did serrano cause a decline in schoolecon.ucsb.edu/~jon/publications/serrano.pdfdid serrano cause a...

DID SERRANO CAUSE ADECLINE IN SCHOOLSPENDING?FABIO SUVA* &JON SONSTELIE*

Abstract - Compared to the national aver-age, California's public school spendingper pupil fell by 23 percent from 1970 to1990. We find that about half of the de-cline can be attributed to Serrano v.Priest, the 1971 California Supreme Courtruling that required equal spending perpupil across school districts in the state.The remainder can be attributed to therapid enrollment growth in Californiaduring the 1980s.

In 1970, California ranked 11th amongstates in public school spending perpupil, 13 percent above the average ofall other states. By 1990, it had fallen to30th, ten percent below that average.To observers of California's fiscal politics,the decline was surely due to Proposition13. By limiting property tax rates androlling back assessed valuations, the ini-tiative curtailed the main source of localrevenue for public schools. According toOakland (1979), Proposition 13 reducedproperty tax revenues in California by 57percent.

*Department of Economics, University of California—Santa

Barbara, Santa Barbara, CA 93106.

However, Proposition 13 was an endog-enous outcome of California's politicalsystem, not an exogenous event. As aconsequence, it cannot be the ultimateexplanation for the decline in schoolspending. Furthermore, it was an out-come of the same political system thatdetermined school spending in the1960s and 1970s. Perhaps it was the in-strument for reversing those spendingdecisions, but then what caused Proposi-tion 13?

Fischel (1988, 1993) has proposed ananswer to that question. In his view.Proposition 13 was caused by the rulingof California's Supreme Court in SerranoV. Priest. In 1971, the Court ruled that,because school districts have unequalproperty values, the local property tax isan unconstitutional method for fundingpublic schools. In 1976, the Court de-creed that a method would be constitu-tional if it were to result in approximateequality in spending per pupil across dis-tricts. While equality in spending wasnot the sole criterion specified by theCourt, equality soon became the stan-dard.

According to Fischel, that standard upsetthe political equilibrium underlying Cali-fornia's public schools. Before Serrano,

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California resembled the model de-scribed by Tiebout (1956) and Hamilton(1975). To protect their tax bases, com-munities practiced fiscal zoning, whichturned the property tax into an efficientprice for local public goods. Given thisprice, families sorted themselves outamong communities according to theirdemands for public goods, particularlypublic education. As a consequence,high-income families resided in schooldistricts with high spending per pupil.

Serrano ended this system and wouldhave inevitably redistributed property taxrevenue from high-spending districts tolow-spending districts. In Fischel's view,voters saw Proposition 13 as a way toshort circuit that redistribution. Leyden(1988) has reinforced this argument byshowing how intergovernmental grantssuch as those required by this redistribu-tion may lead voters to impose state-wide ceilings on local tax rates.

As Fischel further points out, Serranowas a court ruling, not the outcome ofa democratic vote. Unlike Proposition13, it was exogenous to California's po-litical system. It therefore qualifies as apossible explanation for the passage ofProposition 13 and thus of the decline inCalifornia's school spending.

The last step in this argument is not asobvious as it initially appears to be,however. Proposition 13 did reduceproperty tax revenue, but why did notthe state simply replace the revenuewith sales or income tax revenue? Onepossible answer is that the Gann spend-ing limit prevented the state from doingso. However, as we point out in thenext section, the limit was not bindingfor school spending. Consequently, inour view, 1990 school spending in Cali-fornia ought to be regarded as a choicethat was not constrained by institutionalrigidities. This view leads us directly tothe following question: Is there some-

thing about equalization itself that couldcause a decrease in average spendingper pupil?

The second section addresses this ques-tion, using a standard model of localpublic finance. We find that equalizationmay have two effects: an income effect,which acts to decrease school spending;and a price effect, which can act in theopposite direction. Consequently, thenet effect of equalization cannot be de-termined on purely theoretical grounds.

We then estimate the magnitude of thetwo effects. Each effect depends on un-known parameters, so we used datafrom states other than California to esti-mate those parameters and then appliedthose parameters to California. Both theincome and price effect are substantialfor California, and each works in an op-posite direction. The income effect dom-inates, however, so the net effect ofequalization was to decrease spendingper pupil. Equalization explains abouthalf of California's decline in schoolspending.

Finally, we consider an alternative expla-nation for this decline. During the1980s, public school enrollments rose by21 percent in California while falling byfour percent in the rest of the nation. Ifexpenditures are slow to adjust to en-rollment changes, an increase in enroll-ments would lead to a decrease inspending per pupil. We find that Califor-nia's enrollment growth during the1980s also contributed to its relative de-cline in school spending.

DID TAX AND SPENDING LIMITSCONSTRAIN SCHOOL SPENDING?

In the late 1970s, the voters of Califor-nia approved two constraints on govern-ment spending: Proposition 13, ap-proved in 1978, and the Gann Initiative,approved one year later. Not only did

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DID SERRANO CAUSE A DECLINE IN SCHOOL SPENDING?

Proposition 13 reduce local property taxrevenue, it also required a two-thirdsmajority of the state legislature for anincrease in state taxes, thereby limitingthe state's ability to replace this lost rev-enue. The Gann Initiative limited eachstate and local government entity to aspending growth rate that was not toexceed its population growth rate plusthe minimum of either the inflation rateor the growth rate in personal income.

We have argued that Proposition 13cannot be an explanation for the declinein school spending because it was en-dogenous to the political system. Thesame argument applies to the Gann Ini-tiative. Nevertheless, many have arguedthat the two initiatives represent a fun-damental shift in voter attitudes. Accord-ing to that view, the two initiatives areexogenous events. In this section, we ar-gue that, even if one holds that view,the initiatives cannot explain the declinein school spending because they did notactually limit school spending in the1980s.'

Both initiatives had a direct effect on thestate legislature's response to Serrano. Inthe period before the two initiatives, thelegislature had devised a two-part re-sponse. First, it increased foundation aidfor schools, thus pushing up the low-spending districts. Second, it introducedrevenue limits, which imposed a ceilingon the expenditure growth rate of eachschool district. High-spending districtswere given lower limits than low-spending districts, thus pulling down thehigh-spending districts.

Proposition 13 upset this scheme just asit was being implemented. In reality,however, the Proposition strengthenedthe state's control over school spending.In the wake of Proposition 13, the statelegislature established a formula for allo-cating property tax revenue amongschool districts, cities, counties, and spe-

cial districts. Using its huge surplus, esti-mated by Oakland (1979) to be $10.1billion in 1979-80, the state also sup-plemented the property tax revenue withits own funds. In the case of schools,the legislature allocated enough propertytax revenue and state aid to bring eachdistrict's expenditures within about 90percent of its revenue limit.

This arrangement made the revenue lim-its a more effective tool for equalization.The state no longer had to depend onlow-spending districts to bring their ex-penditures up to their revenue limits;the state itself determined their expendi-tures. According to the California Com-mission on State Finance (1986), by1985-6, 91 percent of California's pub-lic school students attended schools thatwere within $100 of the statewide aver-age in expenditures per pupil. A few dis-tricts remained above this band becausetheir property tax revenue exceededtheir revenue limits and they were notrequired to return the excess to thestate. No districts were below the band.As Downes (1992) notes, this equaliza-tion in spending did not result in anequalization in student performance.Nevertheless, it satisfied the court.

The state's program to equalize expendi-tures per pupil was at odds with theGann Initiative, however. The Initiativerequired each government entity to limitthe growth rate of its real spending tothe growth rate of its population. In thecase of school districts, population wasinterpreted to mean the district's enroll-ment. Thus, taken literally, the Initiativewould have limited each school districtto its 1978-9 level of real expendituresper pupil. Under this constraint, equal-ization could only be achieved by bring-ing spending per pupil in every schooldistrict down to the level of the lowestspending district. Faced with this conflictbetween Serrano and the Gann Initia-tive, the state legislature chose to ignore

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Gann. In Senate Bill 1352, enacted in1980, it exempted school districts fromthe Gann limits.

The exemption created an avenue forstate revenues to escape the Gann lim-its. Under the Gann Initiative, state sub-ventions to local government count aslocal spending, not state spending. If thestate had tax revenue that would put itover its Gann limit, it could transfer therevenue to school districts that were notrequired to abide by the Gann limit.

In fact, the state almost used this devicein 1987. The Tax Reform Act of 1986broadened the base of the federal in-come tax, which Galifornia uses as abase for its own tax, and created a reve-nue windfall for the state. Ladd (1993)estimated this windfall to be nearly $2billion per year. As a consequence, inthe 1986-7 fiscal year, the state had asurplus of $1.7 billion. At the time, thestate was approximately $600 millionunder its Gann limit, so the surplus putthe state over by $1.1 billion. As de-scribed by Sweeney (1987), some legisla-tors argued that the excess ought to betransferred to the local schools, but thelegislature voted to reduce income taxrates instead.

We conclude that neither tax nor spend-ing limits were effective constraints onschool spending in the 1980s. The statewas always free to increase schoolspending. State aid to schools did notcount as a state expenditure, and schooldistricts were exempt from the Gannlimit. The restrictions on tax increasesembodied in Proposition 13 could havebeen a constraint on government spend-ing, but the state actually decreased taxrates in 1987.

Though tax and spending limits werenot a binding constraint In the 1980s,California's state and local governmentsdid reduce expenditures relative to other

states. Figure 1 compares California andthe United States in state and local ex-penditures per capita. In 1969-70, Cali-fornia spent about $650 more per capitathan the rest of the country. The gapnarrowed to a minimum of $336 in1983-4 and then widened again to$455 in 1989-90. At the end of the1980s the gap was about $200 lessthan in 1969-70.

Figure 2 shows real, current expendi-tures per capita on public schools. Asthe figure indicates, about half of Cali-fornia's $200 per capita decline in totalexpenditures is due to its relative declinein school spending. California spentabout $100 more per capita on publicschools than did the nation in 1969-70.That gap persisted until 1977-8 andthen declined steadily toward the na-tional average. It fell slightly below thataverage in 1983-4 and remained at ap-proximately that level for the rest of thedecade.

The relative decline in school spendingper capita led to an even greater relativedecline in spending per pupil. In 1969-70, there were 0.88 public school pupilsper family in California and 0.87 pupilsper family in the rest of the country. By1989-90, pupils per family had fallen to0.68 in California and 0.60 in the rest ofthe country. Spending per pupil in Cali-fornia thus fell from 13 percent abovethe national average in 1969-70 to tenpercent below the average in 1989-90.

This brings us back to our basic ques-tion; Why did Californians choose tospend relatively less on their publicschools? Throughout the 1980s, Califor-nia continued to have high state and lo-cal government spending. The gap be-tween California and the rest of thenation narrowed somewhat, but abouthalf of that decline is due to a relativedecrease in school spending. Why wasschool spending the target? Is equaliza-tion an explanation?

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FIGURE 1. Real State and Local Government Expenditure per Capita (Direct, General, Current Expenditures in

1990 Dollars)

$3,500

$3,000

$2,500

$2,000

$1,500

$1,000

$500

$0 'P-V

• United States

D California

Source: Bureau of the Census, Government Finances, annual editions from 1969-70 to 1989-90.

DOES EOUALIZATION LOWERTHE AVERAGE?

Before Serrano, each local school districtchose its own level of spending, andfamilies chose among districts. After Ser-rano, all districts were required to spendthe same amount per pupil, and thestate legislature chose that level. It wasas if all school districts were to mergeinto one, statewide district. Such amerger would have increased spendingin some districts and decreased it in oth-ers. Our question is: What would hap-pen on average?

We address that question in the contextof a standard model of local public fi-nance. All families have the same de-mand function for spending per pupil.

where q is a family's demand for spend-ing per pupil, p is its tax price forspending per pupil, y is its income, andthe /3's are parameters. A family's taxprice is the increase in its taxes resultingfrom a one-dollar increase in spendingper pupil. The price depends on the av-erage number of pupils per family. Tomake matters simple, we assume that allfamilies have the same number of schoolchildren, a number we denote by s.

Now consider a family's options in theenvironment described by Tiebout (1956)and Hamilton (1975). There are manyschool districts, and each finances itsschools through a property tax. To pro-tect its tax base, each district establishesa minimum zoning requirement, whichturns the property tax into a head tax.As a consequence, each family pays anequal share of district taxes, an amountequal to sq. The tax price is therefore s,the number of pupils per family. The tax

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FIGURE 2. Real Public School Spending per Capita (Current Expenditures in 1990 Dollars)

$800

$700

$600

$500

$400

$300

$200

$100

$0

• United States

• California

o I - oj CO Tj- in COh - h > c o o o c o c o c o c o o o o o c o c o a >

Source: Bureau of the Census, Government Finances, annual editions from 1969-70 to 1989-90.

price is the same across districts, but dis-tricts spend different amounts per pupil.

Families may deduct property taxes fromstate and federal taxable income. Forfamily /, let A, be the cost of one dollarof property taxes, net of this deduction.The family then faces a net tax price ofA,s.

Given its tax price, each family deter-mines its demand for spending per pupiland then chooses a school district thatsupplies the level of spending that it de-mands. The average level of spending inthe state is therefore the average ofthese demands. This average is

Now suppose that all school districts aremerged into one district. Within the dis-trict, families have a wide range of in-comes and thus may pay quite differenttaxes. Unlike the Tiebout-Hamiltonworld, families in the same district mayhave different tax prices. To analyze thissystem, we assume that each family paysa certain fraction of total school taxes, afraction that does not vary with the levelof spending. Let e, be the fraction oftaxes paid by family /. The family's totaltax bill is G.nsq, where n is the totalnumber of families. The family may de-duct some of this bill from state andfederal taxable income. Let /a, be the netcost to family / of one dollar of schooltaxes, incorporating this deductibility.The family's net tax price is

where A is the average A, and y is aver-age family income.

Because tax prices and incomes differamong families, their demands forspending per pupil may also differ. Thedistrict resolves the difference through

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majority rule, which results in the leveldemanded by the median voter. Themedian voter is the family with the me-dian income, which is denoted y.

Therefore, spending per pupil is

where / i and 0 are the values of ju., and0, for the median income family.

Subtracting equation 2 from equation 3yields the difference in spending perpupil with and without the merger:

q-q = - \)s - y)

The first term in equation 4, Pp(pi.0n —A)s, is a price effect. The parameter 6 isthe tax share of the median-incomefamily. Because taxes generally increasewith income and median income is lessthan average income, this share is lessthan the average tax share, 1 /n. Thus,0n is less than unity. On the other hand,because median income is generally lessthan mean income, the marginal incometax rate of the median income familywill be less than that of the average in-come family, so /I is greater than A. Fur-thermore, the percent of school taxesthat can be deducted may be less with aSerrano-type school system than with aTiebout-Hamilton system. With a Ser-rano system, school spending may be fi-nanced, in part, by state income andsales taxes. State income taxes are onlydeductible at the federal level, and statesales taxes are not deductible at anylevel. In contrast, with the Tiebout-Hamilton system, schools are financedthrough a property tax that is deductibleat both state and federal levels. We con-clude that (iJidn - A) could be positive or

negative. If the tax system is quite pro-gressive, however, Bn is small, and it islikely that (/i0n - k) is negative. In thatcase, because /3p is also negative, theprice effect is positive. This occurs be-cause the merger lowers the tax price ofthe median voter. Fisher (1979) makes asimilar point in his analysis of revenuesharing. If local taxes are less progressivethan federal taxes, revenue sharing maydecrease the tax price of the medianvoter and thus increase governmentspending.

The second term in equation 4, /3y(y -y), is an income effect. When familiesare sorted by income and each receivesthe level it demands, the average levelof spending per pupil is the average ofthese demands and is therefore deter-mined by the average level of income.When families are not sorted by income,only the median-income family receivesthe amount it demands and thus themedian income determines the level ofspending per pupil. Because median in-come is less than average income, theincome effect decreases the level ofspending per pupil.

This conclusion is consistent with the re-sults in Leyden (1992). He considers amodel in which there are high-spendingdistricts and low-spending districts. Iflow-spending districts dominate in thestate legislature, as would be the case ifmedian income is less than average in-come, average spending per pupil is lesswith one statewide district than withmany local districts.

The model thus predicts that a mergermay have two opposing effects onspending per pupil. We are left with theempirical task of evaluating the relativestrengths of these opposing effects. Be-fore taking up that task, however, let usacknowledge four limitations of ourmodel.

First, in the model without Serrano, we

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have assumed that all families within agiven school district have the same de-mand for spending per pupil and thusthat the statewide average of spendingper pupil is the average demand. In real-ity, of course, school districts are notthat homogeneous, so the statewide av-erage of spending per pupil is the aver-age of the median demand in eachschool district. Nevertheless, we maintainthe homogeneity assumption because itsimplifies the analysis and illuminates thefundamental forces at work.

Second, we have ignored the possibilitythat the public schools in one districtmay confer external benefits on the resi-dents of neighboring districts. As Rose-Ackerman (1981) has shown, in the faceof these beneficial spillovers, voters mayapprove higher levels of spending at thestate level than they would support fortheir own local district, considered inisolation.

Third, we have assumed that the medianvoter is in the family with median in-come and thus implicitly that the incomedistribution of voters mirrors the incomedistribution of families. Inman (1978) ex-amined this assumption in his study ofthe spending decisions of 58 Long Islandschool districts. He found that he couldreject this assumption for at most one-fourth of the districts and that, even forthose districts in which the assumptionappeared to be violated, the bias in thepredicted level of school spending wassmall. While these findings appear tosupport the use of median income indetermining local school spending, itdoes not necessarily imply that the sameassumption would hold for statewidespending decisions. Nevertheless, ourmodel maintains this assumption.

Fourth, at the state level, school expen-ditures decisions are part of a multidi-mensional budget process in whichschools compete with welfare, correc-

tions, transportation, and so on. As Ar-row (1963) demonstrated, this processmay not have a simple, majority-ruleequilibrium. In that case, the outcomemay be partly due to elements of thelegislative structure such as who sets theagenda and who votes on what issues.Craig and Inman (1986) use this conceptof a "structure-induced equilibrium" asa basis for an empirical examination ofstate spending. While this multidimen-sional model gives a more satisfying ac-count of state politics than the one-dimensional model on which we haverelied, it is also much more complicated.In what follows, we ask how much ofCalifornia's relative decline in schoolspending can be accounted for by thesimple, one-dimensional model. We donot deny that a more sophisticatedmodel might produce a different an-swer.

WHICH EFFECT DOMINATES?

While our principal concern is to explainCalifornia's spending in the 1989-90school year, we first ask whether itsspending in 1969-70 is consistent withthat of other states during the same pe-riod. According to the model in the pre-vious section, spending per pupil in astate is a linear function of average taxprice and average family income. We es-timated this function with data from allstates except California.

The average tax price is the number ofpupils per family multiplied by the aver-age cost of one dollar of property taxes.To determine this cost, we began witheach state's income distribution from the1970 Census. The Census reported thenumber of families in each of 12 incomegroups. Using data from the Statistics ofIncome, we estimated the percentage offamilies in each group that itemize de-ductions. For those who do not itemize,the cost of one dollar of property taxes

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is one dollar. For those who do itemize,the cost of one dollar of property taxesis 1 - t, where f is the family's marginalincome tax rate.

A family's marginal income tax rate is afunction of both its federal and statemarginal income tax rates. For stateswithout an income tax, the rate is thefamily's federal marginal tax rate, whichwe determined for each income groupfrom the 1969 federal tax schedule, tak-ing account of exemptions and the aver-age itemized deduction for each group.For states with an income tax, we alsodetermined each group's state marginalincome tax, using state tax schedules.Some states permit federal taxes to bededucted from state taxable income; inother states, state income tax is just afraction of a family's federal income tax.These special features were incorporatedto yield a combined state and federal in-come tax rate for each group in everystate.

The combined rates were then averagedacross the groups in each state, usingthe number of families in the groups asweights. The weighted average is theaverage of the marginal income tax ratesof families in the state. The average taxprice is one minus this average rate mul-tiplied by the number of pupils per fam-ily in the state. These calculations aredescribed in more detail in Appendix B.

Hawaii was treated differently because ithas one statewide school district. Follow-ing the model of the previous section,school spending in Hawaii ought to bedetermined by the tax price and incomeof the median income family. Thus, inthe regression, family income for Hawaiiis median family income, not averagefamily income as in other states. Ha-waii's tax price was calculated in the fol-lowing way: For each income group, weestimated the sales and income tax pay-ments of a representative family. These

payments were multiplied by the num-ber of families in each group and thenadded across groups to determine totalstate taxes. The tax share for each repre-sentative family is its tax payment di-vided by this total. The median taxshare, 0, is the tax share of the repre-sentative family in the median incomegroup. We assumed that the median-income family itemizes deductions andthus deducts state taxes from its federaltaxable income. The parameter /I istherefore one minus the federal mar-ginal tax rate for the family with medianincome.

Following equation 3, the tax price forHawaii is iiOns, where n is the numberof families and s is the number of stu-dents per family. Appendix B summa-rizes these calculations.

Table 1 reports the results from an ordi-nary least-squares regression of spendingper pupil on tax price and income. Bothtax price and income coefficients havethe hypothesized signs, though the tax-price coefficient is not significantly dif-ferent from zero. The model explains 70percent of the cross-state variation inspending per pupil.

Table 2 reports the tax price and aver-age family income for California in the1969-70 school year. California's taxprice was nearly equal to the average ofother states, but California's averagefamily income was 18 percent higherthan the average of other states. Com-

TABLE 1DEMAND FUNCTION FOR SPENDING PER PUPIL:

1969-70 (VARIABLES EXPRESSED IN 1990DOLLARS)

Variable

ConstantTax priceIncome

Number of observations

Coefficient

246-660

0.0801

490.70

StandardError

629548

0.0095

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DEMAND VARIABLES:

Spending per pupilTax priceFamily income

TABLE 21969-70 (VARIABLES

California

$2,921$0,72

$41,187

EXPRESSED IN 1990

Mean

$2,584$0,73

$34,996

DOLLARS)

Other States

StandardDeviation

$541$0,09

$5,227

bining the California values of tax priceand average family income with the esti-mated coefficients for tax price and in-come, the model predicts that Californiashould have spent $3,093 per pupil. Infact, it spent $2,921 per pupil, which iswithin one standard error of the model'sprediction. We therefore conclude thatCalifornia's school spending in 1969-70was roughly consistent with that inother states.

We repeated this exercise using datafrom 1989-90, As in the previousregression, family income is median fam-ily income for Hawaii and average familyincome for the 48 other states, and taxprice is median tax price for Hawaii andaverage tax price for the other states.The calculation of average and mediantax prices follows the same format as for1969-70, For 1989-90, however, thereare 25 income groups instead of the 15groups for 1969-70, Furthermore, as aresult of the Tax Reform Act of 1986,state sales taxes are no longer deduct-ible from federal taxable income. Appen-dix B describes the 1989-90 tax pricecalculations in detail.

The regression results are in Table 3, Aswas the case with the 1969-70 regres-sion, the 1989-90 regression explainsnearly 70 percent of the cross-state vari-ation in spending per pupil. The tax-price and income coefficients have theanticipated signs, and the income coeffi-cient is significantly different from zero.

We combined the regression coefficients



Variable

ConstantTax priceIncome

Number of observations

Coefficient

446-21540,1345

490,67

StandardError

13361470

0,0186

in Table 3 with California's income andtax price listed in Table 4, The modelpredicts that California should havespent $6,132 per pupil in 1989-90, Infact, it spent $4,391 per pupil, a gap of$1,741,

These calculations ignore the price andincome effects of equalization. The in-come effect of equalization is the in-come coefficient, Py, multiplied by thedifference between median family in-come and average family income. Thatdifference is -$10,639 in 1989-90, andthe estimate of py is 0,1345, so the in-come effect of equalization is -$1,431,

The price effect of equalization works inthe opposite direction, however. Theprice effect is PpOiens - As), The firstterm in the parentheses is the tax priceof the median-income voter under theSerrano system, and the second term isthe average tax price of families underthe Tiebout-Hamilton system. Using thesame method described above for Ha-waii, we estimated that the Serrano taxprice is $0,43, As noted in Table 4, the

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DEMAND VARIABLES:

Spending per pupilTax priceFamily income

TABLE 41989-90 (VARIABLES

California

$4,391$0.56

$51,198

EXPRESSED IN 1990

Mean

$4,890$0.51

$41,128

DOLLARS)

Other States

StandardDeviation

$1,306$0.09

$7,079

Tiebout-Hamilton tax price is $0.56. Weestimated pp to be -2,153, so the priceeffect of equalization is $278. Conse-quently, the net effect of equalization isto decrease spending per pupil by$1,153. This is two-thirds of the gap be-tween predicted and actual spending perpupil in California.

According to Theobald and Picus (1991),six other states had court rulings similarto Serrano between 1973 and 1983.Though none of these states appear tohave equalized as completely as Califor-nia, we did estimate the model withoutthose states. There was no significantchange in the price and income coeffi-cients and thus no significant change inour estimate of the price and income ef-fects of equalization in California.

POPULATION GROWTH WAS ALSO AFACTOR

Equalization was not the only significantfactor affecting California schools in the1980s. Over the decade, schools werealso forced to accommodate a 21 per-cent increase in enrollments. This rapidgrowth strained school resources andmay therefore be a competing explana-tion for California's relative decline inspending per pupil. In this section, weconsider this explanation.

The enrollment growth was caused byimmigration. During the 1980s, Califor-nia's population grew by 25 percent,and the number of families in the stategrew by 21 percent. While the popula-

tion growth increased enrollments andthus the demand for school services, italso increased the tax base and thus thesupply of tax revenue. In terms of ourmodel, because the number of familiesincreased at the same rate as the num-ber of students, the tax price of educa-tion did not change. In that sense,growth did not affect the demand forspending per pupil.

However, growth may affect spendingper pupil through a second channel. Ifschools are slow to adjust to enrollmentchanges, an increase in enrollment willlead to a temporary decrease in spend-ing per pupil. A large increase in enroll-ment requires new classrooms and newteachers. A school district may takesome time to build new classrooms, andit will not hire new teachers until theclassrooms are completed. During thisgrowth period, class sizes may increaseand current spending per pupil may fall.Similarly, a decline in enrollment maylead to a rise in spending per pupil. Thedecline should lead to teacher layoffsand school closures. But teachers' unionsare often quite effective in opposing lay-offs, and neighborhoods usually fight tokeep their own schools open. As a resultof union and neighborhood resistance,class sizes may fall as enrollment de-clines, so spending per pupil may rise.

To determine whether enrollmentchanges affect spending per pupil, weadded enrollment growth to the 1989-90 regression. The growth variable is thestate's enrollment growth rate between

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1984-5 and 1989-90, The OLS regres-sion results are reported in Table 5,

The coefficient of enrollment growth isnegative, as hypothesized, and signifi-cantly different from zero. In fact, thesize of that coefficient indicates that,over a five-year period, total spendingmay not change as enrollment changes.According to the estimates, a ten per-cent decline in enrollments will increasespending per pupil by $592 per pupil,which is 12 percent of the sample aver-age of spending per pupil.

The estimated coefficients from thisregression were then applied to Califor-nia, Without Serrano and with no enroll-ment growth between 1984-5 and1989-90, the regression predicts thatCalifornia should have spent $6,414 perpupil in 1989-90, In fact, Californiaspent $4,391 per pupil, leaving a gap of$2,023,

California's enrollment growth rate was18 percent from 1984-5 to 1989-90,so the regression predicts its spendingper pupil should be $1,066 less on thataccount. After incorporating enrollmentgrowth, the difference between pre-dicted and actual spending per pupil isnarrowed to $957,

Equalization explains the remainder.With the estimated tax-price and incomecoefficients, the income effect of equal-ization is -$1,512, the price effect is



Variable

ConstantTax priceIncomeEnrollment

Number ofR'

growth rate

observations

Coefficient

-183-12220,1422

5926

490,76

StandardError

11791307

0,01641519

$158, and the net effect is -$1,354,We conclude that these two factors,equalization and enrollment growth,completely explain the decline in schoolspending in California, Equalization Isslightly more important.

Our estimate ignores the important rolethat foreign immigration played in Cali-fornia's growth during the 1980s, Dur-ing the decade, the number of foreign-born persons in California increased bythree million, which is approximately halfof the increase in California's populationduring the decade. Many of these immi-grants were not yet citizens in 1990, sothe immigration of the 1980s may havedecreased the percentage of residentswho were active voters. Furthermore, ac-cording to Johnson (1993), foreign im-migrants during the 1980s were pooreron average than California's nonimmi-grant population. As a consequence, thegap between the median income of vot-ers in the state and the median incomeof families probably widened during the1980s, In predicting the income effect ofequalization, we have used the medianincome of families rather than the me-dian income of voters, so our predictionmay be too high. If that is the case, wehave attributed too much of the de-crease in school spending to Serrano.

Conclusions

In a symposium in the June 1994 editionof this journal, Reschovsky, Oakland, andLadd and Yinger lay out the pros andcons of fiscal equalization. They also de-scribe possible approaches to equaliza-tion, California has taken a radical ap-proach—state control of local schoolspending. Other states have experi-mented with less extreme approaches,such as district power equalization.While Rothstein (1992) suggests that dis-trict power equalization may also lead toa decline in average school spending perpupil, our analysis does not directly ap-

210


ply to these moderate approaches.

As Reschovsky notes, however, recentcourt decisions in Kentucky, New Jersey,and Texas do seem to favor a California-like approach. The recent school financereform in Michigan, described in Cour-ant, Gramlich, and Loeb (1994), has alsoresulted in a more centralized system.Will these reforms lead to lower schoolspending? While California's experiencesuggests that they will, one ought to becautious in extrapolating from that expe-rience. Our model does not predict thatcentralization always leads to a declinein school spending. In the model, thereare two opposing effects, and the out-come depends on the relative strengthof the two. In California, the income ef-fect dominates the price effect. In an-other state with a different income dis-tribution and a different tax system, theprice effect could dominate.

This point is reinforced by two recenteconometric studies. In a panel dataanalysis of school spending across states,Manwaring and Sheffrin (1994) find thatspending per pupil is actually higher instates in which the school finance sys-tem has been successfully challenged inthe courts. Downes and Shah (1994)perform a similar analysis but allow theeffect of school finance reform to de-pend on the extent of the reform andthe state's characteristics. They find thatextensive reform, such as California's,has a negative effect on spending insome states and a positive effect in oth-ers. This finding is consistent with ourmodel: equalization does not necessarilydecrease school spending; the net effectof equalization depends on the state'scharacteristics.

APPENDIX A

DATA SOURCES

Spending per Pupil by State

Table 157, p. 160, Digest of Educational Statistics,1992. National Center of Educational Statistics, U.S.Department of Education.

Average Daily Attendance by State

Table 45, p. 59, Digest of Educational Statistics,1992, National Center of Educational Statistics, U.S.Department of Education.

Average Family Income, Median Family Income, and

Number of Families by State

1970: Table 178, p. 539. 1970 Census of tfie Pop-ulation, Characteristics of the Population,U.S. Summary, volume 1, part 1.

1990: 1990 Census of the Population. SummaryTape File IC.

Consumer Price Index for All Items, 1970 and 1990

Table 760, p. 477, 1991 Statistical Abstract of theUnited States.

APPENDIX B

CALCULATION OF AVERAGE AND MEDIAN TAX

PRICES

Average Tax Prices

The tax price of school spending is s, the number ofpupils per family. The net tax price takes into ac-count the deductibility of property taxes from stateand federal taxable income. For family /, the net taxprice is AiS, where A; is the cost of one dollar ofproperty taxes net of any reduction in state and fed-eral income tax that results from deducting this onedollar from state and federal taxable income. Theaverage tax price, which is used in the empiricalanalysis as the tax price for all states except Hawaii,is Xs, where A is the average of the A, across fami-lies within a state. Table B-1 illustrates the calcula-tion of A. The data is from California in 1969, butthe same method is used in other states and for1989.

Column 1 lists the income groups reported in the1970 Census. Column 2 lists the percentage of fam-ilies in each group in California in 1969. Column 3lists the mean income within each group. This is theaverage of the upper and lower limits for the first11 groups. For the top group, the mean income isassumed to be $50,000. The average income foreach group was considered to be the income of arepresentative family for that group. The remainderof the table is concerned with calculating the A; foreach of these 12 groups.

Column 4 lists the percent of each group that item-izes. This number is from the Table 1.6 of Internal

211

TABLE B-1CALCULATION OF A FOR CALIFORNIA IN 1969

Income($1,000)

(1)

Percentof

Families(2)

MeanIncome($1,000)

(3)

Percentwho

Itemize(4)

MeanDeduct.($1,000)

(5)

TaxableIncome($1,000)

(6)

Fed.TaxRate(7)

StateTaxRate(8)

Comb.TaxRate(9)

A(10)

0-11-22-33-44-55-66-77-88-10

10-1515-2525+

22444556

1228216

0.51.52.53.54.55.56.57.59.0

12.520.050.0

1617242931333640517290

0.130.520.720.871.021.081.281.391.692.143.288.34

0.370.981.782.633.484.425.226.127.31

10.3616.7241.66

0.000.150.170.190.190.220.220.250.250.320.420.58

0.010.010.010.020.020.030.040.040.050.070.100.10

0.010.160.160.210.210.240.250.280.290.370.480.62

$1.000.990.970.950.940.920.920.900.890.810.680.44

Revenue Service, Statistics of lncome-1969. Individ-ual Income Tax Returns. Column 5 lists the averagededuction of those who itemize, a number which isalso from Statistics of lncome-1969. Column 6,taxable income for itemizers, is column 3 lesscolumn 5.

Columns 7 and 8 are the federal and state tax ratesfor individuals with the taxable income of column 6.The state tax rates are from Table 40 of the Advi-sory Commission on Intergovernmental Relations,State and Local Finances, 1967-70. The table liststax rates for single individuals. To be consistent, wealso used the schedule for single individuals to de-termine the federal tax rate. In determining thesetax rates, we assumed one exemption.

Column 9 lists the combined state and federal in-come tax rate. It is the increase in the sum of stateand federal income taxes resulting from a one dollarincrease in taxable income. For states like Californiathat do not allow federal taxes to be deducted fromstate taxable income, this tax rate is t = t, -F t, -tjf, where t, is the state marginal tax rate and f, isthe federal marginal tax rate. For states that do al-low the deductibility of federal taxes, the formula ist = (f, -H f, - 2t,t,)/0 - t,t,). Finally, some statesdetermine state taxes as a fraction of federal taxes.In those states, f = (1 + fs)f,/(1 + t,t,).

For those families that do not itemize. A, is unity.For those families that do itemize. A, is 1 - f. Col-umn 10 lists the average A, for each group. It is1 - TT -̂ iT l̂ - f), where TT is the percent of fami-lies in the group that itemize. The parameter A isthe weighted average of the A,. It is the sum of col-umn 10 weighted by the percentages in column 2.

This number was 0.81 for California in 1969. Theminimum was 0.78 for Alaska, and the maximumwas 0.90 for Arkansas and Mississippi.

The calculations for 1989 are basically the same.There are 25 income groups instead of 12. The topgroup is income greater than $150,000. The aver-age income of this group was assumed to be$200,000. Information on the percent itemizing andthe average itemized deduction is from Table 1.2 ofInternal Revenue Service, Statistics of lncome-1989.Individual Income Tax Returns. The data on state taxrates are from the Advisory Commission on Inter-governmental Relations, Significant Features of FiscalFederalism: 1990, M-169. For 1989, A was 0.82 forCalifornia. The minimum was 0.81 for Maryland andNew Jersey, and the maximum was 0.91 for WestVirginia.

Median Tax Prices

Under a statewide school system, the tax price ofthe median voter is ilSns, where /i is the cost to themedian income family of one dollar of school taxesnet of the deductibility of those taxes from federaltaxable income, 6 is the median voter's share ofschool taxes, n is the number of families, and s isthe number of school children per family. This me-dian tax price is used as the tax price in the regres-sion analysis for Hawaii and to estimate the effectof Serrano in California. Table B-2 illustrates the cal-culation of 6 for California in 1989.

Column 1 lists the income groups in the 1990 Cen-sus. Column 2 gives the number of families in eachgroup in California in 1989. Column 3 gives the in-come of a representative family in each group. For

212


TABLE B-2CALCULATION OF 9 FOR CALIFORNIA IN 1989

Income(Thous,)

(1)

0-55-10

10-12,512,5-15

15-17,517,5-20

20-22,522,5-25

25-27,527,5-30

30-32,532,5-35

35-37,537,5-40

40-42,542,5-45

45-47,547,5-50

50-5555-6060-7575-100

100-125125-150

150+

Families(Thous,)

(2)

207348238230255234279237278230300226271213275201234186406331780649275117216

MeanIncome

(Thous, $)(3)

2,507,50

11,2513,7516,2518,7521,2523,7526,2528,7531,2533,7536,2538,7541,2543,7546,2548,7552,5057,5067,5087,50

112,50137,50200,00

SalesTax(4)

176176217217271271319319363363405405444444482482519519571571636758869869869

Percentwho

Itemize(5)

1477

111120202929464646466666666679797992919191

Avg,Deduct,

(Thous, $)(6)

8,88,58,28,27,17,17,37,37,47,48,48,48,48,49,99,99,99,9

12,712,712,716,924,224,224,2

Inc, TaxItem,

(Thous, $)(7)

0,00,00,00,00,10,20,30,40,50,70,81,01,21,51,61,82,02,32,42,83,85,26,99,2

15,0

Inc, TaxNonitem

(Thous, $)(8)

0,00,00,10,10,30,40,60,70,91,11,41,61,82,12,32,52,73,03,33,84,76,68,9

11,217,1

TotalTax

(Millions $)(9)

36667189

135154231234329316457394545478632508655564

1272119235833954218112003469

the first 24 groups, this family has an income that isthe average of the upper and lower incomes for thegroup. For the top group, the family has an incomeof $200,000, To determine each representative fam-ily's tax share, its sales and state income tax for1989 are estimated.

Column 4 gives the sales tax of the representativefamily for each group. The first step in computingthis tax was to take the tax listed for a one-personfamily in California from the 1986 Optional StateSales Tax Table in the IRS Instructions for PreparingForm 1040, The second step was to multiply thisnumber by 5/4,75, because California increased itssales tax rate from 4,75 percent in 1986 to five per-cent in 1989,

The state income tax was estimated for families thatitemize deductions and for those that do not. Col-umn 5 lists the percent of families that itemize ineach group. This information is from Table 1.2 ofthe Internal Revenue Service, Statistics of Income-1989, Individual Income Tax Returns, Column 6gives the average deduction of those who itemize.This information is also from Statistics of Income-1989, The taxable income of the representative

family if it itemizes is its income less this itemizeddeduction and less the exemption granted by thestate tax laws. The family was assumed to take oneexemption. Column 7 gives the state income tax fora single taxpayer with that taxable income. The taxschedule and exemption are from the AdvisoryCommission on Intergovernmental Relations, Signifi-cant Features of Fiscal Federalism, 1990, Column 8gives the state income tax if the representative fam-ily were not to itemize. The state standard deduc-tion is from Significant Features of Fiscal Federalism,

The total state taxes paid by each group is the salestax multiplied by the number of families in thegroup plus the income tax of itemizers multiplied bythe number of itemizers in the group plus the in-come tax of nonitemizers multiplied by the numberof nonitemizers in each group. These numbers arelisted in column 9. A family's tax share is the sumof its sales and income tax divided by the sum oftaxes across all groups (the sum of column 9),

The median income family is assumed to be anitemizer. In California in 1989, the median family in-come was $40,559, According to our estimates, itpaid $482 in sales tax plus $1,573 in income taxes

213

for a total of $2,055. Its share of taxes multiplied bythe total number of families, 6n, was 0.81. Thefamily's state income tax can be deducted from fed-eral taxable income, but its sales tax cannot. Thus,77 percent of its state taxes can be deducted fromfederal taxable income. Its federal marginal tax ratewas 28 percent. Assuming the fraction of state in-come and sales taxes remains the same as totalstate taxes are changed, the net cost to the familyof one dollar of state taxes is 0.77(1 - 0.28) -f0.23 = 0.78. This is the parameter / i .

The same procedure was followed for Hawaii in

1969 and 1989.

ENDNOTES

We thank Eric Brunner, William Fischel, DennisLeyden, Eugenia Toma, and three anonynnousreferees for valuable comnnents on a previousdraft of this paper.

' Most of the history of California school fi-nance in this section is based on PIcus (1991).We have also benefitted from conversationswith Paul Goldfinger, School Services of Cali-fornia, and Raymond M. Reinhard, Governor'sOffice of Child Developnnent and Education,State of California.

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