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'Il't‘ nu...” J_J 1,1”, J1, I Am. We} gooS@®ZH ~ 111*1 1mm; 111111111llllxllllxllljl 1 1115111.... '21... 3 1293 00099 Diversity INTERGOVERNMENTAL GRANTS AND THE DEMAND FOR LOCAL EDUCATIONAL EXPENDITURES presented by Michael Francis Addonizio has been accepted towards fulfillment of the requirements for Ph.D. degreein Economics Majomrofessor Date May 1 9 8 8 MS U is an Affirmative Action/Equal Opportunity lmtitutiou 0-12771 MSU LIBRARIES RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. och \W 351° MAFllflé ton ‘ 0 8 I .112 ‘! ‘IAYO 8199‘ a“ '1 2 19%| INTERGOVERNMENTAL GRANTS AND THE DEMAND FOR LOCAL EDUCATIONAL EXPENDITURES BY Michael Francis Addonizio A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1988 3LQ3-752x' ABSTRACT INTERGOVERNMENTAL GRANTS AND THE DEMAND FOR LOCAL EDUCATIONAL EXPENDITURES BY Michael Francis Addonizio School district expenditures in Michigan are determined by a simple majority of eligible local voters. The school tax effort chosen in each district is assumed to depend upon voters' marginal tax prices, income levels, and preferences. Because the state allows the school expenditure decision to be, made by the local electorate, voter response to the price and income effects of education grants are important means by which the state can influence local school expenditures. This study extends past research in four ways: first, the price term is specified to incorporate the effects of both. Michigan's guaranteed tax base (GTB) school aid formula and homestead property tax relief program ("circuit breaker"), as well as the composition of the local property tax base; second, the expenditure equation is specified to test whether the expenditure- income relation is U—shaped rather than monotonic and, if so, to allow variation in the level of family income at which the minimum level of desired school spending Iv Michael Francis Addonizio occurs; third, the model empirically tests whether the two samples of school district voters-—those in districts receiving GTB grants ("in-formula" districts) and those in districts which do not ("out-of—formula" districts)-— represent different demand structures; and fourth, the study recognizes the nonlinear budget constraint created by Michigan's GTB formula for some school districts. Dummy variables are used to reject the null hypothesis that in-formula and out-of—formula districts are drawn from the same population and infer, instead, that a structural difference in education demand exists between the two samples of district voters. Econometric evidence is then presented indicating that demand is more elastic among residents of out-of—formula districts than among in—formula district residents. The low price- and income-elasticities of demand estimated for in-formula. district voters suggest that their relatively low desired school expenditure levels are unlikely to be altered by increases in either matching' or lump-sum state aid. The price-inelastic demand of in-formula district voters would likely render any program of increased matching aid for such districts ineffective in stimulating spending increases, since such aid would likely induce recipients to lower their school tax effort. IIV Copyright by MICHAEL FRANCIS ADDONIZIO 1988 IV For Joan, Matthew, Craig, and Mark iv ACKNOWLEDGMENTS No dissertation is written without considerable help and encouragement of others, and this one is no exception. As Chairman of the Guidance Committee, Dr. Ron Fisher provided valuable counsel and great patience, as his pupil committed errors of omission and commission during the many drafts of this work. The opportunity cost of his time spent on this project was undoubtedly high, and as the beneficiary of' his efforts, I cannot claim this project was a Pareto improvement. I can only express my deep gratitude. I am also indebted to the other members of the committee: Professors John Goddeeris, Byron Brown, and Christine Amsler for their time spent reading this research and their suggestions for improving it. Finally, I owe a special thanks to Professor Jack Meyer, without whose skillful instruction in basic microeconomic theory I would never have had the opportunity to complete this project. other essential inputs to this project were a large data base and a substantial amount of computer time. I am indebted to Jacob Silver and Bob Witte of the Michigan Department of Education for their assistance in assembling portions of the data base and to James Phelps of that Department for access to their computer facilities. This research was funded, in part, by a grant from the National Institutes for Education, No. NIE—G—83-0049. I an grateful for their support. The advice and assistance of these people have undoubtedly improved the quality of this project, and responsibility for remaining errors rests solely with me. On more than one occasion, I harbored serious doubts that my dissertation would ever reach completion. On such occasions, it was the support and encouragement of my wife, Joan, that pulled me through. She was also helpful with our three sons, Matthew, Craig, and Mark, who often asked "When is daddy going to finish that book?" vi Table of Contents Page LIST OFTABLESOOOIOOOO OOOOO OOOOOOOODDOCOOOOC. 000000 .ix LISTOFFIGURESOO00.000.000.000... 0000000000 OOOOOIOOXi Chapter I. INTRODUCTION.. ............. ........ l The Theoretical Analysis of Inter- governmental Grants ......... .............2 Lump—Sum Categorical Grants .............. 6 Matching Grants..........................8 Revenue SharingOOOOOOOCOOOOOIOOOOCCOOOOOO9 Block Grants............................12 II. INTERGOVERNMENTAL GRANTS IN EDUCATION: RESEARCHTODATE.............. ............... 16 A Survey of Past Research ............ ...... 16 The Median Voter Model...................19 Education Demand: A Monotonic Function of Income?........... ........ .24 Refining School Tax Prices: The Importance of Tax Base Composition.......35 A Summary of Empirical Findings ........... .42 Empirical Literature: Summary and Conclusions....... ................ .......59 Methodological Issues........... ......... ..61 Michigan: A Case in Point........ ......... 66 III. STATE EDUCATION GRANTS, PROPERTY TAX RELIEF, AND EDUCATION DEMAND INMICHIGANCOOOCOOOOOOOOOO ...... .IIOOOO. CCCCC 69 The Michigan GTB School Aid Formula........70 The Michigan Circuit Breaker Program.......89 A Model of Education Demand in Michigan.... 96 Estimating Circuit Breaker Price Effects........... . ...............99 Education Demand: Alternative Price Specifications........ .. ..... ..103 In— Formula and Out- of- Formula Districts: Two Structures or One?... ........ .......105 vii IV. DATA AND DESCRIPTIVE STATISTICS ............ .112 Marginal Tax Prices of School Expenditures..................... 115 V. REFINING THE PRICE TERM AND ESTIMATING THE MODELOOOOOOOOOIOOQO ....... O OIIOOIOOI00123 Empirical Results ...... ...................128 Price Elasticity of Demand .............. 129 otherResultsfiOOOOIIIOIOO0.00......0....136 VI. NONLINEAR BUDGET CONSTRAINTS AND MICHIGAN SCHOOL SPENDING DECISIONS: EMPIRICAL RESULTS ........................... 142 which Marginal Tax Price?..... ..... .......151 other Results........................ ..... 153 VII. THE INCOME—EXPENDITURE RELATION: EMPIRICAL RESULTS ................... ........156 Impact of Intergovernmental Grants........161 VIII. SUMMARY AND CONCLUSIONS.............. ....... 165 Voter Response to Local Tax Base Composition. ........... ........ 167 Income-Elasticity of Demand For School Expenditures ..... ...... ...... 169 Policy Implications........... ....... .....172 BIBLIOGRAPHY......... ....... ................. ..... . 180 viii III. III. III. III. IV. IV. 1. 2. 3. 4. l. 2. LIST OF TABLES Page Taxonomy of Intergovernmental Grants......15 Estimated Parameter Values of Major School Expenditure Determinant Studies...... ...... . ..... ........... ...... 44 Provision of Public Education.............65 Kink-Point Per Pupil Expenditure Levels for Michigan School Districts, 1982—83....80 District Spending Levels and Kink- Point Levels: Examples...................82 Michigan Homestead Tax Credit Parameters................................91 Circuit Breaker Credit Types ............. 102 Marginal Tax Prices: Alternative Specifications, Descriptive Statistics: Out-of—Formula Districts.. ............... 115 Marginal Tax Prices: Alternative Specifications, Descriptive Statistics: In—Formula Districts......... ............ 117 Marginal Tax Prices: Alternative Specifications, Descriptive Statistics: All Districts... ........... ........ ...... 118 Prices, Incomes, Millage Rates, and Public School Expenditures In—Formula vs. Out—of—Formula Districts, 1982—83.... 122 Perceived Tax Price and Tax Base Composition.................. ...... ...... 125 Variables Associated with Public School Expenditures: Descriptive Statistics—— 1982—83000000000 ooooooooooo cod-oooovoooool30 WLS Regression Coefficients for Michigan K-lz Districts, 1982—8300000000000900000' 131 ix VI.l. VI.2. VI.3. V1.4. VII.l. Estimated Point Price Elasticities of Demand for School Expenditures..... ...... 133 Estimated Point Income Elasticities of Demand for School Expenditures ........... 135 District Spending as Compared with Kink Level.............. ......... ........144 WLS Regression Coefficients for Michigan K-12 Districts, 1982—83 ......... 145 Estimated Point Elasticities of Demand for Public School Spending: Evidence from Three Samples.............. 150 Price Elasticity of Demand for School Spending: Alternative Price Specifications .......... .................152 WLS Regression Coefficients: Estimating the Income—Expenditure Relationship, In-Formula vs. Out- of—Formula Districts-—1982—83.... ....... .157 Figure III.1. III.2. III.3. III.4. III.5. III.6. LIST OF FIGURES Page Michigan GTB Formula Tax Base Guarantee ......................... . ........ 75 School District Budget Sets Resulting from Michigan GTB Aid Formula, 1982—83 ..... 79 Millage Rate and Tax Base Combination Placing Districts at Per Pupil Expenditure Kink ................. . ....... ..81 Piecewise—Linear Nonconvex Budget Setii ..... 0... ....... 0 0000000 O 0000000000000 85 Nonconvex Budget Set and the Nominal Tax Base Guarantee ....... . ..... ............88 A Family of Linear Demand Curves..........109 xi CHAPTER I INTRODUCTION In the wake of tax limitation movements in some states (e.g., Proposition 13 in California, and Proposition 2 1/2 in Massachusetts), school finance researchers and policymakers have renewed interest in the use of intergovernmental grants for education” Such interest also stems from the New Federalism, which shifts some responsibilities from the federal government to state and local governments, and restructures the system of federal grants to these governments. The so-called "property tax revolt" and the New Federalism have combined to increase the state role in financing local schools. This strengthened state role, along with the consolidation of federal categorical grants into block grants to state and local educational agencies, gives rise to a need for reexamining intergovernmental grants for education in terms of their rationale, design, and effects. Of particular interest is the relationship between the design of an intergovernmental grant and its fiscal impact. Different types of intergovernmental grants can be expected to have different. effects on. ‘the educational spending of recipient levels of government” The .leVel and distribution of education spending have received attention in the last five years by state legislatures. This dissertation examines the response of local school district voters to the fiscal incentives provided by Michigan's Guaranteed Tax Base (GTB) state school aid formula and its Homestead Property Tax Credit Program, commonly known as the "circuit breaker." Specifically, a model of local school district spending in Michigan will be estimated in order to measure the extent to which these two intergovernmental transfer programs, both of which reduce the local tax price of education, elicit increased local tax effort for public elementary and secondary schools. The Theoretical Analysis of Inter- governmental Grants Intergovernmental education grants education generally take four forms: categorical grants, matching grants, general revenue sharing, and general aid to education. Such grants include federal aid to state and local governments and state aid to local governments. The theory of intergovernmental grants uses assumptions from the theory of consumer behavior, which holds that the consumption decisions of an individual or household depend upon prices, income, and preferences. The governmental unit receiving the grant is viewed as a consumer with regard to these behavior determinants. Preferences refer to the priorities assigned by the recipient government to various public goods and to the relative desirability of changing residents' utility through public, as opposed to private, consumption. The price of public goods is a weighted average of the prices of such goods expressed in terms of a tax rate or local tax price required for access to them. The budget constraint of the recipient government is the portion of the residents' income allocated to the purchase of public goods. Given a set of preferences, a set of prices of public goods and a budget constraint, the governmental unit chooses the combination of public goods, including education, that maximizes its residents’ utility. Thus, the theory of intergovernmental grants assumes that each potential grant recipient is in equilibrium, with its resources allocated so as to Inaximize its own. welfare (Gramlich and Galper, 1973). However, this allocation of resources may not be optimal from the perspective of a higher level government. That is, it may provide for an overall education expenditure level which is lower than that preferred by the higher level government or it may assign a lower priority to the education of particular pupil populations, such as handicapped or economically disadvantaged pupils. It is these disparities between local decisions and state and federal priorities that become the object of state and federal grant—in-aid policy. Intergovernmental grants become a vehicle by which higher levels of governmental attempt to change lower level behavior. From the analytical framework presented above, it is clear that the higher level of government can alter the behavior of the lower level by changing their preferences, the relative prices of goods, or income. Intergovernmental grants attempt to do all of these. Legislative initiatives focusing on particular educational goals provide a basis of grant policy designed to alter the preferences and priorities of the recipient government. At the same time, by paying all or part of the cost of the educational services of interest to the higher level government, the grant program reduces the price of those services to the recipient level of government. Finally, the degree to which the grants increase the income of the recipient governmental unit, a larger budget is available to provide all public goods, including those educational initiatives of interest to the higher government level. Thus educational grants can be analyzed according to their effects on the recipient governmental unit through each of these three factors. Because of these different possible effects of intergovernmental grants, one cannot assume that a grant provided to a lower level of government will be allocated entirely to the targeted program. There are, in fact, three responses that can be made by the recipient government. First, the grant can be used to increase the amount of the targeted educational service beyond the level that would be provided in the absence of the grant. Second, the grant can be used to reduce the amount of local revenue allocated to the targeted educational service, enabling the recipient government. to redirect. local revenue 'to other public goods. In this case, the grant substitutes for funds that. would. have been. spent: on. the intended educational service. Finally, the grant can be used for local tax relief. In the first case, the grant is used for its intended purpose. Indeed, in some instances, the grant may succeed in stimulating increased local support for the targeted service. In the second and third cases, however, a part of the grant is used to replace local revenue that would have been spent on the intended service in the absence of the grant. In these cases, resources are shifted to nonaided services or back to the private sector in the form of tax cuts. In general, the fiscal response of the recipient government depends on the form of the intergovernmental grant and the preferences of the recipient. Lump-Sum Categorical Grants Lump-sum categorical grants are provided to state and local educational agencies to increase the total level of resources devoted to particular educational services beyond the level that would be allocated in the absence of the grant. Prominent examples include special education, bilingual education, and compensatory services for educationally disadvantaged children. Such grants can increase support for the targeted services in three ways. First, by increasing the income of the recipient government (e.g., a local district), more of all educational services, including the targeted service grant, may be provided. Second, the grant ensures a minimum level of expenditure on the targeted 1 service. Finally, the grant may succeed in altering the 1This type of grant is sometimes described as exerting a price effect; i.e., reducing the price of the targeted service to zero up to the level purchasable with the grant. However, since this grant type exerts no such effect at the margin if, in the absence of the grant, expenditures on the categorical service would have equalled or exceeded the amount of the grant, reference to the price effect in this case is trivial and leads to a confusion‘ between lump-sum grants, which exert no marginal price effect, and matching grants, which do. preferences of the local district by calling attention to particular state or national priorities. While categorical grants are intended to be used only to jprovide the specific intended service, it is virtually impossible for the grantor to prevent some portion of the grant to be used for other purposes.2 In most cases, some portion of categorical grants will be allocated to the intended service; some will be used to support other educational services and allow a shift of some resources from education to other public goods; and some will be used to reduce local taxes. While the exact distribution will be difficult to ascertain because of accounting limitations, accountability requirements, such as annual audits, will tend to increase the amount of the grants that are used for their intended purposes. A major feature of categorical grants is precisely that the purpose of the program can be expressed in grant regulations and guidelines that increase the probability that the funds will indeed be used for their intended purpose (Barro, 1978; Gurwitz and Darling-Hammond, 1981). 2Regulations for some programs, such as Title I of the Elementary and Secondary Education Act of 1965, stipulate that such funds cannot be used to supplant funding from state and local sources that would otherwise be provided for the categorical service. However, the accounting necessary to determine compliance or noncompliance is virtually impossible. Matching Grants An alternative to lump—sum categorical grants are matching grants, which are a mechanism by which a higher level government contributes a specified proportion (m) of the lower level government's outlay on the educational service of concern. Such grants, which reduce the effective price of the targeted good faced by the local government, denote the proportion of local expenditures that the higher level of government will pay as well as the maximum amount, if applicable. (The imposition of a maximum grant amount M, of course, eliminates the marginal price reduction for local governments whose local expenditures exceed M/m. Such grants effectively operate as lump—sum grants.) Analyses based on the local community acting like a single individual (e.g., Wilde, 1968) suggest that a matching grant, offering the recipient government the same tax/expenditure possibility as a lump—sum grant, will lead to a higher level of local spending. The reason is that matching grants involve a compensated price change and result only in a substitution effect. Thus, for example, federal matching grants have been used to stimulate the provision of educational services that serve national priorities by reducing the cost to state and local educational agencies of providing such services. If the lmatching rate is high. enough, the desired response of increased provision of the priority service will be obtained. The precise matching rate to achieve the desired spending response depends on the local governments' price elasticity of demand for the service in question. as well as the interests of' the grantor. The major theoretical advantage of matching grants is their efficiency in stimulating the provision of particular services. The local government must demonstrate that it has spent its own resources on the selected program in order to receive the matching funds. In this way, there is likely to be less leakage to other educational programs or public services or to tax reduction. Revenue Sharing Revenue sharing refers to a system of unrestricted lump—sum cash grants from the federal government to state and local governments. Such grants are intended to share national tax revenue with states and localities and are not based on a national concern over the state and/or local provision of any particular public goods. Thus, revenue sharing grants can be used to increase the provision of any and all public goods, to 10 reduce state and/or local taxes or some combination of the two. Economists generally view the effects of lump—sum revenue sharing on public expenditures as similar to that of any increase in community income on expenditures. About 10 percent of additional community income is allocated to increased spending on public goods, so presumably about 10 percent of revenue sharing receipts would be so allocated, with the remaining aid used for state-local tax relief (Gramlich, 1977). However, while many of the theoretical individual utility-maximizing models of state and local government expenditure, including the full-information median—voter model (described below), would predict. that the increase in educational expenditures stemming from a lump-sum education grant would be roughly equal to the increase arising from an increase in community income of an equal amount, such recent econometric work on the effects of intergovernmental grants on state and local government expenditure contradicts this theoretical expectation. Specifically, much of this empirical work has shown that lump-sum grants increase state and local government expenditures more than equivalent increases in private personal incomes. In view of this result, dubbed the "flypaper effect" because "money sticks where it hits," ll (i.e., money received in the public sector tends to remain in the public sector, while money received in the private sector tends to remain there), we might expect that a greater proportion of lump-sum education aid would be retained for education than would be retained from an equal increase in private income.3 Since revenue sharing addresses issues of national concern only insofar as the more progressive federal tax system is used to raise revenue for state and local public goods, it is hardly a precision instrument for addressing specific national priorities such as education. Rather, general revenue sharing will exert an income effect on state and local governments, increasing the amount of all goods purchased, including education. 3The size, and even the existence of the flypaper effect, remains uncertain. As Fisher (1982) notes, the theoretical and empirical studies of the flypaper effect can be divided into four categories: explanation based on (1) some form of fiscal illusion, (2) features of particular political institutions, (3) the income effects resulting from tax substitution, and (4) some statistical or information problems in interpreting grants. Based on his review of the literature, Fisher offers the following two views of the flypaper effect: first, any difference in the estimated lump—sum grant and income effects in econometric studies is unexpected and represents a flypaper effect. Alternatively, only differences in the estimated and theoretically predicated effects represent a flypaper effect. According to the second view, a more complete version of the standard government expenditure demand model (incorporating, for example, the financing of lump—sum grants or allowing for fiscal illusion) may predict different grant and income effects so that the flypaper effect, the unexplained difference, is reduced or eliminated. 12 Although some of the funds will be spent on education, the amount will be relatively' small and will not be targeted to any particular educational service. Rather, the specific allocation decisions will be left to state and local political processes and preferences.4 Block Grants In contrast to matching grants, block grants generally have no local matching requirement. Rather, such grants provide general aid to a state or local education agency for educational purposes only. An example of such general aid is the pupil membership or average daily attendance grants common. to) many state school finance systems. Such state grants provide a flat amount for each child attending the school district and the grants can be used for any educational purpose. As such, education block grants are theoretically indistinguishable from lump-sum categorical grants, the only practical difference being that the use of block grants is often less restricted than the use of categorical grants, which are usually earmarked for particular educational services (e.g., special education, bilingual education, etc.). As with any lump-sum grant, 4Strictly speaking, general revenue sharing grants provided under the State and Local Fiscal Assistance Act of 1972 do expert a small local price effect, since the grants are determined, in part, by local tax effort. 13 the absence of a matching requirement is expected to elicit a different local response than that which would be elicited by a matching grant. Specifically, while the latter is normally expected to increase local provision of educational service by lowering the locality's service price, a block grant exerts no such price effect. Rather, since a block grant does not alter the local price of the targeted service relative to other goods and services, it provides the locality with no incentive to spend relatively more on the targeted service and relatively less on other services. Indeed, although some of the grant is expected to augment the targeted public good, economic theory holds that some will be used in a way similar to any increase in community income—-that is, to increase expenditures on all goods, public and private. In the case of block grants for education, this is accomplished through a reduction in local school spending, with this reduction being divided between increased expenditures on other public goods and a reduction in local taxes. Economic theory would predict that the increase in educational expenditures resulting from a block grant would be roughly equal to the increase stemming from an increase in community income of an equal amount. That 14 is, for each dollar of increase in community income, the proportion allocated to public goods, including education, would be about the same as that a resulting from an additional dollar of general education aid. However, in view of the above—noted evidence of a flypaper effect, we expect that a greater proportion of education aid would be retained for education that would be retained from an equal increase in income. In summary, higher levels of government use four major grant types to increase the provision of educational services by lower levels of government. However, while each has the potential for increasing local school expenditures, each also has the potential for increasing spending on other public goods and for reducing local taxes. The differences among these grant types are summarized in Table 1.1. 15 quowmm xmu Hmooa ma synod CH .omcflfiumumc mum museum map modem pommmw moaum HmooH HHmEm m unmxm on mhma mo pom mocmumflmmé Hwomflm Hmooq can wumum on» wound wmofiwonm mucwum mafia—mam msam>mu Hmumcmm .mCMxmmmm wauofluum... uommEH m>flumasawum o>flpsuflumnsm Hmomflm o>fiusuflumosm m>fiusuflpmn5m manmnoum uomwmm QEOUCH AycsoEm éucsofim AmmOHHm m>Hu o ucmum on as onwu mm Damnm CD as oumu Imamu CH mmcmno * 2 Op condom“ moaum w on omoocou ooflum Hmoonv pomwmm Aamooav sanflmmom LamooH. sflnflmmom conusuuumnsm ucmuw mo me ”on ummmq 3mm mam: umoz mucwawnflwvmu m>fiumuumflcfieod mofl>umm mcflccmmm moH>Hmm HmH wEoocfl Hmumcmm ca HMDO» IDOflunm o How Hmooa Hm>ma mcflocwmm cam HMUOH Hm>ma ocHUGwmm mmmmuocH Edaflcflfi whammfl opmHsEflpm EDEHCHE whamm< mmomusm uamuw acmuo mcflumnm DMMHO m mmcfimmwmzHo HmOHHommpmu msco>mm x Hm u to .m Edmlmfisq mumnlwanmaum> mpcmuw Hmwcmficum>omHchH mo >EOCOMMBII.H.H mHQMB I' CHAPTER II INTERGOVERNMENTAL GRANTS IN EDUCATION: RESEARCH TO DATE A Survey of Past Research Studies of the impact of intergovernmental grants on educational spending, dating from about 1960, address both. state and .local governments, employ' various statistical techniques and examine cross-sectional, time- series and pooled data sets. The earlier studies examine the "determinants" of school spending by state and local governments by means of a single-equation regression model explaining total per pupil. or per' capita educational expenditures in. terms of' intergovernmental grants and a set of socioeconomic variables, generally including income, property wealth and education level, intended to proxy residents' preferences. These "first generation" studies, which generally employed a least-squares estimation technique, often revealed a strong and statistically significant effect of intergovernmental grants on school expenditures. These studies, however, suffered from both theoretical and methodological shortcomings. Many were based on ad hoc 16 17 models which lacked an adequate underlying theory of the fiscal behavior of governmental units. Often, for exampLe, both supply variables (e.g., teacher salaries) and demand variables (e.g., education levels of community residents, percent of families with school—age children) were included in one equation.5 Additionally, many studies simply lumped all types of grants into one intergovernmental aid variable, thereby failing to account for the differences in fiscal incentives and expected recipient responses associated 6 with the grant types, as noted above. Consequently, the demand elasticities estimated with these models provided 5One such empirical study was done by Miner (1963), who examined the impact of state education grants on local school districts. Specifically, Miner considered the determinants of per pupil educational expenditures in 1,127 school districts in 23 states. He constructed a single equation relating per pupil educational expenditures to more than a dozen explanatory variables, including demand factors (e.g., percent of school—aged children in the district population), supply factors (e.g., teacher salaries), and variables reflecting differences among the state school aid systems (e.g., grant types, state shares of total school spending). He found that total per pupil school expenditures were negatively related to the state share of school expenditures, reflecting the fact that poor districts spend less on education than wealthy districts, although they receive more aid. 6One example is Brazer (1959), who examined the educational expenditures in 1953 of 40 large cities (population more than 250,000) across the 0.8. He found that for every additional dollar of state education grant received, a city would increase its school expenditures by 29 cents. 18 an unreliable basis for designing a system of inter— governmental grants. Finally, most of these studies were cross-sectional, examining the response of state or local governments in a single year. Results obtained in this way may not accurately describe the spending behavior of educational units as they respond over time to the incentives of intergovernmental grant system. Studies since the late sixties have paid more attention to these conceptual and statistical questions. Some of these studies (e.g., Brooms and Hu, 1971), involve a system of simultaneous equations that explicitly model the interaction of the supply and demand forces which determines educational expenditure levels. A two-stage least-squares procedure (TSLS) is then used to estimate the impact of various factors affecting the level of educational expenditures. Some authors (e.g., Black, Lewis, and Link, 1979) have specified an education demand function based on a median—voter, majority—rule model. (The theoretical foundation. of' this :model is developed below.) Others (e.g., Booms and Hu) have constructed a utility-maximizing model, in which the government unit seeks to maximize the welfare of its constituents, subject to a budget constraint. With regard to the inadequacy of cross-sectional studies for predicting the spending behavior of local governments over time, some authors (e.g., Adams, 1980; 19 Carroll and Park, 1982) combined cross-sectional data for several years into a pooled, cross-sectional, time—series statistical analysis. Such pooling generates more variance in the data set for statistical analysis. A second method for predicting government spending over time is "change" analysis, in which changes in expenditure levels between two years are regressed over changes leii set of explanatory variables over the same period. (For a discussion and application of this method, see Adams, 1980.) The Median Voter Model Until quite recently, nearly all empirical studies of intergovernmental education grants and local school district spending behavior have relied on median voter and related models, tested with data aggregated at the local district or precinct level. This literature builds upon the work of Bergstrom and Goodman (1973), who drew a logical connection between a community demand function and individual demand functions in a way that is useful for empirical analysis. Their application of the median voter model of local fiscal choice focuses on the voter-resident and the election process. Voters determine school spending. The model implicitly assumes that voters are well—informed on budget issues, voting costs are negligible and, since all voters are interested 20 in public education, all voters vote. In this way, the complex interactions that generate school district spending decisions are reduced to the choice of a single consumer. The model allows us to assume that school districts act as if a single household-—the household that is most typical of the community, that is, the median voter—-made all spending decisions.7 Bergstrom and Goodman (1973) have derived five conditions sufficient for the preferences of the voter in the median position of the town's demands for local services to correspond to the preferences of the median— income family: 1. All sample cities have income distributions that are simple proportional shifts of each other's distributions 2. Each family's share of local tax cost (T) is a constant elasticity function of family income (T = dIE) 3. All families have identical log—linear demand for public services as a function only of income and tax shares (G = AIaTB) 7A5 applied in empirical analyses, the median voter model assumes that each local government supplies only one service financed by a fixed tax structure. This guarantees that local budgets are one—dimension issues—— is there to be more or less spending? (Extension of the median voter logic to multidimensional issues demands improbable restrictions on voter preferences). Ilbr 21 4. The relevant elasticities do not violate the condition a + B E ,4 0 5. All families vote their preferences (i.e., no strategic voting). Expenditures are set by majority rule and through a process of spending proposal adjustments, the spending level favored by the median (50th percentile) voter stands to win.8 Deviation from the expenditure level preferred by the median voter will ensure that spending will be revised by the electorate so as to coincide with the level most preferred by the median voter. Thus, the model assumes that school district voters face a series of dichotomous choices between alternative school spending levels. Second, the model assumes that each 8The adjustment process always moves to the median position in the distribution of preferred spending levels. From a starting position below the median, more than 50 percent of' the ‘voters will prefer increasing expenditures. Likewise, from a starting position above the median, more than 50 percent of the voters will prefer a reduction in spending. Regardless of the initial spending level, expenditures will always converge to the single equilibrium at the median position. This single equilibrium position, independent of the starting budget, occurs only with 50 percent majority rule. Political choice decision rules requiring more than a 50 percent majority for victory (e.g., two-thirds or three— fourths) will yield outcomes that are contingent on the original spending level. For empirical analysis, the single equilibrium is obviously advantageous. School districts' millage elections, along with most local political decisions generally, are settled by majority vote. See Duncan Black, "On the Rationale of Group Decision Making," Journal of Political Economy, Vol. 56 (February 1948): 23-24. 22 voter's preferences are "single-peaked"; that is, each voter is characterized by a preferred expenditure level and suffers a uniform decline in utility as the actual expenditure level increases or decreases from that preferred level. The median voter model assumes that the tastes and incomes of the consumer—voter are given as are all prices, except that of education. It is left for the model to determine the price of education and the quantity demanded. We define a unit of educational services as $1 of expenditure and assume that a district can produce any level of educational services at a constant average of $1 per unit. We further assume that each district voter pays some share of the cost of each unit of educational serviced provided. This share is the "local tax price" of education. The distribution of these voter shares is determined by the district's tax system. For example, if, as in Michigan, education is financed locally by property taxes, the share of each dollar of local school expenditures paid by a household is that household's share of the district's total property tax base. In representing the preferences of the school district electorate by the preferences of the median voter, we identify the characteristics of the median 23 voter as the Inedian characteristics of the electorate. The income of the median voter is taken to be the median income of the district households.9 The median voter's educational atttainment is the median level in the district. If more than half of the families in the district have school-aged children, then the median voter has school-aged children, and so on. In this way, consumer demand theory is used to determine the consumption choices of the median voter. As with any consumer, the spending choices of the median voter depend on income, prices, and taste. As Beck (1984) points out, school district expenditures offer the best prospect of following the predictions of a median voter model because direct voter approval of school taxes is required in Michigan and other states. Enrther, because school districts serve a single purpose, it is unlikely that total expenditures are determined by a logrolling process in which special interest groups obtain majority approval of spending levels for particular public goods which deviate from 9It has been shown that the use of median family income to represent the income of the median voter in cross-sectional analysis can be justified even if the demand for education is not a monotonic function of income as long as income distributions across communities meet certain regularity assumptions. See Bergstrom and Goodman, "Private Demands for Public Goods," American Economic Review 62(3) (June 1973): 380—97. 24 spending levels that would have been supported by a majority of voters had they been voted upon in isolation. Education Demand: A Monotonic Function of Income? Previous cross-sectional studies of local public expenditures using a nedian voter model have generally assumed that the desired level of public expenditure is a monotonic function of income and, therefore, have included only median family income in the expenditure equation. The associated coefficient is then. used to estimate the income elasticity of demand for public services. Bergstrom and Goodman (1973) have shown that even in certain cases where the median voter does not have the median income, inclusion of median income in the expenditure equation will yield a coefficient which gives an unbiased estimate of the individual's income elasticity of demand for the public good. Such cases might include those where different subgroups of the population have different tastes for the public good (e.g., parents and nonparents) or if different subgroups faced different tax prices (e.g., homeowners and renters). As noted earlier, the Bergstrom-Goodman theorem imposes certain restrictions on the income distribution among these subgroups. Further, it requires 25 that the demand function for each subgroup be a monotonic function of income. That is, the median-voter model assumes that, when families in each subgroup are ordered by income, this ordering is identical with an ordering of the same families by preferred level of spending on the public good. It is precisely this assumption of monotonicity that guarantees that the spending level preferred by the median-income voter is the only level to get a bare majority when paired against any other proposed level. Brown and Saks (1983), however, identify two troublesome empirical consequences of this standard model. First, it is impossible to disentangle price and income effects unless median income and SEV (i.e., property wealth) have some independent variation across communities. Second, and more serious, no aspects of the wealth distribution other than its mean and median are relevant for explaining community choice in the model. Thus, the distribution of wealth in a community could be substantially altered, but if the change is mean- and median-preserving, demand for schooling would be unaffected. The authors argue that this is not a realistic restriction and provide evidence to support their claim. They begin their theoretical analysis by demonstrating that if the income-expenditure curve for 26 public education of families in a community is either U— shaped or inverted U-shaped, a mean— and median— preserving decrease in the variance of the community's income distribution would lower the desired school spending level, while an increase in the variance would raise it. More importantly, given a U—shaped function, the spending chosen at a given community median income lies abgye the demand curve, not on it, thus destroying the one—to—one correspondence between individual and group behavior. Consequently, estimates of school spending by income class obtained with the standard median voter model will be biased upward. Likewise, if the income—expenditure curve is an inverted U, the error will be negative and the estimate derived from the assumed monotonic equation will be biased downward. In each case, the reason for the bias is the possibility of coalitions of voters from noncontiguous portions of the income distribution. The theoretical possibility that demand for public goods is not a monotonic function of income arises from the combination of two effects: 1. The pure income effect depends on the income elasticity of demand. Unless public goods are inferior goods, the quantity demanded is expected to be a monotonically increasing function of income, holding the price constant. 27 2. The tax price, the individual's share of the cost of public expenditures, may vary systematically with income. Consider, for example, a public service financed by a local property tax. The tax price of the public service per family for voter i is Vi/TB, where Vi is the assessed value of voter i's residence and TB is the total assessed value of all property (including nonresidential property) in the district. If housing values are proportional to family income, this tax price ‘will be proportional to income. The combination of these two factors may result in the demand for public goods being a U—shaped function of income when both the price and income effects are taken into account. The poor may want to spend more on the public good because of their low tax price while the rich may favor higher expenditures because of the pure income effect.lo Bergstrom and Goodman provide some evidence supporting the monotonicity assumption. They included 10This line of reasoning is presented in Beck (1984, pp. 55—56). Increased demand for public goods at higher levels of income may reflect greater "public- regardiness" on the part of high-income voters. Stiglitz (1974, p. 355) presents an indifference curves graph illustrating this for the case of public education. Romer and Rosenthal (1979, p. 156) present another reason demand may not be a monotonic function of income. While the arguments of Brown and Saks, Beck, and Stiglitz involve a combination of price and income effects, Romer and Rosenthal base their argument on the combined effects of income and family size. 28 the percent of the population with annual income below $3,000, and the percent above $10,000 (in 1959) as explanatory variables in their estimated expenditure equations. In nearly every case, these variables were found to have coefficients which were not significantly different from zero.11 Using a sample of 500 Michigan school districts, Brown and Saks test the monotonicity assumption by testing the statistical significance of including parameters, other than the median, describing the distribution of income of each district in an equation for local revenue per family. They include median family income, the square of median family income, the Gini coefficient for the distribution of income in each district, and the Gini coefficient multiplied by median income and median income squared, respectively. The authors find the joint significance of the three 11One exception was the equation for expenditures for California municipalities, which showed a sta— tistically significant, positive effect for the proportion of the population with income under $3,000 (Bergstrom and Goodman, 1973, p. 291). However, as Beck (1984) has observed, Bergstrom and Goodman's use of a variable measuring the proportion of population below a constant income level such as $3,000 is an inadequate test of the monotonicity assumption if, as is argued by Beck (1984), demand is a U-shaped function of income with a minimum point that varies across communities. In communities in which the minimum point occurs at a fairly high income level, the lower—income part of the pro— spending coalition will include a much larger share of the population than those below the poverty line. 29 variables involving the Gini coefficient to be significantly different from zero at the 0.01 level, thus rejecting the assumption of monotonicity. Brown and Saks present two demand curves for their regression estimates, assuming all variables, except income and the Gini coefficients, are at their means. Assuming the Gini coefficient is equal to 0.32 (the mean value of the sample), the estimated equation implies a demand curve that rises monotonically with income. However, only if the income distribution within each school district were perfectly equal (i.e., only if the Gini coefficient in each district were zero) would the effect of differences in median family income in a cross-section of districts represent the effect of family income on individual demand for public school expenditures. Thus, to obtain an unbiased estimate of individual demand of public school expenditures as a function of income, Brown and Saks set the Gini coefficient equal to zero and derive a U-shaped demand curve with a minimum at a family income of about $8,300 in 1969.12 12Brown and Saks hypothesize that the error in the specification of the demand for public school expenditures resulting from the association of school spending with the preferences of the median—income family will be nonnegative (nonpositive) if the demand curve is U—shaped (inverted U-shaped) and approaches zero as the Gini coefficient approaches zero. 30 Brown and Saks interpret the statistically significant effect of the Gini coefficient as evidence of a nonmonotonic demand for public education, hypothesizing that the distribution of income affects the outcome of the school tax voting process because of the way in which the process aggregates individual preferences.l3 Specifically, the significance of the set of terms involving the Gini coefficient is consistent with a "substitute—voter effect," whereby voters from nonadjacent parts of the income distribution other than the median form coalitions to select an expenditure level other then that desired by a family with the median income. In the case of a U—shaped demand curve, an increase in the variance of the community's income distribution would result in an increase in equilibrium spending. Thus, the Gini coefficient (or set of terms involving the Gini) would be positively associated with school spending. 13An alternative hypothesis is that individual demand depends on the community income distribution. For example, Baird and Landon (1972) hypothesize that income inequality could affect the demand for police, while O'Brien (1971) suggests that greater income inequality could increase demand for public assistance spending. In these cases, the presence of poor people in the community increases the demand for public spending on the part of higher income households. In contrast, the Brown—Saks hypothesis holds that the demand of higher—income households is unaffected by the presence of low-income households, but the latter themselves add to the .pro- spending vote. 31 Brown and Saks include SEV per family as a separate independent variable in their regression equation to estimate the effects of SEV per family on the tax price and thus the desired level of school spending. However, while SEV per family was found to be positively and significantly associated with increased school spending at any given level of income, the Brown—Saks specification does not allow U , the minimum point of the income—spending curve, to vary with SEV per family. The Brown—Saks expenditure equation included both median family income (Y) and Y2 to reflect the U—shape of the individual's desired level of per pupil expenditures. The equation also included the Gini coefficient, G, along with. GY and GY2 since, by their theory, individual U— shaped income—expenditure curves would result in the selection by majority rule of a level of spending in excess of that preferred by the individual with the median family income if' people at the extremes of the income distribution prefer more spending than those in the middle. Thus, G is expected to be positively associated with school spending. However, the size of this effect depends on how far the median income is from u If the median income, Y, is very much above u, most of the population will be on a monotonically increasing portion of the income-—expenditure curve. The decisive 32 median voter will then be close to the voter with the median income. That is, the error which results from associating school expenditures with the preferences of the median-income family when the income-expenditure curve is U—shaped should approach zero as G goes to zero. Thus, Brown and Saks specify the error (E) resulting from the substitute—voter effect in estimating the expenditure equation as where Y is the median family income. In the case of a U-shaped demand curve, if 81’ 32 and are all greater than zero, the error is greatest at Y = and diminishes for increases or decreases in Y until it becomes zero at Y = u i /—§?7§Z This functional form has the disadvantage of becoming negative at extreme values of Y. Beck (1984) modifies the Brown-Saks specification of the public school expenditure equation to allow for the theoretical implication that the minimum point of the U-shaped expenditure-income demand curve will vary across communities because it depends on tax price. Beck assumes that an individual's tax price for public school expenditures is proportional to Y/B, where Y is the 33 individual's income and B is assessed property (including nonresidential) per family in the district, and that the tax price and income have additive effects on the demand for public services. Thus, the demand for public expenditures can be separated into two components, one reflecting the pure income effect and the other the price effect: D(Y;B) = D1(Y) + D2(Y/B) With this specification, the demand curve will shift down as the tax base falls and the: minimum point of the income-expenditure curve will shift. Thus, recognizing that u is a function of B, Beck adds the interaction terms of BGY and BZG to the expenditure equation, which included G, GY, and G3!2 in the Brown and Saks specification. Beck's expenditure equations were estimated using observations of 219 California municipalities with populations of at least 10,000. His dependent variable was general expenditures per capita and his estimated equation included BGY, BZG, and B/Y as explanatory variables for theoretical reasons explained above. His results show that, contrary to the Brown-Saks model, the value of B affects the level of income at which the desired expenditure function attains a minimum. value. 34 Both B/Y and logeY have the expected statistically significant positive coefficients.14 To obtain an estimate of the individual's desired public expenditure as a function of income, G is set equal to zero. As in the Brown—Saks study, the resulting function is U-shaped. At the sample mean value of B, assessed value per family, the expenditure fUnction attains a minimum at a family income of $1,761. As Beck notes, if the demand for public expenditures were a monotonically increasing function of income above this level of income in all communities, inequality in the distribution of income and the pro-spending votes of the very poor (Brown and Saks "substitute voter" effect) would not be expected to exert a significant effect on municipal spending. However, the minimum point of the income-spending function varies substantially across the local units of Beck's sample. Assessed value per family, varies from a minimum of $599 to a maximum of $109,154, with a standard deviation of $8,088. At the 14Contrary' to ‘theoretical expectations, the coefficient of B, assessed value per family, was negative and statistically significant. However, evaluated at the sample means of the other variables, the total effect on expenditures of an increase in B (including the effects of all terms including B) was positive, as expected. Beck argues that the significant negative coefficient of 1B may be attributable to the individual's tax price not being strictly proportional to ‘Y/B as assumed and to possible error in the assumed functional form for terms involving G. 35 maximum value of B, the income—spending function attains a minimum at a family income of $21,239. Thus, Beck concludes that the U—shape of the income—spending curve may have a significant effect on public spending even in communities with relatively few poor families if the assessed property value per family is high. Refining School Tax Prices: The Importance of Tax Base Composition Perhaps the most difficult task in conceptual— izing school district financial decisions within the framework of traditional consumer demand theory is the correct specification of the tax price of educational services. To estimate demand functions for public goods using the median voter model, one must define the relevant public finance variables (e.g., taxable wealth, disposable income, tax rates and expenditure levels) in terms that can be analyzed within the framework of traditional consumer demand theory. In deciding which public and private goods to buy, consumers consider their disposable income, their tastes, and relative prices. The median voter model assumes that the tastes and incomes of the voter are given, along with the prices of all goods except education. The researcher must then measure the quantity and price of education. 36 As a matter of convenience, researchers define a unit of educational services as one dollar's worth and assume that any quantity of educational services can be produced by any school district at constant average cost.15 Such. is the basis of the empirical studies summarized above, which take total per pupil expenditures as their dependent variable. Correct specification of the tax price of educational services, however, has been more difficult. The marginal tax price of educational services for a school district resident is that resident's share of the cost of each unit of educational services provided. The distribution of these shares is determined by the tax system of the district. For example, if the district's tax system levies equal tax shares on each household, and if there are N resident households and no taxes are exported to nonresidents, the share of the cost of each unit of educational services paid by each household will be 1/N. More typically, since most local school revenue comes from property taxes, each household's share of each dollar of school revenue is that household's share of the total property value in the district. 15Median voter models can be built to define educational services and the cost of providing them more realistically . However, as Gurwitz (1982) notes, the predictions of these more realistic models are quite similar to the predictions of the simpler model. 37 Other factors determining the tax price of educational expenditures are the state aid matching rate,16 the median voter's federal and state marginal income tax rates, and the .number of' pupils or average daily attendance (ADA) of the district. This tax price, which is the amount the median. voter must pay if' per pupil expenditures in the district are to be increased by one dollar, is the controllable variable that, along with income, most influences behavior in the median voter model. If per pupil expenditures are to be increased by one dollar, then total district expenditures must be increased by $ADA. Given a state matching rate of m, then the portion of the increase which must be raised locally is 1/1+m. Thus, the increase in local tax revenue must be $ADA (1/1+m). Assuming for the moment that school district residents perceive no tax shifting (that is, they perceive as their share of the tax burden only that part that falls on them directly in their capacity as homeowners, and that some proportion, n, of the local tax 16Guaranteed tax base, percentage equalization, or power equalization state school aid formulas are matching grants systems. For a demonstration of the mathematical equivalence of these three state—local shared-cost school aid formulas and the older Strayer— Haig Foundation formula, see Peter Jargowsky, Jay Moskowitz, and Judy Sinkin, "School Finance Reform: Decoding the Simulation Maze," Journal of Educational Finance 3 (Fall, 1977): 199-213. 38 base consists of nonresidential property, then the residents as a group must pay $ADA (1/1+m)(1—n). Since residents divide their share of the total tax bill in proportion to the value of their houses, the share of the median voter will be Vm/VT, where Vm is the assessed value of the median voter's house and VT is the total assessed value of housing in the district. Thus, the median voter must pay $ADA (1/1+m)(1—n)(Vm/VT) more in taxes for each one dollar increase in district per pupil spending. However, since property tax payments are deductible from gross income for computing federal and state income tax liability, the median voter who owns a home and itemizes his federal tax deductions will sustain a decrease in after-tax income of ADA (l/1+m)(1-n)(Vm/VT)(l—f) for each one dollar increase in per pupil expenditures, where f is the proportion of the local tax increase offset by the income tax liability reduction.17 This tax price expression would be modified, however, if resident voters indeed perceive that they 17This assumes that the median voter is a homeowner. If the median voter is a renter, then the tax price term must be modified to include the multiplication factor r, the proportion of property taxes on rental housing shifted forward from the owner to the tenant. Thus, if the median voter is a renter, then the tax price will be ADA (1/1+m)(l-n)(Vm/VT). 39 bear part of the property tax levied on local commercial and industrial property. Such shifting of taxes to local residents could take two forms: first, firm migration, which reduces the tax base; and second, higher prices for locally consumed private goods. Were either form of the tax shifting perceived by resident voters, the tax price expression given above would understate the price perceived by local residents and the expression (1—n), the residential fraction of the school district tax base, would have to be modified as follows: (l—n)* = 1 — xC — BI where: C and I are the commercial and industrial fractions, respectively, of the local property tax base.18 The parameters x and B represent the fractions of the commercial and industrial property tax n9: shifted onto local residents. As Ladd (1975) has noted, the parameters need not be equal. If resident voters are concerned about the future size of their local tax base, x may well be larger than B. This hypothesis is based on the view that industrial property is more mobile and more responsive to local fiscal factors than is commerciaI l8This adjustment in the tax price term is based on Ladd (1975). 40 property. Alternatively, if firms shift their property tax burden onto local residents in the fonn of higher prices, B may likely exceed x; that is, the proportion of the tax not shifted is greater for industrial than for commercial firms. The reasoning in this case is that industrial firms, producing for a market larger than the local community, are unlikely to command the market power necessary to raise prices. Moreover, a smaller proportion of industrial output than of commercial output is bought locally.19 Other independent variables often included in median voter model regressions of school expenditures are median income of district residents, some measure of the distribution of income among district residents, the proportion of residences that are owner—occupied, the dollar amount of state and federal categorical grants per pupil, and a set of variables intended to represent differences in preferences for public education among school districts. Such variables include median 19In her study of communities in the Boston metropolitan area, Ladd (1975) obtained estimates of x ranging from .71 to .79 and of B ranging from .39 to .45, indicating that the residential fraction of the local tax base is indeed an underestimate of the perceived tax base composition component of the tax price. Further, the higher value of x implies that resident voters believe that industrial property is more likely than commercial to relocate in response to inter-community fiscal differentials. 41 education level of taxpayers, the proportion of residents who are elderly, the jproportion. of 'taxpayers who are professionals, and the proportion of children who attend private schools. Of course, the explanatory variables included in empirical models are selected not only on theoretical grounds, but also on. the basis of'wu cmflm may .wocwn “mmusuwecmoxw Hagan mom wwocmcfim NHHmooH we w~nmaum> Dcwvcmmwom NIKE mflcwo 2.th ms.o n we\me uuefimo sh muofluumee shame Hooeom ewfloflcs «mm a ensue MUMU . . eaeooe asafiuflsafl Amuse. moo O NO OI Gmmflfioflz CH mnvOflHu. 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Summon 302 :H whoa .mwumo me e mm o. mnonesmne Hooeom a eeoueaem «6.0 em.o- meafl .eaafleoflz :H mDoHHumfle Hoonom dongs mm ObmH .BoHumm . msmfiuosmfi .outsmaoa eh mesa .xenq a em 0 mDOHHumflc Hoosom mHBDQ .xomam sbfloflumaam suooenmaam sufloflbwaam seesaw yahoo soon How QEDA wymum @EOOEH mUHHm XMB sesum eoscflueooul.H.HH wanes 46 analyzed different data sets.22 Nevertheless, the results of all the studies do appear to be generally consistent with theoretical expectations. The price elasticities, with one exception, are negative, indicating, as expected, that total per pupil expenditures fall as the tax price of educational services rise.23 The income elasticities all have the expected positive signs. The findings also indicate that lump—sum block grant increases lead to relatively smaller expenditure increases than do matching grant increases, reflecting the stimulative price effect exerted on recipients by the latter grant type. We do find, however, disparities among the parameter estimates sufficiently large in) pose problems for policymakers wishing to predict voter responses to various programs of intergovernmental school aid. The most notable disparity is that between the findings of Grubb and Michelson and Park and Carroll, on the one hand, and those of the other authors, particularly Perkins, Feldstein, Ladd, Inman and Peterson. The latter 22Interestingly, however, Park and Carroll (1979) did reproduce the methodologies used by Ladd (1975) and Feldstein (1975) and obtained markedly different results, as indicated. 23The positive tax price elasticity obtained by Grubb and Michelson (1974), indicating that local per pupil expenditures rises as tax price rises, is the sole anomaly. 47 studies found a relatively elastic demand for educational resources with respect to both tax price and income. Thus, by those findings, policymakers could expect sizeable increases in school district per pupil expenditures resulting from even relatively small percentage decreases in education tax price or increases in income. Such findings lend support to the advocates of matching grant programs, such as Guaranteed Tax Base (GTB) or District Power Equalizing (DPE) for stimulating school expenditures and reducing interdistrict disparities in per pupil spending without disturbing local school district autonomy in setting school tax rates. While the anomalous tax price elasticity estimated by Grubb and Michelson. was not significantly different from zero at the 10 percent level, the statistically significant findings of Park and Carroll indicating a very inelastic demand for education suggest little effectiveness of state school aid in altering local district fiscal behavior. Large interdistrict spending disparities will continue to exist, according to these findings, regardless of changes in relative tax prices among districts. If these elasticity estimates are accurate, the social welfare goals of equal expenditures and local district fiscal autonomy are incompatible and a choice must be made between the two. 48 Equal expenditures would be attained by a fully state— funded system which precludes local district taxing and spending discretion. Of course, the differences in the findings may be due to differences in behavior between Michigan voters and voters in Massachusetts and New York. Such behavioral differences would pose problems for policymakers since important school spending determinants would remain 113 be identified through further research. However, once the significant determinants are identified in a particular state, the school aid system could be designed to provide incentives (for the socially-desired behavior, assuming that the determinants are controllable policy variables. However, in view of the significant differences between the Park and Carroll findings, and those of Peterson and, to a somewhat lesser extent, Barlow, all of whom examined voting behavior in Michigan, one is led to suspect that the disparities arise from different models and estimation techniques. The sensitivity of findings to various models of school district spending behavior is demonstrated by Grubb and Michelson. The authors specified four different models of spending behavior: a utility function specification” a linear additive specification, a log linear specification, and a linear expenditure function. For unrestricted block grants, 49 they found that locally-financed educational expenditures would decrease by an amount ranging from 19 cents to as much as $1.18 for each additional dollar of such grants. Likewise, estimates of the tax price elasticity of locally financed school expenditures ranged from 0.14 to 1.2. The results of Grubb and Michelson, reported in Table II.1, are those obtained from the authors' linear additive specification of school district expenditures and the inclusion of a number of explanatory variables. In this case, the authors found that, for every additional dollar of state education block grants received, locally financed education expenditures would fall by 74 cents (and, thus, total expenditures would rise by 26 cents). The effect of state education categorical grants, on the other hand, was found to be stimulative, with locally financed expenditures rising by $1.21 for each $1 increase in categorical grants. Finally, as noted in Table III.1, the authors found, in this case, that the elasticity of locally financed educational expenditures with respect to tax price was 0.5. As noted above, however, this anomalous estimated elasticity was statistically indistinguishable from zero. Feldstein (1975) specified a log—linear relationship between total per pupil educational expenditures and nine explanatory variables, including 50 per pupil property wealth, income, state block grants, federal grants, the residential share of the local property tax base, the number of private schools per capita, the number of public schools per capita, and the ratio of the town's pupil population to that population five years earlier.24 For eight different forms of the log—linear expenditure function and different data sets, Feldstein obtained price elasticity estimates ranging from —0.940 to —1.599 and wealth elasticity estimates between 0.101 and 0.361. In contrast to the results obtained by Grubb and Michelson, these results are quite stable, despite differences in estimation methods. For the 1970 cross—sectional data, the estimated price elasticity was —1.0; the elasticity of total educational expenditures with respect to state education block grants was 0.066, which corresponded to a marginal propensity to consume such funds of approximately 0.6. Feldstein notes, however, that this high value is misleading because, in 1970, most block grants were paid to towns that passed the limit of matching aid, thus making the block grants endogenous and the estimated coefficient 24Feldstein notes that if town residents are reluctant to raise the school tax rate quickly, then a rapid growth in pupils will lower per pupil spending. To allow for a more general lagged response of educational spending to all of the explanatory variables, Feldstein also examines a proportional adjustment model by including, as an explanatory variable, the value of the dependent variable lagged five years. 51 biased upward. The estimates in Feldstein's 1965 equations show that an unbiased estimate is not significantly different from zero (coefficient = 0.006, standard error = 0.032). Feldstein was concerned with the problem of how to finance local public education in a way that partially or completely neutralizes the effects of intercommunity wealth differences without sacrificing the opportunity for local choice. Interest in this issue, which has been the center of attention of public school finance policy for at least the past fifteen years, followed from a series of judicial decisions, including the landmark Serrano vs. Priest, which held that education is a responsibility of the state government and that local educational expenditures may not be a function of the taxable wealth of the local community. In his paper, Feldstein develops a theoretical model from which is developed a means of achieving "wealth neutrality," that is, a condition whereby per pupil educational expenditures of a district is unrelated to a measure of local wealth that emphasizes property value, income, and other aspects of community wealth. Measuring wealth neutrality by the elasticity of local school spending with respect to local per pupil wealth, Feldstein demonstrates that a state can achieve any desired degree 52 of wealth neutrality by using matching grants that cause the local tax price of educational services to vary with wealth in the appropriate way.25 Ladd (1975) analyzed 1970 data for the 78 communities in the Boston SMSA. Using a log—linear equation relating total educational expenditures with ten explanatory variables, including state education block grants, local tax price, state and federal categorical grants, property wealth, and median family income, she found that the estimated price elasticity associated with state matching grants for education ranged between -0.65 and —0.49, considerably less elastic than the range estimated by Feldstein. The elasticity for state education block grants was about 0.03, in line with Feldstein's estimate, and the elasticity for combined state and federal categorical grants was 0.11. (The implied marginal propensity to spend out of block grants and categorical grants was 0.5 and 1.1, respectively.) 25The specific parameter estimates of Feldstein's educational demand function imply that complete wealth neutrality (i.e., E = 0) could be achieved in Massachusetts with ‘hdtching grants that involve a relatively low elasticity of price with respect to wealth (between 0.33 and 0.37). Interestingly, these estimated price-wealth elasticities indicate that the widely advocated and employed district power equalizing formula for state school grants, which has by definition a price- wealth elasticity of 1, would not be wealth neutralizing, but rather is more likely to result in an inverse relation between local wealth and local educational spending. 53 Ladd's central purpose was to examine the effect of local tax base composition on local decisions to provide educational services. As noted earlier, the possibility of such an effect is clear. If local voters assume that they bear less than the full cost of taxes raised from nonresidential property, those towns in which the residential property proportion of the local tax base is relatively high should prefer a lower level of school spending. If local residents assume that they bear none of the local tax on nonresidential property, the effective tax price of educational services is reduced by a fraction equal to the nonresidential property proportion of the local tax base. However, local residents will bear the tax on nonresidential property to the extent that it affects local wages and prices and, more importantly, through its long-run effects on the size of the nonresidential property tax base. Ladd found that the residential fraction of the tax base is an underestimate of the perceived tax base composition component of the tax price (i.e., voters perceive that they indeed bear some of the tax on nonresidential property), and that resident voters believe that industrial property is more likely than commercial to relocate in response to inter—community fiscal differentials (i.e., commercial property has a 54 stronger positive effect on educational expenditures than does industrial property).26 Black, Lewis, and Link (1979) and Grubb and Osman (1977) examined the impact of state education block grants on the total educational expenditures of local school districts. Analyzing pooled, time—series, cross— sectional data for the 23 regular school districts in Delaware with a median—voter model, Black et al. found a surprisingly large difference in the relative sizes of the expenditures elasticities of state and federal block grants, .66 and .04, respectively. However, the marginal impacts on expenditures of an additional dollar of each type of grant, computed at the means of the same, are quite similar: .77 for state aid and .70 for federal aid. Their result with regard to the state block grant is very close to that of Grubb and Osman (1977) who found a coefficient of .78 per dollar of state aid for California unified school districts. Black et al. estimate the income elasticity of demand for educational services at 0.44, implying that a 26Ladd calculates the expenditure elasticities of commercial and industrial property as 0.58 and 0.33, respectively. That is, a 1 percent increase in a community's commercial (industrial) property measured as a fraction of the local property tax base will result in a 0.58 (0.33) percent rise in per pupil educational expenditures. 55 dollar increase in real income would raise per pupil spending by 4 cents. Black et al. also examine the hypothesis that the assumption of full exporting of nonresidential taxes will produce an underestimate of the tax price elasticity of demand. Assuming such full exporting, the authors obtain a price elasticity of -0.15. However, when the model's tax price term is modified to allow for less than 100 ‘ 1 percent tax exporting, the estimate price elasticity is -O.23.27 This estimate is considerably lower than Ladd's comparable estimate of -0.65. The authors note that the relatively low price elasticity from Delaware is probably due, in large part, to the state's relatively large share of public elementary and secondary education expenditures as compared with Massachusetts and other states where 27Assuming 100 percent exporting of nonresidential taxes, Black et al.'s tax price t is: t = Pu . n ' Hm l tax-base x Matching-rate TAS 1+m component component where P is the resource cost per unit of education, n is the number of students, u is the units of education per student (U = E/Pu), TAS is the total assessed value of taxable property, Hm is the assessed value of the median voter's home, m is the matching rate of state school aid. Allowing for less than 100 percent exporting of nonresidential taxes, the tax base component of t becomes: 56 education demand has been estimated. Further, the authors cite Delaware's substantially lower price elasticity (—0.23) as compared with Feldstein's estimate of -1.00 for Massachusetts as evidence that a perfectly wealth—neutralizing scheme of matching grants may not be possible for Delaware without negative matching rates for the wealthiest districts; that is, a constitutional or statutory provision for the state "recapture" of locally— raised school tax revenue. (Such a provision has been found unconstitutional by state courts in Wisconsin and Maine.) Perhaps the most disquieting studies for school finance policymakers who seek statewide distributional objectives, such as wealth neutrality, without disturbing local district fiscal autonomy are those of Park and Carroll (1979, 1982). Their 1979 study of 451 school districts in Michigan indicates a much lower response of school districts to state school aid than those indicated in other studies of Michigan and other states. The authors found that a Michigan school district would T* = Pu [anm + (1+e) (TAS - nfhm)] - n1 "h where nf is the number of families e is the fraction of the nonresidential tax burden which voters perceive is not shifted back to district residents. 57 increase its total educational expenditure by only 6 cents and 32 cents for each additional dollar of state educational block grant and categorical grant respectively. Moreover, their estimated price elasticity of -0.02 would hold relatively little promise for achieving statewide distributional goals by means of state education matching grants. Pooling cross—sectional and time—series data in an econometric model that related per-pupil expenditures to different types of grants, Park and Carroll examined the budgetary behavior of 451 Michigan school districts over the 1971-72 through 1975—76 school years. The distribution of general purpose state aid to local districts was fundamentally changed during this period. Prior to 1973-74, Michigan distributed general aid to school districts through a foundation plan. Each district received an unrestricted block grant equal to the difference (if positive) between a predetermined per pupil expenditure level (the "foundation" level) and the amount that would be raised by the local district levying a predetermined, hypothetical tax rate.28 The state's 28In 1972-73, for example, districts below $17,750 per—pupil property wealth received a per—pupil amount equal to the difference between $715 and the revenue the district would raise if it levied a 20 mill school tax. Districts with per—pupil tax bases in excess of $17,500 received a per—pupil amount equal to the difference between $644 and the revenue that would be raised by a 16 mill tax. 58 guaranteed tax base (GTB) plan was introduced in the 1973—74 school year. In its first year, the state guaranteed each local district $38 per pupil for each mill of' tax effort up to 22 inills. Thus, a district levying less than 22 mills received per—pupil matching grants equal to its tax rate times the difference (if positive) between $38,000 and its per-pupil tax base. A district levying 22 mills or more received per-pupil payments equal to ($38,000 - Vi) (.022), where Vi is the district's per-pupil tax base. Park and Carroll suggest that the considerable differences between their estimated price elasticity and those obtained by Feldstein and Ladd can be partly explained by the different econometric techniques employed in the studies. Specifically, the authors point out that cross-sectional estimates, like Feldstein's and Ladd's (and like similar estimates reported in Park and Carroll, 1979) are biased if the error term is correlated with any of the independent variables.29 The check for such a bias can be done with pooled, time-series, cross— sectional data using Hausman's (1978) specification test, but not with cross-sectional data. Applying Hausman's 29The cross-sectional estimates reported in Park and Carroll (1979) showed price elasticities of up to -0.1, much larger than those estimated with pooled data, but still considerably smaller than those estimated by Feldstein and Ladd. 59 test to their pooled time-series, cross—sectional data on Michigan school Districts, they found that cross- sectional estimates should be rejected. This suggests that, if Feldstein's and Ladd's cross—sectional estimates could be similarly tested, they might be rejected as well. The authors then re-estimate the expenditure equation using five alternative specifications, each providing consistent coefficient estimates. None of the five equations disturbs the conclusion that the effects of state matching grants and unrestricted block grants are too small to be of any use for policy purposes.3o Empirical Literature: Summgry and Conclusions Although the studies discussed above differ both in methodology and the unit of government examined (cities, counties, and school districts), the findings do allow for some generalizations regarding the responses of local units to intergovernmental education aid and identified several socioeconomic and demographic determinants of local educational expenditures, including property wealth, personal income, age distribution, and the composition of the local tax base. Further, the responses of local units to various types of 3oEstimated price elasticities ranged from -0.001 to -0.018, while estimated block grant elasticities were 0.002 in four equations and 0.001 in the fifth. 60 intergovernmental aid were generally consistent across most of the studies. Unrestricted state block grants (e.g., flat per-pupil grants or foundation grants) were generally found to be substitutive-stimulative. The recipient local unit will use part of the grant to increase noneducational expenditures or to reduce local taxes and will spend part of the grant on educational services. Studies of matching grants revealed the expected negative relationship between total educational expenditures and the price of educational services. The estimated price elasticities, however, ranged considerably, from —1.0 in Feldstein's 1975 Massachusetts study to —0.02 for Park and Carroll's 1979 study of Michigan. Recognizing the possible econometric explanations of the sometimes substantial differences among the estimates of price elasticities obtained in the studies discussed above, the precise impact of a state matching grant for education appears to depend at least somewhat on the characteristics of the recipient local government. With regard to categorical grants for education, the estimated coefficients range considerably, from .008 to .66, indicating that such a grant is largely substitutive for some school districts and entirely stimulative for others. Several of the more recent IF I 61 studies (e.g., Adams, 1980; Black, Lewis, and Link, 1979; Vincent and Adams, 1978) indicate that for each additional dollar of state categorical grants, total educational expenditures will increase by approximately one dollar. The research indicates that state categorical grants are more stimulative than state block grants on the average. The most obvious reason for the greater stimulus of the categorical grants is that such grants are accompanied by more administrative requirements regarding their expenditure. Methodological Issues While the empirical literature reveals an unmistakable association between intergovernmental grants and levels of educational expenditures, estimates of the magnitude of this association appear to be sensitive to the formulation of the statistical model used. Consensus appears to be lacking as to the underlying fiscal behavior of the local units of government and the way in which explanatory variables, such as taxable wealth, income, and demographic composition affect school spending. Different theoretical models have yielded different coefficient estimates for the impact of intergovernmental grants on educational expenditures for the same data set. 62 Another difficulty in estimating these behavioral parameters is the nonrandom distribution of state school aid across local governments. With the exception of flat per-pupil grants, most state aid is distributed to local governments according to a redistributive formula which provides proportionately more aid to poorer districts. (Examples include general aid distributed to local units by means of a district power equalizing or percentage equalizing formula, as well as categorical aid for compensatory and bilingual education.) If poor communities have a rugher marginal propensity to spend out of state educational grants than. do wealthy communities, then the estimated coefficients will overstate the average fiscal response of the sample. Alternatively, if the poor districts have a lower marginal propensity to spend out of state school aid than do their wealthier counterparts, the estimated coefficients will understate the average response to intergovernmental grants. The hypothesis regarding the behavior of voters in poor communities must be tested before the coefficients from the full sample regressions can be interpreted. Quantitative relationships between school expenditures and other determinants of local fiscal behavior may also vary considerably within a state. Adams (1980) found that school districts in downstate New 63 York had a much lower marginal propensity to spend out of unrestricted state block grants than had upstate districts, but that the upstate districts spent relatively more out of personal income. Dembowski (1984) found that school districts' marginal propensity to spend out of unrestricted state block grants variedl by geographic location and population density. These findings suggest that the individual characteristics of a local community strongly influence its response to intergovernmental educational aid and that a statistical analysis of average district behavior may differ substantially from the behavior of particular individual districts. Indeed, such differences in local fiscal decision making is entirely consistent with Tiebout's (1956) classic theory that individuals with similar tastes for public goods will live together in jurisdictions that can supply the desired types and levels of public goods with relatively little economic inefficiency and the median voter theory, which holds that local governments will indeed comply with the wishes of the community's median voter when supplying public goods.31 Finally, the different types of local 31For evidence in support of both the Tiebout hypothesis and median voter model, see Edward M. Gramlich and Daniel L. Rubinfeld, "Micro Estimates of Public Spending Demand FUnctions and Tests of the Tiebout and Median Voter Hypothesis," 1984, unpublished manuscript. 64 jurisdictions which have been assigned responsibility for providing elementary and secondary education services, as indicated in Table II.2, and the complexities of their fiscal behavior Inake it extremely difficult to predict the response of a particular locality to a given program of intergovernmental grants. A policymaker pursuing a particular statewide distributional objective through intergovernmental grants, while maintaining local fiscal autonomy, should consider not only the estimated average response of local governments, but the variance of those responses as well. Such variance can be significant. Cohn (1974, interstate study) found that, for every additional dollar of state aid received, local governments increased educational expenditures by' 36 cents (M1 the average. The standard error of the estimated state aid coefficient, however, was 0.21, indicating that a local government at the 16th percentile spent only 15 cents per additional dollar of state aid, while a local unit at the 84th percentile spent 57 cents of each additional dollar of aid.32 32The degree of variability in the responses of local units to intergovernmental aid has been shown to vary by grant type. Park and Carroll (1979), Vincent and Adams (1978), and Adams (1980) have found that the ratio of the standard error to the estimated effect of state categorical grants were smaller than that of block grants. 65 Table II.2.——Provision of Public Education Responsible Government Example State Hawaii Counties North Carolina School Districts Michigan Counties and School Districts Minnesota Counties and Municipalities Virginia Municipalities and School Districts New Hampshire State, Counties, and Municipalities Alaska Counties, Municipalities and School Districts Tennessee Municipalities, Townships, and School Districts Connecticut State, Municipalities, Townships and School Districts Maine Counties, Municipalities, Townships and School Districts New York Source: Adapted from Reischauer, 1977. 66 Thus, in assessing the probable behavioral response to an intergovernmental grant program, one must examine an entire structure of inter— and intra— governmental fiscal relationships, including local tax base composition and the full array of existing intergovernmental grants and tax expenditures, including the federal deductibility of state and local taxes. In the absence of such a full specification of the income and price effects of a state's fiscal system, one cannot differentiate between differences in taxpayer preferences and structural differences when confronted with behavioral parameter estimates differing between jurisdictions. Michigan: A Case in Point As noted above, voter behavior in Michigan has proved a puzzle for researchers, with estimates of behavioral parameters differing significantly between cross—sectional and time—series studies. The disparate results, however, may be attributable to different econometric specifications of the expenditure model, significant structural differences occurring in Michigan's school finance system and differences in the perceived marginal tax price of schooling as voters gradually acquire a better understanding of their state 67 and local tax structure and their system of public school finance. Peterson (1973) examined voter behavior in Michigan prior to the major reforms of 1973, when the state introduced both a Guaranteed Tax Base (GTB) state school aid formula and a property tax credit, or "circuit breaker," program which provides income tax credits or rebates for homestead property taxes which exceed a specified percentage of household income. Rubinfeld (1977) reports no effects of the circuit breaker on school district voter behavior, but his sample was taken only one month after the circuit breaker's inception. Park and Carroll (1979 and 1982) did not consider circuit breaker price effects. More recently, Bergstrom, Rubinfeld and Shapiro (1982) found that the estimated price elasticity of demand for local school expenditures did not change whether the tax price measure included the circuit breaker effect or not. Fisher and Rasche (1984) however, report significant price effects on local property tax use in Michigan when tax price is measured using the circuit breaker price only. Thus, the econometric evidence on Michigan taxpayer reaction to the circuit breaker—induced property tax price reduction is still ambiguous. So, too, therefore, is the taxpayers' demand for public school 68 expenditures. More reliable demand elasticities for public education must be obtained to determine whether Guaranteed Tax Base (GTB) formulas, which make local district tax effort the sole determinant of per pupil spending, can be used effectively in breaking the relationship between wealth and school spending. CHAPTER III STATE EDUCATION GRANTS, PROPERTY TAX RELIEF, AND EDUCATION DEMAND IN MICHIGAN Michigan provides aid to its 565 local school districts in three forms: 1. unconditional matching grants for educational programs allocated by means of a modified guaranteed tax base (GTB) formula; 2. categorical grants earmarked for particular pupil populations (e.g., special education, compensatory education, bilingual education, etc.) or educational support services (e.g., pupil transportation, teacher training, etc.) 3. property tax relief in the form of an income tax credit for all property taxpayers whose tax bills exceed a fixed proportion of their income. Michigan's GTB "general membership" formula was instituted in the 1973-74 fiscal year, while the property tax relief or "circuit breaker" program was initiated in the 1973 tax year. Interestingly, while Michigan's circuit breaker is by far the largest in the nation in 69 Il- 70 terms of total state cost, with approximately 70 percent of the relief reimbursing school district property taxes, the programs' effect on the local tax price of educational programs has been generally overlooked in studies of school district spending behavior. Each component of Michigan's school aid systan is described below and a model of Michigan school district fiscal behavior is presented. The Michigan GTB School Aid Formula Michigan distributes approximately three—fourths of its total aid to local school districts by means of a modified guaranteed tax base (GTB) formula, which may be characterized as a version of a district power equalizing (DPE) formula. In its pure form, a DPE formula effectively equalizes the tax bases per pupil of all local school districts, ensuring that local districts will raise equal state and local per-pupil revenue for equal tax rates. Districts whose local taxable wealth exceeds the tax base guaranteed by the formula are subject to a "recapture" mechanism by which they must return their excess local revenue to the state for redistribution as state aid to poorer districts. As such, the pure DPE formula, along with its conceptually 71 equivalent counterparts, percentage: equalizing, and 33 serves two basic purposes:' guaranteed tax base, 1. It allows the electorate of each school district to determine the tax effort they are willing to make to support their educational goal; and 2. It assures that this choice is not constrained by the district's local wealth.34 Michigan's system of general membership aid to local school districts is based on the DPE formula, but with two modifications. First, as is the case in virtually every state employing a DPE school aid formula, no provision is made for the recapture of local revenue from "out-of—formula" districts-—that is, districts whose per-pupil property tax wealth exceeds the level 33For a demonstration of the mathematical equivalence of these three state-local shared—cost school aid formulas and the older Strayer-Haig foundation formula, see Peter Jargowsky, Jay Moskowitz, and Judy Sinkin, "School Finance Reform: Decoding the Simulation Maze," Journal of Education Finance 3 (Fall 1977): 199— 213. 34As noted earlier, a DPE formula generally will not yield a perfectly wealth—neutral distribution of revenue because district tax effort can be expected to vary systematically with district wealth. See Martin Feldstein, "Wealth Neutrality and Local Choice in Public Education," American Economic Review 65 (March 1975): 75— 89. As a matter of public policy, however, the existence of such a relationship may be far more tolerable than a systematic relationship between district wealth and school revenue per unit of tax effort. 72 guaranteed by the state.35 In 1982—83 Michigan had 199 such districts, accounting for approximately 26 percent of all elementary and secondary school pupils. Second, Michigan's GTB formula includes a "base per—pupil payment" parameter which results in a lower state and local revenue yield per Inill for above—average Inillage districts as compared with below-average districts. The effect of this base payment parameter, which is unique to the Michigan GTB formula, is demonstrated as follows. Michigan's GTB formula can be written as: Gi = Max [A + (v*—vi)ri, 0] (3.1) where Gi is per pupil state aid in the ith district V* is the nominal per pupil tax base guarantee Vi is the ith district's per pupil property wealth (SEVPP) r. is the ith district's millage rate A is the base per pupil payment 35In response to a growing disparity in per— pupil tax revenue per unit of tax effort between out—of— formula districts and their less wealthy in-formula counterparts, Michigan instituted a "categorical revenue recapture" mechanism in 1980-81. This provision deducts from the categorical aid of out-of—formula districts an amount equal to the district's local revenue which exceeds the DPE guarantee. However, while such deductions would be directly proportional to local property wealth, their impact was muted by the restriction that a district's deduction could not exceed 66 percent of its categorical aid, a constraint which was binding for all but a few of the out-of—formula districts. 73 For any Vi > V*, the expression (V*—Vi)ri is negative and thus deducted from A, the base payment parameter. For such districts, then, total per pupil state aid is a decreasing function of school millage rate. That is, marginal state aid is negative: = (v*-vi) < o 1 i Setting Gi equal to zero and rearranging (3.1): v, = v* + _5 (3.2) r . 1 or r. = ——£L——— (3.3) Vi-V* Equation (3.2) indicates that a district's State Equalized Valuation per pupil (SEVPP) cut—off point (i.e., the SEVPP at which the district's state aid falls to zero and the district moves "out—of—formula") falls as its millage rate rises for any V*. Equation (3.3) indicates that a district's millage cut-off point falls as the base payment parameter A falls for any given level of state SEV guarantee V* and rises for any A as the SEV guarantee approaches Vi from below. Thus, as (3.2) and (3.3) indicate, a school district whose local per pupil property wealth exceeds the nominal guarantee of the 74 formula can move out of formula by an increase in either per pupil property wealth or tax effort. Second, for districts whose per pupil property wealth is less than the nominal guarantee (i.e., V* > Vi), marginal state aid is positive, but state aid per unit of tax effort falls monotonically as tax effort rises because of the base payment parameter. That is, i = (v* - V.) > 0 dri 1 G1 A = + (v* -vi) ri ri G. d._1 r. 1 _ -2 d ri - Ari < 0 Thus, while a "pure" GTB formula, with or without a recapture mechanism, provides a tax base guarantee for all school districts which is invariant with respect to school district tax effort, the Michigan GTB formula with its per-pupil payment parameter provides an effective local district tax base guarantee which is inversely related to tax effort, shown in Figure III.1. 75 District Tax Base Guarantee VG v* District Tax Effort, ri Figure III.1.--Michigan GTB Formula Tax Base Guarantee 76 Given any level of the per—pupil payment parameter A, the local district tax base guarantee, VG’ approaches the nominal formula guarantee, V*, asymptotically from above as district tax effort, r1, rises. Conversely, VG approaches infinity as ri approaches zero. Thus, the per-pupil payment parameter exerts two effects on the formula's payout schedule. First, while the formula's marginal matching rate is invariant with respect to district tax effort up to the point where state aid falls to zero, and is equal to (V* - Vi)/Vi, the state average matching rate for local school district expenditures varies inversely with tax effort for any given level of local district property wealth, and is equal to A + (v*-vi)ri Viri Second, the per-pupil payment parameter exerts a potential behavioral effect on some local school districts through its effect on the marginal matching rate, and thus the local tax price of educational expenditures. Specifically, the payment parameter results in a local tax price greater than 1 for districts whose local per—pupil tax base exceeds the nominal per- pupil tax base of the formula. Thus, the per pupil 77 payment parameter operates, in effect, like the recapture provision of the pure DPE formula, except that a local district's tax price of educational expenditures would fall to 1 when its state aid falls to zero. More importantly, this parameter results in a (3TB formula matching rate that can change for a district iri which the local voters change their millage rate. Tfiiat is, while the formula yields a linear budget c<>nstraint for districts with an SEV per pupil which is hxelow the nominal guarantee of the formula ($54,000 in 15382—83), it yields a piecewise—linear, or kinked, budget CCJnstraint for districts whose per pupil property wealth e) $54,000, the marginal 'ta)c price (or local tax share) is: Vi/$54,000 > 1 for Vi > $54,000 and (Vi - $54,000) ri < $328 1 otherwise Conversely, the marginal tax price for any disStrict where V1 5 $54,000 is Vi/$54,000. Thus, while 78 the GTB formula yields a linear budget constraint for districts where Vi 3 $54,000, it yields a piecewise- linear, or kinked, budget constraint (and, correspondingly, a piecewise-linear nonconvex budget set) for districts where Vi > $54,000, as indicated in Figures III.2a and III.2b. The school expenditure level, E*, at which the kink occurs is determined jointly by Vi and ri : E* = E* (Vi, ri*). The school district's decision variable is ri and E* is attained at ri*, where ri* 328/(Vi $54,000). The interaction of V1 and r1* in determining E* is illustrated in Table III.1 and Figure III.3. As Table III.1 indicates, districts which could be located near the kink are those districts with an SEV per pupil (Vi) within the $62,000 to $68,000 range. Districts with Vi below $63,000 would have to levy millage rates in excess of .041 to reach the kink, while districts with Vi above $68,000 would reach the kink only with very low millage rates (.028 or lower) and per pupil expenditure levels, including the GTB grant, that would likely be unacceptably low for these communities (below $1,600). Further, a district within the interval $63,000 3 $68,000 may or may not be located near the kink, depending on its millage rate. As Table III.2 indicates, 79 Y +___r————— Slope = - (Vi/V*) Numer- aire Good P1: Slope = — (Vi/V*) < —1 Numer— aire Good «—_r———-—- P2: Slope = -1 Figure III.2.--School District Budget Sets Resulting from Michigan GTB Aid Formula, 1982—83. 80 Table III.1.--Kink-Point Per Pupil Expenditure Levels for Michigan School Districts, 1982-83. Vi r*i E* = Vi ri* $54,000 —— -— 55,000 .32800 $18,040 56,000 .16400 9,184 57,000 .10933 6,323 58,000 .08200 4,756 59,000 .06560 3,870 60,000 .05467 3,280 61,000 .04686 2,858 62,000 .04100 2,520 63,000 .03644 2,296 64,000 .03280 2,099 65,000 .02982 1,983 66,000 .02733 1,804 67,000 .02523 1,690 68,000 .02343 1,593 69,000 .02187 1,509 70,000 .02050 1,435 N233: The r*i's are school district tax rates expressed in decimals. For example, .02982 represents a tax rate of 2.982 percent or 29.82 mills, which was approximately the average millage rate among Michigan school districts in 1982-83. This rate would raise $29.82 per year per thousand dollars of SEV. 81 * r = 328/(V. - $54,000) 1 1 * ri (Mills) Vi (SEV Per Pupil thousands) Figure III.3.--Millage Rate and Tax Base Combination Placing Districts at Per Pupil Expenditure Kink. 82 .mam>wa ocflccomm can mwumu ommHHflE Mecca mo mmoacummou mpcflmuumcoo pompon Hmocfla 00mm muofiupmflo cosm .ooorewm v mm>mm QOHQB now unflupmflc mew mom m>flummwc on GHDOB mszmee hmm. omN.m mm.vm omm.vm mmo.N NM oooeom mmo.a mmoam w.mm HHH.M© vomrm mm ooo.ww mom.H HmmsH v.mm ommrvw th.N Nm oootmm ohm. mmoamw m.mm omm.vw wmo.m mm ooo.vww MZHmem\me *MZHmem MZHMAHHZ MZHM>mm mmxm mwfiquZ mm>mw moHomem “me>wQ Deflom-xcflm can me>wA mcflccwmm poflwwmfioll.N.HHH THQMB 83 a district with Vi = $64,000 and ri = .032 would be spending at a level equal to .979 of the "kink—level," E*, while a district with Vi = $68,000 and r1 = .032 would be spending at (1.368) E*. Rather, districts spending near the kink of the budget constraint would be districts for which Vi is approximately equal to $54,000 +($328/ri). As a district moves from just below to just above the kink, its marginal tax price of school spending falls from Vi/54,000 to 1. For example, a district with Vi = $64,000 which raised its millage rate from 32.7 mills to 32.9 mills would lower its marginal tax price from 1.185 to 1.0, a reduction of 15.6%. The question arises as to whether such districts near the kink do respond to the change in nmrginal tax price occurring at the kink or whether they intend to simply spend at a level near the kink and likely would be indifferent to being just below or just above the kink. As Moffitt (1986) has noted, the existence of piecewise-linear constraints alters some of the comparative statics of consumer demand. Specifically, if the budget set is nonconvex, as it is in this case, price effects may be positive instead of negative, while income effects may be negative, instead of positive. Conversely, if the budget set is piecewise convex, price 84 and income effects may be zero, instead of negative and positive, respectively. Both results can occur even though the indifference map is conventionally shaped.36 The following derivation of a consumer demand function in the case of the Michigan GTB school aid formula (i.e., a piecewise—linear budget constraint and nonconvex budget set) follows closely the exposition of Moffitt (1986). The local district budget constraint can be written as: M=P1E+Y ifE5E* M = PZE + Y if E > E* where M = M + (P2 — P1)E*. A M, or imputed income, is the intercept of the extended, or linearized, segment 2 in Figure III.4. Given this budget constraint, the conditional demand function for E may be written as: 36For the derivation of a consumer demand function in the case of a nonlinear budget constraint and discussion of its comparative statics, see Moffitt (1986). 85 I-- Segment 1 (slope = —P1) £——— Segment 2 (Slope = — P2) Ek Specifically, the individual's choice of segment is: Pick segment 1 if V (P1,M) :_V (P2,M) Pick segment 2 if V (P1,M) : V (P2,M) F” where V(P,M) = max I U(E,Y:] = U [_g(P,M), M - P (P,M):] is the E,Y — g conditional indirect utility function Figure III.4.--Piecewise-Linear Nonconvex Budget Set. 86 E = g (P1,M) if E 5 E* E = g (P2,M) if E > E* where g (P,M) is the demand function for E resulting from utility maximization The function is called conditional because it describes the choice of E conditional on having chosen a segment on which to locate. In this case, the individual (school district) has two options: to locate on segment 1 or on segment 2. (Utility maximization cannot occur at the kink in the case of a nonconvex budget set if the indifference curves are everywhere differentiable.) A change in V*, the nominal tax base guarantee parameter set by the legislature, would change both P1 and E* (the "zero grant" per pupil expenditure level) for any given district for which Vi > V*. This can be demonstrated as follows: = *— Gi A + (V vi) ri Rearranging and setting Gi = 0, *_ = A + (v vi)ri o A = r. (v. - v*) 1 1 and 87 r = A . i _— (vi - v*) Since by definition E* = A + V* ri, by substitution * = _ * * , = E ri(Vi V ) + V rl V r i i and V.A E*= V. — V* 1 Finally, because P1 = Vi/V*, dPl/ dV* = — ViV* < 0. The functional relationships between the policy parameter V* and both E* and P for districts with Vi > 1 V* are illustrated in Figure III.5. A consistent estimate of the elasticity of demand for districts spending near the kink could be obtained by the method of maximum likelihood. Such an estimate would suggest whether districts near the kink do respond to the change in marginal tax price occurring at the kink or whether they intend to simply spend at a level near the kind regardless of marginal tax price. If the latter is true, a consistent estimate of the price elasticity of demand for Michigan school district voters would be obtained by the method of least squares. This method was 88 Assume: Vi > V* and * V* lowered to VN < V* Y Numeraire Good Efi E* E Figure III.5.—-Nonconvex Budget Set and the Nominal Tax Base Guarantee. 89 used by Johnson (1979), who investigated school district spending in Wisconsin in the presence of a kinked budget constraint. Johnson estimated an expenditure equation after eliminating from his sample those districts which were spending within a small interval about the kink. The Michigan Circuit Breaker Program The Michigan circuit breaker provides an income tax credit to all property taxpayers who qualify regardless of their age, income, or homeownership status. Program benefits are determined In! a threshold formula which reimburses all eligible property taxpayers for all or a portion of the amount by which property taxes on their homes (or on farmland, buildings, equipment, and homes for farmers) exceed a specified percentage of their income. Both the credit rate and the threshold percentage of income vary by type of household. Renters receive similar relief, with 17 percent of their income 37 being imputed as property tax. The amount of the credit is determined by: 37The 17 percent presumably attempts to account for the shifting of the property tax by landlords onto renters and is based on Netzer (1966, p. 28). 90 where CR.. amount of credit received by the 13 ith taxpayer in household class j PTi. = homestead property taxes paid (actual 3 or imputed to renters) by the ith taxpayer in household class j 1' household income of the ith taxpayer 3 in household class j The tax credit parameters aj and bj are given in Table III.3. The ceiling on credits is $1,200, up from $500 prior to 1975. Beginning in 1982, program benefits were reduced for households with annual incomes over $65,000. Specifically, a family's credit is reduced by 10 percent for each $1,000 by which the family's income exceeds $65,000,a figure indexed to the CPI. Michigan's total program cost is by far the highest in the nation, and its average benefit is third, behind Minnesota and Oregon. The Michigan circuit breaker is thus designed to serve an equity goal of providing more tax relief to low- income households than to high and a political goal of reducing the tax burdens of high property taxpayers, 38 regardless of their income. In addition, as a 38For a discussion of the incidence of the property tax, see Aaron (1975). For an analysis of the income and geographic incidence and the incentive effects of the Michigan circuit breaker, see Fisher and Rasche (1980). For analysis of the Michigan circuit breaker in terms of these equity and political objectives, see Rubinfeld and Wolkoff (1983). .wocmwmfisouflo m.me%mmwa mew co unaccwmwc ooo.>w ow oom.mw Scum mmflum> SUASB wocmonHm 05Hm> u > wDHm> hvmwmoum Umsflamsvw wvwwm u >mm DHCSB slam"? > D n .Aommfiv mcommm wcm mocmflm Eoum :wxmu m0 manmu manev .mEoocH caoammsom .n I xmu hpmmmoumv .m n mo ma MHSEHOM Honocmm omen 91 mmo. 00. mmo. 00. 0.0 an- mmo. 00.H 000.0 A mmo. 00. 0m0. 00. 0.0 all 000. 00.H 000.0-H00.m mmo. 00. 0N0. 00. 0.0 on- 0N0. 00.H 000.m|H00.e mmo. 00. 0H0. 00. 0.0 all 0H0. 00.H 000.0I000.m mmo. 00. 000. 00. 0.0 nu- 000. 00.H 000.mu0 a . detail“ a Ian .. Imdmsaexme AemHhmmflm Leenflm new lemonaOAeeame mmo Hmnuov haamuoev wcwuwew>v can UEOOGH waoswmsom emu mmo mmo Amemhflpflo neecomv Hmo mmumpwfimumm Dflcwmo xma cmwummfiom cmmflcOHzll.m.HHH mange 92 mechanism to reduce the local tax price of public services financed by the property tax, the‘ circuit breaker can be expected to influence household behavior. Specifically, circuit breakers may alter the level of support for property tax increases, resulting in increased consumption of public services. Since the local property tax is the sole source of local public school revenue in Michigan, the circuit breaker alters the local tax price of educational expenditures for all households eligible for property tax relief and not receiving the maximum credit. For example, if a resident were eligible for an income tax credit equal to 60 percent of his property tax bill in excess of the percentage of income threshold, his marginal tax price of school expenditures would fall by 60 percent. That is, assuming each individual in a community lives in an identically valued home and that nonresidential taxes are fully exported, his tax price without the circuit breaker would be (ns/n)(R/V), where nS is the number of public school students, n is the number of families, R is the aggregate residential per pupil property value, and V is the value of all taxable property per pupil in the school district. However, households eligible for property tax relief and not receiving the maximum credit would face a marginal tax price of school expenditures of 93 (.4)(ns/n)(R/V), while the price for households either ineligible for property tax relief or already receiving the maximum credit remains (nS/n)(R/V). In addition to the credit for recipients whose net marginal private cost of local property tax increases is 0.4, the 100 percent credit for property taxes of senior citizens and the handicapped implies a net marginal private cost of zero for these taxpayers who are eligible for a credit and receive less than the $1,200 maximum. Fisher and Rasche (1984) provide the following distributions of marginal property tax prices in Michigan for 1976 and 1977: Marginal Property Tax Price Percentage of Tax Returns 1976 1977 1.0 65.0 67.0 0.4 23.6 22.0 0.0 11.5 11.0 Using 1976 and 1977 data, Fisher and Rasche found large reductions in net marginal property tax costs because of the circuit breaker, with the property tax credit reducing the net private cost of property taxes by 23 or 24 percent on average for the state. They also found wide variation in the marginal price of local property 94 tax increases across counties in Michigan, ranging from 0.85 to 0.66 with an average of 0.77 for 1977.39 In view of the substantial reduction in marginal property tax costs, and thus in the cost of local school expenditures, the question arises regarding the extent to which local property tax rates, and particularly school tax rates, are influenced by the property tax credit. As noted earlier, the econometric evidence as to whether taxpayers indeed respond to the circuit breaker is ambiguous. Such information regarding taxpayer response can be important for policy purposes. For example, Fisher and Rasche (1984) have shown that the incentive to increase property taxes created by the circuit breaker is greater in jurisdictions with higher per capita property values ceteria paribus. At the same time, it was demonstrated above that Michigan's GTB school aid formula, instituted in the same year as the circuit breaker, provides a substantial incentive for low property value districts (which are typically low spending districts) to increase school spending. Because the circuit breaker creates a greater incentive to raise property taxes (and thus spending) in the higher property 39As the authors note, Michigan counties are hardly homogeneous and the marginal prices of local property tax increases for the counties must be interpreted as average for all the separate local jurisdictions in each county. 95 value districts, it works in opposition to the incentive of the GTB school aid formula. Determining the extent to which the circuit breaker incentive offsets the GTB formula incentive and prevents the desired equalizing of per pupil spending across districts requires estimates of the elasticities of local school revenues and expenditures with respect to properly specified price terms. Accordingly, this study will attempt to provide these estimates with a model in which the price term is specified so as to include the effects of each of the following: (1) the: GTB school aid formula; (2) the circuit breaker; and (3) the composition of the local district property tax base (to test for perceived tax shifting by homeowners onto business and industry). The study will focus on changes, if any, in the estimated price elasticity of demand as the tax price measure is changed by the sequential inclusion of these effects and will address the existence of kinked budget constraints for specified districts, which arises from the particular form of Michigan's GTB formula. The income elasticity of demand will also be estimated with the model, which will include as independent variables proxies for local voter tastes and the cost of educational services. 96 A Model of Education Demand in Michigan The demand for education is initially assumed to be derived from a median-voter, majority-rule model where it can be shown that, under conditions outlined above, a community's effective demand for education. per family will be that of its median voter (see Bergstrom and Goodman, 1973; Robert Deacon, 1977). As with nearly all previous work on local public good demand, the model will initially assume that an individual family's demand function is a monotonic function of family income. That is, the model assumes that, when families are ordered by income, this ordering is identical with an ordering of the same families by preferred level of spending on the public good. It is this assumption of monotonicity which ensures that the spending level preferred by the median- income voter is the only level to get a majority of votes when paired against any other level. (This assumption is discussed and empirically tested in Chapter VII.) The median-voter model of demand for education is specified as follows: where PRICE INCOME STCAT FEDERAl PCTPRIV COST PCTCOLL FAMILIES The 97 b0 + bl PRICE + b2 INCOME + b3 STCAT + b4 FEDERAL + b5 PRIV + b6 COST + b7 PCTCOLL + b8 FAMILIES (3.4) Educational expenditures per public school pupil, including local, state, and federal funds Marginal tax price faced by the median incme family of the district Median family income in the district State block grants to the district per pupil Federal block grants to the district per pupil Percent of district pupils who attend private schools An index of teacher salaries, adjusted for experience and educational preparation. Percent of distict residents with some college education Number of families in the district effect of Michigan's GTB formula on the median voter's marginal tax price, PRICE, can be specified within. a framework developed by Ladd (1975). Ladd has characterized the matching rate for a local district in [hatching grant schemes such. as GTB as the state share of an additional dollar in locally financed educational expenditures. In the presence of matching grants, PRICE becomes 98 1 PRICE = n (Vm/Vt) (1-f) Tim _ tax base matching-rate (3 5) ' component component ' where n is the number of students in the district V is the assessed value of the median voter's house t is the total assessed value of property in the district f is the proportion of the local tax increase offset by reduction in federal or state income tax liability m is the district matching rate40 As formulated by the median voter model in Equation (3.1), P is a multiplicative function of ‘two separate factors: the tax base component and the matching—rate component. Equation (3.5) would understate the price perceived by local districts if they believed that they bear a part of the property tax levied on nonresidential property. Ladd (1974, 1975) has provided evidence that 40For districts receiving GTB aid, m equals (V*-Vi)/Vi. It is zero otherwise. Feldstein (1975) employed a slightly different notion, where 1n* is the state share of an additional dollar of total (as opposed to only the locally financed portion) education expenditures. In that case, Equation (3.1) beComes PRICE = n (Vm/Vt)(l—f)(l—m*) 99 voters indeed perceive less than full exportation of nonresidential property taxes. Adjusting for this possibility, the tax—base component of PRICE becomes n v+(1+e)(v—nv p* = f m t f m . (3.6) Vt where nf is the number of families 0 is the fraction of the nonresidential tax _ burden which voters perceivglis not shifted back to district residents. A final adjustment to the marginal tax price term must be made for households eligible for state property tax relief and not receiving the maximum income tax credit. Estimating Circuit Breaker Price Effects Fisher and Rasche (1984) specify the marginal private cost of a property tax increase, P, as the following: 41Equation (3.2) requires the assumption that the average assessed value of housing in the school district is equal to the median value. The formulation can be modified to allow for differences in tax shifting between owners of commercial versus industrial property. In that case, the tax—base component of P would be nf ' vn + (l-o) (Vt-nfvm + vc) + (1-8) (vt - anm + VI) . p' = Vt "PP where V and V are the commercial and industrial fractiong and th£ parameters a and B represent the fractions of the commercial and industrial property tax not shifted onto local residents. where CR = Since the Mic CRij where CRij PT.. 1] Yij then the marginal private cost of a property tax increase 100 the amount of credit received by the taxpayer the amount of homestead property taxes paid (actual or imputed to renters) by the taxpayer higan property tax credit is determined by r =Lm1n a..(Pt.. — b.Yij), 1200] = the amount of credit received by the ith taxpayer in household class j = the homestead property taxes paid by the ith taxpyaer in household class j = the household income of the ith taxpayer in household class j for a taxpayer in household class j is given by: Thus, property tax depends upon household class, l-aj if PTij - ijij > O and CRij < 1200 1 if PTij - ijij < 0 or CR1]. _>_ 1200 the perceived marginal private cost of increase for the decisive, median voter the voters' property taxes paid, income, and whether or not a credit was indeed 101 claimed. To estimate the price effect on the median voter, the average marginal price of property tax increases was calculated for each local K-12 school district in Michigan. Specifically, the marginal price of a $1 increase in local property tax is calculated as the average of the marginal price for each. credit type, weighted by the number of credits within each type.42 The credit types and their respective marginal prices, or marginal private costs, are shown in Table III.4 Using aggregate data from the Michigan Department of Treasury on the number of taxpayers in each local school district receiving each type of credit, along with the total number of taxpayers in each district, an average marginal private cost of a $1 increase in property tax for a school district is estimated by the following formula: 42As an alternative to the average marginal property tax, the property tax price faced by the median voter (i.e., the median—income, median-SEV householder) could have been used. 102 Table III.4.—-Circuit Breaker Credit Types Credit Type Marginal Private Cost (T) CR 1 (Seniors) 0 CR 2 (Veterans/Blind) 1 CR 3 (Paraplegics) 0 CR 3 (Disabled) .4 CR 4 (General) .4 4 Z T _ CR2i + .2CR3i + .4CRi + (Ti - j=1 CRj) i— T. 1 where Ti = average marginal price of a $1 increase in local property tax in the ith school district T. = total number of taxpayers in the ith district 43Data were not available on the number of taxpayers receiving the maximum amount of each type of credit. Examining data for the 1976 and 1977 tax year, Fisher and Rasche (1984) found that less than 1.4 percent of credit claimants received the maximum credit. Hp 103 Education Demand: Alternative Price Specifications The model of demand for public school spending in, Michigan will be estimated with each. of the following marginal tax price specifications: 1 PRICEl = N(Vm/Vt) m (3.7) where N = number of students in the district Vm = median household SEV in the district Vt = total SEV of the district (V* - Vi)/Vi if district receives formula aid 0 otherwise As such, specification Pl incorporates only the GTB school aid component into the price term. Specification P2, however, incorporates the effect of the Michigan circuit—breaker on the marginal tax price of education, as follows: PRICE2 ='TP1 where T is the district's average marginal property tax price under the circuit—breaker, as defined above. Specification P3 incorporates the GTB school aid formula, the circuit breaker, and the composition of the 104 local district property' tax base, providing a test. of perceived tax shifitng by homeowners onto nonresidential property owners, as follows: PRICE3 = N *’T/(1+m) * Vm/VTRES * (1— GPCTNRES) where N = Number of students in the district T = District's average marginal tax price under Michigan's "circuit breaker" property tax relief program, weighted by credit type m = District's matching rate under the Michigan GTB formula, or (V*—V.)/V. if the district is in—formula ahd 0 otherwise. V* = Nominal GTB formula SEV per pupil guarantee Vi = District's actual SEV per pupil Vm = Average residential SEV in the district (proxy for median household SEV in the district) VTRES = Total residential SEV in the district PCTNRES = Fraction of total district SEV that is not residential or agricultural a = Fraction of nonresidential or non— agricultural property tax not shifted back to district residents The case where o = 1, which yields PRICE3 = N * T/(1+m) * Vm/VTRES * (l-PCTNRES) represents perfect perceived tax avoidance by school district residents. This can be demonstrated by as follows: PRICE3 = N * T/(1+m) * vm/vt That is, the tax price for the median household voter is proportional to his share of the total property tax base of the district. Tax price specification PRICE3 is derived as follows: Vm/V = Vm/VYTES * VTRES/V t t = Vm/VTRES * PCTRES Since PCTRES = 1 - PCTNRES, by substitution we get: = * - Vm/Vt Vm/VTRES (l PCTNRES) the tax base component of the tax price specification for the case of perfect perceived tax avoidance. School expenditures should also vary with school staff costs and the demographic characteristics of the community. In-Formula and Out—of—Formula Districts: Two Structures or One? A question raised by this dissertation is whether the voters in the in—formula districts and the out-of— formula districts are drawn from the same population. On 106 the one hand, there is no a priori reason to expect that voters in out-of—formula districts have significantly different preferences for public education from voters residing in in-formula districts. The division of Michigan school districts into in-formula and out-of— formula groups arises solely from particular public choices regarding both an allocation mechanism (i.e., the GTB formula) and a state aid dollar amount. There is no reason to assume that the Michigan GTB formula divides the Michigan population along a nonarbitrary line. Rather, there may indeed be one demand curve for all district voters in the sample, rather than a separate demand curve for each district group. On the other hand, the in-formula and out—of— formula district groups may indeed differ in their preferences in public school expenditures because their division created by the GTB formula is the result of a Tiebout self—selection process whereby individuals with a relatively strong demand for education locate in communities with rich tax bases and high school expenditures. Log-linear expenditure equations indicating more price-elastic demand for out—of—formula district residents shed no light on this question. Such a demand formulation, which assumes a constant elasticity of demand on the part of Michigan voters, is often used h 107 in empirical work because results so obtained are easy to interpret and may, in fact, provide a good approximation to the data.44 Suppose in this case, however, that Michigan voters' demand for public school spending is linear rather than log-linear. Is such a hypothesis also consistent with regression results indicating that the estimated price elasticity of demand is higher among out— of-formula district voters than among in—formula voters? In the case of a single linear demand curve, the price elasticity of demand rises with price, of course, from zero at P = 0 to .0 at P = some positive. Such a single, linear demand curve is inconsistent with the evidence presented thus far, since out-of—formula districts face lgggr marginal tax prices than in—formula districts, and yet, were found to have more elastic demand for school spending. The price effects of Michigan's GTB formula, which reduce the Inarginal tax prices faced by in-formula district voters, but have no bearing on the tax prices faced by out-of—formula district voters, are more than offset by the TAXBASE 44If the tax price-expenditure function is actually long—linear, the multiplicative components of PRICE2 could be entered separately into a log—linear expenditure equation and the same coefficient would be estimated for each component. However, estimated coefficients on the PRICE2 components were found significantly to be different from zero and from each other at the .01 level in both the in—formula and out—of- formula distict equations. 108 price components, which reflect the relatively high proportion of nonresidential property in the out-of- formula districts. At the same time, however, the data reveal that household income is higher among the out-of—formula districts. Consequently, their higher per pupil expenditure levels should be illustrated not by a single demand curve, but by a second curve to the right of the first, representing their higher income levels. Such a family of linear demand curves is presented in Figure III.6. The two demand curves y = yI and y = y0 correspond to the average household incomes of in-formula district and out-of-formula district households, respectively. First, it is clear that school spending is assumed to be a normal good. At any given marginal tax price, (e.g., p*), expenditures will be higher among the higher income group (i.e., the out—of-formula school districts ) or I t x E > E Certainly, then, given a 12:33; marginal tax price among out-of—formula districts, expenditures will be higher among these higher income districts, with the expenditure disparity exacerbated by the lower price in the out-of- formula districts Marginal Tax Price (P) I J * * I EI o o Expenditures Per Pupil (E) Figure 111.6 .-- A Family of Linear Demand Curves. 110 However, the hypothesis of a linear demand curve, or family of curves, is still inconsistent with the evidence presented in the regressions presented above, since demand was found to be more elastic among out—of-formula district voters, not less as indicated in Figure V1.1. Further testing is required to determine ‘whether the price and income elasticities estimated by dividing Michigan school districts into: two samples——in—formula and out-of-formula--do, in fact, represent two different structures or indeed belong to the same population. One appropriate test for structural differences between in-formula and out-of-formula districts is the test employed by Gregory Chow for compring sets of coefficients in two linear regressions.‘15 However, the hypothesis of structural unity may be tested with regard to each independent variable by means of dummy variables. Here, one regression is estimated for the entire sample, using dummy ‘variables for’ the intercept. and for each explanatory variable. The model to be estimated is: 45See Chow (1960) and Dutta (1975). 111 EXPENDPP = 80 + 81D + BZPRICE + 83 (D*PRICE) + 84 INCOME + 85 (D*INCOME) + B6STCAT + 87(D*STCAT) + BSFEDERAL + 89(D*FEDERAL) + BIOPCTPRIV + 811(D*PCTPRIV) + BIZCOST + 813(D*COST) + 814PCTCOLL + 815(D*PCTCOLL) FAMILIES = D*FAMILIES) (3.1) 816 816( where 0 if district is in—formula 1 otherwise CHAPTER IV DATA AND DESCRIPTIVE STATISTICS The dependent variable in the lnodel of school spending behavior is district operating expenditures per public school pupil, which is financed by local property tax revenue, state (hatching grants distributed through the DPE formula, state aid for categorical programs (e.g., special education, pupil transportation, etc.), and federal aid. The data on local school district SEV, revenues, operating expenditures, millage rates, public and private school enrollments, average teacher salary, average teacher experience, and the proportion of teachers with a master's degree or higher were obtained from the Michigan Department of Education. The data on homestead and farmland property tax credits for the 1982 tax year were obtained from the Michigan Department of Treasury.46 46Not all income tax returns are represented in these data, since 11 percent of the returns filed listed no school district code or a nonexistent code. Further, the Treasury Department was unable to check whether some taxpayers may have listed incorrect school district codes. 112 113 The data on the number of families per school district, median family income, and the number of families with school-age children were obtained from the 1980 Census of Population and Housing, Local Education Summaries. A Gini coefficient for the distribution of family income in each school district was computed with data from the 1980 Census, which provides a frequency count of families across 15 income intervals for each school district. The coefficient was calculated for each district using the method outlined by Lows (1984). Because breakdowns of individual school district SEV by property classification are not available from the state, these data were obtained for the 1982 tax year from either county equalization offices or intermediate school districts. With the exception. of school district SEV distributions by property classifications, data were obtained for all 530 local school districts in Michigan, providing instruction for grades kindergarten through 12 for the 1982-83 school year. Data on SEV distributions by property classifications were obtained for 345 districts. Since such data on SEV distributions are necessary for the calculations of each alternative local marginal tax price for public school expenditures, the study is limited to a sample of 345 local school districts in Michigan. These districts accounted for 83.6 percent of Michigan's total kindergarten through 114 12th grade enrollment, and received 87.7 percent of the state's total membership aid in 1982-83. In addition to the local marginal tax price of public school spending, income, and socioeconomic characteristics of school district households, the cost of schooling relative to the cost of other goods should affect the level of school spending; While average teacher salary of a district is often used as a proxy for schooling cost, such a measure fails to control for variation in teacher quality. Following Brown and Saks (1983), school district average teacher salaries were adjusted for quality differences due to variations in years of experience and the proportion of teachers with master's degrees. This was done by regressing the (natural) log of average teacher salary in a school district on the average years of teacher experience and the district's proportion of teachers with master's degrees (both in quadratic form). The estimated regression equation was then used to determine the difference between the observed and predicted salary level for each district, given its teacher quality. This difference, residual average teacher salary, is a measure of the interdistrict differences in costs for teachers of comparable quality. 115 Marginal Tax Prices of School Expenditures As noted above, a GTB school aid formula, such as Michigan's, is designed to equalize combined state and local revenue yields across school districts levying equal school tax rates. The formula accomplishes this by providing state aid to school districts on a Inatching rate basis, with each district's matching rate being inversely proportional to its per pupil property wealth. Descriptive statistics for the alternative measures of the marginal tax price of public school expenditures in the 345 sample school districts are provided in Tables IV.1, IV.2, and IV.3. Statistics are provided for the entire 345 district sample, as well as for the 242 in— formula districts, and the 103 out-of—formula districts. The separation of the sample into in—formula and out-of- formula groups was done antecedent to the execution of separate regressions on each group and a cmow test to test the null hypothesis that there is no statistically significant difference between the estimated price and income coefficients of the two regression equations (i.e., that both samples are drawn from the same population). Recall that PRICEl consists of two components: TAXBASE and MATCHP, as follows: 116 mofi 0H0. 0 mmH. 0mm. ozHeom 00H moe. 0H0. H00. 00H. ssooeom mod 0N0. mmo. mam. 0mm. mmmzeom M00 mom. 000. N00. New. mmonm mofi 0H0. 0M0. 000. NHN. mmonm mofi 000. 000. 000. mew. e mofi 000. 000. 00H. mmm. Hmonm z EDEflxmz , EDEMGMZ coaumfl>mo cumocmvm cow: GoaumUHMAUOQm muofluumflo wHSEHomImoIDSOIImoflumMDMDm w>flemfluomwo .mcoflDMOHMHoQO w>flumcuwDH< "mmoflmm MMB HmcflmuwSII.H.>H mqmde 117 New mom. o hmo. evo. QZHBUm New wow. 0 moo. omo. EEOUBum New mww. Hoo. HmH. mmm. mmmZBum New ewe. NNo. Nmo. mam. mmonm New mom. mac. wmo. Hum. NmUHmm New 0mm. omv. «mo. Hum. e New man. oeo. mMH. awe. HmUHmm z Edaflxwz EDEHCHE COHDMH>mQ oumocmwm cow: coauwoamaowmm muofluymflo MHDEHOMICH "moapmHDMDm ®>Huofluomwo.mGOHPMUAMMODQm w>flwmcuwpam umwoflum xma Hocflmumzll.m.>H mqm<fi 118 mam 0H0. 0 N0H. 000. ozHeom mam 000. 0 mso. 000. 2206968 mam 0N0. H00. 00H. sew. mmmzeom mam mom. mmo. 000. mam. mmonm mam pom. 0H0. H00. mmm. mmonm mam 0mm. 000. 000. 0mm. e mam mns. 0N0. HeH. 000. Hmonm z EDEmez EDEHQMZ COHDmH>mD oumocmvm cmwz GOHDMOMMMUQO muonnnmao Hue "monumnuabm m>HpmflHommD smcoHDmoflwflowmm w>flumcuwwa< "moveum Mme Hmcflmuczll.m.>H mqmde 1 = * '— PRICEl N (Vm/VT) 1+m TAXBASE MATCHP where N number of students in the district < u median household SEV in the district (proxied by average residential SEV in the district) V = total SEV of the district T (v*/V./Vi if district received formula 1 aid m = 0 otherwise V* = nominal GTB formula SEV per pupil guarantee Vi = district SEV per pupil The full sample mean of PRICEl is considerably less than one, ranging from a low of .02747 to a high of .713, with a mean of .388. This relatively low PRICEl is due not to the price effects of the GTB school aid formula, but to the TAXBASE component; that is, to the presence of considerable nonresidential property in the school districts. The impact of the TAXBASE price components on the Michigan school finance system is apparent upon comparison of TAXBASE and PRICEl for in—formula and out- of—formula school districts. The lower TAXBASE price components for the out-of—formula districts, .332 as 47A case—by—case listing reveals that this minimum taxprice is for the Bridgeman School District, which enjoys an SEV per pupil of $637,246, due principally to the presence of the Cook nuclear power plant in its local tax base. 120 compared with .500 for the in—formula districts, more than offsets the higher MATCHP component for the out-of— formula districts. That is, while the out—of—formula districts receive no state aid through the GTB membership formula and have, therefore, a MATCHP price component equal to unity, their lower average TAXBASE component yields a lower average PRICEl for the out—of—formula districts. Assuming for the moment that taxpayers believe they completely avoid taxes levied on nonresidential property (a hypothesis which is empirically tested in the next chapter), voters in out—of—formula districts make their school spending decisions on the basis of a lower perceived marginal tax price than do their in-formula district counterparts. The GTB formula, designed to yield a marginal tax price inversely related to per pupil property wealth in each local school district, merely reduces the marginal tax price advantage enjoyed by out- of—formula districts because of their relatively high property wealth, both residential and nonresidential. Moreover, when adjusted for income tax credits provided through the property tax circuit breaker, the relative price advantage enjoyed by the out—of—formula districts actually increases, with their average marginal tax price falling from 80.8 percent to 78.2 percent of the average marginal in-formula tax price. 121 The expenditure disparities between the two district groups, which are a function of differences in marginal tax price, family incomes, and preferences, are correspondingly large, as indicated in Table IV.4. Mean expenditures per pupil among in—formula districts for 1982-83 were $2,246, while out-of—formula districts enjoyed average expenditures of $2,989, or 33.1 percent higher than their in—formula counterparts. 122 hmw.m mmm.mm nam.o mmo.mm omm.m omm.om mwwo .oum cow: .>mo .owm com: .>oo .ppm cow: mDOHuumfiD Ham _ wHSELOMIMOIDDO MHSEHomncH mwlmmma .mwofluwmflo MHDEHomleIDDO . m> MHDEHOMIGH meSpflocmmxm Hoonom OHHQDm pom .mmumm wmmHHHE .wwEoocH..mwoflHmll.v.>H mange CHAPTER V REFINING THE PRICE TERM AND ESTIMATING THE MODEL While specifications PRICEI and PRICE2 implicitly assume perfect avoidance by homeowners of taxes levied on nonresidential property, specification PRICE3 allows for the possibility that the burden of such taxes, particularly those levied on commercial and industrial property, can be shifted onto residents, principally in the form of higher product prices or the out—migration of capital and consequent shrinking of the tax base. When the tax price specification that implies perfect avoidance is modified to explicitly incorporate perceived tax shifting from commercial and industrial property owners to homeowners, the goodness of fit of the estimated linear expenditure equations, as measured by the adjusted R2, is increased for both in—formula and out—of—formula districts. Specifically, the residual sum of squared errors of the estimated expenditure equation is minimized, and the adjusted R2 maximized in the case of a = .74 for out-of—formula district voters and 123 124 o = 1.31 for in-formula voters, where represents the fraction of commercial and industrial property 293 shifted onto local residents. Using data for 242 in-formula school districts, a series of estimates for expenditure equation 3.4 were obtained, each incorporating a different hypothesized value for a . The same procedure was repeated for the sample of 103 out—of—formula districts. These results are presented in Table V.1.48 As shown in the table, residents of Michigan's in-formula districts perceive that 131 percent of the nonresidential property tax burden is avoided, as compared with 74 percent for residents of out—of-formula districts. This relatively large difference in the estimates of the perceived incidence of nonresidential property taxes by the two school district voter groups serves to narrow the disparity in average per pupil spending between the two groups. That is, in the case of "perfect" exporting of nonresidential taxes (i.e., a = 1.0), the local marginal tax price of school spending for 48Since the study involves grouped data from the individual school districts, all regressions use weighted least squares where the weights are the square root of the number of families in the district. Ordinary least squares would be an inappropriate estimation technique because the error term is a function of the size of the population tested (heteroscedasticity; see, for example, Kmenta, 1971, pp. 322—6). 125 Table V.l.--Perceived Tax Price and Tax Base Composi- tion, PCTNRES = 1 PCTRES, where PCTRES =[£% Res. + % Agric.)+ 100] Linear Form Out-of-Formula Districts Regressions a RZ SSR SEE .67 .63335 1343545750 429.06620 .68 .63386 1341681006 428.76834 .69 .63429 1340096072 428.51501 .70 .63465 1338791068 428.30631 .71 .63493 1337765732 428.1422? .72 .63513 1337019430 428.02283 .73 .63526 1336551153 427.94786 .74 .63531 1336359529 427.91718 .75 .63529 1336442826 427.93052 .76 .63519 1336798963 427.98753 In-Formula Districts 1.27 .46310 983726294 257.35348 1.28 .46318 983595642 257.33639 1.29 .46323 983502461 257.32420 1.30 .46326 983446016 257.31682 1.31 .46328 983425578 257.31414 1.32 .46327 983440422 257.31609 1.33 .46324 983489300 257.32255 1.34 .46320 983573090 257.33344 1.35 .46313 983689497 257.34867 1.36 .46305 983838352 257.36814 126 in—formula districts is .271. However, given the estimated exportation of more than 100 percent of such taxes by in—formula district residents (i.e., d = 1.31), the perceived local marginal tax price for these voters falls to .246, a decline of 9.2 percent. Since the price elasticity of demand for school spending for these voters is estimated at .149891, the 9.2 percent reduction in perceived marginal tax price raises per pupil expenditures by 1.37 percent, or approximately $31. By this reasoning, the 14.15 percent increase in the perceived marginal tax price of out—of—formula residents, from .212 to .242, results in a 4.11 percent decrease in per pupil expenditures, or approximately $123, in these districts. In this way, differences in perceived property tax shifting between residents of in— formula and out—of—formula district residents have the effect of reducing the disparity in average per pupil spending between the two groups by approximately $154, or 17.2 percent. The result suggesting that residents in in- formula districts perceive an exporting of more than 100 percent of taxes levied on nonresidential property would be difficult to explain in a world where information is costless or Where political competition assures accurate perceptions of tax burdens. However, as has been argued 127 by Greene and Munley (1981), there is no a priori reason to reject the hypothesis that local residents can indeed perceive the ability to export to nonresidential property owners more than 100 percent of the taxes levied on such property. Filimon et al. (1982) examined the possibility that it could be in the interests of individuals attempting to maximize the size of the local budget to create fiscal illusion whereby voters underestimate levels of intergovernmental aid or overestimate the share of local taxes paid by others. In this way, voters may perceive exportation of more than 100 percent of taxes levied on commercial and industrial property even if they recognize the possibility of some shifting of 49 nonresidential property taxes onto themselves. Thus, 49Published research examining the question of perceived property tax exportability is scarce. In addition. to Ladd (1975) and Nelson (1984), Greene and Munley (1984) addressed this question. The results obtained here, while indicating greater perceived tax shifting than do the results obtained by Ladd and Nelson, are considerably lower than the estimate of 2.46 for the tax shift parameter obtained by Greene and Munley with their log—linear expenditure equation. In view of the estimate's large standard error, however, the authors reject this estimate as imprecise and accept their estimate of .88 obtained using a Box—Cox transformation. Since the estimate value for the transformation parameter is .98 with a standard error of .32, the null hypothesis that the parameter equals one cannot be rejected and the authors conclude that a linear demand equation provides a better fit than a log—linear equation. FUrther, their results cannot rule out some values of the tax shift parameter in excess of unity. 128 the results fbr inrformula district residents are consistent with a high degree of fiscal illusion.‘ While this method of estimating the extent of perceived shifting of nonresident property taxes is useful, Megdal (1984) notes several problems with it. First, a school district could enjoy fiscal benefits associated with the presence of commercial and/or industrial property, such as reduced costs of commuting to work or shopping. Such benefits would result in higher real incomes, ceteris paribus, and, therefore, school spending could be positively correlated with PCTCOMM and/or PCTIND. Further, if the amount of commercial and industrial property is a function of community income (see Fischel, 1975), interpretation of would be further confounded. Empirical Results The. model of school expenditures presented in Chapter III (Equation 3.1) is now estimated with tax price terms PRICEI, PRICE2, and PRICE3, as specified above. The model is also estimated with specification PRICE4, which includes the GTB component adjusted for perceived tax shifting from commercial and industrial property owners, but not the circuit breaker. Descriptive statistics for each variable are presented in 129 Table V.2. Regression results are summarized in Table v.3. In view of possible behavioral differences between residents of in—formula and out—of—formula districts, dummy variables are used to test for structural. unity with regard to each individual independent variable. Theequations are estimated by weighted least squares, where the weighting factor is the square root of the number of families in the school district. Price Elasticity of Demand As shown in Table v.3, the coefficients on all four price terms have the expected negative sign and are significant at the .01 level. The same is true for each of the dummy price ‘variables, indicating a structural difference between in- and out-of-formula district voters in the price elasticity of demand for public school expenditures. Estimated point elasticities of demand, calculated at the mean per pupil expenditure levels, and mean prices, are presented in Table v.4. While the estimated point elasticities vary somewhat for the out—of—formula voters, the results indicate that their demand is substantially more elastic than that of their in—formula counterparts. This finding raises a concern for state policymakers, because the group of voters less responsive to price effects is that group which participates in the state's major school 130 00H 000 z 000. 0H0. 00H. 000. >Hmmaom 000.0 000.00 000.0 000.H0 msoozH 00H. 000. 00H. 000. .0monm 000. 000. 000. 000. mmonm 000. 0H0. 000. H00. 0mone 00H. 000. 00H. H00. Hmonm 0H00 0000 000.0H 0000 mmHHHs00 00H. 000. 000. 000. HHooeoe 00.0HH 00.H0 00.00 00.H0 00000 00.00 00.00 00.00 00.00 H0mmomm 00.0000 00.0000 00.0000 00.0000 0000 00.000 00.0000 00.0H0 00.0000 mmozmmxm c00#MH>0Q Unmwcmum cow: c00000>wo oumccmum com: wHQMHHm> mflOHHu.mHQ MHSEHOMIMOIHVDO meofluumflo masfinomch m>0maflwomwo "monswficcmmxm Hoooom 00-000H--06H00H0000 ,oflaoom c003.UchHUOmm< moHQmHHc>II.N.\w mqmfie 131 TABLE V.3.-—WLS Regression Coefficients for Michigan K—12 Districts, 1982-83 Predictor Price Specification Variable PRICEl PRICE2 PRICE3 PRICE 4 CONSTANT 1673.620** 1704.852** 1691.135** 1664.547** (20.691) (20.498) (20.283) (20.343) DUMMY 206.299** 236.493** 573.612** 546.232** (28.290) (28.041) (29.613) (29.521) PRICEl -506.810** (25.831) D*PRICEl -l629.333** (44.482) PRICE2 -909.026** (40.494) D*PRICEZ -2893.595** (71.325) PRICE3 -887.948** (35.937) D*PRICE3 -3519.465** (75.407) PRICE3 -511.748** (22.947) D*PRICE4 —2198.973** (47.859) INCOME .00916** .00968** .00948** .00928** (.00110) (.00106) (.0010) (.00105) D*INCOME .03405** .03655** .0386** .03861** (.00143) .00139) (.0013) (.00140) COST .02577** .02448** .0238** .02490** (.00062) .0062) (.0006) (.00061) D*COST —.004455** —.007l93** -.0087** -.008157** (.001015) (.001020) (.0010) (.001019) TABLE V.3.--Continued. 132 Predictor Price Specification Variable PRICEl PRICE2 PRICE3 PRICE 4 FEDERAL 1.8027** l.7177** 1.7039** 1.7808** (.0425) (.0424) (.0421) (.0418) D*FEDERAL 1.1007** .75867** .4158** .84314** (.0891) (.08923) (.0900) (.08844) PCTCOLL 645.543** 691.284** 667.082** 626.723** (34.218) (33.414) (33.271) (33.753) D*PCTCOLL 348.172** 390.113** 249.351** 154.5946** (46.183) (45.110) (45.112) (45.9330) PCTPRIV -69.618* -61.32612* -47.999* —57.4446* (24.155) (23.74579) (23.580) (23.7544) D*PCTPRIV 211.126** 172.987** 98.994** 137.735** (25.186) (24.787) (24.704) (24.843) FAMILIES -.00121** -.00124** -.00124** -.00122** (.00005) (.00005) (.00005) (.00005) D*FAMILIES -.000273 -.001228** —.00205** -.001069** (.000492) (.000486) (.00048) (.000486) STCAT 2.3651** 2.31665** 2.2849** 2.33555** (.0707) (.06966) (.0693) (.06967) D*STCAT -2.5051** -2.4155** —2.3328** —2.42266** (.0766) .0755) (.0751) (.07550) R2 .788 .795 .797 .795 N 345 345 345 345 SEE 285.464 280.995 279.271 281.179 NOTE: Standard errors are in parentheses. *Statistically signifciant at the .05 level. **Statistically significant at the .01 level. TABLE VI.3.-—Continued. 133 Predictor Price Specification Variable PRICEl PRICE2 PRICE3 PRICE 4 FEDERAL 1.8027** 1.7177** l.7039** l.7808** (.0425) (.0424) (.0421) (.0418) D*FEDERAL 1.1007** .75867** .4158** .84314** (.0891) (.08923) (.0900) (.08844) PCTCOLL 645.543** 69l.284** 667.082** 626.723** (34.218) (33.414) (33.271) (33.753) D*PCTCOLL 348.172** 390.113** 249.351** 154.5946** (46.183) (45.110) (45.112) (45.9330) PCTPRIV -69.618* —6l.32612* -47.999* —57.4446* (24.155) (23.74579) (23.580) (23.7544) D*PCTPRIV 211.126** l72.987** 98.994** 137.735** (25.186) (24.787) (24.704) (24.843) FAMILIES —.00121** -.00124** -.00124** —.00122** (.00005) (.00005) (.00005) (.00005) D*FAMILIES —.000273 -.001228** -.00205** -.001069** (.000492) (.000486) (.00048) (.000486) STCAT 2.3651** 2.31665** 2.2849** 2.33555** (.0707) (.06966) (.0693) (.06967) D*STCAT -2.5051** —2.4155** -2.3328** -2.42266** (.0766) .0755) (.0751) (.07550) R2 .788 .795 .797 .795 N 345 345 345 345 SEE 285.464 280.995 279.271 281.179 NOTE: Standard errors are in parentheses. *Statistically signifciant at the .05 level. **Statistically significant at the .01 level. 134 finance policy tool, viz., the GTB general membership formula. If the state were to increase district participation in the formula in an attempt to reduce interdistrict disparities in per pupil spending, the larger stimulative effect upon spending in property wealthy districts would likely increase such disparities.50 That is, the lower marginal tax price for current in—formula disticts which would result from an increase in GTB aid would have little stimulative effect on the voters, given their price inelastic demand. These voters are currently spending at their desired levels and cannot be induced to change these levels by the price effects of state funding changes. As indicated by the price elasticities shown in Table v.4, such price effects would likely result in expenditure increases in districts 50Such an increase in formula participation could be achieved, for example, by raising the level of state aid from current revenue sources or by exempting certain classes of property (e.g., commercial or industrial) from local ad valorem taxation and imposing a state tax to be distributed to school districts through the general membership formula. 135 currently out-of—formula, given their substantially more price-elastic demand for school spending. As shown in Table v.3, the coefficients on both INCOME and D*INCOME are positive and significant at the .01 level in each of the four equations. Estimated point elasticities of demand, calculated at the means of the variables, are presented in Table v.5. In each equation, the estimated income elasticity of demand is substantially higher among out-of—formula district voters, suggesting that unconditional grants would have substantially more stimulative effect in these districts. Put another way, increases in state block grants to in— formula districts would likely prove inefficient in reducing spending differences between in—formula and out- of—formula districts, since voters in the former group would merely reduce their tax effort in response. TABLE V.5—-Estimated Point Income Elasticities of Demand for School Expenditures Voter Group Equationl Equationz Equation3 Equation4 In-Formula .0899 .0864 .0935 .0828 Out-of— Formula .3857 .4127 .3916 .4275 136 Other Results All remaining coefficients are also of the expected sign and statistically significant at the .01 level, with two exceptions. First, the coefficient on state categorical aid (STCAT) for out-of—formula districts is not significantly different from zero (2.2849 - 2.3328 = -0.0479, with a standard error of .07).51 The absence of a statistically significant relationship between such aid and total per pupil spending in out—of-formula districts is likely due to the state "recapture" of such funds from these districts. Categorical grants to these districts were reduced by 66 percent in 1982—83. (The mean and standard deviation of STCAT presented in Table V.2 were calculated before the reductions were applied. Under Department of Education accounting procedure, the full categorical program payments are credited to each out-of—formula districts and the recapture applied as a single deduction. 51"Nonmatching state aid" is not an entirely correct name for this variable since it includes payments to local school districts to partially reimburse the cost of some services (e.g., pupil transportation and special education) incurred in the previous year. Such reimbursement constitutes a matching grant scheme, thus exerting a price effect as well as an income effect on local school districts. However, since the data do not distinguish between matching and nonmatching aid distributed to local districts outside the general membership formula, they are treated as a nonmatching block grantq In 1982-83, such. nongeneral. membership state aid accounted for approximately 24 percent of all state school aid. 137 Adjusting the STCAT descriptive statistics for the recapture, the mean falls to 17.51 and the standard deviation to 40.14). Consequently state categoricals are a very small part of out-of—formula district budgets.52 State categorical grants to in-formula school districts appear to be surprisingly stimulative, with a $1 increase in such grants being associated with a $2.28 increase in per pupil spending (PRICE3 equation). Such evidence, however, should not be interpreted as "proof" that such grants would be effective policy tools for stimulating school expenditures if used more extensively (say, by diverting state revenue from ‘the GTB general membership formula). Because these grants do exert some price effects (distributed largely as reimbursement for previous year expenditures on special education, pupil transportation and teacher training), more extensive use of such grants for out-of—formula districts would likely 52The categorical recapture formula for 1982-83 may be criticized on vertical equity grounds. The formula is designed to be equitable by recapturing an amount of categorical aid from each out—of—formula district equal to the amount of the district's local property tax revenue in excess of the amount guaranteed the district by the general membership formula. However, the recapture amount is subject to a cap equal to 66 percent of the district's total categorical entitlement. Since the "excess local revenue" exceeded the 66 percent cap in all but approximately five of Michigan's 199 out— of—formula districts in 1982—83, districts with large variations in per pupil property wealth lost a uniform 66 percent of their categorical revenue to the recapture provision. 138 result in even greater spending disparities as the more progressive price effects of the GTB formula are replaced with those of the categorical reimbursement formulas. Second, for the in-formula districts, the coefficient on PCTPRIV, the percentage of district pupils who attend private schools, has the expected negative sign, but is significant at only the .05 level. Further, while the coefficient is significant at the .01 level for the out—of—formula districts, its sign is positive, an arguably unintuitive result (50.995 in the PRICE3 equation, higher in the others). However, this result for out—of-formula districts (where a substantially higher proportion of pupils attend private schools as compared with in-formula districts) may reflect greater demand for all school spending, both public and private. As indicated by the regression results reported above, residents of out-of—formula districts have revealed a stronger preference for education than as revealed by in- formula residents. Although residents of out-of—formula districts purchase higher per pupil expenditures in their public schools than do their less wealthy in—formula counterparts, their school tax rates are slightly lower-- an average of 29.096 mills among out—of—formula districts versus 30.380 for in—formula school districts in 1982—83. Further, as noted earlier, residents of out-of—formula 139 districts face a lower average Inarginal tax price for education (PRICE3 = .246 for in—formula district residents and .242 for out-of—formula residents), due primarily to differences among the district groups in tax base composition and, to a lesser extent, differential treatment by the circuit breaker property tax relief program. However, residents of out-of—formula districts spend a slightly higher fraction of their income on public education than do their less wealthy in—formula counterparts.53 Thus, out—of-formula district residents have more discretionary income than in—formula district residents, and greater demand for spending on education, both public and private. The findings that out—of— formula district residents send a substantially higher proportion of their children to private schools and that, among these residents greater public school spending is positively associated with higher proportional enrollments in private schools as well as with income, reinforce the finding that these residents spend more on education than can be explained by price and income alone. Federal grants appear to stimulate spending in both in—formula and out-of—formula school districts, the 53This proportion is, on the average (.246 x 2245.79)/21,344, or .026 for residents of in-formula districts and (.242 x 2988.72)/24,372 or .030 for out—of— formula district residents. 140 effect being slightly stronger among the latter group. Such grants, however, which exert primarily an income effect on recipients are relatively ineffective in reducing the substantial disparities in per pupil spending disparities among Michigan's school districts, which stem not only from income and marginal tax price disparities, but also from differences in preferences.54 Such preferences stem, in part, from (and are themselves reflected by) differences in educational levels among school district voters. A higher proportion of residents of out-of—formula districts have some college education than do their in-formula counterparts. Moreover, out-of- formula residents display a somewhat greater willingness to vote for school spending for a given level of educational attainment, with a coefficient of 916 on PCTCOLL as compared with 667 for in-formula residents (PRICE3 equation). Both coefficients are significantly different from zero at the .01 level. Finally, the negative and significant coefficients on FAMILIES and D*FAMILIES indicate the presence of scale effects among both groups of districts, 54Federal aid for special education is dis- tributed to school district as partial reimbursement for prior year expenditures. Thus, these grants, which account for approximately 17 percent of all federal education in Michigan, are matching rather than block grants and exert a price as well as an income effect. 141 with those among out—of—formula districts being the stronger. In summary, the evidence indicates that socioeconomic differences between in—formula and out-of- formula residents reinforce the spending disparities which are themselves associated with differences in marginal tax prices. Significantly, one state policy variable—-the local marginal education tax price effect of the circuit breaker——actually exacerbates, rather than reduces, the interdistrict spending disparities which are also associated with. differences in local preferences. Thus, the effects of both an endogenous factor (local marginal tax price) and exogenous factors (local preferences) combine to yield substantial interdistrict disparities in per pupil spending, disparities which cannot be substantially reduced by the price and income effects of increased state grants for low—spending school districts. Given the inelastic demand for school spending on the part of in-formula district residents, such grants would merely result in reduced local school tax effort. CHAPTER VI NONLINEAR BUDGET CONSTRAINTS AND MICHIGAN SCHOOL SPENDING DECISIONS: EMPIRICAL RESULTS As noted earlier, districts for which Vi _<_ V* ($54,000 in 1982-83) face linear budget constraints at all levels of' tax. effort. and. per jpupil expenditures, while districts for which V > V* face a kinked budget 1 constraint and a nonconvex budget set. However, among the latter group of districts, the kink has a practical bearing on the school expenditure decision for only those districts for which V1 is within a narrow interval about V* + (A/ri). (The parameter A was $328 in 1982—83). No such interval, however, can be designated a priori and no subset of districts can be identified as those facing a kinked constraint on the basis of district spending levels in relation to their kink (or zero—grant) spending levels. A frequency distribution of districts' quotients of actual spending (E1) and kink-level spending (E*) revealed that no districts are located at the kink. This finding is consistent with utility maximization in the case of a nonconvex budget set and indifference curves 142 143 that are everywhere differentiable. Further, only six of the 350 sample districts had a per pupil spending level within 10 percent of E*. The distribution of this statistic, EXPPKINK = Ei/E*, is given in Table VI.1. While the low number of districts near the kink is consistent with utility maximization given the nonconvexity of the budget constraint, the observations do not reveal obvious breakpoints about Ei/E* = 1. Accordingly, two intervals were selected for exclusion from the sample in the reestimation of the school expenditure equation. First, the eight districts for which 0.80 < Ei/E* < 1.15 were eliminated from the sample and the expenditure equation was reestimated. Second, a much wider interval including all districts for which 0.9 i SEVKINK 5 1.1 where SEVKINK = vi/[54,ooo + (328/ri)] were eliminated from the sample. This interval includes 42 districts for which 0.24 < Ei/E* < 1.77. The weighted least squares estimates of the unrestricted coefficients for the complete sample and the two "gap—at-kink" samples are summarized in Table VI.2. Dummy variables are used to test for structural differences between in-formula and out—of—formula districts. That is, one regression is estimated for each sample, using dummy variables for the Table VI.1.—-District Spending As Compared with Kink 144 Level No. of Districts Ei/E* No. of Districts Ei/E* 188a Below 0.0 1 0.78 14 0.0-0.19 2 0.80 1 0.20 l 0.87 1 0.21 l 0.96 2 0.22 1 0.97 2 0.24 0 1.00b l 0.30 2 1.02 2 0.32 1 1.03 1 0.38 l 1.06 2 0.45 1 1.12 l 0.47 1 1.16 l 0.51 2 1.20 1 0.52 1 1.22 1 0.53 2 1.34 1 0.55 1 1.39 2 0.58 l 1.52 l 0.59 2 1.54 l 0.60 l 1.55 1 0.61 l 1.58 l 0.66 1 1.64 l 0.75 1 1.77 _§§_ Over 1.80 350 aDistricts for which vi < v* b (E1 ‘5 E") Table VI.2. 145 —-WLS Regression Coefficients for Michigan K-12 Districts, 1982-83. Predictor Variable Full Sample Gap-at-Kink (1) (o.eiEi/E*g1.15) Gap-at—Kink(2) O.9£SEVKINK£1.1 Constant 1692.135** (20.283) Dummy 573.612** (29.613) PRICE3 —887.948** (35.937) D*PRICE3 —3519.465** (75.407) INCOME .00948** (.0010) D*INCOME .0386** (.0013) COST .0238** (.0006) D*COST —.0087** (.0010) FEDERAL l.7039** (.0421) D*FEDERAL .4158** (.0900) PCTCOLL 667.082** (33.271) D*PCTCOLL 249.351** (45.112) PCTPRIV —47.999* (23.580) D*PCTPRIV 98.994** (24.704) 1713.956** (21.190) 555.050** (30.456) -887.923** 36.438) -3536.738** (77.114) .00803** (.00106) .0401** (.0014) .0245** (.0006) —.00947** .0010) A 1.6839** (.0429) .4311** (.0910) 674.253** (34.195) 240.238** (45.983) -62.782* (24.454) 113.335** (25.559) l767.546** (20.430) 553.728** (29.568) —870.559** (35.395) —3699.251** (76.565) .00508** (.00103) .0481** (.0014) .0256** (.0006) .0173** (.0010) l.6488** (.0407) l.l493** (.0905) l.l493** (33.572) —12.8588 (44.912) (25.072) 79.105** (26.071) 146 Table VI.2.—- continued Predictor Gap-at—Kink (1) Gap-at—Kink(2) Variable FUll sample (0.8gEi/E*gl.15) O.9£SEVKINK£1.1 FAMILIES -.00124** -.00128** -.00129** (.00005) (.00005) (.00005) D*FAMILIES -.00205** -.0020** .00080** (.00048) (.0004) (.00005) STCAT 2.2849** 2.3566** 2.2926** (.0693) (.0709) (.0680) D*STCAT -2.3328** —2.404** -2.4154** (.0751) (.0767) (.0733) R2 .797 .799 .833 N 345 337 303 SEE 279.271 281.525 264.048 Note: Standard errors are in parentheses. *Statistically significant at the .05 level. **Statistically significant at the .01 level. 147 intercept and for each independent variable. The estimated model is EXPENDPP = BC + BID = BZPRICE3 + B3(D*PRICE3) + B4INCOME + B5(D*INCOME) + B COST + B7(D*COST) + B PCTPRIV 6 8 + 89(D*PCTPRIV) + BIOPCTCOLL * + B11(D PCTCOLL) + BleEDERAL * + B13(D FEDERAL) + B14FAMILIES * + 815(D FAMILIES) + BIGSTCAT * + B17(D STCAT) 0 if district is in-formula where D 1 otherwise The regression results are substantially the same for the full sample and the "gap-at-kink 1" sample, as expected since the latter sample 'excludes only eight districts, viz. those districts which would have to change their per pupil expenditures by not more than 15 percent to reach the kink. The coefficients on PRICE3 and D*PRICE3 are nearly identical for both samples and are all significant at the .01 level. The estimated 148 coefficients on INCOME, however, differ by .00145, or by more than the standard error on either coefficient (.00100 for the full sample and .00106 for the Gap 1 sample). Similarly, the estimated coefficients on D*INCOME differ by .0015, as compared with standard errors of .0013 and .0014 on the D*INCOME coefficients for the full sample and Gap 1 sample, respectively. -In sum, removal from the sample of those districts which could feasibly reach the budget constraint kink by a change in tax rate makes very little difference in estimating price and income elasticities of demand for school spending. Removal from the sample of the larger group of district for which 0.9 g SEVKINK i 1.1 (Gap 2) does make more of a difference in estimated demand. However, the difference between the estimated PRICE3 coefficients for the full sample and Gap 2 (about 17.3) is only one-half the standard error on both coefficients. The differnce between the coefficients on D*PRICE3 is larger (about 180) and more than twice the standard error of each coefficient, suggesting that the presence of the kink does effect voter decisions in out—of-formula districts where a decline in millage rate could bring the district into-formula. The estimated coefficients on INCOME are also substantially different for the two samples (.0044, as 149 compared with a standard error of .001 for each coefficient), but are small, indicating a significant but low income elasticity of demand for school spending among in-formula district residents. In sum, the regression results are not much changed regardless of which of the three samples is examined. Exceptions to this general finding are to be found only in the insignificance of D*PCTCOLL for the Gap 2 sample, indicating no difference between in— and out—of—formula district residents with regard to the effect of their educational attainment and the insignificance of' PCTPRIV for in-formula district residents. Perhaps most important is the evidence of structural differences between in- and out—of—formula district residents regarding education demand. The estimated point elasticities of demand, calculated at the mean per pupil expenditure levels, are presented for each of the three sample in Table VI.3. In each sample, the price and income elasticity of demand for public school spending are considerably higher among out-of—formula district voters. Estimated elasticities for both voter groups are lowest for the most exclusive sample (Gap 2), but the estimates obtained from the Gap 1 sample are arguably best since that sample excludes only those districts which could reach the budget kink with not more than a 20 percent change in per pupil spending. J 0000. H000. 0H00. 0000.- 0000.- 0000.- mHseHom-mo-uso 0000. 0000. 0000. H000.- 0000.- 0000.- 0Hseuom-EH 0 erm H xEHM 0H0600 0 erm H er0 0H0600 00-606 (um-owe HHsm (00-006 -00-dmo HHsm hufiofiummHm mEoocH mufioflpmmHm moflum "mcflocmom Hoonom 00Hosm How mmaofimm mouse 800m mocmofl>m panama wo mmHHHOHHmmHm pcwom UmumfiflpmMFlkméukmeomB 151 Which Marginal Tax Price? The question as to which price component or components voters appear to be responding when making spending decisions remains unanswered. To obtain more information on this point, the expenditure equations for the full sample and the Gap 1 sample were reestimated with three alternative price terms: PRICEl (the GTB formula price), PRICE2 (the GTB formula and Circuit— Breaker price), and a new PRICE4, which includes the GTB component, adjusted for perceived tax shifting from commercial and industrial property owners, but excludes the circuit-breaker component. Estimated price term coefficients and point elasticities are presented in Table VI.4. All coefficients are statistically significant at the .01 level. Estimated point elasticities are again significantly higher among out-of—formula districts and are nearly identical across the two samples, suggesting that the presence of a kinked budget constraint for some districts is not generally important in spending decisions. The estimated price elasticity of demand among in-formula voters remains essentially unchanged between PRICEl and PRICE4, at an absolute value considerably lower than that obtained from PRICE3 (-.0866 and —.0869), the "complete" price specification. Demand by in-formula district voters appears to be more elastic 152 Table VI.4.--Price Elasticity of Demand for School .01 level. Spending: Alternative Price Specifications Price . Specification Full Sample Gap At Kink 1 PRICEl —506.810 —526.994 (25.831) (26.427 D*PRICEl —1629.332 —1597.228 (44.482) (45.338) Est. Point Elasticity: In-formula districts —.0448 -.0465 2Out—of—formula districts -.1886 —.1876 R .788 .790 SEE 285.464 287.628 PRICE2 -909.026 —932.390 (40.494) (41.187) D*PRICEZ —2893.595 —2881.110 (71.325) (72.893) Est. Point Elasticity: In-formula districts —.0803 -.0824 2Out-of—formula districts -.3359 —.3369 R .795 .796 SEE 280.995 283.133 PRICE4 -511.748 -514.311 (22.947) (23.323) D*PRICE4 -2198.973 -2187.463 (47.859) (48.716) Est. Point Elasticity: In-formula districts -.0452 —.0454 2Out-of—formula districts —.2395 -.2387 R .795 .796 SEE 281.179 283.439 Note: All coefficients statistically significant at the Standard errors are in parentheses. 153 when the circuit—breaker is considered, with estimated elasticities of -.0803 and -.0824 for the full and Gap 1 samples, respectively. In fact, inclusion of the circuit-breaker price component results in nearly a doubling of the estimated elasticities for both in- and out-of-formula districts, suggesting that voters do respond to the price effects of Michigan's property tax relief program. These findings reinforce the proposition that residents of out-of—formula districts have a more elastic demand for educational spending. Such a finding is not surprising in light of the possibility of a Tiebout-type self-sorting of Michigan residents among school districts, whereby individuals with more elastic demand will locate in communities with strong property tax bases, generally including a relatively large share of commercial and industrial property. Again, such large shares, along with generous circuit-breaker credits, serve to lower marginal tax prices for education in these districts. Other Results The results reported in Table V1.1 are substantially the same for all three samples, reflecting the relative insignificance of the kinked budget constraint for the State as a whole. All coefficients 154 for the full sample and the Gap 1 sample are significant at the .01 level, except for the coefficients on PCTPRIV, which are both significant at the .05 level. For the Gap 2 sample, all coefficients are significant at the .01 level, except for those on PCTPRIV and D*PCTCOLL. The significance at the .01 level of all but one dummy variable in the three samples confirms the hypothesis of a structural divergence between in-formula and out—of— formula district residents. The insignificance of PCTPRIV would seem counter—intuitive, were it not for the considerable level of service provided by public schools to private school pupils in 1982—83 in special education, bilingual education, and remedial reading. The coefficient on D*PCTPRIV is significant at the .01 level in each of the three sample, reflecting the fact that private schools in Michigan are concentrated in property- wealthy, high-expenditure school districts (particularly in Oakland County), districts which are attractive to parents with strong preferences for education, public or private. Federal categorical aid (FEDERAL) appears to be more stimulative among out-of—formula districts in the Gap 2 sample than in either of the other two. The out— of—formula districts in the Gap 2 sample are property wealthy and generally affluent and may pursue federal 155 grants for special education and commensatory education more aggressively than other districts. Finally, the coefficient on D*PCTCOLL is insignificant for the GAP 2 sample, indicating no difference between in-formula and out—of—formula districts as to the effect of voters' educational attainment on education demand. This finding differs remarkably from those obtained from the full and Gap 1 samples, both of which indicate a significantly stronger positive association of educational attainment and education demand among voters of out-of—formula districts. IDespite this single anomalous result, all three samples reveal a significant positive relationship between educational attainment and education demand among voters in Michigan school districts, and the "best evidence" (from Sample 1, in particular) indicates that this intuitively expected relationship is stronger among out-of-formula districts. CHAPTER VII THE INCOME-EXPENDITURE RELATION: EMPIRICAL RESULTS In order to test the monotonicity assumption in the context of this study, expenditure equations were estimated for the 1982-83 school year, based on observations of 345 school districts. Again, in conformity with the dummy variable test results presented earlier, separate equations were estimated for in-formula and out-of—formula districts. Descriptive statistics for each variable are presented in Table ‘V.2. Regression results are summarized in Table VII.1. The results in Table VII.1 for the in—formula districts indicate that, in keeping with the Beck approach, the value of B, SEV per family, affects the level of income at which the expenditure function attains a minimum. Both B/Y and lnY have the expected positive and statistically significant. coefficients. Following Brown-Saks and Beck, an estimate of the individual's desired level of per pupil expenditure as a function of income, is obtained by setting G equal to zero. The resulting function is U-shaped. At the sample mean value 156 TABLE ‘VII.l.--WLS Regression Coefficients: 157 Estimating the Income-Expenditure Relationship, In- Formula vs. Out-of—Formula Districts-- 1982-83 Predictor In-Formula Cut-of-Formula Variable Districts Districts CONSTANT -5288.39** 14008.49** (590.74) (971.62) cosr .02326** .03404** (.00042) (.00104) 'FEDERAL 1.7145** 2.3308** (.0288) (.09767) STCAT 2.1647** -.11778** (.0477) (.03307) PCTCOLLEGE 547.879** 888.371** (23.802) (44.120) FAMILIES -.00100** -.00170** (.00004) (.00056) PRICE3 -.1042.13** -4638.966** (26.11) (78.488) BGY 132x10’6** 8.12x10'7 (1.75 x 10-7) (7.58x10’8) LN(INCOME) 676.866** -1077.51** (57.776) (92.20) B/Y 269.55** 166.58** 2 (19.42) (11.85) B G -7.898x10-7** -6.024x10'8 (6.581x10-8) (2.276x10-9)** GINI 753.57** -4226.73** (124.16) (269.58) GINI * (INCOME) -1.17x10-6** 4.144x10'6** (2.27x10-7) (1.619x10-7) PCTPRIVATE -27.31 88.297** (15.79) (8.521) 82 .726 .799 N , 242 103 SEE 183.72 317.89 NOTE: Standard errors in parentheses. **Significant at .01 level. *Significant at .05 level. i I- i 158 of $35,653 for B, this function has its minimum point at a family income of $14,198, well below the sample mean of $21,344. As noted in Beck (1984), if the demand for public expenditures were a monotonically increasing function of income above this (relatively low) level of income in all communities, inequality in the distribution of family income and the pro—spending votes of the poor would not be expected to exert a significant effect on school district expenditures. However, the minimum point of the U-shaped income-expenditure function varies over the sample of in-formula districts. Property tax base per family has a standard deviation of $7,817 and varies from a state equalized valuation per family of $17,278 to a maximum of $62,975. At this maximum value of B, the income—expenditure curve has its minimum point at a family income of $25,079. Thus, the: U—shape of' the income-expenditure curve may have a significant effect on school spending even in districts with relatively few poor families if the property tax base per family is high. With regard to out-of—formula districts, the negative and significant coefficient on the log of income is contrary to theoretical expectations. However, evaluated at the sample means of the other variables, the total effect on school expenditures of an increase in income, including the effects of the interaction terms 159 BGY, BYZ, and B/Y, is positive as expected. The unexpected significant negative coefficient on income may be attributable to possible error in the assumed functional form for the terms involving G. Further, the results in Table VII.2 indicate that when G is set equal to zero, the resulting function is upward sloping, rather than U-shaped. This anomalous result supports these finding reported above on the basis of the Chow and dummy-variable tests--Viz., the behaviors of in-formula and omt-of—formula district voters do, in fact, represent two different structures. Regarding the remaining explanatory variables, the results in Table VII.2 indicate that COST is positively and significantly associated with spending in both in- and out-of-formula districts, as is PCTCOLLEGE, both at the .01 level. PCTPRIVATE, the percent of resident children who attend private schools, is positively and significantly (at the .01 level) associated with spending in the out-of—formula districts, but negatively associated with spending in the in-formula districts (significant at the .05 level). While a negative association between private school enrollments and public school expenditures might be expected in both groups of districts, this seemingly anomalous result may reflect a difference in the causal 160 relationship between the variables for the two school district groups. That is, the lower expenditures and correspondingly lower program quality in the in-formula districts induce residents who can afford private school tuitions to select that option, thus making them less willing to support public school millage increases. Residents of out-of—formula districts, on the other hand, with their lower marginal tax price for education and their higher incomes, enjoy substantially higher public school expenditures, and presumably better quality programs, than their less wealthy in-formula counterparts, while levying a lower school tax rate. Since private school attendance constitutes increased consumption of education, the positive association between such increased consumption and public school spending might be attributable to the income effect of the lower marginal tax price of public schooling in these districts. The income effect may swamp the price effect, leading to greater consumption of public education. Unfortunately, data regarding the tuition levels of private schools are unavailable. Such data could provide insight into the public school-private school choices of school district voters. 161 Impact of Intergovernmental Grants Federal grants, which consist of both matching and nonmatching block grants, are stimulative among both groups of districts, with a $1.00 per pupil grant increase eliciting a spending increase of $1.71 per pupil among in-formula districts and $2.33 among out-of-formula districts. The apparently greater stimulus among the latter group of districts may be attributable, in part, to their substantial local expenditures for special education. While state and federal special education revenue amounted to approximately 20 percent of total special education expenditures in in-formula districts, such revenue amounted to less than 7 percent of such expenditures among out-of—formula districts because of the "recapture" of categorical aid, including special 55 education, to these districts. Consequently, the out- of—formula districts financed approximately 93 percent of their special education expenditures with local property tax revenues.56 55Although the "recapture" of categorical aid is a state, rather than federal, mechanism, federal special education aid to Michigan is commingled with state aid and these funds are distributed to local school districts by means of a single formula and subject to the state recapture provision. 56Special education expenditures are not discretionary for Michigan school districts. Rather, Michigan public schools are required by state and federal law to provide each special education pupil with all 162 Similarly, state categorical aid, which is largely, but not entirely, nonmatching‘ as noted above, was found to be quite stimulative among in—formula districts, with a $1.00 per pupil grant increase associated with a $2.16 increase in per pupil spending. Such a strong stimulative effect is somewhat unintuitive, although consistent with a strong flypaper effect. In contrast, such grants are found to be merely substitutive among out—of—formula districts. Indeed, the negative and significant coefficient on STCAT for these districts is unintuitive. Possible explanations for this finding in 1982—83 are the relatively small share of school expenditures represented by these state categorical funds, the uncertainty regarding the availability of these funds in future years, and the fact that services provided with these funds are not mandated by law, except for special education and bilingual education. The low level of state categorical funding for out—of—formula districts, and possible uncertainty regarding future funding, are attributable to the categorical recapture formula adopted by the Michigan required instructional programs and support services mandated by that pupil's Individual Education Planning Committee (IEPC). As such, the demand for special education expenditures is inelastic with respect to both price and income in Michigan, one of the few states which has adopted special education requirements more stringent than federal statutory requirement. 163 legislature in 1980—81. As noted earlier, this formula provided for a reduction in categorical aid otherwise due out—of—formula districts in an amount equal to the difference between the district's local property tax revenue and the combined local revenue and GTB formula aid that would be available to an in-formula district with the same school tax rate. This amount, however, was subject to a cap equal to 66 percent of the out—of— formula district's total categorical entitlement. Because of the substantial property tax base advantages enjoyed by most out-of-formula district as compared with their in—formula counterparts and the relatively small share of K—12 spending accounted for by state categorical funds (approximately 8 percent), virtually all out—of— formula districts were subject to the 66 percent recapture cap in 1982—83. Further, the recapture was subject to a statewide cap of $26 million, resulting in an effective recapture rate of approximately 64 percent for out-of—formula districts. This $26 million cap on the statewide recapture formula was significantly higher than the $14 million cap effective in 1980-81, the first year of the recapture formula. The increased cap reflected the legislature's concern over the growing number of out-of—formula 164 districts, and provided the state with additional revenue to distribute through the GTB formula.57 Thus it is likely that out—of—formula districts feared future reductions in state categorical aid, and consequently, limited their local spending on nonmandated categorical programs in order to avoid future commitment of increased local spending to compensate for expected state aid reductions.58 Finally, COST, a measure of interdistrict differences in the cost of teachers of comparable quality (proxied by experience and education) is positively and significantly associated with school expenditures among both groups of school districts. 57Because of Michigan's deep recession of the early 1980's and consequent reductions in state aid, the number of out—of—formula districts rose from 150 in 1980— 81 to 199 in 1982-83. The percentage of pupils attending school in such districts rose from 18.8 in 1980-81 to 26.1 in V1982—83. 58As noted in Megdal (1984) and earlier in this study, inverse relationships between nonmatching block grants and expenditures have occasionally been reported in the literature. Grubb and Michelson (1974) found an inverse, although statistically insignificant, relationship when studying a sample of Massachusetts school districts for 1968—69. More recently, Chang (1981) found that a sample of school districts in Virginia would spend slightly less with lump sum grants than without such aid. In their work on agenda control, Romer and Rosenthal (1980) present a ‘theoretical basis for such an inverse relationship in certain circumstances. CHAPTER VIII SUMMARY AND CONCLUSIONS The primary focus of this research has been to examine the response of local school district voters in Michigan to the economic incentives provided by Michigan's K-12 public school finance system. 'Ihese incentives stem from both Michigan's system of intergovernmental grants (including federal pass—through revenue) for school districts and the level and composition of local district property tax bases, which provide virtually all local public school revenue. Since both the intergovernmental grants and the composition of the local district property tax bases exert effects on both the incomes of voters and their marginal tax prices of school expenditures, such an examination requires the estimation of local voters' demand for public educational expenditures with respect to both price and income. Empirical results reported in Chapter V raised the question as to whether the two samples of school district voters-~residents of in-formula and out-of- formula districts, respectively-~represent two different structures or belong to the same population. A Chow test 165 166 led to the rejection of the null hypothesis that the in- formula districts and out-of—formula districts are drawn from the same population and to the inference that a structural difference exists between the two samples of district voters that is not captured by marginal tax price and median family income. Econometric evidence presented in Chapter V indicates that while the demand for public educational expenditures is relatively inelastic with respect to price among both samples of voters, demand is more price elastic among residents of out-of—formula districts. Ironically, it is this more responsive group of voters who do not participate in the state's primary school finance tool, viz., the GTB general membership formula. Thus, if the state were to increase district participation in the GTB formula by substantially increasing such state aid in an attempt to reduce inter— district disparities in per pupil spending, the larger stimulative effect upon spending in the property—wealthy districts would likely increase such disparities. That is, the lower marginal tax price for current in-formula districts which would result from such an increase in GTB aid would have little stimulative effect on these voters, given their inelastic demand for school spending. Such increased GTB aid, however, would likely stimulate 167 spending in districts currently out—of—formula but eligible for the increased GTB aid, because of their substantially more elastic demand for education. Implicit in Michigan's adoption of a GTB state aid formula and local determination of school tax rates is the acceptance, at least within limits, of spending disparities arising from differences in tax rates as opposed to disparities stemming from differences in local taxable wealth. Econometric evidence also indicates a substantially higher income elasticity of demand among voters in out—of—formula districts, suggesting that unconditional grants to lower spending and lower income, in-formula districts would be ineffective as a means to reduce public school spending disparities in Michigan. Voter Response to Local Tax Base Composition Marginal tax price specifications were modified by elimination of the a priori assumption of perfect avoidance of nonresidential property taxes and incorporation of an explicit nonresidential tax avoidance parameter, a. Following the methodology of Ladd (1975), an iterative search over alternative values of a , the fraction of commercial and industrial property not shifted onto local residents, revealed that the residual 168 sum of squares of the estimated expenditure equation is minimized, and the adjusted R2 maximized for 0‘ = .74 for out—of-formula district voters and 0‘ =-"- 1.31 for in- formula voters. Thus, while the latter group perceive that 131 percent of the commercial and industrial property tax burden is avoided, the former perceive the avoidance of 74 percent of the commercial and industrial property tax burden. The substantial difference in perceived tax shifting between in-formula and out-of-formula district residents tends to reduce the difference in the marginal tax price of education expenditures among the two groups of voters. Given the negative and significant (albeit small) price elasticities of demand for school spending of both voter groups, such a reduction in the price difference (a decrease in the in-formula price from .271 to .246 and an increase in the out-of-formula price from .212 to .242) also reduces the expenditure disparities between the two groups to a lower level than they would be were the degree of perceived tax avoidance equal across voter groups. While the result suggesting that residents in in-formula districts perceive an exporting of more than 100 percent of taxes levied on nonresidential property would be difficult to explain in a world of costless information, information is scarce 169 and there is no a priori reason to reject the hypothesis that local residents can indeed perceive the ability to export to nonresidential property owners more than 100 percent of the taxes levied on such property. Thus the fiscal illusion apparently suffered by in—formula district residents serves to increase their per pupil expenditures and reduce the disparity between their spending and that of their higher—spending, out—of— formula counterparts. Income-Elasticity of Demand For School Expenditures Results reported in Chapter VIII are consistent with the hypothesis that the income—expenditure relation among in-formula district voters is a U-shaped function. As noted by Beck (1984), such a result is theoretically possible when the tax price of the public good is systematically related to income. The hypothesis is supported by the significance of both the Gini coefficient and coefficients of the interaction terms between the Gini coefficient and other variables in the income—expenditure equation. Further, the results imply that the level of income at which the U-shaped function attains its minimum is, itself, a function of the property tax base per family in. the community. Thus, the income—expenditure curve may be U—shaped even in school districts with a low 170 percentage of poor families if the property tax base per family is high. Results for out-of—formula districts, on the other hand, indicate an. upward—sloping rather than U— shaped income-expenditure function. That is, for these voters, public school spending rises monotonically with income. Thus, the results of the econometric tests of the income—expenditure relation are consistent with those of the Chow test——viz., the behaviors of in—formula and out—of—formula district voters do, in fact, represent different underlying demand structures. The finding of a significant difference in the income—expenditure relationship between in—formula and out—of—formula districts in Michigan is consistent with the finding of a statistically significant difference in the stimulative effect of nonmatching federal block grants on expenditures in in-formula and out—of—formula districts. Evidence of this difference was presented in Chapter VI. Specifically, an increase of $1.00 per pupil in federal grants was found to elicit a school spending increase of $1.71 per pupil among in—formal district, as compared with a $2.33 increase among out—of—formula districts. Both the great apparent stimulative effect of this nonmatching aid and the statistically significant difference between them require explanation. 171 It is likely that the apparently strong effect of the nonmatching grants, which consist almost exclusively of grants for special education and compensatory education, merely reflects the fact that special education expenditures are mandated by both. state and federal law and that federal special education aid covers only about 6 percent of such expenditures. Further, the higher coefficient obtained in the expenditure equation for out—of—formula districts may merely reflect ‘the relative insignificance of federal special education to out—of—formula districts, since the state's categorical recapture formula includes federal special education aid, as well as nearly all state categorical aid. Thus, while a finding of a greater stimulative effect of nonmatching aid among out—of—formula districts is consistent with both a higher estimated income elasticity of demand among such districts and a monotonically increasing income-expenditure function for these voters, the estimated coefficients associated with federal nonmatching aid to Michigan school districts may simply reflect first, the state and federal statutory mandates for provision of all special education services prescribed by pupils' planning committees and, secondly, more comprehensive plans being prescribed in the wealthier out-of—formula districts. 172 State categorical grants to local districts, on the other hand, were found to be substantially more stimulative among in-formula districts, than among those out—of—formula. An increase of $1.00 per pupil in such aid, which includes both matching and nonmatching grants, was associated with a $2.16 increase in per pupil spending among in—formula districts, while such aid was merely substitutive among out—of—formula districts. Possible explanations for this otherwise unintuitive finding include the relatively small share of school expenditures represented by state categorical aid and the growing amount of such aid whicfll was subject to state recapture. This amount, which was increased to $26 million in 1982-83 from $21.5 million in the prior year, had risen each year since the inception of the recapture formula in 1980—81, creating uncertainty regarding the availability of such funding for out-of—formula districts in future years. Policy Implications In 1973-74, Michigan adopted a GTB state school aid formula in order to achieve a "fiscally neutral" distribution of elementary and secondary public school expenditures in Michigan. By the standard of fiscal neutrality, the quality of a local public school program, measured in terms of per-pupil expenditures, should not 173 be correlated with school district per pupil property wealth. Thus, the GTB formula is designed to provide local school districts with equal per pupil revenue from combined state and local sources for equal tax effort and any disparities among districts in per pupil revenue would stem solely from a difference in district tax rates. Nevertheless, while Michigan's GTB formula was primarily intended to serve the standard of fiscal neutrality, hope was expressed at its inception that per pupil spending disparities among school districts would also be reduced.59 This standard of equality, based on the egalitarian principle that education should be consumed roughly equally by all (i.e., education falls within the category of goods called "merit wants" as defined by Musgrave), does not allow spending disparities among school districts arising from differences in either local tax base or tax rate. Specifically, it was hoped that low—millage, property—poor districts would respond to the price effect of the GTB formula by raising their school tax rates, thereby reducing the variance in school district per pupil expenditures. The local marginal tax prices of school expenditures in Michigan were also altered in 1973-74 by 59See, for example, Phelps and Addonizio, 1981. 174 passage of the Homestead Property Tax Relief Act, or "Circuit Breaker," which provides an income tax credit for property taxpayers whose property tax bills exceed a specified percentage of their income. While the program as introduced was comprehensive, with no restrictions on eligibility other than the formula, the price effects of the GTB formula and the circuit breaker failed to elicit a taxpayer response sufficient to narrow school spending disparities across districts by the middle 1970s. The GTB formula was modified in FY 1976—77 by the inclusion of a base per pupil payment parameter which was invariant with respect to tax effort for most in—formula districts. This parameter, however, raised the marginal tax price of school spending for those in—formula districts in which local SEV per pupil exceeded the nominal guarantee level of the GTB formula. The same modification created an inverse relationship between the SEV per pupil formula cut-off (i.e., the SEV per pupil level at which GTB aid falls to zero) and local tax effort. To the extent that voters' demand for school spending was price—elastic, the base payment parameter did reduce per pupil spending disparities somewhat among in—formula districts by establishing a positive correlation between marginal tax price and tax effort among high-SEV per pupil, in-formula districts. As the analysis indicates, however, such effects were slight, 175 due to the relatively low price-elasticity of demand of in—formula district voters. Indeed, efforts by the legislature to curb interdistrict spending disparities by means of GTB formula price effects have been largely futile for two reasons. First, the GTB formula price effects have remained swamped by the counter—effect of the circuit breaker and the composition of the district property tax bases.60 That is, while the GTB state school aid formula did lower the marginal tax price of school expenditures for in—formula districts, lower marginal tax prices persisted, on the average, in out—of—formula districts due to their greater average proportion of commercial and industrial property. Further, the circuit breaker actually lowered marginal tax prices more, on the average, for residents of out—of—formula district residents. Thus, interdistrict disparities in per pupil expenditures persist, due in part to the combination of lower prices and greater price elasticity of demand among residents of the relatively property—rich districts. 6owhile data on marginal federal tax rates for Michigan school districts are lacking, the deductibility of the property tax from income subject to federal tax would likely reduce marginal tax prices for school spending proportionately more for residents of out—of- formula districts than for those in-formula, since incomes (and therefore, the likelihood of itemizing) are higher among the former group. 176 The evidence presented above strongly suggests that a program of matching grants is quite unlikely to succeed in narrowing spending disparities among Michigan's school districts. Further, the finding of a greater stimulative effect of nonmatching aid among out— of—formula districts, along with a higher estimated income elasticity of demand for these voters than for their lower-spending, in—formula counterparts, suggests that nonmatching grants are also likely to be ineffective in narrowing spending differences across school districts. While some of the results reported here appear to refute the traditional theory that nonmatching grants are equivalent to income factors and are less stimulative than matching aid, this unexpected degree of stimulation occurred in the property-wealthy, high-spending school districts and not in those for which the state would seek spending increases. At best, the expected expenditure effects of increases in nonmatching categorical or block grants to school districts are unclear, with institutional factors such as district budgeting procedures, state mandates regarding program and service levels, and the state recapture formula all contributing to the results presented above in ways that are important, but not fully understood. Evidence does suggest, however, that increases in nonmatching aid would 177 merely induce in-formula district voters to roll back school nullage rates rather than maintain higher school expenditures. The relatively low income elasticity of demand for school spending of these voters indicates that their desired school expenditure levels are unlikely to be changed by the income effects of grant programs. The empirical results reported above suggest also that a system of matching grants would likewise fail to induce spending increased in currently low—spending, in- formula school districts. First, it appears that the price effects of Michigan's GTB general membership school aid formula are more than offset by the countering effects of the state's circuit breaker, the vast differences in commercial and industrial property wealth across school districts, and, likely, the deductibility of the property tax from income subject to federal tax. Second, and more important, the price-inelastic demand of in-formula district voters would likely render any program of increased. matching aid for such districts ineffective in stimulating school spending increases, since such aid would also likely be converted by the recipients into property tax relief through millage rollbacks. Thus, it is both the larger fiscal and economic framework of Michigan K—12 school finance and the relatively weak price—elasticity of demand for educational expenditures that have rendered the GTB 178 formula ineffective as a means to greater equality in school spending. Indeed, the findings reported above strongly suggest that such greater equality, particularly in the form of increased spending among low millage, in-formula school districts, will require that the school spending decision be withdrawn from the local electorate and restored to the state level. Such a reassignment could be rnade, for example, by the adoption of' a foundation program of state education grants, whereby a minimum tax paid to the state would be required of local residents as a condition for receiving a state grant equal to the legislature's chosen minimum school expenditure level. Local districts choosing not to participate in the program (i.e., choosing not to pay the designated state school tax) would receive no state aid and would be limited to an unacceptably low (by local standards) per pupil expenditure level. In effect, local district voter preferences would be overridden by the preferences of the state legislature. Such a course would be politically difficult. 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