The legacy of Serrano: The impact of mandated equal spending on private school enrollment.

Thomas A. Husted (*)

Lawrence W. Kenny (+)

In Tiebout's idealized world, families would sort into homogeneous communities. Each family would get its preferred quality of public schools and there would be no demand for private schools. But limited public school options and a demand for religious instruction not permitted in public schools create a market for private schooling. Recently. many state governments have greatly limited districts' freedom to spend what they wish on education, often in response to court rulings to equalize education spending, such as Serrano in California. Funding equalization also affects the level of public school spending in the average state district; if this rises, as it has in many states, private schools become less attractive. Examining private school enrollment in 159 metropolitan areas in 1970, 1980, and 1990, we find that private school enrollments fall as average public spending rises and increase as public spending becomes more equal.

1. Introduction

The California Supreme Court decision in Serrano v. Priest in 1971 was the first state supreme court ruling to declare a state's education finance system unconstitutional. (1) The suit, originally filed by a class of Los Angeles County public school children and their parents, argued that the California public school finance system was unconstitutional because of its reliance on a local property tax system. Under this system, large differences in property wealth created enormous variations in educational resources across the state. In its subsequent 1976 Serrano II decision, the California Supreme Court found that the state legislature's response to the first Serrano decision was insufficient. The court ordered the state legislature to follow a trial court's requirement to implement a funding formula that reduces wealth-related per pupil expenditure disparities (i.e., property tax revenue exclusive of categorical aid and special needs) to $100 across school districts. The Serrano II decision resulted in a nea rly complete shift of the fiscal responsibility for K-12 education in California from local to state government. In the aftermath of the initial Serrano decision, suits were filed in several other states claiming unconstitutional inequities in the state education system. Many of these suits were successful. Between 1973 and 1983, six state supreme courts (New Jersey [1973], Connecticut [1977], Washington [1978], West Virginia [1979], Wyoming [1980], Arkansas [1983]) found their systems of educational finance unconstitutional. Similar rulings followed in 1989 in Kentucky, Montana, and Texas; in 1993 in Massachusetts and Tennessee; in 1994 in Arizona; and in 1997 in New Hampshire, Ohio, and Vermont. A third of the states' education finance systems now have been ruled unconstitutional. As a result of these rulings and legislative-based education reforms in a number of other states, education expenditure inequality has been reduced. (2) This in turn has left local districts with less latitude in determining spend ing levels. Parents in richer districts are expected to be especially frustrated with the limits on spending that accompany equalization.

Changes in state educational finance systems to gain greater equity affected average spending on education in these states. The initial research on this issue focused on the California experience, where raw expenditure figures reveal the dramatic change in per pupil spending in California since the initial Serrano decision in 1971. In academic year (AY) 1969-1970, per pupil spending in California's public elementary and secondary schools was slightly greater than the national average (106.25% of the national average), ranking 14th among all states. However, by AY 1992-1993, education expenditures in California had fallen to 85.6% of the national average and its rank had dropped to 34th. Silva and Sonstelie (1995) concluded that education spending in California in 1989-1990 was significantly lower than they would have otherwise predicted. They attributed about half of the lowered spending to the legislation following Serrano II and the other half to the growth of the student population in California. But the C alifornia experience of reduced expenditures appears to be atypical. Manwaring and Sheffrin (1997) found spending to be higher in many states as a result of litigation or legislative-based educational finance reform. Downes and Shah (1995) similarly estimated that school finance reform raised spending in some states and lowered spending in other states. Murray, Evans, and Schwab (1998) found state per pupil spending rose with successful state education finance litigation. The variation across states in the spending effects of education finance reforms may be due to the source (court ordered or legislative) and/or degree (e.g., weak reform, strong reform, etc.) of the reforms. In any case, there should be greater interest in supplementing what the public schools do or opting out of the public system if reforms cause spending in a state to fall.

The growing state involvement in education has affected school efficiency in a variety of ways. By centralizing authority, state meddling in school district decisions can make local public schools less efficient, and the evidence suggests that this indeed is the case. But the equalization of state spending also has been shown to lead to less efficiency, perhaps because parents have less incentive to monitor school performance when they have less control over spending. Parental dissatisfaction with public schools is expected to be greater when the schools are less efficient. (3)

There are several ways that parents may respond to policies that make schools less efficient or restrict resources flowing to the schools. One potential response would be to increase voluntary contributions for school activities. Sonstelie, Brunner, and Ardon (2000) report that the number of local educational foundations in California that are set up to funnel private donations into the public schools increased from fewer than 10 prior to the first Serrano decision to more than 500 currently. According to Brunner and Sonstelie (1999), these local educational foundations, along with PTAs and booster clubs, raised over $226 million for the public schools in 1994, or about $45 per student. But California spent nearly $26 billion in 1994 (about $4800 per student). Clearly, voluntary contributions amounting to less than 1% of total expenditures were not nearly enough to undo much of the equalization gained by the post-Serrano ii legislation. Parents also could increase the amount of home educational activities to counteract inefficiency in the school system or any reduction in per pupil school expenditures. Cullen and Somanathan (1999) provide preliminary evidence on this relationship. Using data taken from eighth grade students, they find that parental effort is inversely related to the level of school spending.

An additional and more dramatic response to less effective public schools or restricted public school resources would be for parents to opt out of the public school system and enroll their children in private schools. When public schools do not provide the quality of education desired, some families turn to private schools. Private schools also satisfy a demand for religious instruction and the teaching of values not met in public schooling. Prior empirical research on the use of private schools was based on the demand for value-oriented education and the inability of the public schools to satisfy each family's demand for quality education. (4) With few exceptions, however, this literature has ignored the impact of the recent policies to equalize primary and secondary public school expenditures. As described above, with the increase in state financial responsibility in order to achieve a reduction in state education expenditure inequality, local school districts are left with less latitude in determining spen ding levels. Wealthy school districts in affected states are no longer able to provide the high quality education their citizens demand. This is expected to result in higher private school enrollments, particularly in these wealthier school districts.

The raw data suggest that these education finance reforms have resulted in higher private school enrollment. More precisely, equalization policies have partially offset a trend toward smaller private school enrollments. In the seven states whose educational systems were ruled unconstitutional between 1971 and 1983, the fraction of students in private school fell from 0.0996 to 0.0957, a drop of 0.0039, or 3.9%, between 1970 and 1990. The decline was much sharper in the other 43 states, where private enrollment dropped from 0.1125 to 0.0990, or by 12.0%.

The empirical literature on the effects of school finance reform has primarily focused on the experience in California after the Serrano decisions. Comparing the percentage increases in private school enrollment in California with the rest of the United States between 1970 and 1990, Brunner and Sonstelie (1997) concluded that the effects in California were modest, considering the magnitude of the court-ordered reforms. Downes and Schoeman (1998) documented the rise in private school enrollments in California after its school finance reforms of the late 1970s, but their hypotheses received mixed support. Moreover, they found that the reduction in the variation in school quality played virtually no role in the growth in private school enrollment during the 1970s, contrary to expectations. (5) On the other hand, Sonstelie, Brunner, and Ardon (2000, p. 144) conclude that "the increase in California's private school enrollment has come mainly from higher-income families," as predicted. A few studies have examined private school enrollment outside of the California experience. In preliminary results, Evans, Murray, and Schwab (1999) do not find that court-ordered reforms have increased private school enrollments. Schmidt (1992) found that private school enrollment was higher in rapidly growing areas in states with a limit on expenditure growth but was unexpectedly lower in areas with relatively high tax rates and a state limit on tax rates; also, more children were found to attend private school when state aid was a larger share of school revenue.

We examine the effects of these equalization efforts and centralization on private school enrollment with a sample of 159 metropolitan areas for 1970, 1980, and 1990. Using three measures of the inequality of education spending within the state, we find that private school enrollment has increased in response to new policies that have leveled spending within the state. But state centralization has no independent impact on private school enrollment. We also find that private school enrollments have fallen as educational spending in the state has risen.

The next section explores one model of private school demand. Section 3 describes the data and empirical model. The empirical results are reported in section 4, and section 5 concludes.

2. Theory

Following the theoretical framework in Sonstelie (1979) and Lankford and Wyckoff (1992), we assume that a family has a utility function composed of two goods--the quality of education and a composite (noneducation) good that can be purchased with income net of local (education) taxes. The only way a family can obtain a better education than is provided by its public schools is through private school. This, of course, has a cost--the reduction in consumption of the composite good necessitated by expenditure on private school tuition.

Economies of scale and other impediments to school district formation make school districts larger, and thus less homogeneous, than hypothesized by Tiebout (1956). (6) A district's richer families prefer better schools than the district's median or decisive voter selects, and those who are sufficiently richer than the decisive voter send their children to private school. Metropolitan areas with more districts should have more complete sorting according to preferred school quality (i.e., more homogeneous districts) and thus are expected to have fewer children in private school. Conversely, private school enrollment should be higher in metro areas with greater income dispersion, controlling for opportunities for sorting. In large districts, there are neighborhood schools, which may vary in quality within the district. Schools serving the richer neighborhoods may get more resources or better teachers. If so, desegregation or busing plans would level school quality within a district, causing more families in rich er neighborhoods to choose private school.

It is clear that fewer families will choose to send their children to private school if their district's public schools are better. State education policies can affect the quality of a district's public schools in a variety of ways. As described in the introduction, state policies designed to reduce spending inequality make it more difficult for the richer districts to achieve their desired school quality, which should result in increased private school enrollment in richer areas. In addition, both the centralization of authority over education decisions by state governments and the equalization of school spending have been shown to make schools less efficient, which should also raise the demand for private school. State policies also influence the resources devoted to education in the state. If equalization policies raise spending, as was the case in many states, then more families will be content with the public school system and fewer families will send their children to private school.

As already noted, some parents also care about value-oriented education that is not provided in the public schools. Communities with a larger share of the population with a strong taste for this kind of education will send more children to private school. Similarly, wealthier families will be more willing to pay the tuition required to give their children a values-oriented training or better schooling than is provided by the public system.

The cost of providing children with private schooling is greater in a large family than in a small family. As a result of this quality-quantity tradeoff, private school enrollment should be lower in metropolitan areas with larger families.

In the education production function literature, there is some evidence supporting economies of scale in schooling. (7) In denser areas, the transportation cost associated with adding one more student is lower. As Kenny (1982) showed, this implies that education is relatively less expensive in urban areas and may explain why children in urban areas learn more, go to larger schools, and spend more days but fewer hours per day in school. Since few children attend private school, in many locations it is difficult for private schools to achieve any reasonable economies of scale. In denser areas, it is much easier for private schools to achieve economies of scale, which makes private schooling relatively cheaper. Private school enrollment thus is expected to be higher in denser metropolitan areas.

3. Sample and Variables

We want to estimate the impact of changes in the structure of a state's educational finance system on private school demand. As noted earlier, these changes affect private school enrollment by altering the quality of the average school district in the state and by typically making it more difficult for the state's richer districts to have better schools. We also seek to estimate the impact of the state centralization of control over education.

Sample

Comprehensive data on private school enrollment in each jurisdiction are found in the Census of Population. (8) To cover the period before and after the major reforms of state education finance systems, we have obtained data from the 1970, 1980, and 1990 censuses. None of the other sources of data on private school enrollment span this crucial period in education finance.

In the long-run, the household's school district choice and its private -- public school choice are made in a quasi-Tiebout market in which the set of public school options is determined by the mix of households and the number of school districts in the urban area and by state policies constraining school district choices. As Nechyba (2000) noted, households choosing private schools have a strong incentive to locate in poor communities with low school taxes. Similarly, policies that equalize school spending and thus make it more difficult for rich school districts to have high-quality schools are expected to cause some rich families to relocate to poorer school districts as they opt out of the public school system. Aaronson (1999) presented some evidence that curtailing local discretion in school spending indeed has reduced the amount of sorting across school districts by income. This realignment of households within the urban area weakens the estimated relationship between school reform and income; it could result in private school enrollment rising more in a state's poorer school districts than in its richer districts, even though the growth was coming from the state's richer families.

Since the quasi-Tiebout market for local government services is best described by what the Census defines as the metropolitan area, we follow Clotfelter (1976), Martinez/Vazquez and Seaman (1985), and Schmidt (1992) in using the metropolitan area as the unit of observation. Our use of Tiebout market-level data thus avoids the intraurban area confounding realignment effect that plagues the use of submarket (e.g., school district) data. Our sample initially included 161 metropolitan areas from 43 states that (1) were in existence in 1970, (2) did not cover more than one state, and (3) showed consistency in definition. (9) The first condition produces a balanced sample, which is not dominated by metropolitan areas that emerged in the 1970s or 1980s. The second condition facilitates the determination of the impact of state government policies. The third condition reflects the fact that, for several U.S. metropolitan areas, counties included as part of the area at one time were deleted in subsequent definitions; t hese metropolitan areas were not kept in our sample since there appeared to be some confusion about what comprised the urban area. On the other hand, areas that added counties as they grew are included in our sample. Since our measures of revenue inequality were unavailable for Montana, our two metropolitan areas from that state were dropped, leaving 159 urban areas.

Descriptive statistics and sources for the variables used in our analysis are found in Table 1.

Metropolitan Area Characteristics

The dependent variable is metropolitan area private school enrollment (PRIVATE ENROLLMENT). It is measured by one minus the fraction of elementary and high school students who go to public school. Unfortunately, separate statistics for elementary and high school and for parochial and other private schools are not reported in the 1990 census. In our sample, PRIVATE ENROLLMENT ranged from 0.01 to 0.54, with a mean of 0.102.

Several other metropolitan area characteristics are included as explanatory variables. An increase in the number of school districts allows for more complete sorting and, as Eberts and Gronberg (1981) have shown, results in more homogeneous districts. This is expected to lead fewer families to choose private school. The log of the number of school districts in the metropolitan area (LOG SCHOOL DISTRICT) tests this hypothesis, which has received little attention in the literature. (10,11) The typical urban area in our sample had 18 school districts.

The heterogeneity of the typical school district also reflects the heterogeneity of the metropolitan area. For a given number of districts, there will be more within-district variation in income in an urban area with a wide range of income than in a metro area with very similar incomes. Thus, an increase in the metropolitan area coefficient of variation in family income (COEF VAR FAM INCOME) is expected to be associated with higher private school enrollment.

Since 1970, school integration has become more prevalent, with busing often being used to bring this about. This reduces the range of school quality within a school district and thus makes it more difficult for a district's richer parents to get their preferred school quality, which should result in higher private school enrollment. Clotfelter (1976) showed that parents also may send their children to private schools to avoid integrated schools. If these hypotheses are correct, there should have been a greater increase in private school demand since 1970 in urban areas with a larger black population. FRACTION BLACK equals the fraction of the population that year who are black. The variable FRACTION BLACK: 1970 equals FRACTION BLACK in 1970 and zero otherwise. Both variables are needed to capture the changes that have occurred since 1970. Comprehensive, more direct measures of busing unfortunately are not available. (12)

It is more expensive to send a large family to private school than to send a small family to private school. The variable COMPLETED FERTILITY is the number of children ever born per 1000 women aged 35-44 that year and is included to capture this quality-quantity tradeoff.

In more densely populated areas, it is easier for private schools to achieve scale economies; parents do not have to drive their children as far to the private school. The resulting lower relative cost of private school should lead to greater private school enrollment. There is, however, very little evidence on this hypothesis in the private school literature. Couch, Shughart, and Williams (1993), in perhaps the only other direct test of this hypothesis, found a positive relationship between density and private school enrollment. Our variable LOG DENSITY equals the natural logarithm of metropolitan population per square mile that year.

The Catholic church operates many more private schools than any other religious denomination. It has subsidized the education its schools provide and has strongly encouraged its members to send their children to parochial school. There is strong evidence in the literature that private school enrollment is greater in heavily Catholic areas. CATHOLIC equals the fraction of the population in the metropolitan area that year who are Catholic. (13)

The demand for values-oriented education and for a higher quality education than is found in the public schools is expected to rise as an area's average income increases. REAL MEAN FAM INCOME equals real (1967 dollars) mean family income in 1969, 1979, or 1989.

State Education Policies

In our sample in 1990, half the metropolitan areas comprised no more than 5% of the state's population, and for three quarters of the urban areas, the metro area constituted no more than 13% of the state's population. Thus, it is reasonable to assume state education policies to be exogenous to the individual metropolitan area. Our key results will be shown to be insensitive to the inclusion of metropolitan areas that comprise a large share of the state's population.

State and year dummy variables are included in these pooled regressions to account for otherwise unmeasured year effects and initial state conditions and policies. In this fixed effects specification, the state policy measures described below capture only changes over time in a state's policies. The estimates of the state education policy effects do not reflect any factors that might be correlated with these policy measures but do not change over time.

Private enrollment is expected to fall as the quality of the public system rises since, with higher quality public schools, a larger expenditure is needed to obtain the same quality in a private school. Surprisingly, there is not much support for this hypothesis in the literature. Sonstelie (1979), Gemello and Osman (1984), and Couch, Shughart, and Williams (1993) found the expected negative effect, but others [e.g., Erekson (1982), Martinez-Vazquez and Seaman (1985), Schmidt (1992)] have not. We rely on mean spending at the state level to capture the effects of exogenous (from the district's perspective) changes in state policy on average district spending in the state. LOG STATE REAL EDUC SPENDING equals the natural logarithm of real state and local education spending per student in the state. Between 1970 and 1990, real state public spending per pupil increased by 73% on average.

As previously described, state governments have several different roles in the provision of primary and secondary education. One relatively recent role involves the redistribution of education resources. We are not aware of any studies that estimate the direct impact of changes in the intrastate inequality in school resources on private school enrollment. We use three measures of the inequality of public school per pupil revenues across a state's school districts: the coefficient of variation (STATE EDUC SPEND COEF OF VAR), the Gini coefficient (STATE EDUC SPEND GINI COEF), and the natural logarithm of the ratio of spending at the 95th percentile to spending at the 5th percentile (STATE EDUC SPEND 95/5) (14) With state fixed effects, these variables pick up changes over time in spending inequality, which could be due to legislative initiative or to court-mandated reform. We expect these changes to have a greater impact on private school enrollment in the state's richer areas and allow different effects, depen ding on whether the area's median family income is above or below the state's median family income.

State governments also have a large regulatory role in the provision of education. State governments place and enforce a myriad of rules and regulations on many aspects of local school district policy. Since the percentage of school revenues coming from state government (STATE REVENUE %) is strongly correlated with the centralization of authority over education decisions, this variable is used to measure school centralization. (15) Husted and Kenny (2000) find that the state revenue share lowers school efficiency but has no impact on the inequality of test scores. These results are consistent with their interpretation of the state revenue share as capturing state meddling in local school decisions and not efforts to redistribute education resources. Since state centralization makes the public schools less efficient, it is expected to cause more families to choose private school.

4. Regression Results

Table 2 reports six private school enrollment regressions for our 159 metropolitan areas pooled over three census years, which allow for year and state fixed effects. The t-statistics are based on Huber-White robust errors that allow for clustering by states. The Huber-White robust errors correct for the presence of heteroskedasticity. The second adjustment, clustering by states, assumes the errors to be independent across states but not within states; without this adjustment, the standard errors would be biased downward because our policy measures do not vary among the metropolitan areas within a state. Per pupil revenue inequality in the state's school districts is measured in the first and fourth regressions by the coefficient of variation, in the second and fifth regressions by the Gini coefficient, and in the third and sixth regressions by the natural logarithm of the ratio of revenue at the 95th percentile to revenue at the 5th percentile. The percentage of school revenue coming from the state is utiliz ed in the fourth, fifth, and sixth regressions to test whether state meddling results in greater private school enrollment. We do not report the estimated coefficients for the state dummy variables. The fits are good, and most of our hypotheses are supported.

Tables 3 and 4 report the results of two sensitivity tests. To explore the possibility that our 12-14 socioeconomic and policy variables, 2 year dummies, and 41 state dummies missed some key determinant of private school demand that in turn biased the other coefficients, Table 3 reports the state policy results for regressions using metropolitan area fixed effects instead of state fixed effects; these allow for otherwise unmeasured metro-area effects that do not change over time. Our assumption that state policies are exogenous to the metropolitan area is questionable in states in which a large fraction of the state lives in the urban area. To ascertain the impact of including these influential metro areas, Table 4 shows state policy results for the subsample of areas that comprise less than 20% of the state's population; this restriction excluded 20 urban areas that made up 20-75% of the state.

Educational policies that increase average state public school spending make the public system more attractive and should result in reduced private school enrollment. These changes are captured by the logged real state and local spending per student in the state, which is exogenous to the metropolitan area's districts. The negative and significant coefficients on LOG STATE REAL EDUC SPENDING provide strong support for this hypothesis. A one standard deviation rise is estimated in Table 2 to result in a 0.014-0.016 fall in private school enrollment. Average education spending in the state still has the predicted negative impact on private school enrollment when metro-area fixed effects are used in Table 3 and when very influential urban areas in the state are excluded in Table 4. The latter results are, however, less significant, with one-tailed significance levels ranging from 4 to 8%.

A reduction in the inequality in educational spending in public schools in a state constrains spending in the state's richer school districts. Since more districts in the state's richer metropolitan areas are constrained by this policy change, it should have a stronger effect on private school enrollment in these areas. To test this, the impact of the state's coefficient of variation in public per pupil revenue is estimated separately for areas whose median income is below the state median income (BELOW STATE MEDIAN) and for areas above the state median income (ABOVE STATE MEDIAN). The same specification is followed using the Gini coefficient of educational revenues and the logarithm of the ratio of the 95th percentile to the 5th percentile for revenue per pupil. Recall that the state fixed effects control for state variation in spending inequality and other policies that do not change over time. All coefficients for the spending inequality variables are significantly negative, indicating that private school demand rises as states reduce the inequality in spending. In addition, as expected, the effect on private school enrollment is greater (and more significant) in the state's richer areas than in the state's poorer areas in all six regressions, although the difference in coefficients is significant only in the fifth and sixth regressions. (16) In the richer areas, a one standard deviation fall in these inequality measures is estimated to result in a 0.007-0.010 rise in private school enrollment. Spending inequality still has a negative impact in private school demand when metro-area fixed effects replace state fixed effects in Table 3 and when urban areas that may influence state policies are removed in Table 4.

The share of public school revenue coming from state government is hypothesized to capture the centralization of authority over education. This meddling in school decisions has been shown to make public schools less efficient, which in turn is expected to lead to higher private school enrollment. STATE REVENUE % is, however, unrelated to private school enrollment in Tables 2-4, suggesting that school inefficiency has little impact on private school demand.

Let us turn to the other results. We confirm a large number of studies that find that private school enrollments are higher when Catholics are a larger share of the population. The fraction of the metropolitan population who are Catholic has a positive and highly significant effect on private school enrollment. A one standard deviation rise in CATHOLIC results in a 0.03 1-0.032 increase in private demand.

We expect there to be some interaction between the effects of mean income and the variation in income. An increase in metro-area heterogeneity is unlikely to lead to more private school enrollment in poor metro areas but should raise private school demand in richer metropolitan areas. Similarly, the demand for values-oriented education and for school quality is expected to rise with income, but the latter effect on private school demand should be greater in more heterogeneous areas. The negative coefficients on REAL MEAN FAM INCOME and COEF OF VAR FAM INCOME and the positive coefficient on their interaction are generally consistent with these hypotheses. An increase in mean family income is estimated to raise private school demand when the coefficient of variation in family income exceeds 0.62-0.65, a condition that is met for over three quarters of our sample. A rise in the metro coefficient of variation in family income leads to greater private enrollment only if mean real family income exceeds roughly $12, 000, which is true for only a quarter of our sample. (17)

The coefficients on LOG SCHOOL DISTRICTS are negative, as expected, and are significant at the 0.090-0.098 level under a one-tailed test. (18) In metropolitan areas with more, and thus more homogeneous, school districts, there are fewer families sufficiently dissatisfied with the quality of education chosen by the median voter to opt for private school. A one standard deviation rise in this variable is associated with a 0.008 fall in private school enrollment.

As a result of more pervasive, and sometimes forced, integration, private school enrollment was expected to rise after 1970 in areas with a large black population. The estimates on FRACTION BLACK: 1970 and FRACTION BLACK support this hypothesis. For 1970, the effect of increasing the proportion of the population who are black is given by the sum of the FRACTION BLACK and FRACTION BLACK: 1970 coefficients. Although these coefficients nearly cancel each other out, an increase in the black population had a small but significant impact on private enrollment in 1970; a one standard deviation rise resulted in a 0.004 rise in PRIVATE. On the other hand, for 1980 and 1990, the coefficients of FRACTION BLACK represent the impact of racial composition. The positive and significant coefficients indicate that, in these years, private school demand was greater in metropolitan areas with a larger black population. In these years, a one standard deviation increase in FRACTION BLACK was associated with a 0.019 rise in privat e school enrollment, nearly five times the impact in 1970. Thus, the results are consistent with private school enrollment increasing since 1970 in heavily black areas, perhaps due to busing.

The insignificant coefficients on children ever born to women aged 35-44 (COMPLETED FERTILITY) do not support the hypothesized tradeoff between child quality and child quantity. Perhaps a different measure would better capture the higher cost that parents of large families face in sending their children to private school.

Since it is easier for private schools to achieve scale economies in denser areas, an increase in population density should result in higher private school enrollment. There is, however, very little evidence in the literature on this relationship. The positive and highly significant coefficients on LOG DENSITY provide strong support for this hypothesis. A 0.934 (one standard deviation) rise in this variable is estimated to lead to a 0.011-0.012 increase in private school enrollment.

Interestingly, there is no evidence in the year coefficients of a change in the demand for private school over time that has not been captured by our other independent variables.

5. Conclusion

In the last two decades, the educational systems in a number of states have undergone major changes in response to actual and threatened judicial mandates for equal educational opportunity. The various new state funding formulas that have accompanied state education finance reforms have led to higher spending in many cases and to lower spending in a few others. We find that a metropolitan area's private school enrollment falls as education spending in the state rises, as predicted. Our estimates suggest that the substantial rise in real education spending over time has played an important but unrecognized role in dampening the demand for private schooling.

Most of these reforms reduced the inequality in education resources across a state's school districts. As spending was leveled within a state, richer districts were no longer able to purchase the high-quality education they demanded. We find, using various measures of spending inequality, that this led to higher private school enrollment, especially in a state's richer metro areas. Although the effect of spending equalization on private school demand is not as great as the effects of racial integration, religious composition, or average state spending on education, its impact is comparable with that of the other variables used in this study.

On the other hand, the centralization of authority over education in state government does not raise the demand for private school, even though it makes the public schools less efficient. This suggests that state policies affect private school enrollment principally by altering the resources that can be spent on public schools.

Earlier in this article, we noted that, from 1970 to 1990, private school enrollment had risen 0.0096 more (i.e., experienced a 0.0096 smaller decline) in the seven reform states, whose educational finance systems were ruled unconstitutional between 1971 and 1983, than in the other 43 states. How much of this difference can be explained by the education spending and spending inequality policies that have been the focus of this article? Education spending grew more rapidly in the seven reform states, causing a 0.0025 greater fall in the fraction of students in private schools. The coefficient of variation in revenue fell by 0.0419 in the court-mandated states and rose by 0.0031 in the other states, resulting in a 0.0071 greater growth in private enrollment in the reform states. Similarly, the difference between the fall in the Gini coefficient for school revenue in the seven states (0.0276) and the rise in the remaining states (0.0009) accounts for a 0.0082 greater growth in the court-mandated states. A compar able calculation based on the 95th percentile to 5th percentile ratio coefficients implies a 0.0060 greater growth in the seven court-mandated states. On net, these two policy changes explain 36-59% of the differential private school enrollment growth in these two groups of states between 1970 and 1990.

There are several other novel results. Busing became much more prevalent in the 1970s; this was accompanied by a rise in private school enrollment in cities with large black populations. An increase in the number of school districts permits more homogeneous districts and is found to result in fewer students attending private school. Finally, private schools appear to be much more viable in more densely populated metropolitan areas than in areas with low density.

(*.) Department of Economics, American University, 4400 Massachusetts Avenue, NW, Washington, DC 20016, USA; E-mail [e-mail].

(+.) Department of Economics, University of Florida, P.O. Box 117140, Gainesville, FL 32611-7140, USA; E-mail [e-mail]; corresponding author.

We have benefited from comments received at the University of Florida, Florida State University, and the Public Choice and American Education Finance Association meetings. In particular we thank Jim Adams, Dave Denslow, Jon Hamilton, Thomas Nechyba, Jon Sonstelie, Eugenia Toma, and two anonymous referees. Dirk Commandeur and James Dewey carefully assembled much of the data used in this paper.

Received June 2000; accepted May 2001.

(1.) See Minorini and Sugarman (1999) and Sonstelie, Brunner, and Ardon (2000) for a description of the California Supreme Court decisions.

(2.) This occurred despite efforts by some state legislatures to thwart court edicts by increasing the use of state revenue programs, such as categorical aid, that do not equalize district revenues. Sonstelie, Brunner, and Ardon (2000) describe how this occurred in California.

(3.) Husted and Kenny (2000) review this literature. They also estimate several versions of an education production function and find that schools become less efficient when spending becomes more equal or the state's involvement in education finance rises. Spending equalization also is shown to result in more equal test scores, implying an equity-efficiency tradeoff.

(4.) Clotfelter (1976), Sonstelie (1979), Erekson (1982), Frey (1983), Gemello and Osman (1984), Martinez-Vazquez and Seaman (1985), West and Palsson (1988), Hamilton and Macauley (1991), Schmidt (1992), Couch, Shughart, and Williams (1993), Hoxby (1994, 2000), and Murray and Wallace (1997) have explained differences in area private school enrollment rates, Long and Toma (1988), Lankford and Wyckoff (1992), and Chiswick and Koutroumanes (1996) use household data to examine which families sent their children to private school.

(5.) Most of the growth appears to be due to the deterioration in average school quality during this decade.

(6.) See Kenny and Schmidt (1994).

(7.) See Dewey, Husted, and Kenny (2000).

(8.) Since the various state Departments of Education mainly service the public school systems, many do not gather data on private schools; consequently, no comprehensive data on private school enrollment are available in noncensus years.

(9.) Note that, to be consistent with metropolitan area definitions in other years, the following metropolitan areas were combined into one observation: (1990) Oakland and San Francisco, California; (1970, 1980) Bay City and Saginaw, Michigan; (1990) Erie and Niagara, New York; (1970) Raleigh and Durham, North Carolina; (1990) Houston and Brazoria, Texas; and (1970, 1980) Petersburg and Richmond, Virginia. Our initial sample includes no areas from Alaska, Delaware, New Mexico, North Dakota, Rhode Island, Vermont, or Wyoming.

(10.) The number of school districts reported in the Census of Governments includes a few special districts that provide vocational or college education and not the usual primary and secondary education. To adjust for this, we have multiplied the area's number of districts by the state's ratio of primary and secondary districts to the total number of districts.

(11.) Hamilton and Macauley (1991) and Schmidt (1992) find private school enrollments to be higher when there is more income inequality in the typical district. Martinez-Vazques and Seaman (1985) present some evidence that private school enrollment falls as the number of districts in the metropolitan area rises, presumably because this results in more homogeneous districts.

(12.) Information on court-ordered busing is only available for large school districts, and even this would miss the growth in "voluntary" busing as the legal environment changed.

(13.) This information is from Johnson, Picard, and Quinn (1974), Quinn et al. (1982), and Bradley et al. (1992). Since the data are at the county level, the figures in New England correspond to the counties in which the metropolitan areas are located. In the rest of the country, metropolitan areas are defined by county lines.

(14.) These data, from Evans, Murray, and Schwab (1997), were generously provided to us by the authors of that study.

(15.) Revenue is only one of 36 components in Wirt's (1977) index of state centralization. Nevertheless, the correlation between the state revenue share and his index is 0.40, which implies a correlation between the state share and other components of state centralization. Unfortunately, regularly updated indices such as Wirt's that directly measure state interference in education are unavailable.

(16.) The Wald F-statistics are 2.91 and 3.35, respectively, which are significant at the 0.095 and 0.075 levels.

(17.) The regions for which these variables exert a significantly positive effect on private school demand are correspondingly smaller. In the first regression, for example, mean family income significantly (p = 0.05) raises demand when the coefficient of variation in family income exceeds 0.85; and private enrollment experiences a significant increase as the coefficient of variation increases at mean family incomes above $15,600.

(18.) Clustering at the state level to deal with attributing too many degrees of freedom to state policy variables in effect reduces the degrees of freedom for all variables, making all variables less significant. If, instead, robust errors are clustered at the metropolitan-area level, the school district coefficients are significant at the 0.049-0.055 level under a one-tailed test.

References

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Table 1

Summary Statistics and Data Sources

Metropolitan Area Variables       Mean      Std. Dev.   Minimum

Private enrollment                  0.102     0.060       0.011
Log density                         5.683     0.934       2.944
Log school districts                2.327     1.148       0
 School districts                  18.003    19.70        1
Fraction black                      0.096     0.094       0
Fraction Catholic                   0.224     0.169       0.004
Completed fertility                 2.553     0.510       1.540
Real mean fam income           10,808.2    2159.4      6076.5
Coef var fam income                 0.731     0.104       0.528
State variables
 Log state educ spending            7.851     0.292       7.159
  State educ spending            2679.8     806.0      1286.2
 State educ spend coef of var       0.156     0.046       0
  Above state median                0.084     0.083       0
  Below state median                0.071     0.085       0
 State educ spend gini coef         0.082     0.024       0
  Above state median                0.045     0.044       0
  Below state median                0.038     0.045       0
 State educ spend 95/5              0.464     0.136       0
  Above state median                0.251     0.249       0
  Below state median                0.213     0.252       0
 State Revenue %
  Above state median               25.519    25.011       0
  Below state median               19.795    23.630       0

Metropolitan Area Variables      Maximum

Private enrollment                  0.514
Log density                         9.461
Log school districts                4.799
 School districts                 121.4
Fraction black                      0.458
Fraction Catholic                   0.868
Completed fertility                 4.212
Real mean fam income           30,874
Coef var fam income                 1.265
State variables
 Log state educ spending            8.590
  State educ spending            5375.6
 State educ spend coef of var       0.303
  Above state median                0.303
  Below state median                0.303
 State educ spend gini coef         0.137
  Above state median                0.137
  Below state median                0.137
 State educ spend 95/5              0.849
  Above state median                0.849
  Below state median                0.849
 State Revenue %
  Above state median               89.90
  Below state median               72.40

Sources: Private enrollment, completed fertility, mean family income,
coef var family income: 1970 and 1990 censuses; density, fraction black:
1972 County and City Data Book, 1993 County and City Extra, 1990 census;
school districts: 1972, 1982, and 1992 Census of Governments; fraction
Catholic: 1990, Bradley et al. (1992); 1980, Quinn et al. (1982); 1970,
Johnson et al. (1974); state educ spending: State Government Finances,
1970, 1980, 1990; state educ spend coef of var, state educ spend gini
coef, state educ spend 95/5: data from Evans, Murray, and Schwab (1997)
and provided by authors of that study; state revenue %: Digest of
Education Statistics, various years.
Table 2

Determinants of Private School Enrollment, 1970, 1980, 1990, Full
Sample, State Fixed Effects (a)

                                       1                    2

Log state real educ spending        -0.0513              -0.0507
                                    (2.12)               (2.04)
State educ spend coef of var
  Above state median                -0.1620
                                    (2.39)
  Below state median                -0.1391
                                    (1.80)
State educ spend gini coef
  Above state median                                     -0.2979
                                                         (2.21)
  Below state median                                     -0.2478
                                                         (1.65)
State educ spend 95/5
  Above state median

  Below state median

State revenue %
  Above state median

  Below state median

Log density                          0.0118               0.0118
                                    (2.44)               (2.43)
Fraction black                       0.2033               0.2030
                                    (2.60)               (2.59)
Fraction black: 1970                -0.1607              -0.1616
                                    (4.11)               (4.10)
Fraction Catholic                    0.1908               0.1908
                                    (3.06)               (3.06)
Completed fertility                  0.0103               0.0100
                                    (0.39)               (0.38)
Log school districis                -0.0069              -0.0068
                                    (1.34)               (1.32)
Real mean fam income          -0.22 X [10.sup.-4]  -0.22 X [10.sup.-4]
                                    (2.51)               (2.48)
Coef of var fam income              -0.4223              -0.4 177
                                    (2.37)               (2.35)
Real mean fam income X        0.35 X [10.sup.-4]   0.35 X [10.sup.-4]
 coef of var fam income             (2.48)               (2.47)
 1980                               -0.0064              -0.0064
                                    (0.69)               (0.69)
 1990                                0.0063               0.0052
                                    (0.23)               (0.19)
[R.sup.2]                            0.6742               0.6737
Root mean squared error              0.0366               0.0366
Number of observations             477                  477

                                       3                    4

Log state real educ spending        -0.0538              -0.0478
                                    (2.23)               (1.92)
State educ spend coef of var
  Above state median                                     -0.2086
                                                         (3.14)
  Below state median                                     -0.1216
                                                         (1.55)
State educ spend gini coef
  Above state median

  Below state median

State educ spend 95/5
  Above state median                -0.0530
                                    (1.98)
  Below state median                -0.0427
                                    (1.48)
State revenue %
  Above state median                               0.11 X [10.sup.-3]
                                                         (0.32)
  Below state median                               -0.17 X [10.sup.-3]
                                                         (0.58)
Log density                          0.0121               0.0125
                                    (2.50)               (2.47)
Fraction black                       0.2038               0.2056
                                    (2.60)               (2.69)
Fraction black: 1970                -0.1622              -0.1613
                                    (4.07)               (3.60)
Fraction Catholic                    0.1904               0.1847
                                    (3.06)               (2.91)
Completed fertility                  0.0106               0.0138
                                    (0.41)               (0.52)
Log school districis                -0.0069              -0.0070
                                    (1.33)               (1.37)
Real mean fam income          -0.21 X [10.sup.-4]  -0.23 X [10.sup.-4]
                                    (2.41)               (2.73)
Coef of var fam income              -0.4158              -0.4278
                                    (2.32)               (2.44)
Real mean fam income X        0.34 X [10.sup.-4]   0.36 X [10.sup.-4]
 coef of var fam income             (2.42)               (2.62)
 1980                               -0.0056              -0.0047
                                    (0.62)               (0.47)
 1990                                0.071                0.0093
                                    (0.27)               (0.34)
[R.sup.2]                            0.6735               0.6757
Root mean squared error              0.0366               0.0366
Number of observations             477                  477

                                       5                    6

Log state real educ spending        -0.0470              -0.0498
                                    (1.82)               (1.96)
State educ spend coef of var
  Above state median

  Below state median

State educ spend gini coef
  Above state median                -0.3916
                                    (3.19)
  Below state median                -0.2120
                                    (1.49)
State educ spend 95/5
  Above state median                                     -0.669
                                                         (2.89)
  Below state median                                     -0.0327
                                                         (1.25)
State revenue %
  Above state median          0.14 X [10.sup.-3]   0.22 X [10.sup.-3]
                                    (0.40)               (0.62)
  Below state median          -0.16 X [10.sup.-3]  -0.96 X [10.sup.-4]
                                    (0.57)               (0.29)
Log density                          0.0124               0.0127
                                    (2.46)               (2.56)
Fraction black                       0.2059               0.2073
                                    (2.70)               (2.71)
Fraction black: 1970                -0.1634              -0.1673
                                    (3.58)               (3.60)
Fraction Catholic                    0.1841               0.1835
                                    (2.89)               (2.90)
Completed fertility                  0.0138               0.0145
                                    (0.52)               (0.55)
Log school districis                -0.0069              -0.0070
                                    (1.33)               (1.36)
Real mean fam income          -0.23 X [10.sup.-4]  -0.23 X [10.sup.-4]
                                    (2.72)               (2.63)
Coef of var fam income              -0.4232              -0.4226
                                    (2.41)               (2.38)
Real mean fam income X        0.36 X [10.sup.-4]   0.36 X [10.sup.-4]
 coef of var fam income             (2.62)               (2.57)
 1980                               -0.0047              -0.0047
                                    (0.46)               (0.46)
 1990                                0.0083               0.0096
                                    (0.30)                0.036
[R.sup.2]                            0.6754               0.6755
Root mean squared error              0.0366               0.0366
Number of observations             477                  477

(a)Absolute t-statistics based on robust standard errors, allowing for
clustering by states, are in parentheses.
Table 3

Determinants of Private School Enrollment, 1970, 1980, 1990, Full
Sample, Metro-Area Fixed Effects (a)

                                (1)      (2)      (3)

Log state real educ spending  -0.0555  -0.0550  -0.0561
                              (3.45)   (3.39)   (3.48)
State educ spend coef of var
 Above state median           -0.1254
                              (2.98)
 Below state median           -0.1077
                              (2.62)
State educ spend gini coef.
 Above state median                    -0.2223
                                       (2.63)
 Below state median                    -0.1837
                                       (2.24)
State educ spend 95/5
 Above state median                             -0.0436
                                                (2.84)
 Below state median                             -0.0356
                                                (2.33)
State revenue %
 Above state median

 Below state median

                                     (4)                 (5)

Log state real educ spending       -0.0550             -0.0546
                                   (3.36)              (3.31)
State educ spend coef of var
 Above state median                -0.1076
                                   (2.04)
 Below state median                -0.0939
                                   (1.94)
State educ spend gini coef.
 Above state median                                    -0.1791
                                                       (1.68)
 Below state median                                    -0.1454
                                                       (1.51)
State educ spend 95/5
 Above state median

 Below state median

State revenue %               0.13 X [10.sup.-3]  0.17 X [10.sup.-3]
 Above state median                (0.59)              (0.78)
                              0.15 X [10.sup.-3]  0.19 X [10.sup.-3]
 Below state median                (0.69)              (0.83)

                                      (6)

Log state real educ spending        -0.0548
                                    (3.35)
State educ spend coef of var
 Above state median

 Below state median

State educ spend gini coef.
 Above state median

 Below state median

State educ spend 95/5               -0.0376
 Above state median                 (2.06)
                                    -0.0287
 Below state median                 (1.66)

State revenue %               0.20 X [10.sup.-3]
 Above state median                 (0.93)
                              0.19 X [10.sup.-3]
 Below state median                 (0.87)

Same sample and independent variables as in Table 2.

(a)Absolute t-statistics are in parentheses.
Table 4

Determinants of Private School Enrollment, 1970, 1980, 1990, Subsample:
(Metro Area Pop/State Pop) <0.2 in 1990, State Fixed Effects (a)

                                 1        2        3

Log state real educ spending  -0.0423  -0.0404  -0.0448
                              (1.73)   (1.59)   (1.83)
State educ spend coef of var
 Above state median           -0.2008
                              (2.75)
 Below state median           -0.1733
                              (2.11)
State educ spend gini coef
 Above state median                    -0.3702
                                       (2.47)
 Below state median                    -0.3145
                                       (1.91)
State educ spend 95/5
 Above state median                             -0.0655
                                                (2.28)
 Below state median                             -0.0538
                                                (1.75)
State.revenue %
 Above state median

 Below state median


                                 4                    5

Log state real educ spending  -0.0399              -0.0376
                              (1.58)               (1.42)
State educ spend coef of var
 Above state median           -0.2362
                              (2.80)
 Below state median           -0.1666
                              (2.21)
State educ spend gini coef
 Above state median                                -0.4449
                                                   (2.61)
 Below state median                                -0.2996
                                                   (2.17)
State educ spend 95/5
 Above state median

 Below state median

State.revenue %
 Above state median            0.48 X [10.sup.-4]   0.76 X [10.sup.-4]
                              (0.13)               (0.21)
 Below state median           -0.14 X [10.sup.-3]  -0.14 X [10.sup.-3]
                              (0.41)               (0.39)

                                 6

Log state real educ spending  -0.0416
                              (1.61)
State educ spend coef of var
 Above state median

 Below state median

State educ spend gini coef
 Above state median

 Below state median

State educ spend 95/5
 Above state median           -0.0751
                              (2.88)
 Below state median           -0.0464
                              (1.90)
State.revenue %
 Above state median            0.19 X [10.sup.-3]
                              (0.47)
 Below state median           -0.36 X [10.sup.-4]
                              (0.09)

Same independent variables as in Table 2; 417 observations.

(a)Absolute t-statistics based on robust standard errors, allowing for
clustering by states, are in parentheses.