Abstract
Would you prefer a tighter or a more prolonged exam schedule? Would you prefer to take an important exam first or last? We exploit quasirandom variation in exam schedules across cohorts, grades and subjects from a lottery to identify distinct effects of the number of days between exams, the number of days since the first exam, and the exam order on performance. Scheduling effects are more pronounced for STEM exams. We find a positive and a negative relationship between STEM scores and exam order (warmup) and number of days since the first exam (fatigue), respectively. In STEM, warmup is estimated to outweigh fatigue. Marginal exam productivity in STEM increases faster for boys than for girls. Higherperforming students exhibit higher warmup and lower fatigue effects in STEM than lowerperforming students. Optimizing the exam schedule can improve overall performance by as much as 0.02 standard deviations.
References
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Appendices
A Example of Exam Schedule
B Supplementary Descriptive Statistics
In this section, we provide supplementary descriptive tables of studentlevel data. Table 11, Table 12, and Table 13 provide studentlevel summary statistics for each cohort for students in the 10th grade, 11th grade, and overall, respectively. We find that students characteristics are substantially similar across cohorts and grades.
Year  Female  Age  GPA  Midterm score  Final exam score  Retained  

2002  Mean  0.60  15.84  14.69  16.76  12.81  0.00 
SD  0.49  0.43  2.81  1.80  3.80  0.00  
N  91  91  91  91  91  91  
2003  Mean  0.50  15.76  15.33  17.18  13.50  0.00 
SD  0.50  0.48  2.99  1.79  4.21  0.00  
N  86  86  86  86  86  86  
2004  Mean  0.66  15.88  15.88  17.40  14.21  0.01 
SD  0.47  0.55  2.43  1.61  3.55  0.10  
N  101  101  100  101  101  101  
2005  Mean  0.48  15.81  14.98  16.68  13.05  0.02 
SD  0.50  0.44  3.04  2.12  4.14  0.14  
N  95  95  93  95  95  95  
2006  Mean  0.53  15.95  15.10  17.06  13.14  0.01 
SD  0.50  0.35  2.49  1.62  3.44  0.10  
N  108  108  107  108  108  108  
2007  Mean  0.57  16.06  15.30  17.09  12.90  0.04 
SD  0.50  0.36  2.73  1.99  4.35  0.20  
N  116  116  111  116  116  116  
2008  Mean  0.55  16.03  15.24  17.32  13.20  0.00 
SD  0.50  0.17  2.98  1.92  4.03  0.00  
N  98  98  98  98  98  98  
2009  Mean  0.47  16.02  15.99  17.62  14.38  0.00 
SD  0.50  0.15  2.22  1.44  3.03  0.00  
N  92  92  92  92  92  92  
2010  Mean  0.57  16.04  15.99  17.71  14.09  0.01 
SD  0.50  0.19  2.52  1.52  3.84  0.09  
N  113  113  112  113  113  113  
Total  Mean  0.55  15.94  15.40  17.21  13.47  0.01 
SD  0.50  0.38  2.72  1.79  3.87  0.10  
N  900  900  890  900  900  900 

Notes: This table presents the mean, standard deviation, and number of observations for a set of variables by year (2002–2010) for students in 10th grade. Variables include gender, age, GPA (between 0 and 20), midterm score (between 0 and 20), final exam score (between 0 and 20), and a dummy that indicates whether a student is retained.
Year  Female  Age  GPA  Midterm score  Final exam score  Retained  

2002  Mean  0.61  16.70  12.05  16.54  10.82  0.12 
SD  0.49  0.46  3.17  1.86  3.65  0.32  
N  102  102  90  102  102  102  
2003  Mean  0.63  16.85  14.83  17.18  12.16  0.06 
SD  0.49  0.48  2.80  1.87  4.11  0.24  
N  84  84  79  84  84  84  
2004  Mean  0.52  16.78  15.34  17.44  12.59  0.06 
SD  0.50  0.47  3.04  2.04  4.99  0.25  
N  79  79  74  79  79  79  
2005  Mean  0.66  16.93  15.13  16.81  13.08  0.05 
SD  0.48  0.82  2.69  1.93  4.18  0.22  
N  99  99  94  99  99  99  
2006  Mean  0.50  16.86  15.09  16.88  13.26  0.02 
SD  0.50  0.63  3.12  2.16  4.27  0.15  
N  88  88  86  88  88  88  
2007  Mean  0.56  17.01  15.39  17.39  13.46  0.02 
SD  0.50  0.60  2.43  1.52  3.69  0.14  
N  103  103  101  103  103  103  
2008  Mean  0.58  17.01  15.79  17.76  14.08  0.00 
SD  0.50  0.10  2.59  1.49  3.62  0.00  
N  103  103  103  103  103  103  
2009  Mean  0.59  17.03  15.74  17.72  13.85  0.01 
SD  0.49  0.18  2.84  1.72  4.02  0.11  
N  90  90  89  90  90  90  
2010  Mean  0.47  17.05  15.84  17.93  14.23  0.00 
SD  0.50  0.26  2.47  1.33  3.38  0.00  
N  88  88  88  88  88  88  
Total  Mean  0.57  16.92  15.03  17.29  13.06  0.04 
SD  0.50  0.51  2.99  1.83  4.10  0.19  
N  836  836  804  836  836  836 

Notes: This table presents the mean, standard deviation, and number of observations for a set of variables by year (2002–2010) for students in 11th grade. Variables include gender, age, GPA (between 0 and 20), midterm score (between 0 and 20), final exam score (between 0 and 20), and a dummy that indicates whether a student is retained.
Year  Female  Age  GPA  Midterm score  Final exam score  Retained  

2002  Mean  0.61  16.29  13.38  16.65  11.76  0.06 
SD  0.49  0.62  3.26  1.83  3.84  0.24  
N  193  193  181  193  193  193  
2003  Mean  0.56  16.29  15.09  17.18  12.84  0.03 
SD  0.50  0.73  2.90  1.83  4.20  0.17  
N  170  170  165  170  170  170  
2004  Mean  0.60  16.28  15.65  17.41  13.50  0.03 
SD  0.49  0.69  2.71  1.80  4.30  0.18  
N  180  180  174  180  180  180  
2005  Mean  0.57  16.38  15.05  16.75  13.06  0.04 
SD  0.50  0.87  2.86  2.02  4.15  0.19  
N  194  194  187  194  194  194  
2006  Mean  0.52  16.36  15.10  16.98  13.19  0.02 
SD  0.50  0.67  2.78  1.88  3.83  0.12  
N  196  196  193  196  196  196  
2007  Mean  0.57  16.51  15.34  17.23  13.16  0.03 
SD  0.50  0.68  2.59  1.79  4.05  0.18  
N  219  219  212  219  219  219  
2008  Mean  0.57  16.53  15.52  17.55  13.65  0.00 
SD  0.50  0.51  2.79  1.72  3.84  0.00  
N  201  201  201  201  201  201  
2009  Mean  0.53  16.52  15.87  17.67  14.12  0.01 
SD  0.50  0.53  2.54  1.58  3.56  0.07  
N  182  182  181  182  182  182  
2010  Mean  0.52  16.48  15.93  17.81  14.15  0.00 
SD  0.50  0.55  2.49  1.44  3.64  0.07  
N  201  201  200  201  201  201  
Total  Mean  0.56  16.41  15.23  17.25  13.27  0.02 
SD  0.50  0.66  2.85  1.81  3.99  0.15  
N  1736  1736  1694  1736  1736  1736 

Notes: This table presents the mean, standard deviation, and number of observations for a set of variables by year (2002–2010) for students in 10th and 11th grade. Variables include gender, age, GPA (between 0 and 20), midterm score (between 0 and 20), final exam score (between 0 and 20), and a dummy that indicates whether a student is retained.
Table 14 shows examlevel descriptive statistics for males and females for STEM subjects, nonSTEM subjects, and overall. We find that males and females seem to have similar midterm and final exam scores in STEM subject, while females have slightly higher average midterm and final exam scores in nonSTEM subjects than males.
STEM exams 
NonSTEM exams 


Gender  Midterm  Final exam  Midterm  Final exam  
Male  Mean  16.96  12.26  16.93  13.32 
SD  2.54  6.00  2.52  4.93  
N  5680  5036  5214  5233  
Female  Mean  17.18  12.39  17.78  14.59 
SD  2.46  6.04  2.18  4.76  
N  6651  5995  7138  7150  
All  Mean  17.08  12.33  17.42  14.05 
SD  2.50  6.02  2.36  4.87  
N  12331  11031  12352  12383 

Note: This table presents the mean, standard deviation, and number of observations for STEM and nonSTEM exams, for males and females (but also combined), separately, for the following variables: midterm score (between 0 and 20) and final exam score (between 0 and 20).
C Balancing Tests
One potential concern is whether exam scheduling is consistent with a random process and orthogonal to student characteristics. We deploy balancing tests to examine whether there is any systematic association between the exam scheduling variables and student characteristics, such as age, gender, or prior performance in each subject. Exam scheduling varies across year and grade configurations. To answer whether student characteristics vary along the same dimensions as exam scheduling, we regress each student characteristic on the full set of year by grade dummies. Table 15 presents the results across all students. Columns 1, 2, and 3 show the variation of midterm score, gender, and age, respectively, across all year by grade configurations. Columns 3 controls for grade fixed effects, as age is anticipated to change with grade. The coefficients of the year by grade dummies across all columns of Table 15 are in general small and not statistically significant. The F test for the collective equivalence of the coefficients of the year by grade dummies to zero accepts the null hypothesis of equivalence in each column. We conclude that there is no significant association between exam scheduling and students’ prior characteristics, reinforcing our confidence in the randomization process of exam scheduling.
Variables  (1)  (2)  (3) 

Midterm score  Female  Age  
2002 × Grade 10  0.000  0.000  0.000 
(0.000)  (0.000)  (0.000)  
2002 × Grade 11  –0.058  0.003  
(0.141)  (0.108)  
2003 × Grade 10  –0.037  –0.104  0.000 
(0.092)  (0.089)  (0.000)  
2003 × Grade 11  –0.038  0.027  –0.028 
(0.088)  (0.087)  (0.018)  
2004 × Grade 10  –0.057  0.059  0.004 
(0.123)  (0.073)  (0.004)  
2004 × Grade 11  –0.015  –0.085  –0.015* 
(0.113)  (0.130)  (0.009)  
2005 × Grade 10  –0.085  –0.120*  0.000 
(0.105)  (0.067)  (0.000)  
2005 × Grade 11  0.003  0.052  0.041 
(0.130)  (0.084)  (0.036)  
2006 × Grade 10  –0.008  –0.077  –0.000 
(0.131)  (0.060)  (0.000)  
2006 × Grade 11  –0.065  –0.104*  0.014 
(0.085)  (0.059)  (0.013)  
2007 × Grade 10  –0.078  –0.035  –0.002 
(0.132)  (0.056)  (0.004)  
2007 × Grade 11  –0.006  –0.041  0.009 
(0.120)  (0.060)  (0.034)  
2008 × Grade 10  –0.126  –0.053  –0.000 
(0.128)  (0.064)  (0.000)  
2008 × Grade 11  0.035  –0.022  –0.007 
(0.073)  (0.062)  (0.006)  
2009 × Grade 10  –0.067  –0.137*  –0.000 
(0.108)  (0.073)  (0.000)  
2009 × Grade 11  –0.012  –0.016  –0.021* 
(0.090)  (0.076)  (0.012)  
2010 × Grade 10  –0.061  –0.038  –0.000 
(0.086)  (0.058)  (0.000)  
2010 × Grade 11  –0.020  –0.138*  –0.010 
(0.079)  (0.074)  (0.015)  
Observations  1,736  1,736  1,736 
Rsquared  0.002  0.014  0.939 
FStat Pvalue  0.982  0.296  0.640 
Grade FE  No  No  Yes 

Notes: The dependent variable in column (1) is the standardized midterm score, in column (2) the gender of each student, and in column (3) the age of each student. Results in each column come from a separate OLS regression across all students. Clusterrobust standard errors at the classroom by year level are reported in parentheses. * p < 0.1; ** p < 0.05; *** p < 0.01.
D Variation Sufficiency
Exam scheduling variables vary across years, grades, and subjects. There are two grades (10th and 11th) and nine cohorts. Each subject is tested once for each grade in a given year. Therefore, each scheduling variable takes 18 (two grades × nine cohorts) values for each subject in our data. We illustrate the variation in exam scheduling in Table 16, Table 17, and Table 18. Table 16 shows how Days between Exams varies across subjects. Each entry in Table 16 shows how frequently the subject in that column was tested in the number of days since the previous exam shown in that row. The maximum number of days students have between exams is 5 days, as shown in the first column of Table 16. As an illustration, algebra was tested on the same day as the previous exam zero times, 2 days after the previous exam seven times, and so on. History was tested on the same day as the previous exam zero times, 1 day after the previous exam twice, and so on. At the bottom of Table 16 we report the mean and standard deviation of the number of days elapsed since the previous exam for each subject. We observe considerable withinsubject variation in the time since the previous exam. On average, English and modern Greek have the shortest average time since the previous exam compared to other subjects, although we do not see any systematic differences in the testing pattern of STEM and nonSTEM subjects in terms of the number of days lapsed since the previous exam.
Days between exams  Ancient Greek  Literature  Modern Greek  History  Algebra  Geometry  Physics  Chemistry  English 

–  4  0  2  4  2  0  2  0  0 
0  1  0  0  0  0  0  0  0  0 
1  0  9  9  2  0  0  0  6  13 
2  6  6  4  5  7  7  8  10  4 
3  4  3  3  5  5  9  4  1  1 
4  3  0  0  2  2  0  2  1  0 
5  0  0  0  0  2  2  2  0  0 
Total  18  18  18  18  18  18  18  18  18 
Mean  2.57  1.67  1.63  2.50  2.94  2.83  2.89  1.83  1.33 
SD  1.09  0.77  0.81  0.94  1.06  0.92  1.09  0.79  0.59 

Notes: The table presents the variation of the scheduling variable Days Between Exams across subjects. Each entry shows how frequently the subject in that column was tested in the number of days since the previous exam shown in that row. The variable Days Between Exams takes values from 0 to 5, indicating that from 0 up to 5 days might intervene between two consecutive exams in the sample. For example, modern Greek was tested 1 day after the previous exam nine times and 3 days after the previous exam three times. The first line corresponds to the times each subject was tested first, and thus the Days Between Exams variable is set to missing.
Days since first start  Ancient Greek  Literature  Modern Greek  History  Algebra  Geometry  Physics  Chemistry  English 

–  4  0  2  4  2  0  2  0  0 
2  0  3  0  1  3  0  2  2  1 
3  0  1  0  0  0  0  0  0  0 
4  1  0  1  0  0  1  1  1  0 
5  2  0  0  1  0  1  1  0  0 
7  0  0  1  0  2  1  3  1  2 
9  4  2  0  0  0  2  2  2  0 
10  0  0  0  0  0  0  0  0  0 
11  0  0  0  1  0  1  0  1  0 
12  0  0  0  0  3  1  0  0  0 
13  0  0  0  1  0  0  1  0  0 
14  0  0  3  1  3  2  2  1  0 
15  0  2  1  0  0  1  0  0  1 
16  1  1  0  2  0  1  1  0  3 
17  1  1  0  0  0  1  0  0  1 
18  0  0  2  1  1  2  0  0  0 
19  1  0  1  1  0  0  0  0  1 
20  1  0  0  0  1  0  1  0  1 
21  0  4  2  1  2  0  1  1  1 
22  2  0  1  0  0  0  0  3  2 
23  0  1  1  0  0  0  0  2  2 
24  0  1  2  1  0  1  1  1  1 
25  0  0  1  0  1  0  0  0  0 
26  0  0  0  0  0  1  0  1  0 
27  0  0  0  1  0  2  0  1  1 
28  1  2  0  1  0  0  0  0  1 
29  0  0  0  1  0  0  0  1  0 
Total  18  18  18  18  18  18  18  18  18 
Mean  13.86  15.39  17.69  17.36  12.69  15.17  10.89  16.50  18.06 
SD  7.64  8.92  6.07  8.16  7.24  7.26  6.83  9.15  7.00 

Notes: The table presents the variation of the scheduling variable Days Since the First Exam across subjects. Each entry shows how frequently the subject in that column was tested in the number of days since the beginning of the exam season shown in that row. The variable Days Since the First Exam takes values from 2 to 29, indicating that students take compulsory exams for a maximum duration of 29 days after the first exam. For example, modern Greek was tested 4 days after the exam season started once times and 25 days after the exam season started once. The first line corresponds to the times each subject was tested first, and thus the Days Since the First Exam variable is set to missing.
Exam order  Ancient Greek  Literature  Modern Greek  History  Algebra  Geometry  Physics  Chemistry  English 

1  4  0  2  4  2  0  2  0  0 
2  0  4  0  1  3  0  2  2  1 
3  3  0  1  1  1  3  2  1  0 
4  1  0  1  0  1  0  4  2  2 
5  3  2  0  2  1  2  3  1  0 
6  0  1  1  0  3  4  0  1  0 
7  0  0  3  1  1  2  1  1  0 
8  1  3  1  2  1  1  2  0  4 
9  3  0  1  1  1  2  1  0  1 
10  2  2  2  2  2  0  0  1  3 
11  0  3  2  1  2  0  1  4  3 
12  0  1  1  0  0  1  0  2  2 
13  0  0  3  0  0  2  0  0  0 
14  0  1  0  0  0  1  0  2  1 
15  1  0  0  3  0  0  0  1  1 
16  0  1  0  0  0  0  0  0  0 
Total  18  18  18  18  18  18  18  18  18 
Mean  5.67  7.94  8.11  7.06  5.78  7.50  4.78  8.56  9.28 
SD  4.03  4.32  3.94  5.00  3.49  3.52  2.82  4.41  3.39 

Notes: The table presents the variation of the scheduling variable Exam Order across subjects. Each entry shows how frequently the subject in that column was tested in the order shown in that row. The variable Exam Order takes values from 1 to 16 indicating the order of the tested subject. For example, modern Greek was tested first twice, while it was tested seventh three times. The first line corresponds to the times each subject was tested first, and thus the Exam Order variable is set to missing.
Table 17 shows how Days lapsed since the Exam Season started varies across subjects. Each entry in Table 17 shows how frequently the subject in that column was tested in the number of days since the beginning of the exam season shown in that row. Students take compulsory exams for a maximum duration of 29 days, after the first exam, as shown in the first column of Table 17. For illustrative purposes, algebra was tested on the first day twice, 2 days after the first exam three times, and so on. History was tested on the first day four times, 2 days after the first exam once, and so on. Physics was never tested more than 24 days after the first exam, and algebra was never tested more than 25 days after the first exam. At the bottom of Table 17 we report the mean and standard deviation of the number of days elapsed since the first exam for each subject was administered. We observe considerable withinsubject variation in the number of days since the first exam for each subject. On average, physics and ancient Greek were tested closer to the first exam than the other subjects. We do not see any systematic differences in the testing patterns for STEM and nonSTEM subjects in terms of the number of days elapsed since the first exam.
Table 18 shows how the scheduling variable Exam Order varies across subjects. Each entry in Table 18 shows how frequently the subject in that column was tested in the order shown in that row. Students take a maximum of 16 exams (including electives), as shown in the first column of Table 18. For illustrative purposes, algebra was tested first twice, second three times, third once, fourth once, and so on. History was tested first four times, second once, third once, fourth zero times, and so on. Physics and ancient Greek were the only subjects that were never tested later than the 11th place in the order of exams. At the bottom of Table 18 we report the mean and standard deviation of the place in the exam order at which each subject was tested. We observe considerable withinsubject variation in the order in which each subject was tested across years and grades. On average, physics and ancient Greek were tested at a later place of order than the other subjects. We do not see any systematic differences in the testing patterns for STEM and nonSTEM subjects.
E Overall Scheduling Effects
In this section we provide estimates of overall scheduling effects, without differentiating between STEM and nonSTEM subjects. Table 19 shows estimates from the following model:
where the coefficients α_{1}, α_{2}, α_{3} reflect the average impact of Scheduling Effects I, II, and III, respectively, across STEM and nonSTEM subjects. As shown earlier, STEM and nonSTEM subjects exhibit substantially different scheduling effects. These largely cancel out in an overall analysis of scheduling effects, with the exception of Scheduling Effect I. Table 19 shows that as the number of days between exams increases, the final exam score decreases, on average across subjects.
Variables  (1)  (2)  (3) 

Scheduling Effect III  0.031  0.003  –0.010 
(0.023)  (0.003)  (0.011)  
Scheduling Effect II  –0.013  –0.001  0.001 
(0.011)  (0.002)  (0.005)  
Scheduling Effect I  –0.045**  –0.007**  –0.024*** 
(0.017)  (0.003)  (0.008)  
Scheduling Effect III^{2}  0.000  
(0.000)  
Scheduling Effect II^{2}  0.000  
(0.000)  
Scheduling Effect I^{2}  0.003**  
(0.001)  
Observations  14,258  14,258  14,258 
Rsquared  0.026  0.985  0.985 
Student controls  No  Yes  Yes 

Notes: The dependent variable in each specification is the standardized final exam score at the subject and grade level. Clusterrobust standard errors at the classroom by year level are reported in parentheses. Specification includes grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, and a full set of birth year by cohort fixed effects. Columns 2 and 3 include individual controls. Individual controls include indicators for students’ gender, and a dummy that indicates whether a student is retained. * p < 0.1; ** p < 0.05; *** p < 0.01.
F Nonlinear Scheduling Effects
In this section, we explore nonlinear scheduling effects on exam performance using the quadratic form of each scheduling variable. Specification 4 is an augmented version of specification 1, and includes the square of each scheduling variable.
Column 1 of Table 20 shows the effects for STEM and nonSTEM subjects separately (using specification 1), while column 2 focuses on the difference in each scheduling effect for STEM relative to nonSTEM subjects. Intuitively, the main effects shown in column 2 correspond to the scheduling effects of nonSTEM subjects in column 1, while the coefficients of the interaction terms reflect the additional (marginal) scheduling effects of STEM subjects compared to nonSTEM subjects.
Column 3 of Table 20 shows the estimated nonlinear effects of three distinct channels of exam scheduling on performance separately for STEM and nonSTEM subjects (using specification 4), while column 4 of Table 20 focuses on the differences of nonlinear scheduling effects between STEM and nonSTEM subjects. Scheduling Effect I is found to have nonlinear effects only on exam performance in nonSTEM subjects. The positive coefficient on the squared variable associated with Scheduling Effect I reveals the downward curvature of the effect of the underlying mechanism. Exams in nonSTEM subjects taken further in days from the previous exam are associated with decreasingly lower performance, while controlling for other influences. Scheduling Effect III is found to have nonlinear effects only on exam performance in STEM subjects. The positive coefficient on the squared variable associated with Scheduling Effect III reveals the upward curvature of the effect of the underlying mechanism. Exams in STEM subjects taken at a later place in the exam order are associated with increasingly higher performance, while controlling for other influences. In contrast to the other scheduling effects, Scheduling Effect II is found not to have nonlinear effects in either STEM or nonSTEM subjects.
Variables  (1)  (2)  (3)  (4) 

Scheduling Effect III for nonSTEM  –0.002  –0.016  
(0.004)  (0.015)  
Scheduling Effect III for STEM  0.016***  –0.024  
(0.005)  (0.017)  
Scheduling Effect III for nonSTEM^{2}  0.000  
(0.001)  
Scheduling Effect III for STEM^{2}  0.002**  
(0.001)  
Scheduling Effect II for nonSTEM  0.002  0.005  
(0.002)  (0.006)  
Scheduling Effect II for STEM  –0.006***  0.004  
(0.002)  (0.006)  
Scheduling Effect II for nonSTEM^{2}  –0.000  
(0.000)  
Scheduling Effect II for STEM^{2}  –0.000  
(0.000)  
Scheduling Effect I for nonSTEM  –0.012***  –0.038***  
(0.004)  (0.011)  
Scheduling Effect I for STEM  0.002  0.016  
(0.003)  (0.023)  
Scheduling Effect I for nonSTEM^{2}  0.006**  
(0.002)  
Scheduling Effect I for STEM^{2}  –0.003  
(0.003)  
Scheduling Effect III  –0.002  –0.004  
(0.002)  (0.004)  
Scheduling Effect II  0.002  0.003  
(0.002)  (0.002)  
Scheduling Effect I  –0.012***  –0.012***  
(0.004)  (0.004)  
STEM × Scheduling Effect III  0.019***  –0.015  
(0.005)  (0.017)  
STEM × Scheduling Effect II  –0.008**  –0.001  
(0.002)  (0.007)  
STEM × Scheduling Effect I  0.013***  0.024  
(0.003)  (0.022)  
STEM × Scheduling Effect III^{2}  0.002*  
(0.001)  
STEM × Scheduling Effect II^{2}  –0.000  
(0.000)  
STEM × Scheduling Effect I^{2}  –0.002  
(0.003)  
Observations  14,258  14,258  14,258  14,258 
Rsquared  0.985  0.985  0.985  0.985 

Notes: The dependent variable in each specification is the standardized final exam score at the subject and grade level. Clusterrobust standard errors at the classroom by year level are reported in parentheses. All specifications include midterm score, grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, a full set of birth year by cohort fixed effects, and individual controls. Individual controls include indicators for students who are female, and a dummy that indicates whether a student is retained. * p < 0.1; ** p < 0.05; *** p < 0.01.
G Differential Scheduling Effects by Student Prior Performance
We interact each scheduling effect for STEM and nonSTEM subjects in specification 1 with a continuous variable that captures the standardized prior performance of each student in each subject. Results are relegated to Table 21. For Scheduling Effect I, the interaction of interest is positive and statistically significant for nonSTEM subjects, whereas it is negative and significant for STEM subjects. This indicates that the gap in the effect of an additional day between exams between STEM and nonSTEM subjects decreases with prior performance.
The estimated coefficient of the interaction of interest for Scheduling Effect II in nonSTEM subjects is zero, while the coefficient of the interaction for STEM subjects with prior performance is positive and significantly different from zero. For STEM subjects, higherachieving students benefit more from an additional day since their first exam for STEM subjects; this is not the case for exams in nonSTEM subjects.
The estimated coefficient of the interaction of Scheduling Effect III in nonSTEM subjects with prior performance is zero, while the coefficient of the interaction for STEM subjects is negative and statistically significant. Higherachieving students benefit less from taking a STEM exam one additional place later in the order of exams in the schedule, whereas for nonSTEM subjects, the exam order does not seem to play any important role.
Variables  (1) 

Midterm score  0.470*** 
(0.005)  
Scheduling Effect I for STEM  –0.012*** 
(0.004)  
Scheduling Effect II for STEM  0.018*** 
(0.003)  
Scheduling Effect III for STEM  –0.044*** 
(0.007)  
Scheduling Effect I for nonSTEM  0.025*** 
(0.005)  
Scheduling Effect II for nonSTEM  –0.015*** 
(0.004)  
Scheduling Effect III for nonSTEM  0.038*** 
(0.007)  
Scheduling Effect I for nonSTEM × Midterm score  0.016*** 
(0.002)  
Scheduling Effect I for STEM × Midterm score  –0.004*** 
(0.001)  
Scheduling Effect II for nonSTEM × Midterm score  –0.000 
(0.002)  
Scheduling Effect II for STEM × Midterm score  0.008*** 
(0.001)  
Scheduling Effect III for nonSTEM × Midterm score  0.001 
(0.003)  
Scheduling Effect III for STEM × Midterm score  –0.020*** 
(0.003)  
Observations  14,258 
Rsquared  0.992 

Notes: The dependent variable is the standardized final exam score at the subject and grade level. Clusterrobust standard errors at the classroom by year level are reported in parentheses. Specification includes grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, a linear time trend, a full set of birth year by cohort fixed effects, and individual controls. Individual controls include indicators for students’ gender, and a dummy that indicates whether a student is retained. * p < 0.1; ** p < 0.05; *** p < 0.01.
Table 22 shows the estimated Scheduling Effects by STEM and nonSTEM subjects for four quantiles of prior performance, proxied by standardized midterm score. The estimates are presented graphically in Figure 5.
NonSTEM 
STEM 
Difference 


Coef.  Std. Err.  Coef.  Std. Err.  Coef.  Std. Err.  
Scheduling Effect I  
Quantile 1  –0.060***  (0.008)  0.004  (0.004)  0.064***  (0.007) 
Quantile 2  –0.028***  (0.004)  –0.003  (0.003)  0.025***  (0.004) 
Quantile 3  0.005*  (0.003)  –0.003  (0.003)  –0.008*  (0.004) 
Quantile 4  0.027***  (0.005)  –0.014***  (0.004)  –0.041***  (0.006) 
Scheduling Effect II  
Quantile 1  0.006  (0.006)  –0.021***  (0.004)  –0.027***  (0.006) 
Quantile 2  0.005*  (0.003)  0.000  (0.001)  –0.005*  (0.003) 
Quantile 3  0.002*  (0.001)  0.012***  (0.002)  0.009***  (0.002) 
Quantile 4  0.001  (0.004)  0.024***  (0.005)  0.022***  (0.006) 
Scheduling Effect III  
Quantile 1  –0.014  (0.012)  0.052***  (0.008)  0.066***  (0.013) 
Quantile 2  –0.015***  (0.005)  0.001  (0.003)  0.016***  (0.006) 
Quantile 3  –0.005*  (0.003)  –0.031***  (0.005)  –0.026***  (0.005) 
Quantile 4  –0.001  (0.008)  –0.059***  (0.010)  –0.058***  (0.011) 

Notes: The dependent variable is the standardized final exam score at the subject and grade level. The sample includes 14,258 observations. Clusterrobust standard errors at the classroom by year level are reported in parentheses. Specification includes grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, a full set of birth year by cohort fixed effects, and individual controls. Individual controls include indicators for students’ gender, and a dummy that indicates whether a student is retained. * p < 0.1; ** p < 0.05; *** p < 0.01.
H Differential Scheduling Effects By Exam History
In this section, we provide estimates of differential scheduling effects by exam history. Exam history is measured by the number of STEM and nonSTEM exams taken prior to attempting a subsequent exam. We expand model 1 by adding interactions of each scheduling variable for STEM and nonSTEM subjects with the number of STEM and nonSTEM exams taken prior. Table 23 shows estimates for the interactions of interest.
Variables  (1) 

Scheduling Effect III for nonSTEM × No. of STEM exams taken  0.001 
(0.001)  
Scheduling Effect III for STEM × No. of STEM exams taken  –0.001 
(0.003)  
Scheduling Effect III for nonSTEM × No. of nonSTEM exams taken  0.002 
(0.001)  
Scheduling Effect III for STEM × No. of nonSTEM exams taken  0.004* 
(0.002)  
Scheduling Effect II for nonSTEM × No. of nonSTEM exams taken  0.001 
(0.001)  
Scheduling Effect II for STEM × No. of STEM exams taken  0.001 
(0.001)  
Scheduling Effect II for nonSTEM × No. of nonSTEM exams taken  –0.001 
(0.001)  
Scheduling Effect II for STEM × No. of nonSTEM exams taken  –0.001 
(0.001)  
Scheduling Effect I for nonSTEM × No. of nonSTEM exams taken  –0.000 
(0.001)  
Scheduling Effect I for STEM × No. of STEM exams taken  –0.001 
(0.002)  
Scheduling Effect I for nonSTEM × No. of nonSTEM exams taken  0.003*** 
(0.001)  
Scheduling Effect I for STEM × No. of nonSTEM exams taken  0.001 
(0.002)  
Observations  14,258 
Rsquared  0.986 

Notes: This table presents differential scheduling effects by exam history. We interact each scheduling variable for STEM and nonSTEM subjects with the number of STEM and nonSTEM exams taken prior. The model includes the three scheduling variables by type of subject, controls for midterm score, grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, a full set of birth year by cohort fixed effects, and individual controls. Individual controls include a female gender dummy, and a dummy that indicates whether a student is retained. This table reports only the coefficients of interactions of interest in the interest of space.
I Restricted Models of Scheduling Effects
To increase the empirical intuition behind the size and direction of omitted variable bias when one or more exam scheduling variables are excluded from the regression model, we estimate models using subsets of the exam scheduling variables. Table 24 show the estimate from restricted models across all subjects.
Variables  (1)  (2)  (3)  (4)  (5)  (6) 

Scheduling Effect III  0.002***  0.005*  0.002***  
(0.001)  (0.003)  (0.001)  
Scheduling Effect II  0.001***  –0.002  0.001**  
(0.000)  (0.001)  (0.000)  
Scheduling Effect I  –0.009***  –0.008***  –0.008**  
(0.003)  (0.003)  (0.003)  
Observations  14,258  14,258  14,258  14,258  14,258  14,258 
Rsquared  0.985  0.985  0.985  0.985  0.985  0.985 

Notes: The dependent variable is the standardized final exam score at the subject and grade level. Clusterrobust standard errors at the classroom by year level are reported in parentheses. Specification includes grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, a full set of birth year by cohort fixed effects, and individual controls. Individual controls include indicators for students’ gender, and a dummy that indicates whether a student is retained. * p < 0.1; ** p < 0.05; *** p < 0.01.
J Alternative Modeling Approach to Scheduling Effect III
In this section, we explore an alternative modelling approach for Scheduling Effect III. In particular, we estimate a model using specification Table 20, where the exam order variable is replaced by the ratio of exam order over days since first exam. The estimated coefficient for the ratio of the variables associated with Scheduling Effect III and II is reported in Table 25. The results show that an additional exam per day since the first exam increases test performance by 0.047 standard deviations across all subjects, and by 0.075 standard deviations across STEM subjects. Performance in nonSTEM subjects is not found to be significantly impacted by the number of exams per days since the first exam. The ratio of exam order (Scheduling Effect III) over the number of days since the first exam (Scheduling Effect II) has a positive and significant coefficient for STEM subjects, as does the number of days since first exam variable for STEM subjects. This suggests that providing students with more time to study may be optimal for STEM subjects.
Variables  (1)  (2) 

Scheduling Effect III/II for nonSTEM  0.031  
(0.030)  
Scheduling Effect III/II for STEM  0.075***  
(0.026)  
Scheduling Effect II for nonSTEM  0.001*  
(0.000)  
Scheduling Effect II for STEM  0.002***  
(0.000)  
Scheduling Effect I for nonSTEM  –0.012***  
(0.004)  
Scheduling Effect I for STEM  –0.001  
(0.004)  
Scheduling Effect III/II  0.047**  
(0.021)  
Scheduling Effect II  0.001***  
(0.000)  
Scheduling Effect I  –0.006**  
(0.003)  
Observations  14,258  14,258 
Rsquared  0.985  0.985 

Notes: The dependent variable is the standardized final exam score at the subject and grade level. Clusterrobust standard errors at the classroom by year level are reported in parentheses. Specification includes grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, a full set of birth year by cohort fixed effects, and individual controls. Individual controls include indicators for students’ gender, and a dummy that indicates whether a student is retained. * p < 0.1; ** p < 0.05; *** p < 0.01.
K Day of the Week Effects
One potentially interesting aspect of exam scheduling may be the differential dayoftheweek effects associated with test performance. Table 26 shows our estimated dayoftheweek effects from different specifications ranging from no controls to controlling for subject by grade unobservable effects and scheduling variables. The estimated effects correspond to the marginal effects on test scores associated with each day of the week with respect to Monday (the omitted category). The results show that, without controls for exam scheduling, Tuesday, Thursday, and Saturday may be associated with increases test scores on subject tested on those days, relative to Monday.
Variables  (1)  (2)  (3) 

Tuesday  0.088***  0.090**  0.050 
(0.033)  (0.040)  (0.040)  
Wednesday  0.049  0.053  –0.026 
(0.036)  (0.036)  (0.036)  
Thursday  0.092**  0.076*  –0.030 
(0.039)  (0.039)  (0.046)  
Friday  0.042  0.038  –0.079** 
(0.035)  (0.036)  (0.038)  
Saturday  0.289***  0.326***  0.223*** 
(0.047)  (0.069)  (0.073)  
Scheduling variables  No  No  Yes 
Subject by Grade FE  No  Yes  Yes 

Notes: Sample: 14,258 observations. The dependent variable is the standardized final exam score at the subject and grade level. Clusterrobust standard errors at the classroom by year level are reported in parentheses. Scheduling variables include exam order, days between exams, days since first exam. All specifications include grade by year fixed effects. *p < 0.1; **p < 0.05; ***p < 0.01.
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