284 N. Daneshvary, T.M. Clauretie Economics of Education Review 20 2001 279–287
Table 2 Means and standard deviations for elementary schools’ academic year 1994–95
Variables Traditional schools
Year-round schools Mean
Std. dev. Mean
Std. dev. Per pupil costs US
Instruction 2932.85
449.48 2746.27
284.26 Administration
529.13 136.52
490.00 43.51
Operation 461.16
136.27 387.77
28.74 Support staff
589.53 165.53
556.04 40.95
Real estate 647.68
201.98 436.99
91.98 Total
5161.79 894.90
4635.83 353.02
Enrollment 593.35
163.21 840.69
183.70 Adjusted average daily attendance
555.21 154.39
550.42 190.24
Percent change in enrollment 1.07
15.07 6.88
10.27 Test performance
52.08 15.61
55.76 12.29
Percent receiving special education 13.04
4.33 10.46
3.15 Percent indicating English as a second language
8.38 10.21
9.4 11.04
Percent defined as gifted 7.42
4.09 7.12
0.98 Number of schools
89 26
Source: Clark County School District, District-wide school accountability report, for the school year 1994–95. See the text for a detailed definition of the variables.
Data for this study were obtained for 115 elementary schools in the Clark County, Nevada School District for
the academic year 1994–95.
7
All schools are within the same district so that there is no need to adjust the model
for differences in tax rates, revenues, instructional pay scales, or differences in financial administration. Of the
115 elementary schools, 89 had a traditional schedule and 26 had a year-round schedule in 1994–95. Table 2
shows the descriptive statistics for the variables included in the model, for both the traditional and year-round
schedule schools. Note that the average cost per student is US526 about 10 percent lower for the year-round
schools than for the traditional-schedule schools. Also, the savings extend to each category of costs.
As is shown in Table 2 the average enrollment is about 42 percent higher for the year-round schools. Note that
the adjusted average daily attendance for each school is nearly equal as it should be. The change in enrollment
is also substantial for year-round schools. In addition, a higher percentage 3.7 of fourth graders from year-
round schools than those from traditional schools scored above the national average on the standardized tests. The
year-round schedule schools also appear to have a lower percentage of students with special education needs.
7
As of the 1994–95 school year there were 123 elementary schools within the Clark County School District. Eight schools
were eliminated due to incomplete data.
4. Empirical results
Table 3 contains heteroskedasticity-corrected Ordinary Least Squares OLS estimates of per pupil costs for
instruction, administration, operations, support staff, real estate capital, and total per pupil cost.
8
Note that the coefficient estimates are generally robust across equations and are consistent with other studies
such as that of Barrow 1991 and Duncombe et al. 1995. The adjusted R-squares reveal that, depending
upon the equation, 36–74 percent of the variation of average costs across schools are explained by the model.
The signs and the magnitudes of the intercepts are as expected and are highly significant. Economies of size
are well documented by the negative and highly signifi- cant coefficients elasticities on the average daily attend-
ance variable. The coefficient of the test performance variable is statistically significant for the total per pupil
cost and per pupil instruction cost. Alternative measures of test performance such as mathematics, language, and
reading scores entered separately were tested with no significant alteration in the equations. As expected,
higher special education requirements increase total per
8
Using White’s test, all six estimated equations are tested for an unknown form of heteroscedasticity. The null hypothesis
of homoscedasticity is rejected for the administration and oper- ation equations. The standard errors of the OLS coefficients for
these two equations are re-estimated using White’s Heterosked- asticity Consistent Covariance method.
285 N. Daneshvary, T.M. Clauretie Economics of Education Review 20 2001 279–287
Table 3 Estimates of average cost for elementary schools’ academic year 1994–95. Dependent variable: log of per pupil average cost
a
Independent variables Total cost
Real estate Instruction
Administration Operations
Support Intercept
10.108 9.519
8.722 8.575
8.702 8.321
42.70 17.63
27.59 14.00
14.31 15.86
Log of adjusted average 20.283
20.536 20.161
20.374 20.422
20.319 daily attendance
8.18 6.78
3.49 4.27
4.87 4.15
Percent change in 20.002
20.002 20.002
20.002 20.002
20.0005 enrollment
2.84 1.11
2.25 1.15
1.61 0.311
Dummy variable for year- 20.078
20.370 20.029
20.053 20.131
20.024 round schools
4.00 8.31
1.10 1.40
3.28 0.565
Test performance 0.001
0.001 0.002
0.0006 20.0004
20.0009 1.74
1.11 2.53
0.314 0.241
0.521 Percent receiving special
0.009 0.011
0.010 0.005
0.007 0.007
education 4.25
2.06 3.26
1.04 1.49
1.45 Percent English as a
0.002 0.003
0.001 0.004
0.0007 0.003
second language 1.80
1.57 0.631
1.80 0.402
1.33 Percent defined as gifted
20.0003 0.006
0.0008 20.006
20.002 20.004
0.121 0.950
0.222 1.69
0.736 0.755
Adj-R
2
0.742 0.683
0.436 0.620
0.703 0.364
F-value 44.50
33.58 12.73
25.69 36.81
9.66
a
Note: , , : significant at 0.01, 0.05, 0.10 levels, respectively. Absolute t-values are reported in parentheses. See the text for a detailed definition of the variables.
costs and its components with the exception of adminis- tration and support. Costs are also higher where there
are more students with English as a second language due to an administrative cost component. More gifted stu-
dents appear not to have much impact on costs.
The results also demonstrate that a change to a year- round schedule produces added cost savings. Total costs
are reduced by 7.5 percent about US400 per pupil after controlling for average daily attendance and test
performance.
9
The largest impact of year-round school- ing is on the cost of real estate capital, where there is a
reduction of 31 percent in the per pupil cost. In dollar terms the cost savings is approximately US200 per
pupil. Because operating costs have large fixed cost components it is not surprising to see that there is a 12.3
percent reduction in per pupil costs of operations.
The empirical literature on school district consoli- dation reveals significant cost savings due to scale econ-
omies.
10
As is shown in Table 3, and similar to consoli- dation, a year-round schedule results in significant cost
savings even after controlling for test performance and average daily attendance.
9
The interpretation of a dummy variable where the depen- dent variable is in logarithms can be found by subtracting one
from the antilogarithm of the coefficient on the dummy vari- able: e
20.078
21 =
0.9249621 =
20.075.
10
Economies of scale is multidimensional and refers to quan- tity and quality aspects student achievement, school activities,
and mix of curriculum and economies of size see Fox, 1981; Duncombe et al., 1995.
The year-round versus traditional schedule selection process, described in Section 2, does not suggest that
either endogeneity or sample selectivity is likely to be a problem. The assignment of a school to year-round by
officials depends mainly on overcrowded enrollment and expected future population growth. To be certain, how-
ever, let us assume that, for example, parents of a parti- cular school are very concerned about their child’s edu-
cation, are active participants in the school, support year- round schooling, and help their children at home with
their education. The net effect of this parental involve- ment might be a lower cost of producing a given level
of student achievement. If this were the case, then it is not clear that the lower costs in these schools can be
attributed solely to year-round schooling. This implies potential endogeneity of test performance andor year-
round dummy variables.
11
To investigate the endogeneitysample selection prob- lem, we performed several versions of the Hausman test
Pindyck Rubinfeld, 1991, pp. 303–305; Maddala, 1992, pp. 506–513, 510–511. We tested for the exogen-
eity of the year-round and the test performance achievement variables separately. We also conducted a
joint test, using F-distributions, for exogeneity of the year-round and the test performance variables. The per-
11
We are grateful to an anonymous referee who brought up this potential endogeneitysample selection problem and sug-
gested using a Hausman test to see if our empirical results are affected.
286 N. Daneshvary, T.M. Clauretie Economics of Education Review 20 2001 279–287
Table 4 Estimates of quadratic average cost function for elementary schools’ academic year 1994–95. Dependent variable: per pupil
average cost
a
Independent variable Total cost
Real estate Instruction
Administration Operations
Support Intercept
7944.13 1290.03
2971.81 1275.99
1149.64 1256.65
14.20 8.72
27.84 14.02
13.31 8.07
Adjusted average daily 210.83
22.49 21.81
22.23 22.04
22.25 attendance
8.13 7.07
3.47 10.32
9.94 4.14
Adjusted average daily 0.007
0.002 0.001
0.002 0.001
0.002 attendance square
6.56 7.71
0.91 9.25
8.82 4.14
Percent change in 28.15
20.74 26.87
20.41 20.96
0.83 enrollment
2.25 0.77
2.48 0.69
1.71 0.82
Dummy variable for year- 2546.59 2222.41
2108.30 266.42
290.11 0.83
round schools 5.20
8.00 1.35
3.89 5.55
0.82 Test performance
28.15 1.79
6.81 20.27
20.32 0.07
1.91 1.60
2.11 0.39
0.49 0.06
Percent receiving special 44.65
10.09 26.27
1.39 1.90
4.99 education
3.75 3.21
2.89 0.72
1.03 1.51
Percent English as a 9.54
2.00 2.85
1.95 0.80
4.99 second language
1.96 1.55
0.77 2.46
0.11 1.51
Percent defined as gifted 23.22
2018 2.84
23.41 21.79
20.68 0.23
0.05 0.27
1.50 0.83
0.18 Adj-R
2
0.775 0.736
0.434 0.743
0.766 0.473
F-value 46.65
37.90 11.16
39.29 44.35
12.88
a
Note: , , : significant at 0.01, 0.05, 0.10 levels, respectively. Absolute t-values are reported in parentheses.
centage of students receiving free meals and the percent- age of teachers with a master’s degree were used as
instrumental variables.
12
The null hypothesis that the year-round and the test performance variables are not
exogenous, or that there is no simultaneity, could not be rejected for any of the six equations. In addition, the
significance level and the magnitude of the test perform- ance and the year-round variables did not change. Thus,
we
conclude that
there is
not a
serious endogeneitysample selection problem regarding year-
round and test performance variables in our data set.
5. Conclusion
