3 S. Grosskopf, C. Moutray Economics of Education Review 20 2001 1–14
1994 “. . . the Chicago panel revealed that one third of the targeted funds were being misappropriated and
diverted away from schools into central office bureau- cratic positions”. After the Chicago School Reform Act
of 1988, more of these funds reached the individual schools, which were then able to decide how these funds
would be used. In the 1993–94 school year, new dis- cretionary funds amounted to 491,000 for elementary
and 849,000 for high schools on average.
4
Current evidence on the impact of these reforms—in Chicago and elsewhere—is mixed. For instance, Eub-
anks Levine 1983 describe improvements in test scores in both Milwaukee and New York after school-
based planning committees were instituted to encourage more parent–teacher cooperation. Similarly, Rogers
Chung 1983 find improvements in reading and math scores in New York between 1970 and 1979. Meanwhile,
Sickler 1988a,b notes that standardized test scores rose and student and teacher absenteeism fell when the ABC
District in Cerritos, California gave teachers more con- trol over curriculum. While Steward 1991 finds posi-
tive gains in ACT scores at Tilden High School during the first few years after the Chicago site-based manage-
ment reform, Bryk et al. 1994 find no significant gains in improvement on the Iowa Test of Basic Skills for
grades one through eight in Chicago. In reviewing the literature, Malen, Ogawa Kranz 1990 conclude that
there is no consistent link between school-based manage- ment and student achievement.
Downes Horowitz 1994 provide some econo- metric evidence concerning the results of Chicago’s 1988
reform on outcomes. The authors analyze test score data from the Illinois Goals Assessment Program IGAP and
ACT to determine if decentralization positively or nega- tively affected student performance. They conclude that
IGAP reading test scores for grades 3, 6, and 8 decreased relative to other schools in the state after reform; on the
other hand, post-reform high school graduation rates and
4
In addition to site-based management, many Chicagoans want to establish other types of reforms. For instance, the Illi-
nois legislature has considered a plan that would establish a pilot voucher program similar to the one in Milwaukee. Accord-
ing to Harp 1995, this plan would shift 5 million from the Chicago school district’s budget to provide a 2,500 voucher
to low-income parents. The parents could then opt for a private or parochial school. The pilot program would start in the His-
panic neighborhoods of Pilsen and Little Village. This legis- lation passed the Illinois Senate, but it failed to get enough
votes in the Illinois House in May 1995. Thus, its future is uncertain. The second reform is the establishment of charter
schools that would allow individual schools, by escaping many state rules and regulations, to experiment with new teaching
techniques. According to Dizon Pearson 1996, Governor Jim Edgar signed the bill into law creating 15 charter schools
in Chicago, 15 in the suburbs, and 15 downstate.
ACT scores have increased relatively. The authors find lower outcomes after reform for those Chicago schools
with a larger percentage of students with limited English proficiencies LEP and a larger percentage of students
who qualify for low-income school lunch assistance. Thus, they write the following:
The negative relationship between post-reform suc- cess and the relative size of a school’s at-risk popu-
lation appears to imply that decentralization may not be the answer for urban school systems, since the
result seems to indicate individual Chicago schools failed to benefit from additional control over Chapter
1 funds.
Despite the political and social momentum that appears to be building around changing the status quo,
there is still very little empirical evidence on the success of educational reform in improving school outcomes.
There are several reasons for this. One reason is that the first experiments in reform that do exist are recent, and
therefore, there is little post-reform data. Another prob- lem is the difficulty in measuring performance. For
instance, it is not obvious how to measure outputs, and it is not clear how best to model exogenous factors such
as the role of the family. This measurement debate has been well-documented in the literature; it is perhaps best
summarized in Hanushek 1986.
In this paper, we propose to address some of these problems and measure the performance of Chicago high
schools during the site-based management experiment, i.e., 1989–1994. In terms of a measure of performance,
we follow Grosskopf, Hayes, Taylor Weber 1999 and actually measure potential gains from allowing for
the type of decentralized decision-making that should occur under site-based management. This is achieved by
using cost indirect output distance functions due to Shephard 1953, 1974 which we use to construct our
productivity measures. One advantage of this model and technique is that it readily allows for multiple outputs or
educational outcomes and explicitly includes a budget constraint. As educational outputs we include measures
of changes in test scores which have been corrected for student characteristics and previous performance, i.e., we
include measures of the value-added in terms of test scores due to the school. We also include two other mea-
sures of school success which the current Daley-led sys- tem also employs as school performance benchmarks:
graduation rates and degree of truancy. We turn next to a discussion of our performance measures.
3. Performance measurement
Again, one of the goals of this paper is to model a decentralized system in which local councils have con-
4 S. Grosskopf, C. Moutray Economics of Education Review 20 2001 1–14
trol over their budgets. We follow Grosskopf et al. 1999 and use indirect output distance functions to achi-
eve that goal. Shephard type distance functions are generalizations
of a production function to the multiple output case.
5
They provide a complete description of technology and also have a built-in interpretation as a performance meas-
ure: they are reciprocals of Farrell 1957 technical efficiency measures. We begin with what we call the
direct output distance function. In terms of notation, let x denote a N-dimensional non-negative vector of inputs,
which are used to produce a M-dimensional vector of non-negative outputs, y. The most basic description of
technology in this multiple-output case is the production possibilities set, which we denote Px. It is the set of
all outputs producible from the given input vector x.
The formal definition of the direct output distance function is:
D
o
x,y 5min
q
{ q.0:yqePx} where xPR
N t
, yPR
M t
. 1
In this definition, 1 q is the proportion that the vector
of outputs y could feasibly be expanded to reach the frontier or boundary of the production possibilities set.
This is illustrated for a two output case in Fig. 1. Point A represents a school which is using input vector x, but
is producing an output vector that is interior to the boundary of the production possibilities set, Px; i.e.,
school A is using the given input vector x, but is not achieving maximum potential output. The value of the
direct output distance function for this observation can be written as:
D
o
x,y 5
0A 0U
. 2
Thus, in order to expand an inefficient observation, such as A, up to the frontier, the value of the direct output
distance function would have to be smaller than one. Note that observations on the boundary of the set would
have values equal to one, i.e., no further scaling of out- puts are possible.
More generally, the production possibilities set or output set can be characterized as:
Px 5{y:D
o
x,y 1}.
3 Under site-based management, however, individual
schools have some control over input choices, as long as they do not exceed their budgets. With this in mind,
we follow Grosskopf et al. 1999 and use cost indirect
5
As shown by Shephard 1953, distance functions also satisfying nice duality properties.
output distance functions to model education production under site-based management. Following Shephard
1974, the cost indirect output distance function is defined as follows:
ID
o
p
v
c,y 5min
l
{ l.0:ylPIPp
v
c}. 4
In this equation p
v
represents the vector of variable input prices, and total variable cost is denoted as c. The
indirect production set, IPp
v
c, illustrates the combi- nations of outputs which are feasible given the budget
constraint. This can be expressed as: IPp
v
c 5{y:yPPx, p
v
x
v
c}. 5
Instead of variable inputs being given as in the direct output distance function, they are chosen subject to satis-
faction of the budget constraint. Thus, the indirect dis- tance function helps model the decentralized control over
input choices which is a keystone of site-based manage- ment.
Analogous to the direct output distance function, 1 l
is the proportion that the vector of outputs y could feasi- bly be expanded to reach the indirect production possi-
bilities frontier. In addition, the indirect output distance function at observation A equals:
ID
o
p
v
c,y 5
0A 0T
. 6
Returning to Fig. 1, in order for observation A to be expanded up to the frontier, the value of the indirect out-
put distance function would be smaller than one. Schools are efficient in the Farrell sense for both direct and
indirect output distance functions if they equal one.
Since, at least in principle, Chicago’s site-based man- agement reforms decentralized the overall budget
decisions of the individual schools, the individual schools had more control over the choice of the appropri-
ate choice of inputs subject to their budget constraint. Decentralization, it was hoped, would increase the level
of potential output, which in our model is illustrated by the fact that the indirect output set is “larger than” the
direct output set, giving the school more choice in terms of inputs.
In estimating the distance functions, we use the same techniques employed in data envelopment analysis
DEA. This approach uses linear programming tech- niques to form IPp
v
c and measure the “distance” to the frontier. The standard DEA reference is Charnes,
Cooper Rhodes 1978; see also Fa¨re, Grosskopf Lovell 1985. Those school districts which produce the
most outputs from a given vector of inputs form an “envelope” which approximates the production possi-
bilities frontier. The linear programming problems to
5 S. Grosskopf, C. Moutray Economics of Education Review 20 2001 1–14
Fig. 1. Direct and indirect output distance functions. Source: Grosskopf et al. 1999.
compute the indirect output distance functions are included in Appendix A.
6
The discussion up to this point has concentrated on a static analysis of technical efficiency; next we turn to a
comparative static model, which computes performance over time, namely productivity change. Specifically, we
begin with
the Malmquist
productivity index
as described in Fa¨re, Grosskopf, Lindgren Roos 1989
and Fa¨re Grosskopf 1994 but modified to the indirect case as in Fa¨re et al. 1985. The Malmquist productivity
index was first proposed by Caves, Christensen Diew- ert 1982. Computations in a DEA framework and the
technique of separating this index into technical inno- vation and efficiency change was later developed by Fa¨re
et al. 1989. This procedure has been applied to many
6
Several recent studies have used DEA type approaches in assessing the technical efficiency of individual school districts.
For example, studies applying DEA to education include Bessent Bessent 1980; Bessent, Bessent, Kennington
Reagan 1982 and Charnes et al. 1978. Later, Jesson, Mays- ton Smith 1987 and Barrow 1991 used DEA to analyze
local education authorities in England. In a more recent study, McCarty Yaisawarng 1993 measure technical efficiency in
New Jersey schools. Meanwhile, Fare, Grosskopf Weber 1989 concentrate on Missouri schools, and Grosskopf et al.
1999 compute the potential gain from deregulating Texas school districts.
topics; for example, Fa¨re, Grosskopf, Lindgren Roos 1992 study productivity changes in Swedish phar-
macies, and Fa¨re, Grosskopf, Norris Zhang 1994 analyze productivity growth in industrialized countries.
The aforementioned studies used a Malmquist index based on direct output distance functions. Since we will
be analyzing productivity of Chicago schools under site- based management, we instead use a Malmquist index
based on indirect output distance functions, following Fa¨re et al. 1985.
7
Fig. 2 illustrates the concept of the Malmquist indirect productivity index assuming constant returns to scale.
This diagram uses two technologies, S
t
and S
t +
1
, for two time periods. The total cost of the variable inputs is again
denoted as c. In this situation, all points lying below the technology S
t
are technically inefficient; point F is an example of such an observation. Given the budget con-
straint, the production set S
t
is defined as: S
t
5{x
t
,y
t
:y
t
PIP
t
p
t v
c
t
} where x
t
PR
N +
,y
t
PR
M +
. 7
Time period t +
1 provides another technology S
t +
1
which lies above the first; thus, more output can be achi- eved with the same budget. Point B is an example of a
technically inefficient observation at time period t +
1.
7
See also Fa¨re Grosskopf 1994.
6 S. Grosskopf, C. Moutray Economics of Education Review 20 2001 1–14
Fig. 2. Malmquist indirect output-based productivity index.
The Malmquist productivity index computes the change in performance between t and t
+ 1.
Given the output distance functions defined earlier, Caves et al. 1982 CCD proposed measuring pro-
ductivity as the ratio of two distance functions at periods t and t
+ 1. CCD make the assumption that there is no
technical inefficiency. Fa¨re et al. 1989 relax this assumption and express the output-based Malmquist pro-
ductivity index as the geometric mean of two CCD indexes. Following Fa¨re Grosskopf 1994 and Fa¨re
et al. 1985, the indirect version of this index is:
IM
o
p
v
c
t+1
,y
t+1
,p
v
c
t
,y
t
8 5
F
ID
t o
p
v
c
t+1
,y
t+1
ID
t o
p
v
c
t
,y
t
ID
t+1 o
p
v
c
t+1
,y
t+1
ID
t+1 o
p
v
c
t
,y
t
G
12
This geometric mean can be decomposed into two parts as:
IM
o
5 ID
t 11
o
p
v
c
t 11
,y
t 11
ID
t o
p
v
c
t
,y
t
9
F
ID
t o
p
v
c
t 11
,y
t 11
ID
t 11
o
p
v
c
t 11
,y
t 11
ID
t o
p
v
c
t
,y
t
ID
t 11
o
p
v
c
t
,y
t
G
12
Using this formulation, it is possible to isolate both the change in technical efficiency and the change in tech-
nical innovation between the years t and t +
1. The first term in Eq. 10 is the efficiency change measure. The
square root term is the technical change portion. In geo- metric terms using Fig. 2, the indirect version of the
Malmquist productivity index can be given as:
IM
o
5 0B
0A 0E
0F
F
0A 0D
0C 0E
G
12
10 If there is an improvement in technical efficiency over
the two time periods, the Malmquist index will be greater than one; a decline in productivity will produce an index
that is less than one. The two component measures have a similar interpretation. As mentioned earlier we use
DEA type techniques to estimate the indirect output dis- tance functions used to construct the productivity index.
These productivity indexes allow us to look at whether performance under site-based management improved
over the 1989–94 time period.
To conclude the discussion on the Malmquist pro- ductivity index, Fa¨re Grosskopf 1990 cite its advan-
tages over the Fisher or To¨rnqvist indexes. First, since both the Fisher and To¨rnqvist indexes require price and
quantity data on both inputs and outputs, they might be difficult to use in education and other industries where
output prices, for example, are not available. The Malmquist indirect productivity index, on the other hand,
does not require output price data which makes it the more practical choice for education research. The second
advantage is the fact that, unlike the Fisher and To¨rnqvist indexes, the Malmquist index can be applied to cases
where profit maximization is not presumed to prevail.
4. Chicago high school data
