderlycoefficient from the same model run on various subsamples of districts. It ispossible that the growing elderly population had a larger impact on schoolspending in urban districts or districts in a particular region. The estimated revenueelasticities with respect to the elderly range from 20.048 to 20.173. Poterba(1997) also presents the predicted percentage drop in per-child spending suggestedby his data. He notes that a one standard deviation increase over the mean stateelderly share for his panel, which is a 20 percent increase from 10.8 to 13 percent,would lead to a 5 percent drop in spending per child. For comparison, we presentthe predicted percentage changes in revenues per pupil resulting from a 20 percentincrease in the district elderly share over the weighted district mean for the fullpanel and various subsamples. These percentage changes range from 20.95 to


Table 5aEstimates of district-level model (2) for various subsamples

Predicted change inrevenues per pupil froma 20 percent increase in

Coefficient fraction of elderly(standard error)

Number on population Percentage DollarSample of districts share aged 651 Elasticity change change

Balanced panel 10,753 20.886 (0.077) 20.096 21.91 80Unified districts 9120 20.893 (0.083) 20.097 21.95 80Districts in MSAs 4496 21.220 (0.120) 20.122 22.44 106Northeast region 2323 20.578 (0.152) 20.068 21.35 73Midwest region 4442 20.658 (0.114) 20.073 21.46 59South region 2555 20.445 (0.169) 20.048 20.95 34West region 1433 21.842 (0.219) 20.173 23.46 140

a All regressions include district and year-specific state fixed effects. Other covariates include thoselisted in Table 4, model (2). Observations are weighted by district enrollments.

23.46 percent, and thus in all cases our district-level predictions are well belowPoterba’s predicted 5 percent decline. We also calculated the per-pupil dollarchange associated with each predicted percentage change; the predicted dollarchanges vary from $34 to $140 in revenues collected per student.

4.3. Tiebout sorting

It is possible that single-equation models that treat the elderly (or school-aged)population as exogenous may yield biased estimates. The elderly would beexpected to move to districts where spending is low, and thus the elderlypopulation variable could be negatively correlated with the error term. A similarargument can be made for school-aged children if their parents move to high-spending districts. Likewise, it is possible a mechanical relationship exists betweenschool spending and the fraction of school-aged children that can bias results.Holding the number of elderly constant, in-migration of families will byconstruction lower the fraction of the elderly.

We address the possible bias generated by Tiebout sorting by estimatingdistrict-level models using instrumental variables. We instrument for both thedistricts’s population 65 and older and those 0 to 19 with the share aged 55 to 64

19and the share aged 10 to 54 ten years earlier in the school district’s county. Theelderly instrument, the historical share aged 55 to 64, represents those countyresidents who age into the 65 and older category during the ensuing decade,

19County age distributions come from the Net Migration of the Population by Age, Sex, and Race,1950 –1970 (Bowles et al., 1975), and the Net Migrations of the Population of the United States byAge, Race, and Sex, 1970 –1980 (White et al., 1987).


removing those who move into or out of the county during that time, i.e. itremoves those whose preference changes have led them to choose a new location.The second instrument represents the historical share of the omitted age group,which we use since it is not possible to get a historical share for the youngestgroup, many of whom were born during the previous 10 years. The share aged 55to 64 ten years earlier should be positively related to the share elderly today whilethe historical share aged 10 to 54 should be negatively related. Similarly, both ofthe historical population shares should be negatively related with current fractionof children aged 0 to 19.

There are at least two drawbacks to these instruments. First, we assumeimplicitly that conditional on knowing an individual’s location today, knowingtheir residence 10 years ago provides no information about their willingness tosupport local education. For example, if people who are 55 years old choose acommunity where education spending is low for exactly the same reasons peoplewho are 65 years old choose low spending communities, then this instrument isnot valid.

Second, we must use county data rather than school district data since nationalschool district demographic information is not available prior to 1970. One-thirdof counties have only one school district. For the other two-thirds, our instrumentscannot account for moves between the two or more districts within those counties.Using 1980 PUMS data we can get a sense of how mobile the elderly were during

Table 6aInstrumental variable estimates of district-level model (2) parameter estimates (standard errors)

[elasticity]

Dependent variable

(1) (2) (3) (4)Population Population share Log(Total Log(Totalshare aged 651 aged 0 to 19 revenues /pupil) revenues /pupil)

Covariate OLS OLS OLS IV

County population share aged 0.540 20.760 – –55 to 64 ten years prior (0.013) (0.017) – –

County population share aged 20.080 20.429 – –10 to 54 ten years prior (0.007) (0.009) – –

Population share aged 651 – – 20.886 20.817(0.077) (0.203)

[20.096] [20.088]Population share aged 0 to 19 – – 20.907 21.465

(0.060) (0.155)[20.307] [20.495]

2Adjusted R 0.922 0.932 0.878 0.877a The sample consists of a balanced panel of 10,753 school districts located in the 48 continental

United States and the District of Columbia for the years 1972, 1982 and 1992. All regressions includedistrict and year-specific state fixed effects. Other covariates include those listed in Table 4, model (2).Observations are weighted by district enrollments.


our sample period. Mobility is highest for people in their early twenties; nearly 80percent of this group moved at least once in the 5-year period from 1975 to 1980.Mobility is much lower among the elderly; just 22 percent of those aged 60 to 75and just 25 percent of those over age 75 moved between 1975 and 1980. Themobility early in the life-cycle is associated with the job search. Although themobility rate for the elderly is lower than most of the rest of the population, justover half of the moves the elderly make are within-county moves. As aconsequence, our instruments may not be able to fully purge our estimates ofpotential Tiebout bias.

In the first two columns of Table 6 we report the coefficients on the instrumentsin the first-stage regressions for both the population shares for those aged 65 andover and 0 to 19. In both equations, the coefficients on the instruments areprecisely estimated and have the expected sign. Thus our proposed instrumentsclearly pass the first test of a valid instrument, namely, they are correlated with thevariables we suspect are correlated with the error term. Column (3) reproduces thesingle-equation coefficients of interest from model (2) in Table 4 to provide aframe of reference. In the final column, we report the instrumental variablesestimates of the same model. As expected, instrumenting decreases the magnitudeof the coefficient on the elderly variable, but only slightly. Although thiscoefficient is statistically significant, we cannot reject the null hypothesis that the

20IV and OLS estimates for this variable are the same. In this case, the biasimparted by any type of spending-induced migration appears to be small.

4.4. Interpretation of our results

Our estimate of the impact of the elderly on education spending is much smallerthan Poterba’s (1997) estimate. It is, however, broadly consistent with Ladd andMurray (1999). Ladd and Murray use county-level data and estimate a model thatis similar in many ways to the model we estimate with our district-level data set.Their estimate of the elasticity of state and local revenues per child with respect tothe population share aged 65 and over is just 20.004 and is statisticallyinsignificant. They argue that a state-level analysis overstates the depressing effectof the elderly because it cannot control for within-state sorting of the elderly. Inthe past, the elderly were able to segregate themselves from families with children.This segregation by age forces families with children to bear more of the burden offunding schools, and it is this negative effect on available revenue that the

20We also tested the Tiebout hypothesis on a limited panel of metropolitan school districts where wehypothesized that MSAs with few districts had limited ability for sorting, thus estimates should notreflect a Tiebout bias. We found that metropolitan areas with less than the median number of schooldistricts, 13, had a statistically insignificant coefficient on the elderly share variable while those withmore than 13 school districts had a large negative coefficient on the elderly share. This concurs with theSection 4 results shown above that Tiebout sorting does bias the full panel’s result.


state-level analysis is capturing. Ladd and Murray show that as the elderly share ina state rises, elderly segregation from children falls, diminishing the negativeeffect of the elderly. They try to control for much of the within-state segregation,or sorting, by including county fixed effects in their model.

We would offer a different explanation. We believe that the elderly feel muchmore strongly about state spending on schools than local spending, and that it isthis distinction that accounts for the differences between Poterba (1997) on the onehand and Ladd and Murray (1999) and this paper on the other. At first blush thismight seem paradoxical; after all, an additional dollar of state taxes used to fundeducation would seem to have the same impact on an elderly family as anadditional dollar of local taxes. But this is not necessarily the case. The argumentis as follows. When the state government decides to spend more on education,schools improve throughout the state. Very little of this additional spending iscapitalized into higher house values since the relative attractiveness of com-munities in the state is unchanged. Thus the elderly receive no direct benefit fromthe higher spending — their children finished school long ago — nor any indirectbenefit — the value of their homes is unchanged. At the same time, state spendingon education competes with spending on other state programs which do directlybenefit the elderly, such as Medicaid. Not surprisingly, they oppose proposedhigher state spending on education.

But now suppose the local school district decides to increase spending. Theelderly see that better schools make their community more attractive thanneighboring communities and that as a result the higher spending will becapitalized into higher house values. As a consequence, they are less likely tooppose this increase in local spending on schools than a similar increase in state

21spending.We can offer four pieces of evidence that support our argument. First, a number

of studies beginning with Oates (1969) have shown that people are willing to paya significant premium for homes that offer the best schools. Bogart and Cromwell(1997) looked at the prices of homes that were in the same neighborhood butdifferent school districts and Black (1999) compared the prices of homes withinthe same school district but different elementary school attendance zones. Theirresults are striking. Bogart and Cromwell, for example, found differences in house

21Poterba (1997) offers a different explanation as to why the elderly might support additional localspending on schools but oppose additional state spending. State spending is funded primarily throughthe sales tax and income tax while local spending is funded almost exclusively through the propertytax. In a variation of his model, Poterba introduces an indicator for states with property tax circuitbreakers and an interaction of that indicator with the elderly share. He finds a positive coefficient on thecircuit breaker indicator and the interaction term. The positive coefficient on the interaction implies thatthe elderly are less likely to oppose additional resources for schools if circuit breakers shield them atleast partly from the cost. Any effect of state-wide circuit breakers would be absorbed in our modelthrough the year-specific state effects, and we do not have information on any district-level property taxbreaks for the elderly.


prices within neighborhoods but across school districts of $5600 to $12,000 (in1987 dollars).

Second, as we showed in Table 3, state-level results are driven by the elderly’sopposition to state spending. Using state-level data, we found an elasticity of staterevenues per pupil with respect to the elderly population of 20.513 and anelasticity of local revenues per pupil with respect to the elderly of just 20.021.Since state spending and local spending are roughly equal, our estimated elasticityof total revenues of 20.261 is essentially a simple average of the state elasticityand local elasticity. Similarly, the results for model (3) in Table 4 show that at thedistrict level, local education spending is less sensitive to the size of the elderlypopulation than is total education spending.

Third, we showed that in a fixed effects model that focuses on localgovernments, the variance in local spending is much larger than the variance instate spending. We showed, for example, that in 1982 within-state variation indistrict local revenues per pupil is on average 3.6 times as large as the variation indistrict state revenues per pupil. As a result, in our district-level models variationin total revenues per pupil is roughly equal to variation in local revenues. Astate-level analysis, however, captures variation in both state and local revenues.

Fourth, we included the interaction of our elderly and home ownership variablesin one specification of our model. This model also indicates that increases in theelderly population lower school spending. However, the interaction of the elderlyand home ownership has a positive coefficient, suggesting that capitalizationreduces the negative effects of the elderly on public education spending.

5. Summary and conclusions

In this paper we have used district-level data to estimate the effects of an agingpopulation on support for public education. The fixed effects results suggest thatthe elderly do indeed have a negative effect on public education spending, but thatthis effect is small, about 40 percent of Poterba’s state-level estimate. We attemptto account for possible Tiebout sorting between the local school districts byinstrumenting for the population share aged 65 and older. The second stagecoefficients are slightly smaller and are consistent with the overall conclusion thatthe elderly have a smaller negative effect on school spending than earlier researchhas suggested.

We attempt to determine why we find such a large difference between Poterba’sstate-level results and our district-level results by considering the different viewsthe elderly may have toward education spending at the state level versus thedistrict level. This suggests that a discussion about the policy effects of an agingpopulation depend in large part on which level of government one is concernedabout; our results imply that the aging of the population is not a concern at thelocal level but, as Poterba first demonstrated, it is a concern at the state level. As


more public education finance systems shift toward state financing due tosuccessful court challenges, the negative effect of the elderly on state educationspending may be magnified.

We recognize that we need to be cautious in extrapolating our results to predictthe future effects of aging in America. We should stress that the parameters weestimate reflect the conditions which existed during 1972–1992. Although theelderly represent more than 50 percent of the population in some districts in 1992,the national district weighted average in the entire panel is just 10.8 percent.Attempting to predict what the elderly’s effect will be in 2037, when the first waveof baby boomers will be 90 years old and the national elderly share will be wellover 20 percent, requires an out-of-sample forecast (and perhaps a great leap offaith). What our results do show is that looking back in time, the rise in elderlyconcentrations over the seventies and eighties has not meant all that much at thedistrict level to local public education financing in America.

Acknowledgements

The views expressed here are those of the authors and should not be interpretedas those of the Congressional Budget Office. We would like to thank theparticipants at the University of Maryland brown bag microeconomics seminar,two anonymous referees and the Editor for helpful comments. This research wassupported by the National Science Foundation (NSF) under grant number SPR-9811386. We thank NSF for its support.

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