420 T.A. Downes Economics of Education Review 19 2000 417–429
reveals, however, that, relative to fiscally independent districts, spending levels and aid elasticities could be
higher or lower in fiscally dependent districts. Thus, before venturing into a discussion of solutions to the fis-
cal dependency “problem”, the existence of such a prob- lem must be established. This can only be done empiri-
cally, and this cannot be done by examining only the experience of the fiscally dependent school districts in
New York. The commonly cited problems in these dis- tricts may be attributable to inadequacies and technical
inefficiencies in spending arising from fiscal depen- dency, but these problems could also be a result of the
fact that the fiscally dependent districts are also urban districts. The work of Duncombe and Yinger 1997 sug-
gests that, in New York, cost disparities contribute sig- nificantly to variation in student achievement and that
deficiencies in student performance in the five large city districts cannot be explained fully by technical inef-
ficiencies. Thus, the observed differences between dependent and independent districts in spending levels
and patterns could simply reflect rational responses to differences in circumstances.
The challenge is to isolate the effect of dependency. The next sections of this paper review some initial efforts
to estimate this effect.
3. Data
As has already been noted, examination of only the experience in New York state cannot permit us to deter-
mine if, for example, a one dollar increase in state aid for education translates into a smaller increase in education
expenditures in the five large city districts than in the other school districts in the state. For that reason, I have
assembled data on the revenues, expenditures, and characteristics of school districts in the 12 East Coast
states from Maine in the north to Virginia in the south. What is ideal about this data set is that it includes fiscally
dependent districts in rural, suburban, and urban settings, as well as urban, fiscally independent school districts.
Thus, the separate effects of urbanicity and fiscal depen- dency can be parcelled out.
These data are drawn from the Common Core of Data CCD.
6
Using the CCD assures comparability of rev- enue and expenditure measures. Further, the CCD pro-
vides multiple years of data; information for school years 1989–90 to 1994–95 was used in this analysis.
For both the fiscally dependent and fiscally inde-
6
Financial data for the 1992–93, 1993–94, and 1994–95 school years were acquired from the US Census Bureau’s web
site http:www.census.govgovswwwschools.html. These data will eventually be incorporated into the CCD.
pendent school districts in New York, Table 1 provides basic summary information on revenues, expenditures,
7
and demographics. To observers of New York’s schools, there are no surprises in these numbers. Per pupil expen-
ditures are lower in the dependent districts, while per pupil federal aid and per pupil state aid are higher. The
differences in the means of per pupil state aid are prim- arily attributable to differences in the categorical compo-
nents of state aid; the difference in the means of per pupil operating aid is less than 200. A hint of the higher
costs in the fiscally dependent districts is also provided in Table 1; the means of the percent of children living
in poverty, the percent of schoolchildren at-risk, and the percent of children who do not speak English well are
all substantially higher in the fiscally dependent districts.
What the numbers do not reveal is the adequacy or the efficiency of spending. In dependent districts, spend-
ing is lower while aid is higher, but such an observation does not allow us to conclude that five large city govern-
ments are “stealing” school aid or failing to give proper weight to the needs of schoolchildren. In fact, given the
demographics of these dependent districts, these num- bers could as easily support the conclusion that aid has
effectively promoted spending in localities with extra- ordinary demands for public services.
4. Fiscal dependency and aid elasticities: preliminary estimates
In the CCD, the location of each school district is assigned to one of seven categories.
8
Four of the five fiscally dependent districts in New York fall into the
large central city category.
9
Thus, one avenue for explor- ing the role of fiscal dependency is to compare fiscally
dependent and independent districts in the large central city category. This comparison can be made using the
summary statistics presented in Table 2. From this table, we can see that total and current spending are slightly
lower in the fiscally dependent districts, but so too is state aid, both total and operating, to these districts.
Thus, the table neither supports nor refutes the claim that fiscal dependency matters. What is apparent from the
table is the demographic similarity of the fiscally depen- dent and fiscally independent districts in this category.
There are differences in the means of median income and in the determinants of school district costs, but these
7
All dollar figures have been transformed into 1994 dollars using the Consumer Price Index for all services.
8
These are large central city, mid-sized central city, suburb of large central city, suburb of mid-sized central city, large
town, small town, and rural.
9
The exception is Yonkers.
421 T.A. Downes Economics of Education Review 19 2000 417–429
Table 1 Spending and demographic characteristics of fiscally dependent and independent school districts in New York State, 1989–90 to
1994–95 Fiscally dependent districts
Fiscally independent districts Comparison
of means— T
-values
a
Variable Mean
Standard Number of
Mean Standard
Number of deviation
observations deviation
observations Total expenditures
9852.54 1207.02
30 10,950.13
5974.77 4254
4.60 per pupil
Current 8681.21
1007.43 30
9577.63 4256.63
4254 4.59
expenditures per pupil
Equipment 133.12
58.06 30
171.87 181.95
4254 3.53
expenditures per pupil
Total state aid per 4739.14
1011.74 30
3913.87 1859.96
4254 24.42
pupil Total federal aid
773.55 206.17
30 288.83
271.84 4254
212.80 per pupil
Operating aid per 3278.97
1260.84 20
3021.21 1594.59
2834 20.91
pupil Median income
b
30,160.83 8518.99
5 42,416.62
16,844.23 699
3.17 Median house
138,668.91 96,308.53
5 132,266.55
97,754.88 699
20.15 value
b
Children in poverty 31.76
6.83 5
10.86 7.21
699 26.81
b
Schoolchildren at- 9.76
2.00 5
1.47 1.70
699 29.27
risk
b
Children—limited 3.16
1.78 5
0.86 1.17
699 22.89
English prof.
b a
Variances are not assumed to be equal when t-statistics are calculated.
b
Variable is drawn from the 1990 Census of Population and Housing.
differences are small in comparison to the differences observed in Table 1.
The barrier to drawing conclusions using a compari- son of means is that in such a comparison it is not poss-
ible to control for cross-state differences in fiscal struc- tures. Such conclusions can be drawn on the basis of
estimates of reduced-form expenditure functions. Expen- diture functions are advantageous in this setting also
because they are consistent, as first-order approxi- mations, with the outcomes of a variety of different pub-
lic choice processes.
10
In other words, since ultimately the goal of this research is determining the impact of
dependency on expenditures and is not estimating demand parameters, assuming that the estimating equa-
tions are based on the median voter model is not neces- sary.
Operationally, the log of expenditures per pupil E
j
10
Downes 1992 provides a more detailed discussion of this point.
for locality j, j =
1,...,n, in period t, t =
1,...,T, is assumed to be given by
ln E
jt
5X
it
a1b ln M
jt
1y lnV
jt
1d ln A
jt
1f ln p
jt
1 1C
jt
q1gD
j
1tD
j
ln A
jt
1F
j
1T
t
1u
it
where p
jt
is the price of inputs for community j, C
jt
is a vector of attributes of the community that influence its
cost of providing schooling outcomes, V
jt
is a proxy for measure of the tax base of that community, M
jt
is a proxy for measure of the income of the community’s
residents, A
jt
is intergovernmental aid to the community, X
jt
is a vector of attributes of the residents of that com- munity that individually influence their demand for pub-
licly provided education, and D
j
is a dummy variable indicating whether a district is fiscally dependent. Thus,
the impact of dependency on the level of spending will be reflected in the estimate of
g, and the impact of depen- dency on the elasticity of spending with respect to
intergovernmental aid will be reflected in the estimate of
t.
422 T.A. Downes Economics of Education Review 19 2000 417–429
Table 2 Spending and demographic characteristics of fiscally dependent and independent urban school districts, 1989–90 to 1994–95
Fiscally dependent districts Fiscally independent districts
Comparison of means—
T -values
a
Variable Mean
Standard Number of
Mean Standard
Number of deviation
observations deviation
observations Total expenditures
9006.98 9843.21
271 9717.19
1995.30 66
1.01 per pupil
Current 7653.58
8919.25 271
8729.06 1901.07
66 1.74
expenditures per pupil
Equipment 95.49
305.82 271
106.21 62.45
66 0.58
expenditures per pupil
Total state aid per 3045.82
3774.79 271
3181.59 1843.98
66 0.46
pupil Total federal aid
429.41 587.20
271 360.04
353.19 66
21.27 per pupil
Operating aid per 1681.51
1966.18 177
2315.74 1418.57
44 2.52
pupil Median income
b
45,256.27 14,275.10
44 41,228.97
16,098.23 11
21.01 Median house
180,600.12 55,041.84
44 116,650.76
70,696.81 11
22.76 value
b
Children in poverty 13.75
13.32 44
11.71 13.94
11 20.13
b
Schoolchildren at- 3.78
5.04 44
3.26 5.03
11 0.07
risk
b
Children—limited 1.62
2.42 44
1.41 1.31
11 0.47
English prof.
b a
Variances are not assumed to be equal when t-statistics are calculated.
b
Variable is drawn from the 1990 Census of Population and Housing.
The error term in Eq. 1 has three components: a locality-specific effect F
j
; a time-specific effect Y
t
; and a purely random effect u
jt
. When estimating the expendi- ture function, both the locality-specific effect, F, and the
time-specific effect T can be treated as either fixed or random. In the estimates presented below, the time-spe-
cific effects T are always assumed to be fixed. The approach taken with F is more agnostic since, if F is
treated as a fixed effect, it is not possible to determine how spending levels differ between fiscally dependent
and fiscally independent districts, all else being equal. For this reason, estimates of Eq. 1 in which F is not
treated as a fixed effect are presented below. Treating F as a fixed effect does, however, eliminate bias due to
correlation of included explanatory variables with omit- ted
variables whose influence on expenditures varies across localities but is stable across time within each
locality. The random-effects specification is preferable to the fixed-effects specification not just because the full
impact of dependency can be estimated but also because the random effects estimates are more efficient if the
locality-specific
effect is
uncorrelated with
the regressors. The locality-specific effect F may, however,
include omitted determinants of provision costs or demand that are correlated with included cost or demand
determinants.
11
To avoid pre-judging the question of whether the locality-specific effect is correlated with
included regressors, a Hausman test for the appropriate- ness of the random-effects model i.e. a test of the
hypothesis that F is statistically independent of the regressors was implemented. The relevant test statistics
are reported below.
Implicit in the specification of the expenditure func- tion given in Eq. 1 are several assumptions that warrant
comment. The first of these assumptions is that the deter- minants of the cost of provision can be cleanly divided
from the determinants of demand for the publicly-pro- vided outputs. In practice, such a clean division is neither
11
When estimating expenditure functions like those con- sidered here, Downes and Pogue 1994 found that the locality-
specific effects were correlated with the included regressors.
423 T.A. Downes Economics of Education Review 19 2000 417–429
necessary nor possible.
12
Since the goal of this work is to estimate aid elasticities, it matters not at all whether
the remaining independent variables are interpreted as cost or demand determinants. The second assumption
implicit in the specification given in Eq. 1 is that the structure of the expenditure function is time-invariant. In
reality, this assumption is testable. For the data used in the analysis that follows, the null hypothesis that the
structure is time-invariant can be rejected at the 1 level.
13
None of the fundamental conclusions changed, however, when the parameters in Eq. 1 were allowed
to change from year to year. Thus, so as to avoid over- whelming the reader with numbers, the results presented
below are based on the restricted specification presented in Eq. 1. Finally, as the specification is written, all of
the observable determinants of expenditures save for the dependency dummy are assumed to be time-varying. In
reality, many of the determinants are temporally stable.
14
As a result, the impact of these determinants on expendi- tures cannot be estimated if the locality-specific effect F
is such that a fixed-effects variant of Eq. 1 must be esti- mated.
Since the CCD provides information on operating aid only after 1990–91, two sets of regressions were esti-
mated for both the random effects and fixed effects vari- ants of Eq. 1. First, all components of state aid were
combined into a single measure. Second, the later years of data were used to see if operating aid has an effect
on spending that differs from the effect of the various categorical aid programs.
Estimates of Eq. 1 which treat the locality-specific effect as uncorrelated with the included regressors are
given in Table 3.
15
Since the null hypothesis that the locality-specific effect is uncorrelated with the included
regressors can be rejected for each variant of Eq. 1 presented in Table 3,
16
these estimates are presented sim- ply to provide the best available evidence of how, all
else being equal, total spending and its components differ between dependent and independent districts. With that
cautionary note in mind, what is evident from Table 3 is that these estimates provide a relatively consistent pic-
ture of the effect of fiscal dependency on the level and the mix of spending. At best, total per pupil spending
12
That such a clean division is not possible has long been realized; see Hamilton 1983 for an example that draws out
this difficulty.
13
The relevant F-statistic equals 27.2058 with 34 numerator and 16,161 denominator degrees of freedom.
14
Specifically, a single value is observed for any variable that is drawn from the 1990 Census.
15
The standard errors reported in Table 3 are robust to het- eroscedasticity
and second-order
autocorrelation. Those
reported in Tables 4 and 5 are robust to heteroscedasticity.
16
The Hausman test statistics ranged in value from 127.38 to 6239.1.
and each component of spending are essentially the same in fiscally dependent and fiscally independent districts.
At worst, total spending and each component of spending are lower in fiscally dependent districts. For example,
the estimates imply that current spending per pupil could be as much as 5 lower in the fiscally dependent dis-
tricts, all else being equal.
17
Thus, these estimates imply that fiscal dependency could plausibly be a barrier to
adequate provision of education. For the reasons noted above, conclusions drawn on the
basis of the estimates in Table 3 must be interpreted with caution. Less caution is needed in drawing conclusions
using the fixed-effect estimates in Table 4. Since the underlying specification is in log–log form, the estimates
in Table 4 give the relevant aid elasticities. Thus, for example, the second column of Table 4 implies that a
1 increase in per pupil operating aid will translate into a 0.034 increase in per pupil expenditures.
While this elasticity and the other elasticities given in Table 4 seem low, they are actually reasonably consistent
with other estimates of the responsiveness of spending to aid. Most of the discussion of estimates of the relation-
ship between aid and spending focuses on the implied change in spending that results when aid increases by
one dollar. Fisher 1996 indicates that most estimates of the relationship between aid and spending imply that
a 1 increase in lump sum aid will translate into an increase in spending of between 0.25 and 0.50. Bartle’s
1995 summary of the literature provides some indi- cation of the relationship between aid and spending for
large central cities. For fiscally dependent school districts like those in New York, the responsiveness of total city
spending to aid provides the best available comparisons currently available in the literature, even though, for all
of the reasons noted above, there is no reason to expect that the aid elasticities for total city spending and for
education spending are equal. The estimates that Bartle reports indicate that a 1 increase in lump sum federal
aid could result in an increase in spending of anywhere between 0 and 1, with the sole estimate of the relation-
ship between lump sum state aid and spending equa- ling 0.32.
The case that the aid elasticities given in Table 4 fall inside the range can be made by calculating, for a typical
district,
18
the spending increases that result from a 1 increase in aid. For example, the results in Table 4 imply
that, for a fiscally dependent urban school district with the mean levels of total spending per pupil and operating
17
Using as the base the mean characteristics for fiscally inde- pendent urban districts given in Table 2, these estimates trans-
late into a spending difference of the order of 412 per pupil.
18
Since the expenditure function is in log–log form, the spending changes that result from a 1 increase in aid will vary
from district to district.
424 T.A. Downes Economics of Education Review 19 2000 417–429
Table 3 Estimates of aid elasticities—expenditures in levels model method of estimation: ordinary least squares asymptotic standard errors
in parentheses
a
Independent variables Dependent variable
Log of total Log of total Log of Log of
Log of Log of
expenditures expenditures current current
equipment equipment
per pupil per pupil
expenditures expenditures expenditures expenditures per pupil
per pupil per pupil
per pupil Log of median income
20.0096 0.1901
20.0133 0.0922
20.2912 20.2707
0.0271 0.0308
0.0229 0.0289
0.0792 0.1071
Log of median house value 0.2677
0.1576 0.2247
0.1634 20.0896
20.1394 0.0150
0.0158 0.0136
0.0150 0.0429
0.0549 Children in poverty
0.0022 0.0047
0.0027 0.0038
0.0002 0.0007
0.0007 0.0007
0.0006 0.0007
0.0022 0.0029
Schoolchildren at-risk 20.0019
20.0047 20.0020
20.0047 0.0029
20.0042 0.0017
0.0019 0.0016
0.0016 0.0058
0.0076 Children with limited English profic.
20.0052 20.0029
20.0042 20.0037
20.0054 0.0109
0.0025 0.0031
0.0023 0.0029
0.0102 0.0123
African–American children 0.0032
0.0025 0.0026
0.0018 20.0010
20.0001 0.0003
0.0003 0.0003
0.0002 0.0009
0.0011 Hispanic children
0.0035 0.0042
0.0017 0.0025
20.0049 20.0016
0.0006 0.0007
0.0006 0.0008
0.0022 0.0027
Asian–American children 0.0032
0.0027 0.0029
0.0036 20.0054
0.0005 0.0011
0.0014 0.0009
0.0012 0.0039
0.0055 Adults with hs degree
20.0001 20.0010
20.0004 20.0009
0.0047 0.0044
0.0006 0.0007
0.0005 0.0006
0.0019 0.0024
Adults with college degree 0.0037
0.0022 0.0032
0.0025 0.0164
0.0157 0.0005
0.0005 0.0004
0.0005 0.0016
0.0020 Pop. age 5–17
20.0014 20.0106
20.0013 20.0062
20.0025 0.0028
0.0014 0.0009
0.0011 0.0008
0.0013 0.0034
Log of total number of students 20.1123
20.0940 20.0491
20.0404 20.0438
20.0577 0.0036
0.0039 0.0032
0.0036 0.0104
0.0137 Log of total federal aid
0.0419 0.0440
0.0594 0.0658
0.0684 0.0657
0.0060 0.0073
0.0055 0.0060
0.0180 0.0244
Interaction of fed. aid with dep. dummy 20.0251
20.0031 0.0053
0.0171 0.1176
0.1455 0.0090
0.0117 0.0079
0.0111 0.0302
0.0413 Log of total state aid
0.0662 20.0101
20.0883 0.0069
0.0063 0.0183
Interaction of st. aid with dep. dummy 0.0087
0.0210 20.0099
0.0105 0.0092
0.0328 Log of operating aid
0.0194 20.0118
20.0647 0.0038
0.0036 0.0154
Interaction of op. aid with dep. dummy 0.0006
0.0049 20.0130
0.0060 0.0056
0.0237 Log of categorical aid
0.0486 0.0273
0.0216 0.0046
0.0039 0.0173
Interaction of cat. aid with dep. dummy 0.0186
0.0250 20.0585
0.0105 0.0099
0.0306 Dependent district dummy
0.0459 20.1186
20.2572 20.3434
20.8725 20.6380
0.0904 0.1110
0.0846 0.1109
0.2633 0.2872
Number of observations 16,371
9712 16,371
9712 15,899
9473
a
In addition to the variables given above, each regression includes a constant, year dummies, state dummies, and dummy variables indicating if the district is located in a large central city, mid-sized central city, suburb of large central city, suburb of mid-sized
central city, large town, or small town.
425 T.A. Downes Economics of Education Review 19 2000 417–429
Table 4 Estimates of aid elasticities—fixed effects model method of estimation: ordinary least squares asymptotic standard errors in
parentheses
a
Independent variables Dependent variable
Log of total Log of total Log of Log of
Log of Log of
expenditures expenditures current current
equipment equipment
per pupil per pupil
expenditures expenditures expenditures expenditures per pupil
per pupil per pupil
per pupil Log of total number of students
20.7925 20.8769
20.7943 20.8764
20.6601 20.9942
0.0252 0.0275
0.0234 0.0261
0.0797 0.1660
Log of total federal aid 0.0023
0.0048 0.0046
0.0060 0.0577
0.0733 0.0045
0.0061 0.0024
0.0038 0.0209
0.0440 Interaction of fed. aid with dep. dummy
0.0047 0.0233
0.0010 0.0084
0.0889 20.1597
0.0071 0.0107
0.0044 0.0074
0.0471 0.0862
Log of total state aid 0.0803
0.0543 0.1062
0.0083 0.0051
0.0293 Interaction of st. aid with dep. dummy
20.0281 0.0040
0.0455 0.0124
0.0087 0.0727
Log of operating aid 0.0303
0.0152 0.0507
0.0080 0.0037
0.0442 Interaction of op. aid with dep. dummy
0.0011 0.0214
0.0948 0.0103
0.0074 0.0690
Log of categorical aid 0.0147
0.0113 20.0822
0.0037 0.0013
0.0210 Interaction of cat. aid with dep. dummy
20.0046 0.0131
20.0638 0.0107
0.0056 0.0909
Number of observations 16,801
9903 16,801
9903 16,310
9655 R
2
0.9065 0.9266
0.9710 0.9796
0.5494 0.6119
a
In addition to the variables given above, each regression includes year dummies.
aid per pupil given in Table 2, a 1 increase in operating aid per pupil would result in a 0.1685 increase in total
spending. A 1 increase in operating aid per pupil would translate into a 0.1271 increase in total spending.
Though these aid responses are low, they are within the range given by Bartle and are only slightly outside the
range given by Fisher.
A quick perusal of the estimates in Table 4 reveals that there is little evidence to support the claim that smaller
percentages of the aid increases in fiscally dependent dis- tricts show up in increased spending. In fact, while the
estimates imply that the elasticity of total spending with respect to total state aid is smaller in dependent districts,
the estimates also indicate that the elasticity of current spending with respect to operating aid is larger in the
fiscally dependent districts. In addition, the elasticity of both total and current spending with respect to total fed-
eral aid appears to be slightly larger in these districts, further support for the claim that aid elasticities in depen-
dent districts are not lower.
In conclusion, these estimates suggest that while fiscal dependency may matter, it does not appear to matter in
quite the manner that might have been expected. The results imply that levels of spending may be systemati-
cally lower in the fiscally dependent districts, though this conclusion must be viewed with caution. What does
seem clear is that there is little, if any, evidence that the general purpose governments to which these districts are
fiscally dependent “steal” a disproportionate share of state aid for education.
5. Policy options
