¿ACOTAR LA ESCUELA?

WEEK IMPACT STUDENT

ACTUACIÓN? EVIDENCE FROM

THE FOUR-DAY SCHOOL WEEK

D. Mark Anderson

(Autor correspondiente)

Department of Agricultural

Economics and Economics

Montana State University
Bozeman, MONTE 59717-2920

dwight.anderson@montana.edu

Mary Beth Walker

Andrew Young School of Policy

Estudios

Georgia State University

Atlanta, Georgia 30302-3992

mbwalker@gsu.edu

Abstracto
School districts use a variety of policies to close budget
gaps and stave off teacher layoffs and furloughs. Más
schools are implementing four-day school weeks to re-
duce overhead and transportation costs. The four-day
week requires substantial schedule changes as schools
must increase the length of their school day to meet min-
imum instructional hour requirements. Although some
schools have indicated this policy eases financial pres-
sures, it is unknown whether there is an impact on stu-
dent outcomes. We use school-level data from Colorado
to investigate the relationship between the four-day week
and academic performance among elementary school
estudiantes. Our results generally indicate a positive rela-
tionship between the four-day week and performance in
reading and mathematics. These findings suggest there
is little evidence that moving to a four-day week compro-
mises student academic achievement. This research has
policy relevance to the current U.S. education system,
where many school districts must cut costs.

314

doi:10.1162/EDFP_a_00165
© 2015 Asociación para la política y las finanzas educativas

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3

Four-Day School Week and Student Performance

“There’s no way a switch like that wouldn’t negatively affect teaching
and learning.”

—Tim Callahan, spokesman for the Professional Association of Geor-
gia Educators (Herring 2010)

“We took our budget savings and plowed it right back into instructional
content.”

—Riley Ramsey, Webster County, Kentucky school district director of
personnel and technology (Kingsbury 2008)

1. INTRODUCCIÓN
A surprising number of schools have changed from the traditional Monday
through Friday school week to a four-day-week schedule. This policy has been
in place for many years in rural school districts in western states such as
Colorado and Wyoming and it appears to be spreading, with school districts
from Oregon to Missouri to Florida currently considering it.1 Generally, el
four school days are lengthened in order to meet state-mandated minimum
instructional hour requirements.2

The motivation for the schedule change is most often stated as finan-
cial, with savings related to transportation and overhead costs. Por ejemplo,
Kentucky’s Webster County school district reported substantial savings on
transportation, utility, and insurance costs after adopting a Tuesday through
Friday schedule (Kingsbury 2008). The shortened week has helped the Peach
County, Georgia, school district decrease spending on custodial and cafete-
ria workers in addition to transportation expenditures and utilities (Herring
2010).3

This policy change yields a number of implications that should be evaluated
to understand the cost/benefit impact of the four-day week. Por ejemplo, cómo
much does a four-day week actually affect school expenditures? If school build-
ings and gymnasiums are opened on Fridays to accommodate extra activities
(p.ej., athletic events), cost savings could be modest.4 How do teachers react to
a four-day schedule? Is there less turnover or increased teacher satisfaction?

1. Bowen (2011), Weston (2012), and Seattle Times Staff (2011) describe the current public debate

surrounding the proposed schedule change.

2. Usually, no classes are held on Friday; a small number of schools operating on the four-day week

take Monday as their day off, sin embargo.

3. For additional evidence on financial savings, see Blankenship (1984) and Grau and Shaughnessy

4.

(1987).
If buildings are closed and placed on a weekend cycle, then savings equivalent to a three-day
weekend are possible. It is often the case, sin embargo, that buildings are kept open for extra activities
and for staff use (Dam 2006). A recent report by Griffith (2011) suggested the savings from moving
to a four-day week are modest, although it is worth noting this report was based only on six school
districts from four different states.

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315

D. MARK ANDERSON AND MARY BETH WALKER

Spillover effects on communities could also be present; teens out of school on
Friday might engage more in crime or other risky behaviors.5

Finalmente, and perhaps more critical than the aforementioned issues, es el
question of the effect on student achievement. How do students fare under the
altered schedule? Anecdotally, results and opinions are mixed. Some educators
and parent groups complain that the shorter week harms students academically
(Herring 2010), although others have reported higher grade-point averages
and test scores after switching to the shortened week (Toppo 2002; Tornero
2010). Some accounts indicate that savings on transportation and utilities costs
have been redirected to instructional uses (Kingsbury 2008). Curiosamente,
the articles on the four-day week generally support the notion that student
achievement is not adversely affected by the alternative schedule.6 This work
is entirely descriptive in nature, sin embargo, and often consists of case studies
focusing on only one or a few school districts. Up to this point, no research
has used econometric techniques and panel data analyses to estimate the
relationship between the four-day school week and academic performance. Como
a result, prior studies may be plagued by bias because of confounding factors
that are simultaneously correlated with student performance and a district’s
decision to switch schedules.

We estimate the impact of the four-day school week on student achievement
using fourth-grade reading and fifth-grade mathematics test scores from the
Colorado Student Assessment Program (CSAP). Over one third of the school
districts in Colorado have adopted the four-day schedule. Our primary empiri-
cal strategy is a difference-in-differences estimation that exploits the temporal
and spatial variation in the adoption of four-day-week schedules. Nuestros resultados
generally indicate a positive relationship between the four-day school week
and academic achievement. These positive effects, combined with robustness
checks designed to address selection bias, suggest there is little evidence that
switching to a four-day week harms student performance. Although our data
do not support a full analysis of the mechanisms that generate improved
academic outcomes, some preliminary investigations suggest better atten-
dance results from the schedule change and thus could contribute to improved
actuación.

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5.

Jacob and Lefgren (2003) and Luallen (2006) estimated the relationship between school attendance
and crime by exploiting variation in teacher in-service days and teacher strike days, respectivamente.
Both found that juvenile property crime rates increased on days when school is not in session,
but violent crime rates decreased on these days. The authors speculated that incapacitation effects
caused the increase in property crimes, and concentration effects likely accounted for the decrease
in violent crimes.

6. Daly and Richburg (1984), Sagness and Salzman (1993), Feaster (2002), Lefly and Penn (2009),
and Hewitt and Denny (2011) found little evidence that the four-day week had an impact on test
actuación. Por otro lado, McCoy (1983), Grau and Shaughnessy (1987), and Yarborough
and Gilman (2006) found some evidence of higher test scores.

316

Four-Day School Week and Student Performance

These findings have clear policy relevance to the current situation in the
A NOSOTROS. education system, where many school districts must find ways to cut costs
pero, por supuesto, do not want to hamper student achievement. An important
caveat is that our results speak only to impacts for smaller and more rural
districts; a wider adoption of the policy across more densely populated areas
would be required to allow for a broader understanding of the effects.

The remainder of this paper is organized as follows. Sección 2 proporciona
background information, including a description of the adoption of the four-
day week in Colorado, a review of the relevant academic literature, y un
brief discussion on the possible advantages and disadvantages of the policy.
Sección 3 describes the data. Sección 4 lays out the empirical strategy. Sección
5 discusses the results, y sección 6 concluye.

2. BACKGROUND
Background of the Four-Day Week
It has been reported that school districts in South Dakota in the 1930s were the
first to use a four-day-week schedule (Donis-Keller and Silvernail 2009). Todavía
it was not until the energy crisis of the early 1970s that the shortened school
week gained popularity (ryan 2009). As transportation and utilities costs
dramatically increased, schools in Maine, Massachusetts, New Jersey, Nuevo
México, and Washington experimented with the four-day week (Gaines 2008;
Donis-Keller and Silvernail 2009).7 Schools in Colorado began adopting four-
day weeks following the legislature’s decision in 1985 to alter the minimum
school year requirement from 180 days to 1,080 hours for secondary schools
y 990 hours for elementary schools (Dam 2006).8 This change allowed
schools to meet the minimum instructional hour requirements by increasing
the length of their school day and shortening their days per week.

As of 2008, as many as seventeen states had school districts operating
on a four-day-week schedule (Gaines 2008).9 The four-day week is currently
most prevalent in Colorado, New Mexico, and Wyoming (Dam 2006; Darden
2008). In Colorado, encima 60 del 178 school districts utilize a four-day
week.10 Although this constitutes over 30 percent of the school districts in

7. Cimarron School District in New Mexico has the longest history of the four-day-week schedule;
they switched to the shortened week in 1973–74 and have used it consistently since (Feaster 2002).
8. Although most of the schedule changes occurred after this amendment, some schools were allowed

to pilot the four-day week prior to 1985 (Dam 2006).

9. See Gaines (2008) for a list of these states. Además, Hawaii recently implemented seventeen
mandatory “Furlough Fridays” for state public schools and the Peach County district in 2010 era
the first in Georgia to switch to the four-day week (Herring 2010).

10. All four-day-week schools in Colorado regularly hold school on Tuesday, Wednesday, and Thursday.
The majority of these schools conduct no classes on Friday, but some choose Monday as their day
apagado (Dam 2006). The change to a four-day week usually occurs at the district level, but there are a
few Colorado districts that have individual schools, but not the entire district, on the shortened week

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317

D. MARK ANDERSON AND MARY BETH WALKER

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Cifra 1. Colorado School District Map

Colorado, only about 3 percent of the state’s student population is covered by
the alternative schedule, reflecting the fact that most four-day-week schools
are in rural and sparsely populated districts (Lefly and Penn 2009). Cifra 1
shows a map indicating the school districts in Colorado where at least one
school is on a four-day school week.

A 2010 survey conducted in Colorado by the Department of Education
solicited information from school administrators who had applied to either
switch their school’s schedule to a four-day week or to renew their current four-
day-week status. The responses are tabulated in Appendix table A.1—more than
two thirds of the respondents stated that financial savings were a motivation
for the altered schedule, with another third citing community support.

How Might the Four-Day Week Impact Student Achievement?

There are a host of possibilities that could allow for a changed weekly schedule
to affect student achievement. Primero, consider how teachers might respond to
the changed schedule. It has been conjectured that longer class periods give
teachers flexibility to organize lessons more effectively and incorporate more
varied teaching methods (Rice, Croninger, and Roellke 2002). De hecho, profesores

(Lefly and Penn 2009). Colorado schools on the four-day week generally lengthen their school days
by ending around 4:00 pm. For an example of detailed daily schedules, see the following link to West
Grand Elementary School: www.westgrand.k12.co.us/District/Class/83–5th-Grade-Mrs-Crosby).

318

Four-Day School Week and Student Performance

have claimed less time is wasted during the four-day week, leaving more time
for instruction (Grau and Shaughnessy 1987; Durr 2003). Anecdotal evidence
suggests teachers are able to manage their time efficiently because their in-
struction is more focused and longer lesson blocks enhance curriculum conti-
nuity (Sagness and Salzman 1993; Dam 2006; Yarbrough and Gilman 2006).
In some districts, the day off is devoted to teacher planning and enhances
faculty collaboration (Yarbrough and Gilman 2006). An additional teacher
effect could be reduced turnover and absenteeism—teacher turnover has been
shown to have an impact on student achievement gains (Ronfeldt et al. 2011).
Although it is unclear whether the four-day week has reduced turnover, muchos
school districts have reported fewer teacher absences after switching to the
alternative schedule (Chamberlin and Plucker 2003). Por último, a different effect
could be that teachers are happy with the four-day weeks, and this leads to
higher productivity. This would be consistent with findings from the literature
on the four-day workweek and employee satisfaction (Baltes et al. 1999).11

Although the four-day school week might lead to teacher effects that im-
prove student achievement, potential drawbacks exist. Critics note that teach-
ers could initially face difficulties adapting their lesson plans to the schedule
cambiar (Chamberlin and Plucker 2003). A survey from an Idaho school district
indicated that 24 percent of teachers reported greater stress and fatigue due
to the longer school days under the shortened week (Sagness and Salzman
1993).

From the standpoint of the students, a four-day week may lead to better
attendance and anecdotal evidence suggests this is the case (Toppo 2002;
Kingsbury 2008; Tornero 2010). No es sorprendente, higher student attendance
has been associated with better performance on standardized tests (Ehrenberg
et al. 1991). It has also been reported that students are less distracted, exhibit
improved morale, and behave better on the shortened weekly schedule (Koki
1992; Shoemaker 2002; Dam 2006; Donis-Keller and Silvernail 2009). Out-
side of school, a longer weekend provides students an extra day for homework
and to prepare for class.12 All of these factors have the potential to improve
academic performance.13 In addition, students with long commutes may fare
better on a schedule with fewer trips (ryan 2009).

11.

It has also been shown that the compressed workweek can lead to decreased employee absenteeism
(Pierce et al. 1989).

12. Sixty-five percent of secondary school students from the Shelley School District in Idaho reported
they had more time to complete school work and to prepare for class after their district switched to
the four-day school week (Sagness and Salzman 1993).

13. Sixty-three percent of fourth through seventh graders from the Shelley School District in Idaho
reported that they felt they “learned more in school” after their district switched to the four-day
school week (Sagness and Salzman 1993, pag. 11).

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319

D. MARK ANDERSON AND MARY BETH WALKER

Recent research on cognitive fatigue could also have bearing on the is-
sue of schedule change and academic performance. Fillmore and Pope (2012)
found that test scores fell for high school students required to take Advanced
Placement exams with minimal time between testing. The Advanced Place-
ment exam dates change from year to year, providing a natural experiment
to measure the extent of cognitive fatigue. These findings are relevant to the
four-day-week schedule because, although students have less time to recover
between days during the school week, a longer weekend may positively impact
actuación. Por otro lado, some worry that it is difficult for students to
retain subject matter when given an extra day off (Gaines 2008). Perhaps the
biggest concern is that longer school days require extended focus and atten-
ción, and this could be especially detrimental to younger students (Dam 2006;
Gaines 2008; ryan 2009).14

Aside from these possible advantages and disadvantages, there are several
reasons why the alternative schedule could increase the total amount of instruc-
tional time students receive. Primero, the shortened school week gives parents the
opportunity to schedule medical and other necessary appointments on their
school’s day off instead of on a regular school day (Grau and Shaughnessy
1987). This has the potential to reduce student absenteeism and is particularly
important for those who live in rural communities where long travel distances
for appointments are common (Richburg and Sjogren 1983; Dam 2006).15
Segundo, children may receive additional instruction from a childcare facility
on their day off. A full day of day-care learning could increase the total amount
of instruction children receive. Por último, travel for sporting events results in
missed school time for student athletes. The four-day school week alleviates
absenteeism in this regard as many schools schedule athletics and other extra-
curricular activities on their day off (Dam 2006).16 This is less relevant for our
estudiar, sin embargo, because we focus on the academic performance of elementary
school students.

The four-day schedule also permits flexibility in the event of weather-related
school cancellations—schools can reschedule missed days without increas-
ing the length of the school year (Donis-Keller and Silvernail 2009). Esto es

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14. Some schools have helped elementary students adjust to the longer school days by providing
breakfast and serving lunch later in the day (Hazard 1986). A relevant line of research has studied
whether students retain subject material better in the morning or the afternoon. la evidencia
from these studies is generally mixed (ver, p.ej., Dunn 1984; davis 1987; barrón, Henderson, y
Spurgeon 1994; Muyskens and Ysseldyke 1998; robinson 2004).

15. The same argument applies to teacher absenteeism. Decreases in teacher absenteeism have been
reported as a source of financial savings in terms of substitute teacher costs (Grau and Shaughnessy
1987).

16. This is especially pertinent for rural areas because students at these schools are more likely to
participate in school-sponsored sports activities than students who attend urban schools (Lippman,
Burns, and McArthur 1996).

320

Four-Day School Week and Student Performance

important for us because the CSAP tests are administered during the spring.
Como resultado, if school is cancelled because of winter weather, then students will
generally make up lost time before taking the standardized tests, en vez de
afterward.17

It is helpful to delineate the mechanisms through which the changed sched-
ule may affect academic performance in the hopes that future research can
confirm or reject these hypotheses. Given the data available for this study, nosotros
can only provide a first look at some of the potentially important mechanisms.

Relevant Literature on School Schedule Changes

Although none of the school schedule changes that have been rigorously
evaluated match precisely the change created by the four-day school week,
there are at least three relevant areas of inquiry. Primero, some research deals
with block-scheduling—the reallocation of fixed amounts of classroom time
into longer blocks for some subjects. Implemented at the high school level, el
block schedule is designed to allow for more variety in instructional formats,
encourage more active teaching strategies, decrease disruptions during the
school day, and ultimately better prepare students for college work (Rice,
Croninger, and Roellke 2002; abrazos, Jr. 2004). This educational policy
change is appealing because overall class hours are not increased, so no new
resources are required. Sin embargo, the evidence is mixed regarding the
ability of block scheduling to enhance student performance (Rice, Croninger,
and Roellke 2002; abrazos, Jr. 2004).

Segundo, otro

research has examined the impacts of year-round
schooling.18 Similar to students on the four-day school week, students at
year-round schools are typically expected to receive the same amount of in-
structional time as students on traditional schedules. This alternative school
calendar simply consists of a set number of instructional hours spread over
the entire year. Although past reviews of research on year-round schooling are
inconclusive (Merino 1983; Cooper et al. 2003), recent work by Graves (2010,
2011) found the year-round calendar may impede academic achievement.19

Por último, a number of studies have investigated the effects of an overall
increase in instructional time (ver, p.ej., Brown and Saks 1986, 1987; Link

17. One school district estimated that students were in school approximately one week more per year

after switching to the four-day school week (Richburg and Sjogren 1983).

18. Related to research on year-round schooling, others have examined the effects of mandatory
summer schooling on subsequent achievement. Por ejemplo, Matsudaira (2008) used a regression
discontinuity design based on cutoff scores on year-end exams to show small improvements in
academic performance for those attending summer classes.

19. Tumbas (2010, 2011) specifically focused on multi-track, year-round school calendars. These calen-
dars have the potential to mitigate school overcrowding by serving more students within the same
facility than is possible under traditional or single-track, year-round calendars.

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321

D. MARK ANDERSON AND MARY BETH WALKER

and Mulligan 1986; Coates 2003; Marcotte 2007; Marcotte and Hemelt 2008;
Bellei 2009).20 Generally, this research suggests a positive relationship exists
between instructional time and academic achievement, and instructional time
is subject to diminishing returns.

3. DATA
Data on Test Scores
We use test score data from the CSAP tests to measure student performance.21
The CSAP tests are administered each spring and every public school student
within specified grades is required to take the exams.22 Schools administer
the tests during the period beginning on the second Monday in March and
ending on the third Monday in April. The tests are graded based on one of
four possible achievement levels: unsatisfactory, partially proficient, proficient,
and advanced. Our measures of interest are the percentage of students scor-
ing proficient or advanced in reading and the percentage of students scoring
proficient or advanced in mathematics.23 These measures represent some of
the achievement benchmarks used to evaluate school performance under No
Child Left Behind.

En particular, we focus on fourth-grade reading and fifth-grade mathemat-
ics scores. These data are reported consistently over time and represent the
longest time series of available test scores for Colorado public schools. Nuestro
final data set consists of a school-level panel for the periods 2000–10 and
2001–10 for reading and mathematics, respectively.24 Because there are many
more elementary schools than middle or high schools, these data are perhaps
the most appropriate for examining the effects of the four-day week on student
logro.

Mesa 1 provides descriptive statistics for the test scores. A comparison of
sample averages for schools on four-day-week schedules with those for schools
on traditional schedules indicates that schools on the four-day week have lower

20. Along these lines, research has also considered the effects of full-day as opposed to half-day

kindergarten (DeCicca 2007; Cannon, Jacknowitz, and Painter 2011).
21. These data are available from the Colorado Department of Education.
22. Additional details on the test schedules are available at www.cde.state.co.us/assessment/coassess

-assessmentwindow.

23. Although not our primary focus, we also consider results for all four possible test outcomes (ver
mesa 6). If the proficiency cutoffs for the four categories have changed over time (p.ej., porque
of less or more strict grading), then the effects of this “re-norming” is likely absorbed by the year
effects included in our empirical models.

24. For math, the exams were first administered in elementary schools in 2001 to fifth-grade students.
For reading, the exams were first administered in elementary schools in 1997 to fourth-grade
estudiantes. We do not present reading results for the period 1997–2010 because some of the covariates
were not available for the 1990s. It should be noted, sin embargo, that reading results from models
with school fixed effects and year effects for the period 1997–2010 are similar to those presented
in this paper.

322

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Four-Day School Week and Student Performance

Mesa 1. Estadísticas descriptivas

Four-Day
Week: 5th
Grade Math
Sample

Tradicional
Schedule: 5th
Grade Math
Sample

Four-Day
Week: 4th
Calificación
Reading
Sample

Tradicional
Schedule:
4th Grade
Reading
Sample

estándar.

estándar.
Mean Dev. Mean Dev. Mean Dev. Mean Dev.

estándar.

estándar.

Test scores

Percent scoring proficient

60.3

16.8

63.2

17.0

66.1

15.6

66.9

15.5

or advanceda

County-level variables

Percent povertya,b

Population density (per sq. mile)a,b

School district-level variables

Percent of male teachersa,b

Percent of Hispanic teachersa

Percent of white teachersb

School-level variables

Total studentsa,b

Pupil–teacher ratioa,b

Percent free lunch

Percent of Hispanic studentsa,b

Percent of white studentsa,b

18.7

51.2

29.7

7.6

91.4

9.8

14.4

6.2

92.1 122

108

18.5

50.1

9.7

14.4

6.1

91.6 120

108

10.0

15.8

16.1

26.4

6.5

6.5

90.3

10.7

5.20

29.2

9.2

26.4

5.1

6.5

7.2

91.9

15.2

15.5

6.4

90.5

10.7

228

156

399

150

225

152

399

149

14.2

39.9

21.2

75.4

2.9

21.9

22.3

22.2

16.2

37.3

24.8

67.7

10.2

23.9

21.1

22.0

14.1

39.8

20.3

76.4

2.9

21.0

21.3

21.2

16.3

37.2

24.8

67.9

10.7

23.8

21.2

22.0

norte

282

3,759

326

4,304

Notas: aMeans are statistically different at 5% level for fifth-grade math sample.
bMeans are statistically different at 5% level for fourth-grade reading sample.
Unweighted means for the fifth-grade math sample are based on data from 2001–10. Unweighted
means for the fourth-grade reading sample are based on data from 2000–10.

percentages of fifth graders scoring proficient or advanced in mathematics. El
mean percentage of fourth graders scoring proficient or advanced in reading
is also slightly lower for schools on the four-day schedule, but this difference
is not statistically significant.

Mesa 2 illustrates the mean percentages of students scoring proficient
or advanced for the schools that changed their schedules to a four-day week
during our sample period. For the fifth-grade math and fourth-grade reading
samples we observe fourteen and fifteen schools, respectivamente, that changed
their schedules. We report means for the percentage of students scoring pro-
ficient or advanced for the two years prior to the schedule change, the year in
which the schedule change took place, and the two years after the schedule

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323

D. MARK ANDERSON AND MARY BETH WALKER

Mesa 2. Descriptive Statistics for Schedule Changers: Mean Percentages of Students Scoring Proficient
or Advanced

2 Años
antes
Change to a
Four-Day
Week

1 Año
antes
Change to a
Four-Day
Week

Year of
Change to a
Four-Day
Week

1 Year after
Change to a
Four-Day
Week

2 Años
después
Change to a
Four-Day
Week

estándar.

estándar.
Mean Dev. Mean Dev. Mean Dev. Mean Dev. Mean Dev.

estándar.

estándar.

estándar.

5th grade math

4th grade reading

53.2

60.8

17.4

15.7

55.5

61.5

19.2

14.5

63.1

58.9

16.2

17.4

62.3

70.7

16.8

14.2

72.0

71.0

11.5

15.0

Notas: Unweighted means for the fifth-grade math sample are based on data from 2001–10;
fourteen schools changed their schedule to a four-day week during this period. Unweighted means
for the fourth-grade reading sample are based on data from 2000–10; fifteen schools changed
their schedule to a four-day week during this period.

cambiar. For both types of tests, average performance is significantly higher
after switching schedules.

Covariates
Mesa 1 also shows descriptive statistics for the remaining variables used in
this paper. The independent variable of interest is the Four-day week indicator.
The Colorado Department of Education provided the majority of information
on school schedules and the timing of schedule changes. For the cases where
schedule information was incomplete, we contacted school districts individu-
ally to fill in the missing data.

At the county level, we control for the percent living in poverty and popula-
tion density.25 Given that four-day-week schedules are implemented primarily
for financial reasons in rural areas, these variables are of particular importance.
School district-level controls include the percentage of teachers who are
masculino, the percentage who are white, and the percentage who are Hispanic.26
These demographic characteristics vary across districts and are likely to be
correlated with unobservables that influence academic outcomes.27

Por último, we control for the following school-level variables: total enrollment,
pupil–teacher ratio, percentage of students who receive free lunch, porcentaje

25. More specifically, the poverty measure represents the percentage of people aged 0 a 17 years in
families living in poverty. This variable was imputed for 2010. The poverty and population density
data are from the U.S. Census Bureau.

26. All district-level data are from the Colorado Department of Education.
27. Some research has found that teacher demographic characteristics such as gender and race directly

influence student achievement (Dee 2005; Hoffman and Oreopoulos 2009).

324

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Four-Day School Week and Student Performance

of students who are white, and percentage of students who are Hispanic.28
Some specifications also include the cohort’s previous year’s percentage of stu-
dents scoring proficient or advanced to control for variation in ability. Whereas
the county- and district-level variables control for important time-varying char-
caracteristicas, the school-level variables perhaps better capture environmental
factors that impact test scores and are associated with four-day-week status.

Because the four-day-week schedule is implemented in rural areas and
sparsely populated school districts, we base our estimation sample on restric-
tions to the Population density and Total students variables. Our control group
includes only schools with Population density and Total students values that
are less than the maximum values for these variables for the four-day-week
escuelas. Específicamente, we restrict our focus to schools with enrollments not ex-
ceeding 1,100 students and that are in counties with fewer than 300 persons
per square mile.29

Mesa 1 indicates that, despite the sample selection criterion, diferencias
across schools persist. Por ejemplo, schools on the four-day-week schedule
are generally smaller and in poorer areas. The four-day-week schools also
have slightly lower student–teacher ratios and somewhat lower percentages
of Hispanic students than the traditional-schedule schools. De nuevo, porque
of these differences, we examine the robustness of our results to alternative
control group specifications.

4. EMPIRICAL STRATEGY
We use a difference-in-differences approach to estimate the effect of the four-
day school week on student performance. This method allows us to exploit
the panel nature of our data by estimating a model that includes school fixed
effects and year effects. The baseline estimating equation is:

%Prof/Advs dct

= β0 + β1Four-day weeks dct

+ X 1s d ctβ

+ X 2d ctβ

3

2

+ X 3ct

b

4

+ νs + ωt + εs dct ,

(1)

28. The school-level data are from the National Center for Education Statistics’ Common Core of Data

(see http://nces.ed.gov/ccd/).

29. Frontier Academy is the largest four-day-week school, con 1,108 students in 2010. Ellicott Elemen-
tary is the four-day-week school in the most densely populated county, with over 290 persons per
square mile in 2010. We also drop observations from schools that have fewer than five years of
available test performance data. Appendix table A.2 lists the Colorado elementary schools in our
sample that changed to a four-day week schedule during the period 2000–10. It is important to note
that we examined the sensitivity of our results to alternative sample selection criteria. En particular,
when we restricted our sample based on the U.S. Census’s definition of “rural” the results changed
little from baseline. According to the census, a “rural” county has a population density of fewer
than 1,000 persons per square mile (Ricketts, Johnson-Webb, and Taylor 1998). Results based
on specifications with no sample restrictions were also similar to our baseline estimates reported
herein.

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325

D. MARK ANDERSON AND MARY BETH WALKER

where the dependent variable represents the percentage of students scoring
proficient or advanced in a particular subject (math or reading) and s indexes
escuelas, d indexes districts, c indexes counties, and t indexes years.30 The
variable Four-day week is equal to 1 if a school was on a four-day week during a
given year, and equal to 0 de lo contrario. The coefficient of interest, β1, represents
the marginal effect of switching to a four-day week. Because the decision
to switch to a four-day week is generally made by school districts, standard
errors are adjusted for correlation at the district level (Bertrand, Duflo, y
Mullainathan 2004).31

The vectors X1, X2, and X3 are composed of the school-, district-, y
county-level controls, respectivamente. School fixed effects are represented by νs,
and year effects are represented by ωt. The school fixed effects control for
differences across schools that are time-invariant, and the year effects control
for differences across time that are common to all schools.

A potential source of selection bias comes from the possibility that cer-
tain types of parents might opt to enroll their children in a four-day-week
escuela. Por ejemplo, a shortened school week could increase the expense of
childcare arrangements, so that this schedule could appeal more to parents
who are relatively less burdened by childcare costs.32 If children from these
families perform systematically better (o peor) in school than others, entonces
estimates of the effect of the four-day week on test scores will be biased. El
chances of parents moving their children to schools on the four-day week,
sin embargo, are limited due to the rural location of most four-day-week schools.33
School selection is also limited by restrictions on within-district transfers.34

A second selection bias could result from the fact that school districts
choose their schedule. If only schools in poorer areas change to a four-day-week
schedule, then an observed relationship between the four-day week and test
scores may simply reflect the financial status of the school. School fixed effects,
along with the appropriate covariates, help to purge our estimates of this type of
inclinación. It is important to note, sin embargo, that school fixed effects cannot account
for unobserved time-varying factors that simultaneously influence student
performance and the school’s choice of schedule. Además, it is possible a

30. Marcotte (2007), Marcotte and Hemelt (2008), and Papke (2005) used a similarly defined depen-

31.

dent variable to evaluate student performance at the school level.
De hecho, fourteen of the fifteen schedule changes in our sample were a part of a district-wide policy
cambiar. Frontier Charter Academy was the lone exception. Inference is similar when standard
errors are adjusted for correlation at the school level, see tables 10 y 11 for these results.

32. Higher income households, families with a stay-at-home parent, or farm and ranch households

may find the four-day-week schedule appealing.

33. Within our data, we found little evidence that student enrollments increased after schools switched

schedules.

34. Absent restrictions on within-district transfers, parents would still be limited in their ability to
choose their child’s schedule because the four-day week is usually implemented at the district level.

326

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Four-Day School Week and Student Performance

Cifra 2. Math Performance and the Four-Day School Week

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Cifra 3. Reading Performance and the Four-Day School Week

school could switch to a four-day week in response to a downward trend in test
puntuaciones. To address these issues, we include district-specific linear time trends
in a sensitivity analysis.

5. RESULTADOS
Primary Results
Before discussing the results based on estimation of equation (1), it is use-
ful to consider a more explicit test for whether changes in performance take
place after a schedule change. Figures 2 y 3 present point estimates (con
95 percent confidence intervals) from simple regressions designed to capture

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327

D. MARK ANDERSON AND MARY BETH WALKER

Mesa 3.

Four-Day School Week and Student Performance: Baseline 5th Grade Math Results

(1)

(2)

(3)
% Prof/Adv % Prof/Adv % Prof/Adv % Prof/Adv % Prof/Adv
in Math

in Math

in Math

in Math

in Math

(4)

(5)

Four-day week

norte

R2

13.15∗∗∗
(1.48)

4,041

0.659

School fixed effects

Sí

Year effects

County variables

District variables

School variables

No

No

No

No

7.44∗∗∗
(1.68)

4,041

0.707

Sí

Sí

No

No

No

7.43∗∗∗
(1.77)

4,041

0.707

Sí

Sí

Sí

No

No

7.18∗∗∗
(1.69)

4,041

0.708

Sí

Sí

Sí

Sí

No

7.41∗∗∗
(1.71)

4,041

0.711

Sí

Sí

Sí

Sí

Sí

Notas: Each column represents the results from a separate OLS regression. The dependent
variable is equal to the percentage of students within a school scoring proficient or advanced;
the covariates are listed in table 1. Errores estándar, corrected for clustering at the school district
nivel, are in parentheses.
∗Statistically significant at 10% nivel; ∗∗significant at the 5% nivel; ∗∗∗significant at the 1% nivel.

intertemporal effects.35 Two lead indicators, an indicator for the year a schedule
change took place, and three lag indicators are considered as independent vari-
ables in a regression that also includes school fixed effects and year effects.36
The omitted category is three-plus years before a schedule change occurred. En
each regression, the dependent variable is the percentage of students scoring
at the proficient or advanced levels. The coefficient estimates for the lead dum-
mies in both figures support the common trend assumption that is vital to
difference-in-differences estimation. The leads are statistically indistinguish-
able from zero, indicating schools that switched to a four-day week share
similar pre-treatment trends in test scores with schools that remained on a
traditional schedule during our sample period.

For schools that switched to a four-day week, figura 2 indicates there is a
discrete increase in the percentage of students scoring proficient or advanced
in math during the year in which the schedule change took place, y esto
improvement persists over time. For reading achievement, the coefficient
estimates for the lags are all positive and large in magnitude, but none is
significant at conventional levels.

Mesa 3 presents our baseline ordinary least squares (OLS) estimates of the
relationship between the four-day school week and the percentage of students

35. Grinols and Mustard (2006) used this approach to analyze the effects of casinos on crime.
36. Por ejemplo, the first of the two lead dummies takes on a value of one two years prior to a schedule

change for a particular school, and is equal to zero otherwise.

328

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Four-Day School Week and Student Performance

Mesa 4.

Four-Day School Week and Student Performance: Baseline 4th Grade Reading Results

(1)

(2)

(3)

(4)

(5)

% Prof/Adv % Prof/Adv % Prof/Adv % Prof/Adv % Prof/Adv
in Reading
in Reading
in Reading

in Reading

in Reading

Four-day week

norte

R2

5.96∗∗
(2.54)

4,630

0.709

School fixed effects

Sí

Year effects

County variables

District variables

School variables

No

No

No

No

3.32
(2.49)

4,630

0.726

Sí

Sí

No

No

No

3.64
(2.47)

4,630

0.726

Sí

Sí

Sí

No

No

3.71
(2.42)

4,630

0.727

Sí

Sí

Sí

Sí

No

3.80∗
(2.23)

4,630

0.733

Sí

Sí

Sí

Sí

Sí

Notas: Each column represents the results from a separate OLS regression. The dependent
variable is equal to the percentage of students within a school scoring proficient or advanced;
the covariates are listed in table 1. Errores estándar, corrected for clustering at the school district
nivel, are in parentheses.
∗Statistically significant at 10% nivel; ∗∗significant at the 5% nivel; ∗∗∗significant at the 1% nivel.

scoring proficient or advanced on fifth-grade math tests. Each column illus-
trates results from a separate regression and all models include school fixed
efectos. When controlling for county-, distrito- and school-level differences in
socioeconomic characteristics, the four-day school week is associated with a
7.41 percentage point increase in the percentage of students scoring proficient
or advanced in math.

Mesa 4 shows results from similar models estimated using the percentage
of students scoring proficient or advanced on fourth-grade reading tests. El
impact of the four-day week is generally smaller and less precisely estimated,
but even when all covariates are included, we still find a positive point estimate
of over 3 percentage points.37

En mesa 5, we present regression results designed to provide some insight
into the dynamic pattern of test scores prior to and following the change to a
four-day school week. Específicamente, we replace the Four-day week variable with
two lead indicators, an indicator for the year of the schedule change, y
three lag indicators. The omitted category is three-plus years before a schedule
change occurred. This specification is similar to the model used to produce
figuras 2 y 3, with the exception that the covariates are included. Columna 1
shows results for the math scores. The estimated coefficients prior to the pol-
icy change are positive, though not statistically significant, whereas the point

37.

It is fairly common to find stronger effects on math scores than on reading scores; ver, Por ejemplo,
Dee and Jacob (2011).

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329

D. MARK ANDERSON AND MARY BETH WALKER

Mesa 5.

Four-Day School Week and Student Performance: Policy Timing

(1)
% Prof/Adv in Math

(2)
% Prof/Adv in Reading

2 years before four-day week

1 year before four-day week

Year of schedule change

1 year after four-day week

2 years after four-day week

3+ years after four-day week

1.48
(2.49)

4.66
(3.68)

10.34∗∗∗
(2.50)

7.98∗∗∗
(2.52)

11.59∗∗∗
(3.86)

5.75∗
(2.93)

p-value: joint significance of year of

0.000∗∗∗

schedule change indicator and lags

norte

R2

School fixed effects

Year effects

County variables

District variables

School variables

4,041

0.711

Sí

Sí

Sí

Sí

Sí

2.10
(5.44)

2.59
(4.18)

0.70
(3.22)

5.22
(3.57)

8.23∗∗
(4.10)

6.05∗
(3.19)

0.088∗

4,630

0.733

Sí

Sí

Sí

Sí

Sí

Notas: Each column represents the results from a separate OLS regression. The dependent
variable is equal to the percentage of students within a school scoring proficient or advanced;
the covariates are listed in table 1. The omitted category is “3+ years before four-day week.”
Errores estándar, corrected for clustering at the school district level, are in parentheses.
∗Statistically significant at 10% nivel; ∗∗significant at the 5% nivel; ∗∗∗significant at the 1% nivel.

estimates post-change are much larger and estimated with precision. The re-
sults for the leads, to an extent, quell concerns that academic adjustments were
made in anticipation of schedule changes. Further analysis of the sensitivity
of our baseline results to pre-existing trends is included in the subsequent
robustness checks. The results in column 2 provide some evidence that per-
formance in reading goes up after schools switch to a four-day week, a pesar de
only the estimates for the final two lags are individually statistically significant
at conventional levels. The indicator for the year of the schedule change and
the three lag indicators are weakly jointly significant.

Because our results indicate the percentage of students achieving profi-
cient or advanced scores increases when schedules are changed, it is interest-
ing to consider which group of students accounts for the improvement. Como

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Four-Day School Week and Student Performance

Mesa 6.

Four-Day School Week and Student Performance: All Test Score Categories

(1)

(2)

(3)

(4)

% Unsatisfactory % Partially Proficient % Proficient % Advanced

in Math

in Math

in Math

in Math

−2.55∗
(1.47)

4,041

0.593

(1)

−4.59∗∗∗
(1.11)

4,041

0.549

(2)

3.81∗∗
(1.86)

4,041

0.332

(3)

3.60
(2.36)

4,041

0.693

(4)

% Unsatisfactory % Partially Proficient % Proficient % Advanced
in Reading

in Reading

in Reading

in Reading

−2.45∗
(1.39)

4,630

0.638

Sí

Sí

Sí

Sí

Sí

−0.69
(1.69)

4,630

0.580

Sí

Sí

Sí

Sí

Sí

1.65
(1.98)

4,630

0.651

Sí

Sí

Sí

Sí

Sí

2.16∗∗∗
(0.803)

4,630

0.554

Sí

Sí

Sí

Sí

Sí

Matemáticas

Four-day week

norte

R2

Reading

Four-day week

norte

R2

School fixed effects

Year effects

County variables

District variables

School variables

Notas: Each cell represents the results from a separate OLS regression. The dependent variable is
equal to the percentage of students within a school scoring in one of the following four indicated
categories: unsatisfactory, partially proficient, proficient, advanced. The covariates are listed in
mesa 1. Errores estándar, corrected for clustering at the school district level, are in parentheses.
∗Statistically significant at 10% nivel; ∗∗significant at the 5% nivel; ∗∗∗significant at the 1% nivel.

mentioned earlier, the Colorado Department of Education tabulates student
scores according to four possible achievement levels: unsatisfactory, parcialmente
proficient, proficient, and advanced. Mesa 6 shows results where each achieve-
ment level is considered as a separate outcome and is regressed against the
policy indicator and the full set of covariates. For math, we find that the biggest
share of the improvement comes from the students formerly classified as par-
tially proficient. Our results indicate a 4.6 percentage point decrease in the
fraction of students scoring at this level. En consecuencia, we see a large and
statistically significant increase in the percentage of students scoring at the
proficient level. For reading, the only statistically significant results occur in
the lowest and the highest categories. These results show that the percentage
of students rated unsatisfactory fell by nearly 2.5 percentage points after the
schedule change whereas the percentage of students in the advanced category
rose by over two percentage points. Por supuesto, this probably does not imply

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331

D. MARK ANDERSON AND MARY BETH WALKER

Mesa 7.

Four-Day School Week and Student Performance: Interaction with Percent Free Lunch

(1)
% Prof/Adv in Math

(2)
% Prof/Adv in Reading

Four-day week × Percent free lunch

norte

R2

School fixed effects

Year effects

County variables

District variables

School variables

11.9∗
(7.09)

4,041

0.711

Sí

Sí

Sí

Sí

Sí

1.67
(8.39)

4,630

0.733

Sí

Sí

Sí

Sí

Sí

Notas: Each column represents the results from a separate OLS regression. The dependent
variable is equal to the percentage of students within a school scoring proficient or advanced;
the covariates are listed in table 1. Errores estándar, corrected for clustering at the school
district level, are in parentheses.
∗Statistically significant at 10% nivel.

that formerly unsatisfactory students are now scoring at the advanced level. Él
is more likely the four-day week resulted in a relatively uniform shift upward
in test scores across all achievement levels.

To some degree, these results mitigate concerns that the improved scores
result from more affluent parents placing their children in high quality child
care on the fifth day where they receive additional instruction. The percentage
of students rated unsatisfactory fell by substantial amounts for both reading
and math for four-day-week schools. If additional instruction in high quality
child care accounted for the improvement in scores, the usual correlation
between family income and test scores might lead one to expect the effect to
occur primarily in the partially proficient category.

Because the data do not allow us to directly examine whether additional
instruction from quality child care accounts for rising scores, we also estimate
a specification that interacts the schedule change variable with the percentage
of students receiving free lunch. These results are provided in table 7. For both
math and reading scores, the estimated coefficient on the interaction term
is positive, although it is only statistically significant for the math sample.
These results suggest the four-day week may be particularly important for
students from poorer areas.38 Although we cannot pin down the mechanism

38. We also computed the marginal impacts of the schedule change at the 25th, 50th, and 75th
percentiles for free lunch percentages. The estimated impact of the four-day week on math scores
increased from just under 4 percentage points at the lower poverty schools to over 8 porcentaje
points at schools where the free lunch percentage is at the 75th percentile. For the reading sample,

332

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Four-Day School Week and Student Performance

Mesa 8. Random Four-Day Week Assignment

(1)
% Prof/Adv in Math

(2)
% Prof/Adv in Reading

Average Four-day week coefficient estimate

Number of trials

Number of Four-day week estimates that were
positive and significant at 5 nivel porcentual

School fixed effects

Year effects

County variables

District variables

School variables

−0.69

1,000

5

Sí

Sí

Sí

Sí

Sí

−0.12

1,000

31

Sí

Sí

Sí

Sí

Sí

Notas: Each column represents the results from a series of OLS regressions. The dependent
variable is equal to the percentage of students within a school scoring proficient or advanced;
the covariates are listed in table 1.

driving these effects, the positive association between socioeconomic status
and academic achievement has been documented for quite some time (Sirin
2005). Perhaps students from low-socioeconomic-status households are more
likely to benefit from four-day week advantages, such as fewer long commutes
and longer, uninterrupted blocks of instructional time devoted to complete
lecciones.

Robustness Checks and Potential Mechanisms

We first perform a robustness check based on Luallen (2006) that examines
whether the positive policy effects we measure can be reproduced by random
assignment of four-day-week schedules to schools. If the positive and signifi-
cant effects are easily replicated by random policy assignment, then this raises
the concern that our results are spurious. Específicamente, we create a placebo Four-
day week indicator using a random number generator based on the uniform
distribución. Because fourteen schools switched to a four-day week during our
sample period for math performance, we assign fourteen placebo policies for
each of 1,000 trial runs. For the reading sample, we assign fifteen placebo
policies.39

Mesa 8 illustrates the average coefficient estimates for the placebo Four-
day week on the percentage of fifth graders scoring proficient or advanced

the impact of the schedule change was between 3 y 4 puntos de porcentaje, as poverty levels rise.
On a related note, Tumbas (2011) found that low-socioeconomic-status students experienced a larger
fall in performance due to year-round schooling than the general population of students.

39. A year for a schedule change was randomly selected between 2000 y 2010 for the reading test

regressions and 2001 y 2010 for the math test regressions.

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333

D. MARK ANDERSON AND MARY BETH WALKER

in mathematics and the percentage of fourth graders scoring proficient or
advanced in reading. In both regressions, the average estimate is very small
in magnitude. Además, en 1,000 ensayos, solo 5 estimates are positive and
statistically significant at the 5 percent level for math performance and only
31 estimates are positive and statistically significant at the 5 percent level for
reading performance. These estimates demonstrate our results cannot be easily
reproduced by random assignment of the four-day-week schedule.

Como se discutió anteriormente, schools on the four-day-week schedule differ from
schools on traditional schedules along several margins. En realidad, the four-day
week is not a randomly assigned policy and the chief threat to the validity
of our results is the selection of school districts into these schedules. El
inclusion of school fixed effects controls for time-invariant heterogeneity across
schools and the clustering of our standard errors enables us to take into
account some unobserved heterogeneity. Another method that allows us to deal
with selection on observables is a propensity score matching technique used
in conjunction with the difference-in-differences estimator.40 This method
essentially amounts to re-estimating equation (1) on a matched sample, a
subset of the original sample.41

The goal for matching is to find a group among the comparison population
(es decir., the schools that remained on the traditional schedule) that looks as similar
as possible to the schools that changed schedules. De este modo, we predict whether
a school switches to a four-day week during our sample period based on
observable characteristics from 2001. Appendix table A.3 presents descriptive
statistics for the propensity score matching analysis and Appendix table A.4
presents the probit results. Consistent with anecdotal evidence, schools with
higher transportation expenditures are more likely to switch to a four-day week.
Mesa 9 illustrates results from the estimation of equation (1) on the propen-
sity score matched samples. The k-nearest neighbor matching algorithm was
used to construct the counterfactual.42 For math, the estimates are smaller
than those shown in table 3, although they are still relatively large in magni-
tude and two of the three estimates are statistically significant at the 5 por ciento
level even though the sample has shrunk considerably. Although the estimate
for the case where k = 5 is positive and substantial in size, it is not statisti-
cally significant at conventional levels (pag = 0.101). Given these results, es

40. For a practical discussion on propensity score matching, see Becker and Ichino (2002).
41. For research employing similar methods, see Heckman, Ichimura, and Todd (1997), Sabia (2006),

Gilligan and Hoddinott (2007), and Debaere, Sotavento, and Lee (2010).

42. Específicamente, the k-nearest neighbor algorithm matches each four-day-week school to multiple
schools from the comparison group. We consider values of k = 25, k = 10, y k = 5; the choice of k
involves a trade-off between reduced variance and increased bias. Eso es, variance is reduced when
a higher value of k is chosen because more information is used to construct the counterfactual
for each treated unit but increased bias results from poorer matches on average (Caliendo and
Kopeinig 2005).

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Four-Day School Week and Student Performance

Mesa 9.

Four-Day School Week and Student Performance: Matched Samples

(1)
% Prof/Adv in Math

(2)
% Prof/Adv in Math

(3)
% Prof/Adv in Math

5.37∗∗
(2.50)

k = 25

1,042

0.711

(1)

5.44∗∗
(2.60)

k = 10

822

0.713

(2)

4.29
(2.66)

k = 5

569

0.687

(3)

% Prof/Adv in Reading % Prof/Adv in Reading % Prof/Adv in Reading

4.02∗
(2.20)

k = 25

1,129

0.704

Sí

Sí

Sí

Sí

Sí

3.54∗
(2.00)

k = 10

777

0.720

Sí

Sí

Sí

Sí

Sí

2.66
(1.84)

k = 5

607

0.731

Sí

Sí

Sí

Sí

Sí

Matemáticas

Four-day week

k-nearest neighbors

norte

R2

Reading

Four-day week

k-nearest neighbors

norte

R2

School fixed effects

Year effects

County variables

District variables

School variables

Notas: Each cell represents the results from a separate OLS regression. The dependent variable is
equal to the percentage of students within a school scoring proficient or advanced; the covariates
are listed in table 1. Errores estándar, corrected for clustering at the school district level, are in
parentheses.
∗Estadísticamente significativo al 10% nivel; ∗∗significant at the 5% nivel.

probably best to view the estimates from table 3 as upper bounds. For reading,
the magnitudes of the estimates are on par with those from table 4 and two of
the three estimates are weakly statistically significant.

For completeness, we perform the following additional robustness checks.
The sensitivity analyses for the math results are reported in table 10. In col-
umn 1, the baseline estimate for the fully specified model (see column 5 de
mesa 3) is reported for comparison. Columna 2 de mesa 10 reports results from
a model where the school fixed effects are replaced with district fixed effects.
No es sorprendente, the coefficient estimate on the Four-day week indicator is
larger in magnitude and highly statistically significant. As expected, el modelo
with district fixed effects explains less variation in the percentage of students
scoring proficient or advanced. This implies that school-level time-invariant

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335

D. MARK ANDERSON AND MARY BETH WALKER

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3

Four-Day School Week and Student Performance

unobserved characteristics explain much of the variation in test performance
across schools.

As mentioned previously, the reason we cluster our standard errors at
the school district level is due to the fact that schedule changes are generally
district-wide policies. Columna 3, sin embargo, provides results where the standard
errors are adjusted for correlation at the school level rather than the district
nivel. The standard error for the Four-day week indicator increases but the
coefficient remains significant at the 1 nivel porcentual.

The results in column 4 come from a regression weighted by the school-
level student population. This robustness check examines whether our positive
coefficients result from improvements in small schools wherein larger swings
in scores are easier to achieve. Aquí, the coefficient estimate remains relatively
large in magnitude and is statistically significant at the 5 nivel porcentual.

Columna 5 shows results from a specification that controls for a cohort’s
previous year’s test performance. As long as cross-district migration is limited,
this helps to account for variation in cohort ability. Desafortunadamente, for the math
resultados, this specification requires that we drop five years of data. This is due to
the fact the math exams were not administered to fourth-grade students until
2006. Como resultado, we lose much of the policy variation in our sample.43 These
results yield a smaller point estimate of the impact of the schedule change
y, not surprisingly, show a much larger estimated standard error.

For the results in column 6, we restrict the sample to only schools that
were on traditional schedules at the beginning of our sample period. Iden-
tification in our difference-in-differences framework comes from the schools
that we observe switching schedules. Como consecuencia, our results should change
little from baseline when excluding schools that enter our sample already on
the four-day week. The estimate in column 6 confirms this is the case.

Por último, columna 7 shows results where school district-specific linear time
trends are added to the right-hand-side of equation (1). The district-specific
trends more effectively account for potential selection issues and control for
the influence of difficult-to-measure factors at the district level that evolve
smoothly over time. Although the coefficient estimate remains relatively large
in magnitude, it is measured with less precision and is no longer statistically
significant at conventional levels.44 Of course, because this model uses up
degrees of freedom, less precision is to be expected.

43. Appendix table A.2 illustrates when schools switched to a four-day week.
44. Results based on district-specific trends are presented as opposed to results based on school-
specific trends because the policy change almost always occurs at the district level. Como resultado, él
is conceivable that unobserved time-varying characteristics that drive the decision to switch to the
four-day week are more likely to be district-level factors. Sin embargo, it is important to note that
results are similar when controlling for school-specific linear time trends (coefficient estimate on
Four-day week = 5.95; standard error = 4.33).

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3

337

D. MARK ANDERSON AND MARY BETH WALKER

To push the issue of selection bias further, we subjected the estimate
from the specification with district-specific trends to the method developed
by Altonji, Elder, and Taber (2005). The approach is based on estimating
the ratio of selection on unobservables to selection on observables required
to attribute the entire four-day week effect to selection. Implementing this
method suggests that selection on unobservable dimensions would need to be
roughly twice as strong as selection on observable dimensions to explain away
the effect reported in column 7 de mesa 10.45 The estimate of bias is imprecisely
measured, sin embargo, so it is probably best to interpret the findings in this paper
as high-end estimates.46

The results from the sensitivity analyses for the reading scores are pro-
vided in table 11. Although the reading results are more sensitive than the
math results to model specification and sample selection, all coefficient es-
timates remain positive in sign. With the exception of the column 7 resultado,
the magnitudes of the coefficient estimates remain substantial. When district-
specific trends are added, the estimate becomes much smaller and is not
measured precisely. Note that for the reading results, the specification that
controls for the cohort’s previous year’s test performance yields a positive and
statistically significant effect of the policy change. Unlike for math, this spec-
ification requires that we drop only two years of data. Because reading exams
were first administered to third-grade students in 2002, we retain all of the
policy variation in the sample.

Mesa 12 provides results for a further examination of the potential for
selection bias arising from parents choosing schools because they prefer the
four-day-week schedule. We regress the following school-level student char-
acteristics on the full set of fixed effects plus the policy variable: Percent free
lunch, Percent of Hispanic students, Percent of white students. In each of the
three regressions, the coefficient on the policy variable is small in magnitude
and statistically indistinguishable from zero, yielding no evidence that student
composition is influenced by the schedule change.47

45. The Altonji, Elder, and Taber (2005) method is estimated under the assumption that the selection
on observables equals the selection on unobservables. Sin embargo, as Krauth (2011) points out, este
argument is unlikely to hold because researchers do not select their control variables at random.
This might lead us to expect the selection on unobservables to be less than the selection on
observables.

46. Específicamente, under the assumption that the selection on observables equals the selection on un-
observables, our bias estimate is 2.26, with a standard error of 3.35. The Altonji, Elder, and Taber
(2005) method is summarized nicely in Elder and Jepsen (2014). We are thankful to Todd Elder
who provided the code used to implement the method.

47. We also looked at simple descriptive statistics to observe whether student characteristic means
differed before and after schools switched to a four-day week. The only characteristic that was sta-
tistically significantly different after the schedule change was the percentage of Hispanic students.
Upon closer examination of the data, sin embargo, this simply reflected a Colorado-wide trend where
the percentage of Hispanic students has increased across all schools in the sample.

338

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Four-Day School Week and Student Performance

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