Chicago high school data

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

Like many states, Illinois publishes a “school report card” every year to assess the performance of each school. All data in this paper are taken from the Illinois State Board of Education’s School Report Card except for data on teachers and administrators. The number of teachers and administrators for each school and the aver- age teacher and administrator salaries are from the Chicago Panel on Public School Policy and Finance. Since the Chicago Panel’s data starts in fiscal 1989, Chicago’s high schools will be assessed here using the data for the fiscal years 1989 through 1994. 8 Several studies argue that the most appropriate method of measuring educational output is the value-added effects of school outcomes. The idea is that the school should be credited with producing improvements in edu- cational outcomes above and beyond previous test per- formance and the effects outside the control of the school including student background and parental input. Examples of this approach include Aitken Longford 1986, Boardman Murnane 1979, Hanushek 1986 and Hanushek Taylor 1990. In this paper we use the marginal effects method described in Aitken Longford 8 Fiscal 1995 is omitted because the Illinois State Board of Education changed its definition of the high school graduation rate in that year. The number of observations changes each year since schools were omitted when high school graduation rate and ACT score data were missing. 7 S. Grosskopf, C. Moutray Economics of Education Review 20 2001 1–14 1986, Hanushek Taylor 1990 and Grosskopf, Hayes, Taylor Weber 1998. 9 This is achieved by regressing test scores on measures of previous performance and other exogenous factors. Specifically, the following ordinary least squares regression is computed for each fiscal year t for the two ACT tests, math and English: TEST i,t 5b 1b 1 TEST i,t − 1 1b 2 LEP i,t 1b 3 LOW i,t 11 1b 4 MOB i,t 1e i,t In this equation TEST i,t is the average ACT score for a particular high school for fiscal year t. Similarly, TEST i,t 21 is a school’s average ACT score for the pre- vious fiscal year. 10 LEP i,t is the limited English pro- ficiency rate, and LOW i,t is the rate of students who qual- ify for school lunch assistance. MOB i,t is the mobility rate for each school and each fiscal year. According to the Illinois State Board of Education, this rate can exceed 100 percent since it counts both the number of students entering and exiting a school during the year. Finally, the estimated residual, e i,t , captures the average value- added effects. This model was estimated separately for ACT math and English scores. Using this method of estimated value-added effects, school districts that add less than the average of all Chicago high schools will have negative output meas- ures. Following Grosskopf et al. 1998, these residuals are normalized in the following manner to ensure non- negative values. YTEST i,t 5TEST t 1e i,t ∗TAKERS i,t 12 This measure of value-added effects for each school multiplies the number of students taking the ACT exams TAKERS i,t times the sum of the average ACT test score in either English or math for all Chicago high schools TEST t and the value-added residuals from Eq. 11 for each fiscal year e i,t . Adding the mean to the residual eliminates negative values. Multiplying by the number 9 For the purposes of comparison, we also estimated our model using levels rather than value-added effects. This did not produce significantly different results, and they are not reported here. 10 It would be preferable to regress the ACT English and math scores against some other exam, such as the tentheleventh grade Illinois Goals Assessment Program IGAP test scores. This would allow us to truly measure the value-added effects of a specific group of students. This is not possible, though, since the IGAP scores are not available for all of the years studied. Thus, Eq. 12 serves as a proxy for these value-added effects. We note that using ACT scores means that our measure ignores the value added to students who don’t take the ACT test. of test takers gives us an aggregate measure of the value- added in test scores, which is consistent with notions of production or distance functions. In all, our model includes four measures of output. The first two are the value-added effects from Eq. 12 for math and English. The two other outputs are based on the attendance and high school graduation rates for each individual school, which we include to capture other aspects of school performance. To be consistent with the specification of aggregate inputs and outputs rather than “rates”, we scale the rates up by enrollment in the high school for each fiscal year: ATT i,t 5ATTEND i,t ∗ENROLL i,t 13 HSG i,t 5HSGRAD i,t ∗ENROLL i,t 14 Thus, ATT i,t measures the average number of students attending school on the average day in a particular fiscal year. In Eq. 13, ATTEND i,t is the attendance rate, and ENROLL i,t is the total school enrollment. The state report card defines HSGRAD i,t as the number of entering 9th graders who end up graduating. However, since the ninth grade enrollment that serves as the denominator in this ratio is unknown, HSG i,t in Eq. 14 attempts to give the total number of high school graduates. We also include two variable and two fixed inputs. The variable inputs include the number of teachers and administrators. 11 We also include what we refer to as fixed inputs 12 to control for factors outside the control of the individual schools. Following Grosskopf et al. 1998, these fixed factors are computed as the predicted values from equation 12R. We transform these so that they are in levels rather than rates: XTEST i,t 5TEˆST i,t ∗ENROLL i,t 15 In this equation, TE ˆ ST i,t is the predicted value of the ACT score for a given fiscal school year. Recall that there are two tests: math and English. Table 1 reports means for a variety of variables for the public high schools in Chicago and for the rest of the state as a whole. Table 2 includes means and standard deviations of the variables used in our model for Chicago public high schools. The data are taken from the Illinois State Board of Education’s school report card and the 11 This data, as well as data on salaries, was provided by the Chicago Panel since the school report card only contains this information for each school district. 12 We have notified the definition of the indirect distance function to allow for a partition of the input vector into fixed and variable components. See Appendix A for how this is achi- eved computationally. 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