8 S. Grosskopf, C. Moutray Economics of Education Review 20 2001 1–14
Table 1 Means for Chicago and Illinois high schools, 1989–1994
a
1989 1990
1991 1992
1993 1994
Chicago n
= 60
n =
60 n
= 60
n =
60 n
= 61
n =
61 Illinois
n =
677 n
= 667
n =
664 n
= 657
n =
648 n
= 647
Percentage of white students Chicago
11.997 11.307
10.598 10.135
9.964 9.890
Illinois 84.036
83.691 83.001
83.042 82.560
82.162 Total school enrollment
Chicago 1728.417
1647.250 1610.267
1624.167 1605.639
1584.919 Illinois
767.532 752.936
749.566 769.254
793.111 805.685
Percentage of LEP students Chicago
2.817 4.155
4.972 5.805
6.841 7.536
Illinois 0.694
0.933 1.085
1.160 1.324
1.430 Low-income students
Chicago 36.295
37.650 43.415
57.302 56.792
69.282 Illinois
14.376 14.689
15.945 17.121
18.132 20.530
Mobility rate Chicago
27.872 28.352
27.895 27.215
28.439 24.221
Illinois 15.011
14.910 15.149
14.489 14.690
14.927 Attendance rate
Chicago 80.483
79.982 79.707
79.879 77.656
77.656 Illinois
92.355 92.516
92.416 92.537
92.363 92.021
HS graduate rate Chicago
45.615 46.460
43.347 48.028
49.562 49.562
Illinois 85.301
84.600 85.284
85.226 85.606
80.666 Average ACT English score
Chicago 15.050
b
15.363 15.063
14.898 14.618
14.618 Illinois
20.152
b
20.521 19.950
19.866 20.046
19.985 Average ACT math score
Chicago 15.883
b
15.893 15.908
16.061 15.830
15.830 Illinois
19.318
b
19.818 19.814
20.005 20.185
20.075 Number of teachers
c
Chicago 110.443
107.642 107.492
106.802 105.962
94.780 Average teacher salary
c
Chicago 33044.754
34904.138 35018.49
37787.151 41887.728
41036.428 Number of admin.
c
Chicago 4.063
4.093 3.828
2.813 3.358
3.423 Average admin. salary
c
Chicago 43070.100
44128.171 45377.372
52057.411 53480.715
52834.667
a
Sources: Compiled by the authors using data taken from the Illinois State Board of Education, Chicago Panel on Public School Policy and Finance, and ACT 1989.
b
Concordant value.
c
State averages not available.
teacher and administrator data compiled from the Chicago Panel on Public School Policy and Finance.
Table 1 illustrates the striking difference in character- istics between public high schools in Chicago and in the
state as a whole. Chicago schools have relatively more nonwhite students, bigger enrollments, lower graduate
rates, higher truancy, and lower scores. As shown in Appendix C, these differences are often statistically sig-
nificant based on simple z-tests.
13
Turning to Table 2 which includes descriptive stat- istics of the variables included in our model, we see that
the data are fairly stable over time. In addition, standard deviations are generally smaller than the means, suggest-
ing some degree of homogeneity within the sample.
13
It should be noted at this point that since the American Collegiate Test ACT changed its format in 1989, the scores
for 1989 are not automatically comparable with those for 1990– 1994. Thus, the earlier scores for each individual school have
been adjusted using a concordance table distributed by ACT; the new scores approximate those consistent with the newer
“enhanced” ACT test given in recent years. A copy of the con- cordance tables appears in Appendix B .
5. Chicago high school malmquist productivity index
In this section we explicitly account for changes in the performance of Chicago high schools over time by
estimating productivity change using the Malmquist pro- ductivity index described earlier.
In calculating this index for Chicago high schools, only the sixty observations that appear in all six fiscal
years are included. Although we estimate indexes for each high school for each pair of years, we summarize
the results in Table 3. Included are the geometric means of the indirect Malmquist productivity index and all of
its components, the efficiency change and the technology change indices for each pair of fiscal years. The last col-
umn, which is outlined, shows the overall changes between fiscal year 1989 and 1994, averaged over the
60 schools.
Recall that values equal to one represent no change for the pairs of years; improvement is signified by values
greater than one. In glancing over the numbers in the last column, since the technical innovation change index
for all Chicago public high schools is 0.977, the pro-
9 S. Grosskopf, C. Moutray Economics of Education Review 20 2001 1–14
Table 2 Means for Chicago high school inputs and outputs, 1989–1994 Standard deviations in parentheses
a
1989 1990
1991 1992
1993 1994
Inputs: Number of teachers
110.443 107.642
107.492 106.802
105.962 94.780
38.212 35.839
36.892 35.838
37.203 31.463
Avg. teacher salary 33044.754
34904.138 35018.149
37787.151 41887.728
41036.428 899.388
933.360 1019.953
1240.670 1195.129
1124.551 Number of administrators 4.063
4.093 3.828
2.813 3.358
3.423 1.517
0.948 1.048
0.869 1.309
1.336 Avg. admin. salary
43070.100 44128.171
45377.372 52057.411
53480.715 52834.667
2526.711 3445.006
3368.020 4326.771
4115.021 4330.407
XTEST English ACT 26439.294
25837.269 24845.766
24681.069 24450.248
23651.386 12318.535
12349.963 12366.053
12366.053 12670.123
12359.530 XTEST Math ACT
27788.364 26621.969
26087.068 26518.869
26170.135 25591.733
12015.385 12045.309
12292.520 12394.690
12820.066 12607.778
Outputs: ATT
1405.999 1335.103
1302.979 1315.845
1283.241 1251.470
578.836 565.805
579.766 579.182
593.876 583.523
HSG 823.128
791.992 740.131
818.316 805.533
819.209 559.918
483.784 532.303
562.745 517.026
547.751 YTEST English ACT
2242.069 2266.313
2202.348 2166.948
2208.623 2130.208
2046.988 1799.375
1775.004 1749.573
1737.715 1848.956
YTEST Math ACT 2352.207
2336.398 2327.326
2334.563 2371.899
2304.535 2064.253
1819.594 1887.275
1866.835 1864.369
1955.770
a
Sources: Compiled by the authors using data taken from the Illinois State Board of Education, Chicago Panel on Public School Policy and Finance, and ACT 1989.
Table 3 Geometric means of Chicago high school Malmquist productivity index results
a
Fiscal years Fiscal years
Fiscal years Fiscal years
Fiscal Years Fiscal years
1989 and 1990 1990 and 1991
1991 and 1992 1992 and 1993
1993 and 1994 1989 and 1994
Malmquist productivity 0.973
1.005 1.006
0.987 1.013
0.982 index
n =
60 n
= 60
n =
60 n
= 60
n =
60 n
= 60
Malmquist ,1
0.941 0.971
0.946 0.985
0.952 0.931
n =
37 n
= 37
n =
26 n
= 39
n =
23 n
= 35
Malmquist .1
1.027 1.053
1.054 1.042
1.053 1.058
n =
23 n
= 26
n =
34 n
= 21
n =
37 n
= 25
Efficiency change index 0.995
1.011 1.006
0.994 0.999
1.006 n
= 60
n =
60 n
= 60
n =
60 n
= 60
n =
60 Efficiency change
,1 0.953
0.970 0.956
0.960 0.955
0.941 n
= 26
n =
21 n
= 24
n =
29 n
= 27
n =
24 Efficiency change
.1 1.028
1.034 1.040
1.028 1.037
1.051 n
= 34
n =
39 n
= 36
n =
31 n
= 33
n =
36 Technical change index
0.978 0.995
1.000 0.992
1.013 0.977
n =
60 n
= 60
n =
60 n
= 60
n =
60 n
= 60
Technical change ,1
0.967 0.980
0.971 0.983
0.991 0.964
n =
46 n
= 38
n =
23 n
= 44
n =
26 n
= 48
Technical change .1
1.015 1.020
1.018 1.018
1.031 1.029
n =
14 n
= 22
n =
37 n
= 16
n =
34 n
= 12
a
Sources: Compiled by the authors using data taken from the Illinois State Board of Education, Chicago Panel on Public School Policy and Finance, and ACT 1989.
10 S. Grosskopf, C. Moutray Economics of Education Review 20 2001 1–14
Table 4 OLS results of time trend equations for the Malmquist productivity index, 1989–1994 Standard errors in parenthesis
a
Dependent variable Intercept Time
change in change in change in Adjusted R
2
F-value Durbin-
adm.teacher personnel the of
Watson ratio
expenditures white per student
Students Malmquist
1.005
b
0.002 0.00002
20.001
b
0.00002 0.0721
6.812 1.933
productivity index 0.004
0.003 0.0001
0.0003 0.00007
Efficiency change 1.005
b
20.002 0.00003
20.0005
d
0.00001 index
0.003 0.002
0.00001 0.0003
0.00006 0.0001
1.008 2.012
Technical change 1.002
c
0.004
c
20.00001 20.001
c
0.000006 0.1553
14.745 1.921
index 0.002
0.002 0.00006
0.0002 0.00004
a
Sources: Compiled by the authors using data taken from the Illinois State Board of Education, Chicago Panel on Public School Policy and Finance, and ACT 1989.
b
Significant at the 1 percent level of significance.
c
Significant at the 5 percent level of significance.
d
Significant at the 10 percent level of significance.
duction possibilities frontier for these schools has shifted inward slightly on average between 1989 and 1994.
There is, however, a slight increase in efficiency on aver- age at the high schools. The overall average change in
productivity, however, is negative.
Looking at the more disaggregated results, we see that there is a nearly even split between schools that
improved in terms of productivity and those that declined. In addition, the average productivity vacillates
around one on average over this time period. The same pattern occurs for the two components of productivity
change. Note, however, that over half of the schools con- sistently achieve improvements in the efficiency change;
i.e., they are catching up to the frontier over time.
To determine if there are any significant changes, we include a regression model in which our productivity
change, technical change, and efficiency change meas- ures are dependent variables. Independent variables
include a time trend, the change in the ratio of adminis- trators to teachers, the change in per pupil expenditures,
and the change in the percent of students who are white. The results are summarized in Table 4.
Although we find no significant time trend in the pro- ductivity index or the efficiency change index, there is
a small but significant improvement in the technical change index. The only other significant variable is the
per pupil expenditure variable, which is consistently small but negative in all three regressions, i.e., schools
with greater per pupil expenditure are associated with lower productivity. Finally, if we interpret the intercept
term as the average value of our measures after con- trolling for our independent variables, we find that we
can reject the hypothesis that the efficiency change inter- cept is equal to one at the ten-percent level of signifi-
cance, based on a simple t-test.
14
This suggests that there has been a measured improvement in the efficiency of
Chicago high schools on average over this time period. On the other hand, we cannot reject this hypothesis for
the other index measures.
6. Concluding remarks
