Private school enrollment and public school ...

Public Choice 76: 301-312, 1993. © 1993 Kluwer Academic Publishers. Printed in the Netherlands.

Private school enrollment and public school performance*

JIM F. COUCH Department of Economics and Finance, University of North Alabama, Florence, A L 35632

WILLIAM F. SHUGHART II AL L. WILLIAMS Department of Economics and Finance, University of Mississippi, University, MS 38677 Accepted 1 July 1991

I. Introduction Federal, state, and local expenditures for public education amounted to $184 billion, or $4,538 per pupil, in 1987-88 (Lieberman, 1989: 29). At the same time, educational achievement in the United States, whether measured in terms of student performance on standardized tests, literacy rates, or other dimensions of learning, has been stagnant for a decade or more (National Commission on Excellence in Education, 1983). As a result, public concern with public education has reached a level not seen since the Soviet Union launched its Sputnik satellite in 1957. Calls for educational reform are rampant in many states, with proposals being advanced for increasing teacher salaries, implementing merit pay for teachers, adopting more stringent teacher training and certification requiremens, and introducing various other initiatives designed to improve the quality of education delivered by the public schools. Experiments with introducing choice into the public education process are also beginning to be undertaken. In 1987, for example, Minnesota implemented a plan allowing students to enroll at any public school within the state. Similarly, public school officials in Boston are considering a proposal that would divide the city into three autonomous zones and allow elementary and middle school students to attend any school within their zone of residence (Kelly, 1990). All such experiments are designed to improve the quality of public education by weakening the monopoly power of local school districts. The premise of this approach to educational reform is that by allowing greater freedom of * We benefitted from comments by James Coleman, John Conlon, Artie Powell, Lewis Smith, Keith Womer, Beverly Pearson, and participants in a Department of Economics and Finance seminar at the University of Mississippi. The suggestions of an anonymous referee were particularly helpful in improving the paper. The usual caveat applies.

302

choice within the public school system, individual schools and school districts will be forced by the threat of lower enrollments to offer curricula and instruction that more closely match the demands of the consumers of public education. Competition within the public educational system is still quite limited, though, and so there is at present little "basis for testing empirically the influence of choice on educational quality" (Eberts, Schwartz, and Stone, 1990: 4). Fortunately for our purposes, however, there is an established educational alternative to the public schools - the private schools - which can provide the basis for such a test.1 Critics of policies designed to allow greater freedom of choice in public education have long argued that such policies will lead to a decline in the quality of public schools. This position, which has been taken by one side of the current debate about educational reform, was first advanced some time ago in opposition to proposals that were aimed at encouraging competition between public and private schools by providing parents with tuition tax credits or vouchers that could be used to offset part of the cost of financing a private education for their children. The basis for this argument is an assumption that individuals' preferences for expenditures on public education may be "double peaked," leading to the possibility that two equilibria for public school quality may exist (Sonstelie, 1979; also see Barzel and Deacon, 1975; Flowers, 1975; and Stiglitz, 1974). In one equilibrium, the public schools are of high quality and most students are educated in the public sector. In the other equilibrium, the public schools are of low quality and most students attend private schools. While both equilibria are locally stable, a cutback public school funding caused, for example, by tax limitation initiatives or by the adoption of policies that reduce the cost of attending private schools, "could trigger a progressive decline in public school quality accompanied by an accelerating exodus from the public schools - an unravelling of the public school system" (Sonstelie, 1979: 343). The flaw in this argument is that it assumes that the quality of education delivered by the public schools is exogenous and, moreover, that quality is determined solely by the level of public education funding appropriated by the legislature. If, on the other hand, public school quality is endogenous, that is, if public school administrators and teachers can respond to the threat of declining enrollments by improving the quality of instruction provided to their students at a given level of funding, then making a wider range of educational choice available to parents may enhance rather than erode the quality of public education. The impact of market forces on public school quality is thus an empirical question. Do public schools provide improved instruction to their students where they face more competition from the private sector? Using data on public and private schools in North Carolina, we find that, other things being the

303 same, performance on a standardized algebra test administered to public school students statewide is significantly higher in those counties where a larger percentage of school-age children are enrolled in private schools. Our evidence thus suggests that competitive market forces lead to improved performance in public education as they do in all other areas of the economy. Far from causing the public school system to unravel, policies that enhance freedom of educational choice hold the promise of improving the quality of public education at current (and perhaps lower) spending levels. The paper is organized as follows. Section 2 presents our empirical model and results. Some brief concluding remarks are offered in Section 3.

2. Empirical model and results

Those supporting the introduction of market forces into public education all assume that alternative educational choices will force public schools to do a better job of educating their students. Tuition tax credits and vouchers have been advocated as means to this end (Friedman and Friedman, 1981: 140-178). The presumption is that breaking up the public school monopoly will force the public schools to be more accountable to the "consumers" of education. This is precisely what we wish to test - does the presence of competition exert any influence on public students' performance on standardized tests? As mentioned previously, however, competition within the public school system is quite limited. In order to test for a "competition effect," we therefore examine the relationship between private school enrollments and public school performance. The results reported below suggest that market forces do indeed raise the level of educational achievement in the public schools. Actual and potential competition from private schools apparently motivates educators to act in such a manner that tangible improvements in the quality of public education are produced. Data from North Carolina's 100 counties were used to test for the existence of a competition effect. Our measure of educational achievement is average county scores on the Algebra I part of the End-of-Course Testing Program administered to public school students. This statewide testing program was established in 1985-86 to provide comparative information about student performance in North Carolina's public schools. The average county scores used in the analysis are based on the universe of 60,183 students throughout the state who took the Algebra I test in 1988-89. These test-takers comprised a subset of the public school population in the eighth through twelfth grades.a Student achievement in mathematics was chosen over other subject tests because mathematical skills have been shown to be influenced more by effective teaching than other subjects (Madaus et al., 1979). It has been argued in the literature that public education actually produces

304 two types of output (West, 1990). The first involves privately beneficial human capital formation whereby individuals acquire the skills and abilities that will make them more productive when they subsequently enter the labor force. The second relates to the production of external (public) benefits such as those associated with general literacy and with indoctrination in a common set of values and attitudes (Cohn, 1979; Benson, 1981; Hettich, 1969; Krashinsky, 1986; Lott, 1987; 1990). By using public school students' test scores on a standardized test of mathematical skills as the dependent variable in our analysis, we focus primarily on the first type of output. It is worth noting, however, that insofar as competition leads to improved performance on this narrow margin, public school resources will be freed for use in the production of other types of output. 3 Our first task is to explain variations in private school enrollments across North Carolina's counties. The determinants of enrollment in private schools are important to the analysis because attendance decisions may be in part based on factors such as race and public school quality which themselves influence student performance on standardized tests. We specified the following regression equation to account for this possibility. PRIV = f(BLACK, COLLPCT, TOTFPS, PCY87, POVERTY, DENSITY, e),

(1)

where PRIV

= the percentage of school-age children enrolled in private schools, by county; BLACK the percentage of the county's population that is black; COLLPCT = the percentage of the county's population that is college educated; TOTFPS = total funding per student in the county's public schools; PCY87 = t987 per capita personal income in the county; POVERTY = the percentage of families in the county below the poverty line in 1979; DENSITY = county population per square mile (thousands); and e = regression error term. =

BLACK is included as an explanatory variable to control for so-called white flight. Do private school enrollments increase as whites exit from the public schools in order to avoid contact with classmates from minority backgrounds? If so, we expect the estimated coefficient on this variable to be positive in sign. POVERTY is included to test the possibility that white flight is a response to increased numbers of classmates from low-income backgrounds. 4

305 C O L L P C T represents the " t a s t e " for education in the county population base. T o the extent that college-educated parents are more likely to send their children to private schools than are parents with fewer than 16 years o f education, we expect a positive ceteris paribus relationship to hold. 5 T O T F P S is our measure o f public school quality. If more resources per student make public education a more attractive alternative, we expect private school enrollments to decline. It is worth noting, however, that evidence has been reported suggesting that not all public school funding is equally productive. Increased expenditures on public education that find their way into the classroom improve student performance on standardized tests. But resources spent on administrative and other nonteaching-related inputs tend to lower educational achievement in the public schools (see Anderson, Shughart, and Tollison, 1991). Total funding per student is nevertheless a standard measure of school quality (e.g., Summers and Wolfe, 1977; Eberts, Schwartz, and Stone 1990), and we enter it on the right-hand side of equation (1) in that spirit. PCY87 controls for variations in income across counties in North Carolina. We expect private school enrollments to be higher in high-income counties, assuming that private education is a normal good. DENSITY is included to control for differences in private school enrollments between rural and urban areas. Our main interest is in testing whether variations in private school attendance have an impact on educational achievement in the public schools. The regression equation that serves as the basis for this test is specified as follows. ZSCORE = g(PRIV, BLACK, P A R E N T E D , POVERTY, TOTFPS, DENSITY, u),

(2)

where ZSCORE

= the deviation of the county average Algebra I test score from the statewide average, measured in standardized units; P A R E N T E D = the percentage of students taking the Algebra I test whose parents have less than a high-school education; = regression error term; and all other variables are defined as before. The dependent variable in equation (2) measures the performance of public school students in terms of the amount by which the county average Algebra I test score was above or below the statewide average on that test. The formula for the Z-score transformation is ZSCORE = (X i - ?~)/s, where X i is the observed test score average in a county, J~ is the mean value across the 100 counties, and s is the sample standard deviation of the X i. This variable definition

306 was adopted to take account of the fact that the range of the Algebra I test scores is bounded both above and below (the maximum possible score is 60; the minimum is zero). 6 The specification in equation (2) assumes that the direction of causality runs from private school enrollments to public school test scores. In particular, we do not allow for the opposite possibility that average scores on the Algebra I test rise as low-achieving students leave the public school system seeking less stringent educational standards. A substantial amount of empirical evidence exists showing that the education provided by private schools is of higher quality than that received by students attending public schools. Specifically, students in private schools outperform their public school counterparts on standardized tests (Coleman and Hoffer, 1987), and they also exhibit greater growth in academic achievement between their sophomore and senior years (Coleman, Hoffer, and Kilgore, 1982).7 Our assumption concerning the direction of causation thus seems justified. The estimated coefficient on PRIV will provide evidence on the strength of the hypothesized competition effect. A positive sign will be consistent with the idea that market forces motivate public educators to take actions that lead to higher levels of student achievement. The remaining explanatory variables control for other factors that are expected to influence student achievement in the public schools. TOTFPS again provides a measure of the variation in public school quality across the 100 counties in North Carolina. Does more spending translate into "better" public schools? What about the students themselves? Do the disadvantages associated with a minority (BLACK), low-income (POVERTY), or rural (DENSITY) background have an impact on test score performance? Are lower test scores recorded by the children of less highly educated parents? The data will speak as to the relative importance of these considerations, The observations on all of the variables used in the analysis were taken from standard government sources. 8 Descriptive statistics are shown in Table 1. Because the system of two equations is recursive, we are able to estimate them separately. 9 Equation (1) was estimated using the Tobit procedure to account for the leftcensoring of the dependent variable, PRIV, at zero--13 of the 100 counties in North Carolina reported having no students enrolled in private schools. 1° The regression resuks reported in column (I) of Table 2 show evidence of "white flight." This effect is small in magnitude, however: Private school enrollments increase by only three one-hundredths of a percentage point for every 1 percentage point increase in the proportion of a county's population that is black. The coefficient is nonetheless statistically significant at the 10 percent level.ll Private school enrollments are also apparently driven by a desire to avoid classmates from low-income backgrounds. Each 1 percentage point increase in the

307 Table 1. Descriptive statistics

Variable

Mean

Standard deviation

Minimum

Maximum

ZSCORE PRIV (o70) BLACK (%) POVERTY (%) COLLPCT (o70) PARENTED (%) TOTFPS ($) DENSITY PCY87 ($)

0.0046 2.99 23.15 14. I 1 10.12 11.19 3,705.21 ' 131.45 11,645.98

1.0000 2.7181 16.6303 4.9751 5.2614 3.5649 300.3263 144.6384 2,122.14

- 2.2679 0.00 0.00 6.20 5.00 4.30 3,048.00 10.00 8,101.00

3.6483 10.50 60.70 25.00 41.00 20.00 4,562.00 854.00 17,709.00

Table 2. Regression results

Dependent variables

PRIV

ZSCORE

Intercept

- 2.5241

Intercept PRIV

BLACK

0.0336 (1.75)* 0.1902 (2.11)** - 0.0017 ( - 2.49)** 0.1816 (2.04)** 0.0005 (2.47)** 0.0060 (2.07)** 0.522 16.95

BLACK

COLLPCT TOTFPS POVERTY PCY87 DENSITY R2 F

PARENTED TOTFPS POVERTY

DENSITY

0.2961 0.0782 (2.02)**

- 0.1243 ( - 4.47)*** 0.0006 (1.91)* - 1.0636 ( - 2.97)***

0.2952 0.0897 (2.23)** - 0.0066 ( - 1.06) - 0.1204 ( - 4.29)*** 0.0005 (1.81)* - 0.0517 ( - 2.14)**

0.0025 (-2.97)*** 0.332 9.35

- 0.0024 (-2.87)*** 0.340 7.99

-

Note. t-statistics in parentheses; asterisks denote significance at the 1 percent (***), 5 percent (**),

and 10 percent (*) levels. p r o p o r t i o n o f f a m i l i e s b e l o w t h e p o v e r t y level in a c o u n t y is a s s o c i a t e d w i t h a t w o - t e n t h s o f a p e r c e n t a g e p o i n t i n c r e a s e in t h e p r o p o r t i o n o f s c h o o l - a g e children attending private schools. P r i v a t e s c h o o l a t t e n d a n c e is also s i g n i f i c a n t l y h i g h e r in t h o s e c o u n t i e s w h e r e a l a r g e r p e r c e n t a g e o f t h e p o p u l a t i o n is c o l l e g e e d u c a t e d a n d w h e r e p e r s o n a l i n c o m e s a n d p o p u l a t i o n d e n s i t y a r e h i g h e r . F e w e r s t u d e n t s t e n d t o e n r o l l in p r i v a t e s c h o o l s in c o u n t i e s w h e r e t h e p u b l i c s c h o o l s a r e o f h i g h e r q u a l i t y , at least

308 as measured in terms of spending per student. This result is itself evidence of market forces at work in the provision of education. Parents apparently base their choice of school (public versus private) at least in part on the perceived quality of the education offered by the public sector. Overall, the regression results reported in the table explain more than half of the statewide variation in priVate school attendance in the State of North Carolina. We estimated a second version of equation (1) including a dummy variable set equal to 1 if the local public school system contained separate county and city units and set equal to zero for consolidated county school districts (see North Carolina Department of Public Instruction, 1989). This specification was adopted in order to test whether or not a rough measure of increased choice within the public school system has an impact on enrollments in private schools. Martinez-Vazquez and Seaman (1985) reported such an effect. They included a variable computed as the number of independent public school districts times the number of schools in a regression model explaining variations in private school enrollments across 75 of the largest SMSAs in the United States during the early 1970s. The estimated coefficient on this variable was negative and statistically significant, suggesting that fewer parents send their children to private schools where more choices are available within the local public schools system. Our dummy variable is in the spirit of West and Palsson's (1988: 738) interpretation of this finding, namely "that the increase in private school enrollment will be g r e a t e r . . , if the process of consolidation (into fewer districts and fewer schools) continues." However, the estimated coefficient on the dummy variable was not statistically significant, suggesting that increased choice within the public school system is not viewed as an adequate substitute for increased choice in terms of public versus private schooling, at least in our data set. 13 Regression estimates for equation (2) are reported in the second and third columns of Table 2. The results suggest the existence of a significant competition effect. For every 1 percent increase in private school enrollments, public test scores increase by .08 standard deviations above the statewide mean. By offering parents a choice in educating their children, the presence of private schools in a county has a significant impact on the quality of the public schools that thereby face stronger competitive pressures. The Algebra I test scores recorded by students in North Carolina's public schools are significantly lower in counties where a greater proportion of families earn incomes that fall below the poverty line. Racial differences in academic performance are not significant once this factor is accounted for. Algebra I test scores are also lower in counties where the parents of the test-takers have fewer years of education. This finding supports the conventional wisdom that parents' education is an important input into the academic performance of

309 their children. Indeed, the coefficient estimates suggest that the "taste" for education on the part of parents is more important than any other factor in explaining student achievement in the public schools. The critical point, however, is that competition strongly reinforces parental influence on test score performance. Test scores also tend to be lower in more densely populated counties. This result suggests that, other things being the same, urban public schools are not as effective in teaching math skills as their counterparts in rural areas. 14 Finally, while public school funding per student does appear to have a positive impact on test score performance in North Carolina, the estimated coefficient is different from zero at only the ten percent level of significance. Moreover, the magnitude of the effect is quite small. This result is broadly consistent with trends at the national level (National Commission on Excellence in Education, 1983). 15 The regression estimates explain 34 percent of the variation in deviations from the mean score on the Algebra I test. The evidence presented here seems to contradict some of the conventional wisdom espoused by (public-school) educators which holds that policies designed to encourage educational choice will only weaken public school systems, impairing their ability to meet the challenge of educating students in an increasingly technological age. On the contrary, our results suggest that making alternatives to public education available to more students will improve the quality of education delivered by the public sector.

3. Concluding remarks This paper has presented evidence that competitive market forces lead to improved performance in education as they do in all other areas of the economy. In particular, using data from the results of a standardized algebra test taken by a large number of public school students in North Carolina, and controlling for factors like poverty, total spending per public school student, and the educational attainment of parents, we find that educational achievement in the public schools is higher in those counties where a larger percentage of schoolage children are enrolled in private schools. This result will not surprise economists, who are accustomed to arguing that a wider range of choice always improves individual welfare. It is to our knowledge, however, the first empirical support for this basic point in the case of public education. The opinions of professional educators notwithstanding, the evidence shows that when faced with market competition, the public schools can respond by improving the quality of education they provide for their students.

310

Notes 1. An important question concerning whether increased choice within the public school system will produce the same effects on educational quality as those imputed here to competition between public and private schools is addressed more fully below. 2. Algebra I is an elective course for North Carolina's public school students. Course enrollment rates (and the corresponding participation rates in the statewide testing program, which is required of all students taking Algebra I) is nevertheless quite high. The 60,183 students who took the Algebra I Test in 1988-89 represent over two-thirds (68.6 percent) of the ninth graders enrolled in North Carolina's public schools. See Averett, Ward, and Evans (1989: 46). 3. West (1990: 374) makes this same point in relation to the public good hypothesis of public education when he criticizes the "erroneous practice of treating the public good output from schooling as an absolute demand rather than as one desirable output from education that can be traded off for anotherr (human capital creation)." 4. Conlon and Kimenyi (forthcoming) have shown recently that "white flight" is less a response to race than it is to poverty. Their empirical results suggest that prejudice leading to declining enrollments in Mississippi's public schools is directed against poor blacks rather than against nonpoor blacks or poor whites. 5. Our results are not affected materially by instead using the percentage of the county population with 12 or more years of education as a proxy for the taste for schooling. 6. These are raw scores (the number of items answered correctly) from the 60-question "core" of the Algebra I Test. The actual average raw test scores in 1988-89 ranged from a low of 32.5 (Washington County) to a high of 50.5 (Dare County). See Averett, Ward, and Evans (1989). 7. It is worth noting that private schools produce these results at a lower cost per student. Average public school expenditures per pupil amounted to $2,016 in 1980, compared to $1,837 spent per private school student in the same year (Coleman and Holler, 1987: 35). By 1990, the comparable figures were about $4,000 per public school student and $1,700 per private school student (Kelly, 1990: 18). 8. The 1989 North Carolina Directory o f Non-Public Schools was used to determine the percentage of children attending private schools in each county (see Office of the Governor, 1989). Total funding per student was obtained from North Carolina Department of Public Instruction (1989: Table 4); per capita personal income by county came from the same source, Table 9. Population per square mile, the percentage of the population that is black, the percentage of the population that is college educated, and the percentage of families below the poverty line were taken from U.S. Department of Commerce (1988). The Algebra I test scores and the percentage of test-takers whose parents have less than a high-school education are reported in Averett, Ward, and Evans (1989). 9. The residuals from the two equations are uncorrelated (r = - .05) and PRIV is independent of the residuals from the ZSCORE equation (r = 1.849E -09). See Kmenta (1986: 719-720). 10. See Amemiya (1985: 360-411) for an extended discussion of the Tobit procedure. 11. This weak evidence of "white flight" is similar to that of West and Palsson (1988), who found using data from the late 1970s that private school enrollment rates across the 50 states tended to be lower (although not significantly so) the greater the proportion of whites in the public schools. 12. Race, per capita income, poverty, and educational attainment are obviously correlated with one another, but apparently not enough so to introduce symptoms of mulficollinearity in the regression estimates. The simple correlation coefficients between these four independent variables are given below:

311

BLACK POVERTY COLLPCT PCY87

BLACK

POVERTY

COLLPCT

PCY87

1.00

.48 1.00

-.12 - .38 1.00

- .21 - .76 .64 1.00

13. All other coefficient estimates retained the signs and significance levels reported in Table 2 when the dummy variable denoting school district consolidation was included. These results will be made available upon request. 14. This finding is consistent with Maloney and McCormick (1990), who report that athletes who graduate from smaller high schools tend to grade higher in college (earn higher overall grade point averages) than their counterparts from larger high schools, ceteris paribus. They suggest that this resnlt could be due to the fact that"smaller [public] high schools m a y . . , be spuriously mimicking (higher quality) private schools, which typically have fewer students than public schools." 15. Student achievement in North Carolina is also not affected by the type of administrative organization adopted by the various county public school systems. When included on the righthand side of the score equation, the estimated coefficient on the consolidation dummy variable described above was negative but not statistically significant. This result suggests that improved student performance should not appear on the list of benefits claimed for schooldistrict consolidation.

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