ATTITUDES TOWARDS RACE AND POVERTY
IN THE DEMAND FOR PRIVATE EDUCATION:
THE CASE OF MISSISSIPPI
John R. Conlon and Mwangi S. Kimenyi
Most studies of the demand for private education have treated "white
flight"as a response to the proporlion of the population that is black in
a particular area. The present article, by contrast, considers the possibility that this flight may be from poverty rather than race. The article
develops an aggregate demand function for private education from
which individual behavior may be inferred, and then applies the model
to data from Mississippi. The results suggest that prejudice is directed
against poor blacks rather than against nonpoor blacks or poor whites.
Though most primary and secondary education in the United States is
provided by public institutions, private schools also play a significant
role. In 1980, for example, 10.6 percent of all elementary and high school
students in the United States were enrolled in private schools. There are
significant inter- and intrastate differences in the proportion of students
enrolled in private schools. In the state of Mississippi for example, while
11.8 percent of all elementary and high school students in the state were
enrolled in private schools in 1980, this number was 22.7 percent in
Hancock County and only 0.6 percent in Union County.' Private school
choice is influenced by a number of factors, including religious preferences
and dissatisfaction with the quality of public schools. One important
factor that influences private school choice and has been studied extensively is aversion to the racial composition of public schools-what is
commonly referred to as "white flight."
Several studies show that the demand for private education is influenced by the rq~ial omp position of the public ~ c h o o l However,
.~
while
.
6
The Revicw of Black Political Econom)/Fall 1991
these studies demonstrate that "white flight" is directly related to the
proportion of the population that is black, they do not show how whites
respond to hlacks in different income groups, or how well-off whites
respond to poor whites. It is therefore difficult to determine whether
"white flight" is flight from black students because they are black or
because they are poor. This question has public policy implications going
beyond those dealing with education.
The prominent sociologist William Julius Wilson in his controversial
book, The DecLning Significance of Race3 has suggested that although an
individual's race remains important, social class is becoming an increasingly significant determinant of life chances or opportunities in the black
community. In Wilson's view, this difference in opportunities is caused
by the different positions of middle-income and poor blacks in the shrcture of an economy with a declining and changing industrial base?
Wilson does not view discrimination as the source of this difference in
life chance^.^ A factor closely related to the relative opportunities of
middle- and low-income blacks, however, is the differential attitudes of
whites towards these two groups. Do whites exhibit stronger prejudice
against poor blacks than against middle-income blacks? And, if class is
important, do well-off whites avoid poor whites as well as poor blacks?
A test of these hypotheses can be conducted in the context of demand for
private education. Such a test may not only contribute to an understanding of the nature of prejudice, but may also help to locate the areas of
greatest resistance to integration under alternative systems such as, for
example, vouchers60r "magnet schools" In addition, it may cast some
light on the political economy of public school finance.
This article looks at the factors that influence the demand for private
education in the slate of Mississippi.7 Unlike other work in the field, the
present study looks at the demand for private schools by white families
in response to the combined race and class characteristics of potential
public school classmates of their children, rather than simply focusing on
their response to race alone. The article i:, organized as follows: Section I
provides a theoretical model of the demand for private education, combining individual demand functions to obtain an aggregate demand function from which individual behavior can be inferred. Section I1 presents
empirical results, examining the reaction of well-off whites to the presence
of poor blacks, poor whites, and nonpoor hlacks. Section 111 concludes
with remarks on some public policy implications of the study.
Conlon and Rimensi
7
I. THE MODEL AND EMPIRICAL SPECIFICATION
In this section a model is constructed that focuses on the response of
white families in different income and religious groups to the characteristics of public schools.Tonsider N white families living in a given county.
Assume that the ith family has income Yi and other characteristics 6. In the
discussion that follows, r, will represent religious group, specifically
Catholic versus non-Catholi~.~
The family has the option of sending its
children to a free public school with a vector of characteristics So, including expenditures per student, characteristics of the student body, and so
on. Alternatively, the family can send its children to a private school,
with school characteristics S and tuition T(S).lo
Suppose the family has utility function u,(S, X), where S is the characteristics of the school attended by the family's children, X is expenditure
on other goods and services, and r represents the family's religious group.
Then the ith family chooses its most preferred private school characteristics and tuition (say Si* and Tia) by maximizing u,;(S, Yi T(S)) with
respect to S and setting Ti* = T(Sie). The family then compares u,;(S;*,
Y;- T(Sje)) obtained from sending its children to private schools with the
utility uCi(So,Yi) obtained from sending its children to public schools,
making the choice that yields the higher utility. The ith family's choice
of school would thus be a function of Yi, r,, and Su.
The demand by individual families is now combined to yieid an aggregate demand function. This can be done most easily if the incomes of
potential private school demanders in a county are incorporated through
the proportion of families in the county with income above some specified
level, rather than through mean or median county income. Let Yl represent
a cutoff income level below which very few non-Catholics are assumed
to send their children to private schools (since any cutoff income level
would be somewhat arbitrary, we will check for robustness by reporting
results for three different values of Y,).
Since the main focus of this article is on attitudes towards poor whites,
poor hlacks and nonpoor blacks, and since religion will be included only
as a control variable, ignore the religious characteristics variable q for the
moment. For a full treatment of the religion variable, see the Appendix.
Represent the fraction of white families with incomes above Y1 by the
variable WWOFF (for "white well-off'), and let P(S) be the average
number of children enrolled in private schools per white family with
income above Y,, as a function of the school characteristics S in a county.
Also, let N be the total number of white families. Then N WWOFF is the
-
8
The Review of Black Political EeonomyIFall 1991
Conlon and Kimenyi
total number of white families with incomes above YI, and P(S) N
WWOFF is the total number of white children in private schools (assuming these come piimarily from families with incomes above Yt). Finally, let
b be the average number of children per white family in the county
enrolled in primary and secondary schools (public or private). Then b N
is the total number of white students in primary and secondary schools.
Putting this all together, the fraction of white school children in private
schools (FWPRIV) will be
Table 1 lists means and standard deviations of these variables, as well as
those of FWPRIV, WWOFF, and FCATH, defined previ~usly.'~
Any aversion toward blacks or the poor would be captured by the
effect of the variables BPR, WPR, and BNPR (fraction of population
A large per
poor black, poor white, and nonpoor black, respecti~ely).'~
student expenditure (PSE), by raising the quality of public schools, should
have a negative effect on demand for private schools. A large number of
school districts (NSD) implies a wide range of choices of public schools
in a given area. For example, different school districts in a county may
have different racial compositions or school qualities. Thus, demand for
private schools should be lower in counties with more than one school
district.I3
Finally, the functional forms for PznYS)and D(S) are specified. Let
(1) FWPRIV = [P(S) N WWOFF]/(b N) = (lib) P(S) WWOFF
Equation (1) is the general form of the model we intend to estimate.
However, this equation does not contain a control for Catholic versus
non-Catholic. The derivation of an equation that controls for this characteristic is provided in the Appendix. The result (see equation (A3) in the
Appendix) is
(3) (lib) Ppc (BPR, WPR, BNPR, PSE, NSD) = % + a, BPR
+ a * WPR + a3BNPR + a, PSE + asNSD + el
(2) FWPR1V = (lib) PpC(S)WWOFF + (lib) D(S) FCATH
where D(S) is the difference between Catholic and non-Catholic behavior, FCATH is the fraction of the population which is Catholic, and
PznYS) the average number of children enrolled in private schools per
white nonCatholic family with income above Y , , as a function of the
school characteristics S in a county (see Appendix for details).
This is the general form of the equation that will be estimated in
Section 111. PZW(S)will then reveal the well-off non-Catholic income
group's private school choice in response to the public school characteristics, S, and D(S) will reveal the difference between the private school
choice behavior of Catholics and non-Catholics.
To implement equation (2) empirically, the vector S of public school
characteristics in a county is specified as follows:
S, = BPR, the fraction of population that is poor black;
S, = WPR, the fraction of the population that is poor white;
5
2 ajSi+€~
=au+
i.1
where E, represents the effect of unobserved public and private school
characteristics, and Iet
5
(4)
(lib) D(S) = Bu + 2
11
.
PI Si + 6'
Plugging (3) and (4) into (2) gives:
(5) FWPRIV = % WWOFF +
5
1 a,S, WWOFF
1-1
5
+ puFCATH + C Pi Si FCATH + WWOFF + FCATH
-
i-1
.
I
S, = BNPR, the fraction of population that is black nonpoor;
1
S, = PSE, the per student expenditure in the county;
I
1
S, = NSD, the number of school districts in the county.
9
,
The coefficient aimay be interpreted as the effect of school characteristic S, on well-off white families' private school choice decisions. Remember that b represents the average number of school children in the
t y p i d white family. Equation (3) therefore indicates that baj is roughly the
increase in the number of children from well-off non-Catholic white
families enrolled in private schools, when Si increases one unit. Since
Catholics are a small percentage of the population, bajrepresents roughly
the increase in the number of children in private schools from well-off
white families, generally, when Si increases one unit.
Notice that (5) bas no constant term, and that BPR, WPR, BNPR, PSE
and NSD appear only in interactions with WWOFF and FCATH. This
Canlon and Kimengi
The Review of Black Political EconomyIFall 1991
I0
Equation (5) measures the reaction of well-off white families to the
presence of other racial and income groups: Positive coefficients on the
terms involving poor blacks, poor whites and nonpoor blacks (BPR
WWOFF, WPR WWOFF and BNPR WWOFF, respectively) would suggest that well-off white non-Catholics avoid poor blacks, poor whites,
and nonpoor blacks, respectively, by sending their children to private
schools. If the coefficient on the nonpoor black term is greater than or
equal to the coefficient on the poor black term (a, 2 a,),
then well-off
white non-Catholics are avoiding nonpoor black people at least as strongly
as they are avoiding poor blacks. In other words, they do not care about
the income class of blacks. Similarly, if the coefficient on the poor white
term is greater than or equal to the coefficient on the poor black term
(az r a,), then well-off white non-Catholics are avoiding poor whites at
least as strongly as they are avoiding poor blacks. That is, they do not
care about the race of poor people. The difference in behavior between
Catholics and non-Catholics depends on the 6, (see equation (A2) in the
appendix and (4) above).
TABLE 1
Variable Definitionsand Descriptive Statistics (N=82)
Delinitton
FWPRIV
fraction of white children
in private schools
0.214
0.216
fraction of white families
with income above $15,000
0.542
0.082
fraction of while families
with income above $20,000
0.371
0.085
fraction of white families
with income above $10,000
0.724
0.064
WWOFF (I)
WWOFF (2)
WWOFF(3)
BPR
WPR
BNPR
PSE
NSD
FCATH
Mean
Standard
Deviation
Variable
$1. EMPIRICAL RESULTS
fraction of population which
is poor black
0.157
0.099
fraction of population which
is poor white
0.073
0.034
fraction of population which
is black nonpoor
0.216
0.093
1394.829
171.037
number of school d i s t h s in
the county
1.865
0.952
fraction of the population
which is Catholic
0.020
0.039
per student expenditure
in the county
11
yields a testable hypothesis. Equation (5) also suggests some heteroskedasticity in the error term:I4
(6) Var[WWOFF E, + FCATH aC]= (WWOFF2+ FCATH2) as2
assuming that a, and aC are independent with common variance qZ.
I
Equation (5) was estimated using 1980 data for counties in the state of
Mississippi (see Table 1 for means and standard deviations, and footnote
11 for data sources). A Weighted Least Square procedure was used to
allow for the heteroskedasticity suggested in equation (6). The results for
Y, = $15,000 (that is, for WWOFF representing the fraction of white
families with incomes above $15,000), are reported in Table 2. Table 3
reports the results for Y, = $10,000, and Table 4 reports the results for Y,
= $20,000. As a further check of robustness to specification, regressions
with various insignificant interaction terms removed are also reported in
each table.
It was felt that the cutoff income level Y , = $15,000 was most appropriate because Y,= $20,000 excluded many families which were sending
children to private schools and Y, = $10,000 included families which
would not send children to private schools under most circumstances. In
fourteen counties out of eighty-two, the fraction of white students attending private schools exceeded the fraction of white families with incomes
above $20,000, twice by a factor of two. On the other hand, in only four
counties did the fraction of students in private schools reach 90 percent
of the fraction of families with incomes above $10,000, and in only
fourteen counties did it reach 60 percent. Thus, the cutoff Y, = $15,000
The Review olBIack Political Eeonamy/Fall 1991
12
TABLE 2
The Determinants of Private School Enrollment (FWPRIV)
(WWOFF = families with income greater than $15,000)
Variable
(1)
(2)
(3)
(4)
(5)
Intercept
0.05
(0.34)
-0.15
(-0.38)
0.09
(0.69)
0.09
(0.70)
0.01
(0.12)
0.10
(0.76)
-0.06
(-0.24)
-0.08
(-0.39)
-0.06
(-0.32)
2.88
(7.36)
2.87
(7.46)
-1.53
(-1.00)
3.03
(8.60)
-0.03
(-0.16)
2.98
(8.97)
-1.88
(-1.35)
0.26
0.25
(0.57)
(0.57)
-0.00002
(-0.11)
-0.074
-0.074
(-3.13)
(-3.15)
1.03
1.03
(3.02)
(3.05)
0.42
(1.06)
WWOFF
BPR WWOFF
WPR WWOFF
BNPR WWOFF
PSE WWOFF
NSD WWOFF
FCATH
BPR FCATH
WPR FCATH
BNPR FCATH
PSE FCATH
NSD FCATH
t-test for:
BNPR s BPR
WPR z BPR
R2
2.93
(5.62)
-1.07
(-0.62)
0.61
(0.88)
0.00004
(0.18)
-0.073
(-2.27)
8.57
(0.66)
-3.81
(-0.20)
-1.52
(-0.99)
-0.070
(-3.04)
-0.075
(-3.27)
0.97
(2.92)
1.02
(3.07)
-13.72
(-0.45)
-8.68
(-0.42)
-0.004
(-0.51)
0.13
(0.32)
2.21
3.62
3.69
3.66
2.46
0.775
3.08
0.781
3.11
0.784
0.784
Note: 82 observations; t-statistin for coefficientsin parentheses.
4.20
0.786
Conlon and Kimen).i
13
seems to be an appropriate compromise, with regressions using Y, =
$10,000 and Y , = $20,000 reported to check robustness. The results for
the case Y , = $15,000 are therefore discussed first, with only differences
highlighted for the other two income cutoffs.
We first discuss some of the other terms in the model before focusing
on the terms involving attitudes towards race and class of potential ctassmates.
The constant terms are insignificant in all regressions in Table 2, as
expected (see discussion under equation (5) above). This lends some
initial support to our model. Regressions with the constant term removed
gave similar results. Next, per student expenditure (PSE) has no effect in
any of the regressions, which might reflect the small coefficient of variation
(12.3%) of this variable. (See next section for a discussion of this small
variation.) Number of school districts in the county (NSD) has a negative
coefficient, suggesting that greater choice of public schools in a county
reduces the demand for private education. This may, in part, reflect white
flight between school districts. The coefficient on fraction Catholic
(FCATH) is only significant (and positive) when interactions between
FCATH and public school characteristics are dropped. This may be due
to the combined effect of multicollinearity and the small size of the
Catholic population in Mississippi. The hypothesis that the coefficients
on all of the FCATH interaction terms equal zero was accepted with an
F(5, 69) statistic of 0.596 (5% critical value = 2.35). This means tbat we
cannot reject the hypothesis tbat the difference between Catholic and
non-Catholic behavior involves only a constant term. Additional regressions were therefore also run with the FCATH interaction terms removed.
This made the coefficient on FCATH significant, but had no significant
effects on the other terms.
The only significant coefficient, other than those on number of school
districts and fraction Catholic, is the one on the black poor term (BPR
WWOFF). This coefficient is positive, suggesting that when there are
many poor blacks in a county, well-off white families send their children
to private schools. The coefficients on the white poor and black nonpoor
terms (WPR WWOFF and BNPR WWOFF) are insignificant in all regressions, suggesting that the presence of poor whites and nonpoor blacks
does not have a significant effect on the publiciprivate school choices of
well-off white families.
Furthermore, the nonsignificant effects of poor whites an0 nonpoor
blacks is not due to, say, small numbers in these latter two groups. In the
case of nonpoor blacks this may he seen in two ways. First, the average
14
Conlon and Kimenyi
The Review of Black Political EeonomylFail 1991
fraction of nonpoor blacks in the total population is larger than the fraction of poor blacks (0.216 as opposed to 0.157; see Table I), and the
standard deviation of this fraction is almost as large for nonpoor blacks
as it is for poor blacks (0.093 as opposed to 0.099). It therefore seems
that numbers do not tend to favor finding an effect from poor, as opposed
to nonpoor blacks. Second, the hypothesis that white families avoid the
black nonpoor as strongly as they do the black poor is rejected in all
regressions using a one tailed t-test (t-statistics reported in the BNPR z
BPR row; 5% critical value for all tests = 1.67). This rejection rules out
the possibility that the effect of nonpoor blacks is important, but imprecisely measured due, say, to small numbers or rnnlticollinearity.
Poor whites do form a smaller fraction of the population than poor
blacks. However, the hypothesis that well-off white families avoid poor
whites as strongly as they do poor blacks is also rejected using a one
tailed t-test (t-statistics in the WPR r. BPR row; 5% critical value 1.67).
If the true effect for poor whites was identical to that for poor blacks, but
there were too few poor wbites to have much effect on private school
decisions of well-off whites, then the coefficient on the poor white interaction term would be too imprecisely estimated to reject the above hypothesis, unless the effect were nonlinear, as in "tipping" models. This
possibility merits future research.
Thus, the results of Table 2 suggest that well-off whites avoid poor
blacks more strongly than they do nonpoor blacks or poor whites. In fact,
there may be no avoidance whatsoever of these latter two groups.
The results reported in Table 3, for cutoff income level Y, = $10,000,
and in Table 4, for cutoff income level Y, = $20,000 are similar to the
results in Table 2 with a few exceptions. The terms involving poor blacks
(BPR WWOFF), number of school districts (NSD WWOFF) and (except
in column 1) Catholics (FCATH) are significant just as in Table 2, suggesting that poor hlacks, number of school districts, and fraction Catholic
all influence private scbool enrollment. The hypotheses that the white
well-off avoid the white poor and the black nonpoor as strongly as they
do the black poor are rejected in most, but not all regressions, and the
terns involving white poor and black nonpoor (WPR WWOFF and BNPR
WWOFF) are insignificant in most but not all regressions, suggesting
that there is not much avoidance of nonpoor blacks or poor whites. The
main exceptions here are in the last two columns of Table 4. The term
involving black nonpoor (BNPR WWOFF) in column 4 suggests some
avoidance of nonpoor blacks, though less than that of poor blacks, since
the hypothesis of more avoidance of nonpoor blacks (BNPR 2 BPR) is
TABLE 3
The Determinants of Private School Enrollment (FWPRIV)
(WWOFF = families with income greater than $10,000)
1
I
Variable
intercept
(1)
(2)
(3)
-0.26
(-0.97)
-0.20
(-0.79)
-0.20
(-0.80)
WWOFF
0.15
(0.38)
0.16
(0.56)
0.18
(0.69)
BPR WWOFF
2.19
(5.61)
0.46
(0.33)
0.71
(1.35)
2.20
(7.41)
0.20
(0.15)
0.45
(1.27)
2.21
(7.56)
0.22
(0.17)
0.47
(1.40)
0.00005
(0.33)
0.00002
(0.15)
WPR WWOFF
BNPR WWOFF
PSE WWOFF
(4)
-0.16
(-1.16)
0.16
(0.70)
2.19
(8.38)
(5)
-0.10
(-0.44)
-0.20
(0.74)
2.37
(8.80)
-0.67
(-0.61)
0.44
(1.52)
NSD WWOFF
FCATH
BPR FCATH
WPR FCATH
BNPR FCATH
PSE FCATH
1
1
NSD FCATH
t-test for:
BNPR z BPR
WPR z BPR
RZ
0.773
0.781
0.784
Note: 82 observatiaos;t-statistics for coefficients in parentheses.
0.787
0.782
The Review of Black Political EconomyiFatl 1991
still rejected. In addition, the term involving white poor (WPR WWOFF)
in column 5 is significant and negative, suggesting that well-off whites
prefer public schools with poor whites present, possibly because they
reduce the tendency for public schools to become largely black, since
poor whites have difficulty affording private schools. The constant terms
are also borderline significant in some of the regressions in Table 4.
Nevertheless, the results are fairly similar in the three tables, suggesting
robustness to changes in Y,.
In summary, our results suggest that prejudice against blacks is focused
on poor blacks, hut that a similar sort of prejudice does not seem to be
directed against poor whites. The negative effect of the number of school
districts suggests that wider choice within public schools reduces the
demand for private schools, and the positive effect of the fraction of
population Catholic suggests that Catholics attend private (parochial)
schools more often than non-Catholics.
111. CONCLUSION
This article finds greater aversion to poor blacks than to nonpoor blacks
or poor whites. Our methods are not designed to determine the reasons
why whites tend to avoid poor blacks as opposed to poor whites or
nonpoor blacks, though some possibilities include (I) irrational prejudice,
(2) characteristics of poor black children which white parents fear or
dislike, and (3) poor management of schools with poor black students,
either because of the attitudes of administrators, or greater political passivity of low-income parents. This list, of course, is not exhaustive. We
feel that explanations for the patterns we observe in this article would
form an important area for future research.
Whatever its cause, at any rate, this differential prejudice may be
related to the greater obstacles for poor blacks elsewhere in the economy,
as highlighted by W i f s ~ n . 'It~ may, for example, cany over from relations in school to areas such as employer/employee relations. Thus, poor
blacks may face greater discrimination than nonpoor blacks throughout
the economy.
Our results also have implications for purely educational policy, suggesting that the greatest threat to integration may not be a split along
purely racial lines, hut the isolation of poor blacks from other students.
This might be an effect of "magnet school" programs, which may draw
off the more advantaged students into higher quality selective public
schools. Likewise, a voucher plan as a method of fiancing education,
Conlon and
Kimenyi
Table 4
The Determinants of Private School Enrollment (FWPRIV)
(WWOFF = families with income greater than $20,000)
Variable
(1)
Intercept
0.11
(1.43)
WWOFF
-0.33
(-0.62)
BPR WWOFF
3.79
(5.23)
-2.06
(-0.92)
WPR WWOFF
(2)
BNPR WWOFF
1.37
(1.35)
PSE WWOFF
0.00001 -0.00005
(0.04).
(-0.25)
NSD WWOFF
FCATH
(1.06)
(3)
(4)
(1.04)
(1.89)
(5)
-0.109
(-2.32)
-0.109
(-3.16)
-0.108
(-3.17)
-0.101
(-2.97)
-0.113
(-3.33)
9.91
(0.70)
1.07
(2.88)
1.06
(2.89)
0.98
(2.70)
1.06
(2.91)
BPR FCATH
-3.42
(-0.16)
WPR FCATH
-17.80
(-0.54)
BNPR FCATH
-12.26
(-0.56)
PSE FCATH
-0.004
(-0.51)
NSD FCATH
0.14
(0.32)
t-test for:
BNPR z BPR
1.59
2.98
3.06
2.85
WPR a BPR
2.63
3.37
3.41
R2
0.776
0.781
0.784
0.781
Note: 82 observations;:-statistics for coefficients in parentheses.
5.28
0.783
The Review of Black Political Economy/Fall 1991
IS
even with provisions preventing purely racial segregation, may increase
the isolation of poor blacks from the mainstream ~ociety.'~
Finally, our results may help explain both low education spending in
Mississippi, and the small variation in per-student expenditure from one
county to another. Our results suggest that the well-off whites are most
concerned about avoiding schools with poor black students. Residentially,
however, well-off whites and poor blacks tend to live together (perhaps
because poor blacks tend to work for rich whites). For example, the
correlation coefficient between percent of population poor black and percent of white population with income above $20,000 is 0.248, and the
correlation coefficient between percent of population poor black and percent of white population with income above $35,000 is 0.410. This suggests that if high-income whites wish to avoid poor blacks in school, they
must do so by shifting to private schools, since high-income whites tend
to be concentrated in areas with many poor black families. Thus, the
disparity in per-student expenditure that one observes between affluent
and low-income school districts elsewhere in the United States may not
occur in Mississippi since the affluent whites live close to poor hlacks,
and so, tend to enroll their children in well-funded private schools rather
than sunnorl
.. public
. schools. This mav also reduce the overall suooorl
.. for
public schools among the affluent, thus perhaps providing a partial explanation for low educational expenditure in Mississippi.
Conlon and Kimenyi
19
secondary schools (public and private), so bN is the total number of white
ihildrcn cnrolled i n prlmar) and sccundary schools. Ti,c fra;i$on of whltc school
ch~ldrenin private schools (FWPRIV) will !hen bi'
2
= ( l b ) 1 2 PkYS) (Nkcm +
k-l
2
2 PknC(S)(NknC/N)I
k-l
or, lettingFkr= NkrMbe the fraction of white families in group Gk<
(Al) FWPRIV = (lib) [
2
2
k-i
k-l
2 PkC(S)Fkc+ 2 P,"YS) Fk"q
Two assumptions are used to simplify this equation. First, it is assumed that
no non-Catholic white families with incomes below Y1 send their children to private schools, so PlnYS)= 0.Second, it is assumed that the difference in private
school decisions by Catholic versus non-Catholic families is constant across
income groups, so
(A2) Pkc(S)- PknC(S)= D(S),
where D(S) is independent of k." Thus Plc(S) = D(S) and Pp(S) = PznC(S)
+ D(S).
Plugging these identities into equation (1) gives
FWPRIV = (lib) D(S) FIC+ (lib) [PznC(S)
+ D(S)] FZC
+ 0 + (lib) P2"'(S)
APPENDIX
F2"'
= ( l b ) D(S) [FlS+F25]+ (lb) Pz"qS) [F2=+ P2"=]
Empirical Treatment of the Catholic Variable.
or
Let GI' be the group of white families in religious group r with income below
Y1, and G2' the group of white families in religious group r with income above
Y,. (In the discussion below, this latter group will be referred to as the "white
well-off' families in religious group r.) Let Nkrbe the number of families in group
Gb'.
".and let r = c for Catholics and r = nc for non-Catholics. Then N,C+ NPc +
NZC+NZ"=
= N.
Let Pkr(S)be the average number of children enrolled in private schools per
family in group Gkr,as a function of the school characteristics S of the county.
Then Pkr(S)Nkris the number of private school students from group Gkrand
2
2
k-l
2
2 Px"YS)Nk"c
PkySjN~4
k-I
is the total number of white children in private schools. Let b be the average
number of children pcr white family in the county enrolled in primary and
(A3) FWPRIV = (lib) D(S) FCATH +(lib) PznYS)WWOFF
where FCATH = F,C+ F2=is the fraction of all white families which are Catholic
and WWOFF = FZc+ F206is the fraction of white families which are well-off.
Since we do not have data on Catholics cross-tabulated by race, we used fraction
of total population Catholic to represent FCATH. Equations using Catholics as a
fraction of white population gave similar results. This is not surprising, since the
FCATH variable is being used to control for a concentration of Catholics in a
small number of counties, so the precise specification should not be very important.
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..
.
The Review of Black Political EconomylFall 1991
22
where this occurred, we subtracted data for the reported racial group from the total
numbers to obtain an estimate for the other racial group. Since this "complementary
suppression" is used only when remaining racial groups are very small, this method
should not introduce any biases.
12. Data on public school students cross-tabulated by race and income are unavailable, su we could not use these variables in our model. Moreover, since the final
composition of the public schools is endogenous in our model (influenced by the
movement to private schools), use of actual enrollment numberr on the right hand
side of the equation would lead to simultaneous equatlon bias (in counties with an
unusually large amount of "white flight," the public schools would be left with an
unusually large proportion of black students).
13. See Martinez-Vwuez and Seaman, "Private Schooling," for a similar discussion in connection wilhthc 'Tiebout hypurhcsir. Thc dvcAge number of school
districts in a county is 1.86, wi:h rlighrl) lea, than hali 31 the caunlisr having one
schuol district. There is s puss~b~lit)
that extra srhuul diaricls wcr: esllblirhrd in a
county lo avoid desegregation. This would not necessarily bias our results, but it
uould suggu$$ thnt inLrraser in ihc $numberof school Jlr!rlc~in o ~ i dbe an alienati\e
form of uhile fl!gh!. A cmdr rcgrcssion of SSD dp.nit BPR. LINPR, WPR and
FCATH ie\ealed no effect from BPK or BSPK, houebsr, ruggcsting no attempt to
avoid desegregation by creating new school districts (though there might be white
flight between existing school distriar). Such attempts would, in any case, be difficult
under federal surveillance.
A more precise analysis mighl look at !he number of school disoicts as a function
of the geographic separation of blacks and whites within a county, or at the change
in the number of school districts before and after deseereeation. However. since the
effect of the number of school districts is not the c c n h l i a c u s of this study, it was
felt that such an analysis would take us too far afield.
If new school districts were created to avoid desegregation, this would reduce the
sire of the coefficients on the race and class variables reported in Tables 2 through 4.
Thus, our finding of significant effects would probably be strengthened rather than
reversed by a more careful treatment of the number of school districts. Also, the
differential effect between poor blacks, nonpooi blacks and poor whites would not
be affected unless school districa were more likely to be created to avoid nonpoor
blacks or poor whites than to avoid poor blacks. However, a more careful analysis of
the determinants of the number of school districts would be valuable as a measure of
an alternative form ofwhite flight.
14. Regressions assuming no heteroskedasticity give similar results.
15. Seenote 3.
16. Elchanan Cohn, The Economics of Educaoon (Cambridge. MA: Ballinger
..
Pzzhliohino
n 705
.....-, 10791
. .,,F
17. This is cleail) an unstirfaclury !reatmen1 ai !he bchavior of Cxhalic families Unfonunatsl), data for Catholics arc uns\aillble b) iscr and incdmu gruup,
precluding a mure cnnristrnt treatment. Catholics, hdwrvcr, are onl) a small perccnrage of the popula~ionof Misstssippi (roughiy 3 6 ' i ) , so our rrsulls shauld nor be
sensitive to [hi: precise mnuncr in which Catholics are incorporated inla the madel.
.