Education Vouchers, Dropouts, and the Peer

Education Vouchers, Dropouts, and the Peer Group Problem1

J. Stephen Ferris [email protected]

and

Edwin G. West [email protected]

Comments Welcomed

Draft Date March 10, 2000

Department of Economics

Carleton University Ottawa, Ontario Canada K1S 5B6 Education Vouchers, Dropouts, and the Peer Group Problem

I.

Introduction In a series of recent papers, education economists such as Charles Manski (1992), Dennis

Epple and Richard Romano (1998a, 1998b) and Thomas Nechyba (1999) have emphasized the presence of one particular educational spillover in the use of school vouchers – the “peer group” problem. This is an external effect that vouchers may have on the pool of students remaining in the public school system. By allowing low income students of high aptitude and ability to leave the public school system, a voucher system will encourage for-profit private schools to “skim the cream off” the public school system and so depreciate the average quality of students remaining behind. Because the quality of education received by students is in part a function of the average quality of their classmates, the loss of higher ability students reduces the quality of education received by those remaining. Hence a voucher system, it is argued, will promote inequity across students even as it improves the overall efficiency of the educational system. While recognizing the existence of such negative externalities in the use of vouchers, it is our concern that an excessive focus on the inequity created by the peer group effect will distract attention from an even more pressing horizontal inequity in the current education system. By this we mean the effects arising from the lower education level received by the roughly twelve per cent of students who have dropped out of the education system by the end of high school.2 Thus even though a voucher program may produce a deterioration in the quality of education received by those who do not leave the public school system, a voucher program may improve both educational efficiency and horizontal equity if it helps to retain within the school system more of those who would have dropped out entirely. To illustrate the relative importance of the two problems, consider first the findings of Summers and Wolfe (1977) in their classic study of student achievement. Using the difference in composite achievement scores between grade three and grade six as a measure of schools’ value added, Summers and Wolfe find (p.643) that an increase in the percentage of high achievers in a student’s school has 1

2 two offsetting effects on student scores: one that significantly improves all students’ scores and a second that reduces individual scores by an amount that depends on student ability. The net effect is that average students are largely unaffected by a peer group effect. However, students with the lowest levels of ability experienced as much as a half a year improvement in overall grade performance by the end of that three year period while students with the highest levels of ability are held back somewhat.3 Despite the importance of Summers and Wolfe’s findings for low achievers, it will be recognized that the size of the loss that would be experienced by low achievers in public schools following the adoption of a voucher program would not fall in the same category as the loss experienced by students who did not attend school at all for the same three year period. It is then possible that the loss in public school achievement due to a negative peer group effect could be dominated by an offsetting educational gain. This would require the retention of a sufficient number of students who would otherwise have left school. Hence it is our objective in this paper to reexamine the role of vouchers from the perspective of the dropout problem and highlight the equity tradeoff that arises. The Manski/Epple and Romano externality argument should make us more aware of the needs of students remaining in the public system, but should not blind us to the benefits that vouchers can create for those most in need. Our paper incorporates dropouts in two stages. In the first part of the paper, the model of Epple and Romano (henceforth ER) is adapted to provide an additional rationale for voucher use. In our model, vouchers allow low income students to escape the frustration of having to conform to the educational uniformity of the public school system by attending a private school rather than dropping out of school entirely. The reasons why students choose to drop out of school will, of course, involve more factors than simply the level of their frustration and these factors will be discussed at length later in the paper. However, the dimension of frustration allows us an immediate and straightforward way of modifying ER’s model to highlight the overlooked choice. This means that we need not rely on lower production costs to motivate the emergence of a private school system or a reason for voucher use.4 After abstractly modeling vouchers as an instrument for alleviating the dropout problem in Sections II-V, we turn in Section VI to an empirical examination of whether greater voucher use could

3 actually reduce the dropout rate. That analysis begins with a review of the current education literature in relation to the characteristics held by school dropouts and the set of school characteristics that have been found to be most useful in reducing that problem. This allows us to examine the structure of the competing school systems to assess whether the encouragement of private schooling through vouchers could be expected to alleviate at least part of the dropout problem (as implied by our model). After presenting evidence that private schools do provide more of those characteristics needed to retain students in school, we test the implied hypothesis that the growth of private schooling in the U.S. should be associated with a fall in the overall dropout rate (holding other relevant factors constant). We interpret the outcome of this test as evidence in favour of the hypothesis that greater voucher use can significantly reduce this foremost educational inequity and this reduction could well offset the negative peer group effect. While the relative size of these effects is ultimately an empirical question, it is clearly the case that the presence of a peer group externality is not sufficient in itself to prevent a reconsideration of the benefits of the voucher system for equity as well as efficiency reasons. Our analysis follows that of ER but departs in some significant ways. Unlike ER, for example, we assume a pre-voucher scenario in which private schooling is competitively supplied at a constant cost and paid for by parents through a uniform school fee, p.5 The school fee is then a differential cost to the parents of private school students (who must continue to pay their share of the cost of the public school system). Entry into private schooling is assumed to be open so that while private schools may receive scarcity rents for a speciality, private schools can earn only normal profits.6 As mentioned, we do not motivate the emergence of a private school system from the supply side by arguing, as have others, that competition among private schools will result in a superior product (smaller school/classroom sizes, more student centered learning, greater competition among schools, etc.) at a lower price. Rather, we highlight distributive issues on the demand side by assuming that private schools have no cost advantage and differ only in that they can offer an educational bundle to students and their parents that differs from the single output mix produced by the public system. On the demand side, then, private schools are valued because they offer students and their families distinctive educational variety. Individual private schools provide a different education mix with

4 greater than average focus on, for example, the arts, sciences, mathematics, languages, sports, religion, and/or discipline. We model the demand for variety through the private system’s ability to reduce a consumption bad, called for convenience “frustration”, that is assumed to arise within the public system exclusively. With this assumption we capture the idea that it is precisely the lack of educational uniformity in the private school system that allows for a better matching of some students with the school most suitable for them, particularly those students whose tastes, temperaments, and/or abilities diverge widely from the mean. Setting frustration with the private system at zero is then a convenient shorthand way to highlight the possibility of better matching as the important relative benefit driving this analysis. By being individually specialized but diversified in the aggregate, private schools offer to individual students and their families a menu of different possibilities to avoid having to conform to the uniformity offered by the public system. It is important to emphasize that we are not assuming that the public school system is inherently frustrating, nor will it be frustrating to all. Nevertheless, across a population of students with normally distributed tastes and abilities, any single program (even an optimally designed one) will necessarily produce some degree of frustration for students at the tails of the distribution. To keep our analysis as close as possible to ER’s, we represent the frustration experienced with the public system as a function of the degree to which the individual’s ability diverges from the public system’s mean. Finally, the education choices facing individuals and their families are discrete – students either attend the public school system, attend the private school system, or drop out of school entirely. This means that while many students will be intramarginal, the comparative static effects of regime and policy changes are experienced at the margin and can be analyzed by looking at the incentives facing individuals and their families on the margin. The introduction of a new education regime or a decision to subsidize the cost of one part of a current program will change the net benefits to those on the margin and so signals the direction of change for those who were previously indifferent.

II

The Model We begin by assuming that the decision making agent, the student and/or the student’s family,

5 maximizes a utility function of the following form:

Ui = U(ci, ai) = U(ci) + ai ,

(1)

where ci represents the level of consumption received by the ith family and ai represents the level of educational attainment achieved by the student. Utility is separable in two arguments with U(ci) assumed to satisfy the Inada conditions (so that consumption exhibits diminishing returns in terms of utility).7 The level of consumption received by a household depends on individual income, yi (assumed exogenous in the analysis), the public school tax rate, t, and whether or not the student in the household attends the private school system. That is,

ci = yi(1- t)

if in the public school system (or drops out), and (2)

= yi(1- t) - p

if in the private school system.

In general the school tax rate will depend on the number of students and hence on the scale of the public system. However, we assume that the individual effect on the tax rate is small enough so that each agent ignores the fiscal externality when choosing whether to attend private school. An individual’s educational attainment, ai, is assumed to have four (separable) parts: a minimum level of education arising from innate aptitude and life experience accumulated outside of school (a0i); a level of classroom education that is positively related to the individual’s ability (bi); a peer group effect whereby the classroom education received is enhanced by the quality of the school attended (? j); and lastly a term that reflects the dissipation of classroom education that arises through frustration (fi). More formally, the level of educational attainment received by the deciding agent is assumed to take the following form:

ai = a0i + a1bi + a2(? j - bi) - a3ifi,

(3)

where a0i, a1, a2, and a3i are all positive constants and, because frustration with the public system is

6 measured relative to the most appropriate private school, fi = 0 if a private school is chosen. Students differ in their innate ability, bi, in the degree to which they can learn outside of the school environment, a0i, and in the degree to which their frustration with the uniformity of the public school system diminishes their ability to learn, a3i. On the other hand, a1 and a2 are assumed to be the same across individuals so that educational attainment varies directly with student ability and with the size of the peer group experience. Relative to the ER analysis, our peer group effect has educational benefits that depend directly on the divergence between the individual’s ability and school quality, implying that the size of the peer group benefit of attending a higher quality school is higher for students of lower ability (Summers and Wolfe, 1977). On the other hand, we use ER’s measure of school quality, ? j, as the mean value of the abilities of the n students attending that school, i.e., ? j = 3bi/n (i = 1..n; j = public or private).8 Similarly, we use ER’s variables to express the frustration experienced by public school students as a function of the degree to which their ability departs from the school average. To add specificity we assume that fi = (bi - ? j)2.9 Given the discreteness of the choices facing the family, the student/household would experience three different levels of utility depending on whether the student is: a) in a public school; b) in a private school; or c) has dropped out of the school system. The levels of utility associated with each of these states are:

a) if in the public system, Ui(public) = U(yi(1-t)) + a0i + a1bi + a2(? pub - bi) - a3i(bi-? pub)2,

(4)

b) if in the private system, Ui(private) = U(yi(1- t) - p) + a0i + a1bi + a2(? pri - bi),

(5)

c) if a dropout,

(6)

Ui(dropout) = U(yi(1- t)) + a0i.

where the average quality of public schools (? pub) and private schools (? pri) may differ. Given these choices, the optimizing agent chooses the alternative that generates the highest level of (expected) utility. While there is no particular reason why one of these cases could not dominate the

7 others, we assume that the distribution of parameters across the community is such that some individuals will fall into each category. This corresponds to the situation that arises in most jurisdictions when all three alternatives are present. To utilize these categories analytically, we need to determine the characteristics of those individuals who are likely to change categories as the range of institutional possibilities are increased. To do this we first isolate the net benefit that would accrue to an individual who in the absence of a private school system would choose to drop out rather than continue to attend public school. This sets the characteristics of the decision agent at the margin of choice in our base case institutional setting. We then assess how the marginal individual would respond to institutional innovation – in this case the arrival of private schools. Our interest is the Rawlsian concern with those students who in the base case received the least amount of education – the student dropout – and how the characteristics of those on the school/dropout margin change once private schools enter. This allows us to predict the effect of introducing vouchers into this educational setting.

III

Educational Choices in a Community with only a Public School System Suppose then that we begin by considering an educational jurisdiction that permits only a single

public school system. In this case students and their families have only two choices: to attend a public school or dropout. While many states have mandatory school attendance laws (so that the dropout rate below a certain age might seem to be zero), such laws are not costless to enforce so that large and persistent student dropout rates continue to plague many school districts. Should only public school education be available, our model states that students for whom the net benefit is positive, i.e. Ui(public) $ Ui(dropout), will stay in school while all others will drop out. Inversely, the net benefit of dropping out of school is calculated by subtracting (4) from (6) and is positive for dropouts and zero for students indifferent between staying in school and leaving. That is,

NB(dropping out) $ 0

Y

a3i(bi - ? pub)2 $ a1bi + a2(? pub - bi)

(7)

8 Who then is the educational dropout in our model? First, students dropout only if their level of frustration outweighs the value of their classroom experience as enhanced by the relevant peer group effect. Hence the higher is the degree of frustration experienced by an individual with the uniformity of the public education program (i.e. the higher is a3i), the more likely it is that the net benefit of dropping out will be positive and the student will leave the public school system. Of somewhat more interest is how the decision to dropout varies with the individual’s ability. Are dropouts equally likely at both ends of the ability distribution? If we expand the first term in (7) and set the net benefit equal to zero, we find a quadratic in bi that can be solved for the two ability levels at which such a student would be indifferent between dropping out and staying in school.10 These two values are

2 b*i = ? pub + [(a1 - a2)/2a3i] ± {[2? pub + (a1 - a2)/a3i] 2 - 4[?pub - (a2/a3i)? pub]}1/2(1/2).

(8)

2 Given that a1 > a2 and that a3i?pub > a2? pub,11 the net benefit of a student dropping out from (7) will

begin positively for the lowest level of student ability and then fall as student ability rises. The net benefit falls to zero at the smaller of the two values of b*i in (8) and continues to fall until it reaches its nadir at ? pub + [(a1 - a2)/2a3i]. Beyond that level the net benefit begins to rise and once again becomes positive at the higher value of b*i , i.e., at an ability level in the upper tail of the ability distribution. More generally, the net benefit curve is symmetrically U shaped with the two b*i values distributed symmetrically about a minimum value that is larger than the student population mean, ? pub.12 Given the symmetry of the dropout condition about ? pub + [(a1 - a2)/2a3i], any symmetrical distribution of student abilities will mean that there will be more of the student population below the lower b*i bound than above its upper bound. In this sense, our analysis suggests that the dropout problem will be more severe for those with lower, rather than higher abilities. In terms of the other parameters driving the dropout choice, the greater is the intensity with which frustration is felt (the higher is a3i), the more tightly bound are the symmetric b*i ‘s about the now lowered level at which the net benefit of dropping out is minimized. As expected, greater school

9 frustration increases the scale of the dropout problem. On the other hand, an increase in educational productivity (a1) and/or a diminishing of the peer group effect (a2) will raise the ability level at which the net benefit curve is minimized and spread further apart the two values of b*i. These effects will then reduce the scale of the dropout problem. With lower than average ability dropouts, the equilibrium level of school quality or the average ability and performance level of students who stay in the public system will be higher than the student age population average.13 Somewhat ironically, then, the dropout problem has creates a positive peer group effect for those students who remain in the school system. Such a finding also implies, however, that if by public policy succeeds in increasing the productivity of education to recapture more dropouts, the reduction in dropout numbers will generate a negative peer group effect for the entire public system.14 Confined to the institutional alternatives of either attending the public system or dropping out, there is then the appearance of a somewhat discouraging public policy tradeoff, as higher completion rates are achieved only by lowering the average level of student performance.15

IV

The Entrance of Private Schools Suppose that private schools are now allowed to enter and to service niche educational

markets. In this model, private schools enter at the ability extremes for those students for whom the utility cost of private schooling is low relative to the frustration received in the public school system. There are now three margins of choice: one in which students are indifferent between private and public schooling; a second where students are indifferent between a private school and dropping out; and a third where (as before) students are indifferent between staying in the public system and dropping out. Because the general form of the third remains unchanged from Section III (equation (7)), we examine the net benefit of attending private school relative to the alternatives of attending a public school or dropping out. This allows us to isolate students who would be attracted to a private school out of the public system and the dropout pool. Because the private school system requires the payment of an additional school fee, p, the level of income held by students and their families will be a factor influencing private school choice. Given

10 diminishing returns to income, the utility cost of financing that private school education is also lower for higher income families. To compensate families for the higher cost of education, private schools must provide an additional service (than can the public system) and this service arises through their ability to provide a nonstandard education output mix to students who have experienced frustration with the uniform public school product. More formally, the net benefit of attending a private school relative to a public school is found by subtracting (4) from (5) to get

pub pub 2 NB(Private/Public) = [U(yi(1-t)- p) - U(yi(1-t))] + a2(? pri i - ? i ) + a3i(bi - ? i ) .

(9)

The first term in (9), the utility difference within the squared brackets, represents the utility loss associated with having to pay the additional private school fee, p. The second term, the net peer group effect, reflects the fact that high frustration students attracted into the private system may have different pub levels of ability than those in the public system so that ? pri i can differ from ? i . The last term, a3i(bi 2 ? pub i ) , reflects the net education gain from attending a private school – measured as the loss in

frustration experienced by students who now learn in an educational environment that more closely matches their own preferences. Note from (9) that if we ignored the differential peer group term, the net attraction of the private system to those frustrated by the public system would be symmetrically distributed about the mean level of ability. Private schools would be just as likely to cater to low ability students as those at the higher end of the ability spectrum. The presence of the differential school quality term, however, means that lower ability students who group together in their own specialized private school lose the positive external effect of associating with higher ability peers. In this case the peer group effect is negative, a cost rather than a benefit of choosing the private system. For such higher ability students, the peer group term reinforces their desire to escape the frustration of the public system. This implies that the distribution of private schools will be skewed towards higher ability students.16 It follows that the private system attracts out of the public system nonconformist students from both tails of the ability distribution but with somewhat of a bias towards students with high as opposed

11 to low levels of ability. Such a recruitment bias would introduce into the public school system the negative peer group externality highlighted by ER (diminishing or even reversing the previous peer group effect generated by dropouts). However, whether or not the private system is biased towards drawing out of the public system those students with higher abilities, the students that do withdraw from the public system will have experienced higher than normal levels of frustration and will come from families with higher than average levels of income and wealth. The effect of the entrance of private schools on the dropout problem can be found by subtracting (6) from (5). That is, the net benefit of attending a private school rather than dropping out is

NB(Private school/dropout) = [U(yi(1-t) - p) - U(yi(1-t))] + a1bi + a2(? pri - bi).

(10)

As might be expected, a dropout will choose to attend a private school only if the utility loss associated with paying the additional private school fee is lower than the education gain that can be received by attending a private school. However, private schools attract out of the dropout pool only those students who have already chosen not to attend the public system. Hence combining (10) with (7), the private schools attract out of the dropout pool those students for whom

2 [U(yi(1-t)) - U(yi(1-t) - p)] < a1bi + a2(? pri - bi) < a3i(bi - ? pub i ) .

(11)

In essence, the private school system attracts public school dropouts for whom education is economic only if it can be paid for with income rather than with frustration. The dropout pool that private schools recruit from consists of both high and low ability students, more heavily weighted towards the lower end. However the potential of using the peer group externality in production means that a private system will have a greater probability of success if it sets up catering to higher rather than lower ability students so that the peer group effect provides schools specializing at both ends of the spectrum an incentive for recruiting higher ability students out of the public system. The falling average quality of the public system lowers the peer group effect received by its lower ability students and increases the frustration of the remaining higher ability students. The introduction of a competitive private school system then produces three types of allocative

12 effects. First private schools recruit out of the public system and the dropout pool those students who have experienced a relatively high degree of frustration with public education and who come from families with relatively high levels of income. Second, if the size of the peer group effect makes it relatively attractive to recruit students with higher rather than lower levels of ability, the average ability level within the public school system deteriorates as students with higher income parents leave for the private system. This implies a small offsetting reduction in the frustration experienced by low ability students as their departure from the lower school mean diminishes. Third, for the education system as a whole, the aggregate level of educational achievement rises through a reduction of the dissipation caused by student frustration and the recovery of some students who would otherwise fall into the dropout pool. Note that the average level of student ability and hence average quality of all schools could rise or fall as the private school system absorbs students from both ends of the ability spectrum. The quality of the public school system declines at the same time as retention with the education system as a whole rises. In this sense, both the peer group problem and its interaction with the dropout problem can be seen to have begun well before the arrival of a voucher system. This is because in both our analysis and that of ER there is a tendency for private schools to attract from the public system students who are of higher than average ability. For ER this arises because higher ability students (and their parents) place a higher value on education and this allows private schools that can discriminate in pricing among students to attract higher ability students and so internalize through higher average school fees the positive peer group externality their presence generates. Lower ability students are less willing to pay for the offered higher quality of education and are left behind. In our analysis, income gives families the ability to rescue their nonconformist children from the frustration of dealing with the uniformity of a public system. This is equally true for parents at both ends of the ability spectrum. Because higher ability students provide private schools with an output spillover and such private schools minimize the frustration associated with individual departures from the school mean by specializing in their student body, private schools find it more profitable to enter specializing in higher ability levels. Lower income students experiencing who the same degree of frustration and/or students who experience less frustration choose

13 to stay behind in the public system. In both cases private schools allow income to register intensity and because intensity is provided at lower cost to higher abilities ability, private schools tend to concentrate at the upper end and skim ability from the public system. Stated alternatively, however, the role of the private schools can be seen to be to allow the education system as a whole to match more closely the tastes and aptitudes of students and their families. In this sense, education is provided much more efficiently. In terms of the distribution of these benefits, however, the market basis for allocating education variety means that students from higher income families will be favoured. Because the benefits of variety are not valued equally by students of equivalent ability, lower income families are less likely to exercise private school choice and hence will benefit less from its availability. Dropouts from low income families, in particular, find that additional choice has not been to their advantage. Their relative position in the welfare hierarchy falls, falling behind those who now leave the dropout pool for private school and remaining well below those who stay within the public system and experience only the quality deterioration that follows peer group migration.

V

The Role of Vouchers What then does the introduction of a voucher system do in our model? In large part, of course,

the effects will depend on the particular characteristics of the voucher system. However, the fact that a voucher system is a grant conditional on attending private school does mean that a voucher has no direct effect on the margin between attending public school and dropping out. Vouchers will affect that choice indirectly and only if they alter average school quality. Along the other two margins, however, the giving of a grant conditional on private school attendance will tilt the educational choices towards the private system. The voucher system then encourages the private school system to recruit students out of both the dropout pool and the public school system. Suppose then that a voucher system consists of a uniform grant to all families choosing to attend a private school and that grant is funded out of general tax revenues raised through income taxes. In this case the voucher system is progressive ex ante in its effect on the distribution of income (in that

14 families with higher incomes will pay more than their share of the potential expenditures available in the program).17 Most often, a voucher program will be more restrictive in its coverage – e.g. available only to lower income families – so that the program would be that much more progressive. Finally, because of diminishing marginal utility, the voucher program will be more progressive in terms of utility than it is in relation to income. In short, whether or not a voucher program redistributes education according to ability, the voucher program works primarily to diminish the effect of income on the choice of education alternatives. It is the allocative consequences of the voucher program, however, that are at the root of the peer group externality concern and hence these changes merit closer attention for their effect on the “least well off”. We begin with the effect of the voucher program on the private/public school margin. Using, v to represent the size the conditional grant, the net benefit condition from (9) now becomes:

pub pub 2 NB(Private/Public*voucher) = [U(yi(1-t) - p + v) - U(yi(1-t))] + a2(? pri i - ? i ) + a3i(bi-? i ) .

(12)

From (12) it is apparent that paying a voucher is equivalent to reducing the private school fee and thus the utility cost to all potential entrants.18 The concavity of the utility function, however, means that a uniform voucher will have a proportionally larger on lower income families. In relative terms, more low income students and their families (whose level of frustration with the public school system was previously not quite high enough to merit the utility cost of the private school fee) will now choose to attend a private school. Separate private schools will recruit both high and low ability students, but because the peer group effect in the second term of (12) lowers the relative cost of operating a private school targeted at higher ability students, the students that leave the public system are likely to be those with higher levels of ability. A voucher system increases the size of the peer group effect even as it spreads the benefits of differentiated education more evenly across income. On this margin, then, our model confirms ER’s results. In addition, however, the voucher system alters the marginal condition facing students who had previously dropped out of the education system altogether. These were students who found that the

15 frustration of having to conform within the public system was so high that it dominated any positive education experience. At the same time, the income cost of attending the schooling alternative in the public system was prohibitive. These are students from lower income homes at both ends of the ability spectrum. The arrival of the voucher system now means that the net benefit of attending a private school becomes

NB(Private school/Dropout|voucher) = a1bi + a2(? pri - bi) - [U(yi(1-t)) - U(yi(1-t) - p + v)]. (13)

As was the case in (12), the introduction of a voucher system directly lowers the income cost of attending private school. Because the voucher system leaves the public school/dropout margin unaffected, the reduction in private school fees does lower a binding constraint on educational choice and allows the education system to recapture students who would otherwise be lost. The voucher system increases the scale of the private school system unambiguously but not primarily by raiding the public system of its best students. Rather the private system expands by attracting higher and lower quality students out of both the dropout pool and the public system. This is a net gain for both those individuals and the education system as a whole. It follows that a voucher system reinforces one of the negative equity effects present in the education system while reversing a more pronounced one. The presence of the peer group effect means that the average quality of both the public and the private school system will decline in large part because the voucher system succeeds in recovering some of the previous system’s most striking failures.19 While many voucher models suggest that there will be efficiency gains associated with greater school competition and better streaming of students by ability that will dominate the peer group equity losses experienced by students remaining in the public system, our focus on the Rawlsian concern for the “least advantaged” leads us to believe that appropriate weighing of the equity tradeoff between school quality and dropouts will reinforce the efficiency case for vouchers. The next step is quantitative and empirical. Only if we can show that the actual private system does do a better job in preventing school dropouts can we verify our claim the voucher system can improve horizontal equity.

16 In terms of policy implications, the absence of the dropout problem and the ability of private schools to price discriminate among students in ER’s analysis means that all the benefits of the voucher program will be appropriated by private schools. The consequence is that the subsidization of private schools simply increases student segmentation by ability and results only in peer group losses for students in the public system. To forestall the dissipation of excessive segmentation, ER redesign an income-based voucher program to redirect funds exclusively to those public schools currently cater to low ability students most in need. In our analysis, however, the further subsidization of the public system would do little to assist those truly most in need – those who have dropped out of the education system. Given that school dropouts are the most needy, the traditional strategy of conditionally subsidizing students by income is entirely appropriate. Such a voucher program diminishes the underlying inequality directly and results in wider educational choice, more education in aggregate and less individual frustration within the system. In our analysis, the voucher system promotes greater educational diversity with gains captured primarily by low income students who were most disadvantaged under the previous system. On the other hand, vouchers will also increase the negative scale of the peer group effect working within the public system. Thus even though we question whether ER’s peer group concern would identify the Rawlsian most deserving, our analysis does suggest a legitimate concern for the loss experienced by students within the public system and hence supports efforts to improve the productivity of the public system for the benefit of those students. Ironically, one means of promoting such productivity improvement has been found to be the voucher system itself. That is, the new competition among schools and across school systems that the voucher system will encourage is believed to reduce substantially the real cost of providing public education.20 If so, the savings so generated might profitably be reinvested in improving the quality of the public system.

VI

Vouchers and the Scale of the Dropout Problem: Quantitative Evidence In the previous sections one dimension of educational difference across students was used to

investigate how a voucher program that created a negative peer group migration effect might also

17 alleviate the potentially more serious student dropout problem. That characteristic was student ability. It is immediately apparent, however, that if a voucher system led students to exit the public system on the basis of some characteristic other than ability, the size of the negative peer group effect within the public system would be reduced, perhaps substantially. To use one special example, if a voucher program allowed disruptive students who needed a greater than normal level of attention and discipline to receive better attention in a private school, the peer group migration effect on students remaining in the public system would be positive rather than negative.21 Similarly when discussing the effects of different educational inputs on education outcomes, most often a measure of the school’s achievement such as the average test score received by a certain group of students is used. This is not, of course, the same thing as measuring the effectiveness of these inputs in preventing dropouts. Moreover, to the extent that these scores reflect indirectly the effectiveness of retaining students in school, the results may be the opposite of what they appear to reflect. As Wenger (2000) has emphasized recently, treating schools as firms that produce multiple competing outputs means that “if schools increase expenditure in ways that increase education levels rather than test scores, increasing expenditures per pupil could even lead to falling test scores”(p. 34). And applying this directly to the issue of peer group effects, she writes that “it seems likely that keeping below-average students in school longer may decrease average test scores because the these retained students have relatively low test scores and/or because these students may slow down the rate of learning in the classroom” (p.34).22 In this section, then, we explore the education literature for a more comprehensive description of the characteristics held by school dropouts and a list of those school characteristics that have been found to be helpful in stemming the existing (fairly constant) level of dropouts. Our purpose is to determine whether there are conceptual reasons for believing that the variety provided by the private school system could better supply the inputs needed to retain or reabsorb dropouts and, second, whether in practice the private system has been more successful than the public system in preventing school dropouts. Should these conditions be met, there would be more reason to support the voucher system’s encouragement of the private school system.

18 We begin with the set of individual and family characteristics that the education literature has found to be associated with students who drop out of school. Disproportionately they consist of students who come from single-parent families, families with low income and socio-economic status; students who have performed poorly in school, who have low self esteem, who lack positive relationships with adults and peers, who have experienced pregnancy or delinquency and who have a history of substance abuse (Natriello, 1994). Two things are immediately apparent: first, ability is only one factor that affects the dropout decision and; second, school environment can substitute for only some of these social deficiencies. Nevertheless, the literature does find that the school environment can substitute for at least some and, to the extent that this is possible, there are reasons for believing that a school system that provides a wider range of learning environments is more likely to succeed than one designed to promote instructional uniformity. Many of the dropout conditions (low self esteem, lack of care and support, and the absence of positive adult and peer relationships) describe a dysfunctional family environment coupled with the absence of a supportive social network, a lack of what is now called “social capital”. In this context, the fostering of social capital – the development of stronger supportive personal ties between students and adults – often takes place in a school and that environment can be used to reestablish motivation and interest in students. Not surprising, then, supportive relationships between teachers and their students and an established climate of purpose and concern have been identified as key elements in retaining students in school (Rumberger, 1987). The role of social capital in preventing school dropouts has for many years been the research interest of James Coleman and Thomas Hoffer (hereafter CH). In their widely known study of high school dropout rates in private and public schools, CH (1987) argue that Catholic private schools have a stronger interest in countering what they call the depressive effects of functional or structural deficiencies among many families than do public schools. This leads ultimately to the hypothesis that such social concerns should lower the dropout rate in Catholic schools relative to public schools and/or other private schools. Their results, presented as Table 1 below, are striking in their support of this prediction. Catholic school students experience roughly one quarter of the dropout rate of public

19 school students and one third of the dropout rate experienced by students in other private schools. Such findings lead CH to extend their argument and describe religious communities as one of the few remaining societal organizations that still can induce strong ties of social cohesion between children and adults. This helps to explain the more recent rapid growth of religious affiliated schools within the private school system.23 Table 1 Dropout Rates across Sectors Sector Public Catholic Other Private High Performance Private Source: Coleman and Hoffer, 1987, p. 99.

Percentage dropping out 14.4 3.4 11.9 0.0

Other analysts go beyond dysfunctional families to focus instead on dysfunctional schools. Ekstrom, Goertz, Pollack, and Rock (1986) and Legters, McDill, and Partland (1992), for example, draw attention to organizational features of the public school system that have been conducive to producing school dropouts. Middle and high public schools especially are characterized by large sized schools, with specialized departmental instruction, where teaching roles are defined in terms of the subject matter rather than the interests of their students and where there is little teacher involvement with students or their families. All of these features encourage dropouts. In principle, at least, private schools would seem to have an advantage in providing the positive support relationships lacking in a dropout’s environment. The typical private school is less than half the size of the typical public school and students are taught by teachers who have smaller average class sizes and who stay longer each day with the same set of students.24 To the extent that smaller school size and more focused personal attention can enhance performance, realized academic success can reduce further the likelihood of dropping out. On the other side, the typical public school continues to grow in size with students increasingly being taught by a number of different teachers in area specialties.

20 The consolidated district public school is, in other words, increasingly different from the older neighborhood school.25 While this trend may well have improved both the content and quality of education received by those students who encounter few adjustment problems and who receive greater stimulation in a more academic environment, the greater concern with subject area and professionalism has made the public system, in relative terms at least, more impersonal and less individually flexible. In such an environment teachers are given less motivation to anticipate and react to nonsubject related learning difficulties and find that there is less expected of them in substituting for other family and social deficiencies. In short, the educational focus is on the school’s scholastic achievement and not on retaining potential dropouts.26 While these comments relate to general elements of the public and private systems that affect all student groups, it is often believed that the public system exhibits its greatest failure in its relation to particular subgroups of society. Eugenia Toma (1999) has observed, for example, that “it is the lower socioeconomic groups in the United States whom the system has failed most noticeable over the past three decades. This is the category where dropout rates are greater than graduation rates. In certain inner city schools such as that of Washington, D.C. and Detroit Michigan, [only] 36 percent of the students complete four years of high school” (p.7). Such concerns have led to suggestions for using the voucher system to explicitly target such groups. Florida Governor Busch’s recent plan, i.e., the Bush/Brogan A+ Plan, to target vouchers at lower income students who attend “failing” schools is just one example of the type of experimentation with vouchers that is taking place. There is considerable evidence both that the dropout rate is large (particularly in inner city areas) and that the consequences of dropping out are substantive. In relation to the first, the status dropout rate for individuals between twenty and twenty one in 1997 was 12.7 per cent, a rate that was virtually unchanged from that in 1990 (12.8).27 While the average rate has fallen somewhat through time, the fall in the average hides the considerable degree of variation that can arise even within the same school district. Rumberger (1987), for example, notes that the sixty three high schools in Chicago have dropout rates that vary between ten and sixty two percent. It is also clear that dropping out has a substantive effect on lifetime earnings, an effect that is likely to dominate the earnings consequences that

21 arise from the peer group deterioration of public school quality. Current evidence suggests that not finishing high (elementary) school will result not only in an annual income that is seventy (fifty six) percent of median (full time) income but also result in a much higher probability of unemployment.28 The partial evidence that exists on the relative success of private versus public schools in preventing dropouts is consistent with the hypothesis that dropout rates from private schools are lower. Coleman and Hoffer (1987) report, in the data presented in Table 1 above, that Catholic private schools do have a substantially lower dropout rate than do public schools and that the remaining set of private schools also have lower rates, but less dramatically lower. Mirroring these findings are the suggestive results of a U.S. Department of Education 1993-94 survey of teachers’ perceptions of the seriousness of different problems in their schools.29 This survey found that 14.1 percent of public school teachers identified dropping out as a serious problem in their secondary school while only 1.3 percent of the private school teachers came to the same conclusion. The same concern is reflected in the answers given to broadly similar questions, such as the seriousness of student absenteeism (27.1 to 5.2) and student pregnancy (18.4 to 1.1). When asked about teaching and school conditions, private school teachers report a higher degree of satisfaction than do their public school counterparts with class sizes, participation in education decision making, scope for circumventing school rules, and perception of administrative support for the enforcement of school rules and student disciplining.30 In terms of time series evidence, the inability to attach a particular school dropout to any particular school means that definitive evidence on dropouts by school type is problematic at best. The dropout rate is only meaningful in aggregate. Moreover, time series data is available only for such aggregates as school enrollment and numbers of teachers and/or schools (so that average school size can be measured). In the absence of student/school panel data, many of the other influences on dropout rates, such as the composition of students by socio-economic status, student performances, levels of self esteem, types of adult and peer relationships, and level of care in their school and social environment, are important influences on which we have no observations. We have argued, however, that private schools are much more likely than their public school counterpart to have more of those characteristics that contribute to lower dropout rates. This leads directly to the following test of our

22 hypothesis: an increase in the proportion of private to public schools should be associated with a decrease in the student dropout rate. In Table 2 below, then, we present two OLS regression equations that summarize a test of this hypothesis on U.S. annual data between 1976 and 1996.31 In each regression equation, represented as a column in that table, the dependent variable is the secondary school dropout rate (measured as a percentage of students in the age group between fourteen and seventeen who are not attending any school). Three control variables are used to hold constant other determinants of whether or not to drop out of school: real disposable income per capita, average secondary school size, and, in equation (1), the percentage of students enrolled in elementary school, while in equation (2), the unemployment rate facing secondary school dropouts. Increases in real disposable income per capita (YDIS92) measure improvements in current economic conditions. Because employment is the prime alternative to attending school, improvements in market conditions will encourage students to take market employment and so should be found positively related to the dropout rate. As discussed above, increases in average secondary school size (SSIZE) are expected to produce a less intimate educational environment, discourage the formation of more positive student/teacher relationships and so contribute to a rise in the dropout rate. The predicted sign of the school size coefficient is positive. A rise in the percentage of students attending elementary schools (ENR713) increases the enrollment base of students in secondary schools. By increasing the denominator of the dropout rate measure, a rise in ENR713, holding the number of dropouts constant, will result in a lower observed dropout rate for secondary schools. The expected coefficient sign on ENR713 is then negative. Finally, the unemployment rate facing a high school dropout (DRPURATE) is used in equation (2) as an alternative measure of the availability of employment. A greater prospect of being unemployed should discourage a student from dropping out, leading to the prediction of a negative coefficient sign on DRPURATE. Because DRPURATE is available only from 1980 onwards, its presence reduced the degrees of freedom in the regression equation and led us to use this variable in only one version of the test. The prediction of primary interest is that the secondary school dropout rate will fall with a rise in

23 the proportion of private to public secondary schools (SSRATIO), holding constant other influences on the dropout rate. Note, however, that part of the effect that private schools have on the overall dropout rate comes from the fact that private schools are smaller on average than public schools. Because average secondary school size is held constant when the ratio of private schools is increased, some part of the effect of SSRATIO has already been removed from the variation in the dependent variable. Should a negative relationship between SSRATIO and the dropout rate then be found, we can be somewhat more confident that the private school prediction has been consistent with the data over this time period. The equation results presented in Table 2 support both the general approach and specific hypotheses discussed in this paper. Both equations explain a relatively large part of the variation in secondary school dropout rates over this time period (as measured by the R2 and F statistics) and the Durbin Watson and Q statistics give little evidence of serial correlation among the equations’ residuals. This implies that we have no particular reason to expect systematic bias in coefficient standard errors or t-statistics. In terms of the individual predictions, increases in both YDIS92 and SSIZE have their expected positive effect on dropout rates in both equations with coefficient estimates that are significantly different from zero in equation (2) but not (1). The coefficient on elementary enrollment (ENR713) is signficantly negative, while DRPURATE is positively related to the dropout rate but not significantly so. In combination, the set of control variables can explain eighty eight percent of the variation dropout rates in equation (1) and seventy nine percent in equation (2).32 When we focus specifically on the relative effect of private schools on the dropout rate, both equations find that the increase in the proportion of private to public secondary schools (SSRATIO) is inversely related to the secondary school dropout rate as predicted and that the estimated coefficients measuring this relationship are significantly different from zero at the one percent significance level. In addition, both equations pass the Wald test of the significance of adding SSRATIO as an new explanatory variable to a regression equation (that excluded it) at the one percent significance level. Finally, not only is the proportion of private to public schools statistically significant as a determinant of the aggregate dropout rate, SSRATIO is also economically significant in its ability to explain the fall in

24 the dropout rate that took place over this period. Using the regression coefficient as a point estimate of the effect of the rise in the proportion of private to public secondary schools on the secondary school dropout rate, the rise in SSRATIO from .23 in 1976 to .44 in 1996 would, by itself, have accounted for roughly all of the three percentage point fall in the secondary school dropout rate (from roughly 6.3 to 3.5) over the same time period.

VII

Conclusion In this paper we have argued that even if a voucher system led to the segmenting of the

education system by ability such that the students remaining in the public system were harmed by the deterioration of their school environment, an income based voucher system would rescue from the dropout pool potential students who are far more badly off in terms of their current realizations of education. We have also argued that the migration induced by the voucher system involves more than simply movement by student ability so that the extent to which the private system does expand at the expense of the public need not result in much deterioration of the average ability of the student pool. Finally we have argued that because student dropouts have special needs, private schools are better placed in terms of their structure to help/prevent school dropouts and that in practice they have had better success in keeping dropout rates low. It follows that equality in education might better be accomplished by addressing the dropout problem than by opposing vouchers. This does not mean that instituting a voucher system cannot target for compensation or special attention those groups or individuals who are most likely to be disadvantaged by the development of a more efficient system. Nevertheless, both educational equality and efficiency are more likely to be enhanced a) where the voucher system encourages a private school system that is better able to address the dropout problem than can the public and b) where the dropout problem inflicts more damage on the poor than does the peer group effect. It is the position of this paper that in practice both (a) and (b) are fulfilled.

Appendix on Data Sources All variables are from Digest of Education Statistics: 1998, p.12 Table 3. Enrollment in educational institutions,1950 - 1998, continuous from 1964 STPUBSS, student enrollment, public secondary schools column 6 STPRSS, Student enrollment, private secondary school column 9 STSSTOTAL = STPUBSS + STPRSS Table 37 Gross Domestic Product ....continuous from 1950 YDIS92 Disposable personal income per capita in 1992 dollars

column 9

Table 6 Percentage of the population 3 to 34 years old enrolled in (any type of) school by age ENR713 percentage 7 to 13 enrolled in school col (5) ENR1417 percentage 14 to 17 enrolled in school col (6) Calculation of the Secondary school dropout Rate (Dependent variable in Regressions) DROPSS = (100 - enr1417) Table 90 Public school districts and public and private elementary and secondary schools number of schools SSPUB COLUMN (7) SSPUBREV INTERPOLATED THE MISSING ENTRIES (just a few missing) SSPR SSPRREV averaged the missing entries (pub every second year (on average) SSRATIO = SSPRREV/SSPUBREV SSSIZE = STSSTOTAL/(SSPUBREV + SSPRREV)

Descriptive Statistics

DROPSS

SSIZE

SSRATIO

YDIS92

ENR713

MEAN

4.995238

432.7581

0.340331

16549.71

99.23810

MAXIMUM

6.60

510.1090

0.459883

18989.00

99.70000

MINIMUM

3.30

384.4494

0.232721

13793.00

97.70000

STD. DEV.

1.068399

44.20070

0.081278

1640.956

0.400595

SKEWNESS

-0.051374

0.544502

0.029929

-0.208625

-2.739997

29

30

Table 2 High School Dropout Rates: 1976 (80) - 1996 (t statistic in brackets) High School Dropout Rate

1976 - 1996 (1)

Constant

60.48* (3.46)

Per capita disposable income in 1992 dollars YDIS92

0.0001 (0.937)

0.0008* (2.48)

School Size SSIZE

0.001 (0.301)

0.020* (3.01)

Proportion of Private to Public High Schools SSRATIO

-14.35* (5.95)

Elementary School enrollment ENR713

-11.70** (1.84)

-17.12* (3.86)

-0.533* (3.40)

Unemployment rate of Dropouts DRPURATE

0.022 (0.824)

Statistics: Observations R2 F-statistic DW Q(12) * **

1980 - 1996 (2)

21 .964 106.93 2.13 10.4

significantly different from zero at 5% significantly different from zero at 10%

Data sources in Appendix

31

17 .928 25.6 1.99 9.6

REFERENCES Coleman, J., and T. Hoffer, 1987 Public and Private High Schools, Basic Books, New York. Ekstrom, R., Goertz, M., Pollack, J. and Rock, D., 1986 “Who Drops out of High School and Why? Findings from a National Study” Teachers College Record 87(3), 356-73. Epple, D., and R. Romano, 1998a “Competition between Private and Public Schools, Vouchers, and Peer-Group Effects,” American Economic Review, 62(1), 33-62. , 1998b “Education Vouchers and Cream Skimming”, Working Paper, revised November 1998, 53 pages with appendices. Henderson, V., P. Mieszkowski, and Y. Sauvageau, 1978 “Peer Group Effects and Educational Production Functions” Journal of Public Economics 10,97-106. Legters, N., E. McDill, and J. Partland, 1992, Responses to the Challenge of Educating At-Risk Youth, Center for Research on Effective Education for Disadvantaged Students, Johns Hopkins University, Baltimore Maryland. Natriello G., 1994 “Dropouts, School Leavers, and Truancy”, The International Encylopedia of Education, Volume 3, 2nd ed., Torstein Husen, editor, Pergamon Press: Oxford, 1602-7. Nechyba, Thomas, J., 1998 “Mobility and Private School Vouchers”, Department of Economics Working Paper, Stanford University. Ruggiero J., and D., Vitaliano, 1999 “Assessing the Efficiency of Public Schools” Contemporary Economic Policy, 17 (3), 321-331. Rumberger, R., 1987 “Dropping out of High School: A Review of Issues and Evidence”, Review of Education Research, 57 (2), 199-230. Summers, A.A., and B.L. Wolfe, 1977 “Do Schools Make a Difference?” American Economic Review, 67 (4), 639-652. Toma, Eugenia, 1999 “Will Johnny Read Next Year?” 15th Annual Lecture in the Virginia Political Economy Lecture Series, March 18th. U.S. Department of Education,1998 Digest of Education Statistics: 1998, National Center for Education Statistics, Office of Education Research and Improvement, Washington. 32

Wenger, J., 2000 “What do Schools Produce,” Contemporary Economic Policy, 18 (1), 27-36.

33

NOTES

1. We would like to thank Keith Acheson, Zhiqi Chen and Ambrose Leung for their comments on an early draft of these ideas. 2. Digest of Education Statistics: 1998, Table 106, Percentage of High School Dropouts (status dropouts) among persons 16 to 36 years old by age. The text uses the 12.7 percentage for the twenty and twenty one year old (all races, both sexes) age group in 1997. 3. The work of Henderson, Mieszkowski and Sauvageau (1978) on Canadian data supports the concavity of the Summers and Wolfe peer group effect but dispute whether net effect experienced by high ability students is negative. 4. Most writers on vouchers tend to agree that the competition introduced by vouchers will result in “technical efficiencies” (see Epple and Romano, 1998b). While recognizing the importance of this consideration, we wish to focus on the equity thrust given by Manski (1992). Accordingly we abstract from the efficiency considerations to highlight Rawls’ “difference principle”, a concern with the equity of the least able in society. 5. This allows students and their families to realize different levels of surplus across school systems and so becomes the basis of their choice across educational alternatives. ER assume that private schools can perfectly price discriminate and use fee reductions (scholarships) to attract high ability-low income students and so charge higher income parents for the positive peer benefits of higher ability schools. Open entry into private schooling then produces a school system stratified by ability with lower ability students left in the public system. 6. The analysis assumes that there will be no integer problems arising from insufficient numbers of students capable of supporting private schools targeted at each particular student type. 7. The values of the first derivative at zero and infinity guarantees that individuals will choose some positive level of consumption whether or not they choose to acquire education, i.e., U’(ci = 0) > ai and U’(ci = 4) = 0. 8. This also implies that the peer group effect becomes negative for students who have a level of ability that is higher than the school average. 9. It will be recognized that while we measure the degree of frustration along the dimension of ability, bi could be thought of as a vector of student attributes. The squaring in the definition of fi is to allow frustration to arise symmetrically on either side of the average. 10. At the margin, NB(dropping out) = 0 = a3b2 - (2a3? pub + a1 - a2)b - (a2? pub2 - a3? pub) .

25

11. The former implies that the direct effect of teaching dominates the peer group effect and the latter implies that frustration dominates the peer group effect at the ability extremes. 12. From footnote 12 above, MNB(dropping out)/Mbi = -(a1 - a2 + 2a3i? pub) + 2a3ibi. The slope of the net benefit curve is negative at bi = 0 as long as the direct benefit of learning (a1) exceeds the indirect peer group effect (a2) and then rises in value to become zero at bi = ? pub + (a1 - a2)/2a3i > ? pub. For larger values of bi, MNB/Mbi becomes increasingly positive. 13. High income families often congregate in geographic areas and use their political influence to redistribute resources within the public system. As Eugenia Toma (1999) has written, upper income students “live in nice suburban homes and consume the best the public system has to offer. They get the best buildings, the best teachers, the most rigorous curriculum, and the widest variety of extracurricular activities” (p .7). This implies that in practice the dropout problem will fall that much more inequitably on lower income students and their families. 14. Not incidently, the same factors imply that it is in the teacher’s and the school’s interest to discourage low achievers (costly to teach students) from continuing to attend school. 15. Greater success with the dropout problem here implies less measured success on average. But a lowering of the average achievement score corresponds to lower overall achievement only if the same number and type of students are involved. If the incremental achievement of previous dropouts were recognized and/or a reduction in dropout rates (or rise in the graduation rates) were valued independently, the aggregate outcome would appear quite different. On this see Wenger (2000). 16. ER (1998b) argue that income and education are complements so that the demand for specialized education increases with income. If this were so, the distribution of private school types would be further moved away from symmetry towards higher ability students. 17. Ex post, the fact that vouchers will be utilized primarily by higher income families and financed by all means that the program will be regressive in its outcome. 18. Again we assume that individual’s ignore the consequences of their schooling decision on their tax bill so that t is viewed as independent of school choice. 19. In the absence of the peer group effect, private schools would recruit more symmetrically from both ends of the ability distribution out of both the public system and the dropout pool. Any weakening of the peer group effect further strengthens the equity effect of the voucher program and complements the emergence of any efficiency gains arising from the program. 20. Ruggiero and Vitaliano (p. 329) suggest the availability of gains of up to 15%. 21. More generally, if the voucher program attracts students by features that are independent of ability, there would be no peer group effect in the sense of Manski (1992). 26

22. Similarly, when commenting on the usual finding that teacher experience is unimportant Summers and Wolfe (1977) report “We found that students whose third-grade score was above average benefitted from more experience, but those who were very much below grade level were negatively effected. In fact this group did best with newer teachers who perhaps have undampened enthusiasm for teaching those who find it hard to learn”(p. 644). 23. Note that in fall 1995 Catholic school enrollment (2,519,205) was roughly fifty percent of total private school enrollment (5,032,200), with enrollment in other religious private schools (1,743,791) accounting for roughly two thirds of the other fifty percent. Recent court decisions have allowed some states (e.g. 1998 for Wisconsin) to extend the benefits of such voucher programs as the Milwaukee Parental Choice Program to Catholic schools. 24. The average public school size was 527 students with a pupil-teacher ratio of 17.3 in 1995. The corresponding numbers for private schools were 182 and 14. U.S. Department of Education, Digest of Education Statistics: 1998, National Center for Education Statistics, Table 89 for Public Schools and Table 60 for Private. 25. Between 1988 and 1995 the total number of public school districts declined in each year (15,376 to 14,766) as the proportion of students in the largest sized districts continued to grow. Over 30 percent of students are now taught in schools districts of over 25,000 in size. Digest, Table 91. 26. An increasing focus on subject disciplines can be seen in the rise in the average level of educational achievement required of public school teachers relative to their private counterparts. Similarly the increasing disadvantage that public school’s have in dealing with low achieving (difficult) students can be seen in the rising gap in student/teacher ratios with private schools and indicators of an increasing distance from their students through such factors as the rising average age of public school teachers and their length of job tenure. Digest, Table 65 and Table 70. 27. Status dropouts are those individuals in the age group who are not in school and have not graduated. This is contrasted with event dropouts who are those students who dropped out that year. The status dropout rate then measures the accumulated event dropout rate for that age group. The text figures are from Digest,1998, Table 106, p.125. 28. Digest, Tables 380 and 383. 29. U.S. Department of Education, “Schooling and Staffing Survey,” 1990-91 and 1993- 4, Digest, Table 27. 30. U.S. Department of Education, “Schooling and Staffing Survey,” 1993- 4, Digest, Table 28. 31. All of the data is taken from National Center for Education Statistics, U.S. Department of Education, Digest of Education Statistics: 1998 Washington: US Government Printing Office.

27

32. The significance of the constant in both equations suggests that the set of independent variables does not include all of the important determinants of student dropout rates. Their absence form the equation, however, does not appear to bias the sign or significance of the included variables.

28