Abstract
This article exploits highly detailed data on teacher absences from a large urban school district in the northern United States to shed light on the determinants and effects of teacher absences. The topic is important because both school and district policies can influence teachers’ propensity to be absent. The authors estimate the impact of teacher absences on academic achievement of students matched to elementary school teachers. Models include fixed effects for teachers to control statistically for potential correlation between time-invariant levels of teachers’ skill and effort and their rates of absence. The authors estimate 10 additional days of teacher absence reduce mathematics achievement of fourth-grade students by 3.2% of a standard deviation. They employ an additional instrumental variables strategy to bolster the case for a causal interpretation of results. Instrumental variables results indicate the impact of unexpected teacher absences on student achievement is larger than the impact of anticipated absences.
Keywords
I. Introduction
Over the past 30 years, many quantitative studies have shown that students enrolled in some classrooms learn more over a school year than those enrolled in other classrooms (Kane, Rockoff, & Staiger, 2006; Rivkin, Hanushek, & Kain, 2005; Rockoff, 2004). The explanation favored by most researchers is that some teachers are more effective than others. However, attempts to explain differences in teacher effectiveness by variables describing teachers’ training and backgrounds have had only very modest success. This article explores a hypothesis that to date has received little attention: namely, that part of the class-to-class variation in student learning stems from differences in teacher absences. The hypothesis has face validity in that teachers cannot instruct if they are not in school. It also has potential policy implications because school and district policies can affect the distribution of teacher absences.
This article describes the results of a study examining the causal impact of teacher absences in a large urban school district in the northern United States, where the importance of quality instruction and any negative effects of teacher absence are arguably magnified by the poverty in which the majority of children attending public schools live. The remainder of the article is organized as follows. Section II provides background on teacher absences. Section III presents our data and documents patterns of teacher absence. Section IV explains the analytic strategies we use to assess the impact of teacher absence on student achievement, and Section V presents findings. Section VI discusses these findings and their implications.
II. Teacher Absences
How Often Are Teachers Absent?
On average, public school teachers in the United States are absent 5% to 6% of the days schools are in session (Ballou, 1996; Podgursky, 2003).1 This rate of absence is low relative to those in the developing world, where teacher absence rates of 20% are common (Chaudhury, Hammer, Kremer, Muralidharan, & Rogers, 2006). Yet, it exceeds comparable rates of teacher absence reported in other industrialized countries: 3.15% in the United Kingdom (Bowers, 2001) and 3.12% in Queensland, Australia (Bradley, Green, & Leeves, 2007). Within the United States, teacher absence rates are nearly 3 times those of managerial and professional employees (Ballou, 1996; Podgursky, 2003). One contributing factor may be teachers’ daily exposure to large numbers of children, some of whom are carriers for infectious diseases. A second is that the proportion of teachers who are female is much higher than the proportion of managerial and professional employees who are female. Numerous studies have documented higher rates of absence for female employees than male employees (Educational Research Service, 1980; Ichino & Moretti, 2006; VandenHeuvel & Wooden, 1995).
Can Policy Affect Teachers’ Rates of Absences?
A variety of evidence indicates that teacher absences can be influenced by school and district policies.2 For example, teachers’ rates of absence are positively associated with the generosity of available leave provisions (Ehrenberg, Ehrenberg, Rees, & Ehrenberg, 1991; Winkler, 1980) and the number of contractually allowed days of paid sick or personal leave. Rates of absence drop when incentive schemes like buy-backs of unused sick leave (Ehrenberg et al., 1991; Winkler, 1980) or bonuses for exceptional attendance (Freeman & Grant, 1987; Jacobson, 1990; Skidmore, 1984; White, 1990) are implemented. Teachers respond to changes in absence control policies. For example, teachers who are required to report absences directly to their principal by telephone are absent less often than teachers who report their absences indirectly, to either a centralized reporting center or a school-based message machine (Farrell & Stamm, 1988; Winkler, 1980).
The temporal pattern of teacher absences also suggests discretionary behavior. First, teachers are absent most frequently on Mondays and Fridays (Bundren, 1974; Educational Research Service, 1980; Malick, 1997; Pennsylvania School Boards Association, 1978; Strauss & Strauss, 2003), timing consistent with a desire to have longer blocks of leisure time (Rhodes & Steers, 1990). Second, a high proportion of teacher absences are of a duration just short of that requiring medical certification of illness (Educational Research Service, 1980; Rhodes & Steers, 1990).
Why Are Some Teachers Absent More Often Than Other Teachers?
Characteristics of teachers and schools, some easier to measure than others, have been linked to rates of teacher absence. As mentioned earlier, female teachers tend to be absent more often than male teachers. Researchers have also found a positive relationship between the distance that a teacher commutes to school and rate of absence (Beavers, 1981; Bridges & Hallinan, 1978; Educational Research Service, 1980; Scott & Wimbush, 1991; Winkler, 1980). A teacher’s age has also been linked to rates of absence, though this relationship is not monotonic—the youngest and the oldest teachers tending to be absent more often than teachers of intermediate ages (Bradley et al., 2007; Educational Research Service, 1980). Finally, teachers holding permanent status (tenure) with their employer tend to be absent more often than teachers with other types of employment status (Pitkoff, 1993).3
Characteristics of schools also play a role in explaining variation in rates of teacher absence. Numerous studies have documented a positive relationship between teachers’ rates of absence and school enrollment, and teachers in elementary schools are absent more often than teachers in secondary schools on average (Bridges & Hallinan, 1978; Educational Research Service, 1980). In previous work the authors of this article found significant differences in rates of absence among elementary schools, even after controlling statistically for characteristics of teachers that have been associated with rates of absence (Miller, Murnane, & Willett, in press). The theory of absence culture, first posited by Chadwick-Jones, Nicholson, and Brown (1982), has proven useful in explaining this variation in rates of employee absence among work units (Martocchio, 1994; Xie & Johns, 2000).4 In a case study, Imants and van Zoelen (1995) applied a cultural lens to schools in the Netherlands, finding strong relationships between aspects of school climate and rates of teacher absence, and Jacobson, Gibson, and Ramming (1993) found that school-level norms around attendance explained persistent differences in rates of teacher absence among elementary schools in a western New York district.
How Might Teacher Absences Affect Student Achievement?
The literature on the impact of employee absences on productivity in industries apart from education provides a backdrop for the current study. In an article published in 1983, Allen hypothesized that productivity loss from worker absences will depend on the extent to which managers can reassign workers from other positions and can find temporary replacements as productive as the absentees. In a 2006 article, S. Nicholson and coauthors used results of a survey of managers in 12 industries to test a number of hypotheses similar to Allen’s. They found that absences had larger negative effects on productivity the more difficult it was to find a perfect replacement, the more time sensitive the work involved, and the more the worker functioned as part of a team.
This pattern of findings suggests that the negative impact of teacher absences from urban elementary schools may be substantial. Good substitutes are notoriously difficult to find in urban districts. Many districts are responding to accountability pressures by pressing teachers to stick with instructional schedules aligned with state curriculum standards and the content of mandatory state tests. They are also investing in professional development that involves teachers working in teams to improve instruction and make it more consistent.
There are several mechanisms through which teacher absences may reduce student achievement. First, instructional intensity may be radically reduced when a regularly assigned teacher is absent (Gagne, 1977; Varlas, 2001). A substitute teacher showing movies is a time-honored illustration, but low skill levels of substitute teachers may contribute to the reduction in instructional focus. In contrast to policies of similarly industrialized countries (e.g., Canada, Australia), 19 states do not require that substitutes hold a bachelor’s degree (Henderson, Protheroe, & Porch, 2002), much less the equivalent licensure status of the regular teacher. Furthermore, No Child Left Behind specifically exempts substitutes from its otherwise ambitious requirements for teacher quality (U.S. Department of Education, 2004).
A second mechanism through which teacher absences may affect student achievement is through the creation of discontinuities of instruction, the disruption of the regular routines and procedures of the classroom (Rundall, 1986; Turbeville, 1987). Students may have difficulty forming meaningful relationships with multiple, mobile substitutes, and even if substitutes deliver brilliant isolated lessons, they may not be able to implement a regular teacher’s long-term instructional strategies. Furthermore, substitutes’ lack of detailed knowledge of students’ skill levels makes it difficult for them to provide differentiated instruction that addresses the needs of individual students.
Prior Studies Relating Teacher Absences to Student Achievement
Many studies have found a negative relationship between teacher absences and student achievement (Bayard, 2003; Beavers, 1981; Boswell, 1993; Cantrell, 2003; Lewis, 1981, 1991; Manatt, 1987; Pitkoff, 1989; Smith, 1984; Summers & Raivetz, 1982; Womble, 2001; Woods, 1990).5 However, these studies do not provide compelling evidence of a causal link between teacher absences and student achievement because they do not deal explicitly with the potential correlation between measures of teacher absences and unobserved levels of teacher skill and effort. For example, a high rate of absence may signal a teacher’s lack of skill or effort when he or she is in school. If this were the dominant pattern, then the observed negative relationship between teacher absence and student achievement would be an upwardly biased estimate of the causal impact of teacher absence on student achievement. Thus, the research challenge is to develop a strategy that permits unbiased estimation of the causal impact of teacher absence on student achievement.
Duflo and Hanna’s (2006) experimental study in which financial incentives for good attendance were provided to teachers in a random sample of elementary schools in rural India provides strong evidence of a causal relationship between teacher absence and student achievement. A year after the intervention began, test scores for students in the treatment schools were substantially higher (0.17 SD) than those of students in the control schools. This finding however may be peculiar to the context in which the study was done. The rate of teacher absence was extremely high (42%) compared to rates observed in the United States.
A study conducted by Clotfelter, Ladd, and Vigdor (2007) using data from North Carolina provides U.S.–based causal evidence that teacher absences negatively affect student achievement. Using a large data set in which teachers and students were observed in multiple years, they were able to control for time-invariant skill and effort levels of teachers. Their evidence indicates that 10 additional days of teacher absences decreased student achievement by 1% or 2% of a standard deviation. This finding however speaks to the average effect across rural, suburban, and urban districts alike. Our study focuses on one urban district, where the importance of high-quality instruction and the negative effects of teacher absence may be especially large because most students live in families that lack the resources to compensate for poor school-based instruction.
III. Data
We obtained data on students and teachers from the Ormondale School District (OSD),6 a large urban school district in the northern part of the United States. The district has nearly 80 elementary schools, with approximately 200 teachers and 4,000 students at each elementary grade level. OSD has an electronic report card system in place that supports the matching of students to individual classroom teachers. The OSD Office of Human Resources provided information on each of these teachers’ demographic characteristics, home zip code, absences, experience, licensure, and employment status over 3 consecutive academic years (SY03–SY05). For the purpose of constructing a measure of the distance that a teacher commuted from home to school, we obtained the geographical locations of schools from the Common Core of Data of the National Center for Education Statistics, and we purchased a commercial database that matched each zip code to the geographic latitude and longitude of its centroid.7 From the National Climatic Data Center (NCDC), we obtained files containing multiple measures of daily weather conditions in the vicinity of teachers’ homes. We accessed information on aggregate student enrollment, discipline, attendance, and demographics within each school from the Web site of Ormondale’s State Department of Education.
To situate our quantitative work in the reality of OSD, we interviewed four principals of the elementary schools represented in the data. Our open-ended questions explored principals’ views on teacher absence and substitute teachers. We also interviewed three central office personnel to gauge whether themes and tensions that emerged in the interviews with principals were representative of OSD elementary schools.
Demographic Characteristics of Teachers and Schools
Table 1 presents descriptive statistics on selected characteristics of 285 unique teachers and 75 elementary schools in which they teach fourth-grade students. Of these teachers, 125 taught for at least 2 of the 3 years represented by our data.8 Not surprising for U.S. elementary schools, more than 86% of the teachers were female. In all, 32% were African American and 5% were Hispanic. On average, teachers possessed 14 years of teaching experience. More than 8% of teachers were in their 1st year of teaching, and another 7% were in their 2nd year. Their average length of the home-to-school commute was slightly more than 7 miles, with almost 8% commuting more than 20 miles.9
Table 1 also presents means and standard deviations for variables measured at school level. Student enrollment for the schools in our sample ranged from 113 to 948 students, with an average of 364 students. Of the 75 schools, 9 in the sample had students from kindergarten through eighth grade; the others had students from kindergarten through fifth grade. The demographic composition of the student body varied markedly across schools. However, in all but 2 of the schools, at least half of the students were students of color, and 55 of the 75 schools had a student body that was made up of more than 80% students of color. Other indicators showing considerable variation include the out-of-school student suspension rate (M = 4.128, SD = 4.029) and the student retention rate (M = 5.067, SD = 2.493).
Patterns of Teacher Absence
In contrast to many previous studies of teacher absence, which rely on yearly aggregate measures of teacher absence, the data used in the present study include day-by-day information about teachers’ absences and their reported reasons for being absent. This information allows us to construct a measure of absence specifically tailored to estimating the impact of teacher absences on student achievement. Accordingly, Table 1 includes descriptive statistics on a count of absences by teacher and year that take place on instructional days before the late spring administration of the fourth-grade mathematics achievement exam.10
A cumulative measure of teacher absence, though appropriate for our main purpose, obscures two patterns that highlight the policy relevance of this article. Table 2 shows the percentage of teachers reported as absent by weekday over 3 academic years. The weekdays with the highest percentage of teachers absent are Friday (6.00%) and Monday (5.14%). In contrast, only 4.56%, 4.57%, and 4.39% of teachers were absent on an average Tuesday, Wednesday, or Thursday, respectively. These figures suggest that some OSD teachers tend to use their leave privileges to stretch out weekends, a pattern familiar to employers in education and other employment sectors (Educational Research Service, 1980; New York State Office of Education, 1974; Strauss & Strauss, 2003). In conversations with elementary school principals and central office personnel, we learned that the OSD’s Office of Human Resources acknowledges this pattern by supplying principals with periodic reports highlighting teachers with concentrations of absences adjacent to weekends.
When OSD teachers report an absence, they must provide an “excuse” code.11 Based on these codes, we constructed 12 categories of absence, listed in Table 3 in descending order of frequency. The percentage of absences attributed to personal necessity that occurred on a day adjacent to a noninstructional day (59.8%) was considerably higher than the 45.7% of instructional days adjacent to noninstructional days. All four of the principals we interviewed voiced the idea that many teachers viewed their allotment of personal necessity days as an entitlement that they could use to fit their preferences.12 Furthermore, these conversations suggest that high-quality, continuous leadership is critical to creating cultural norms that discourage the abuse of leave privileges. For instance, two of the principals said that they require teachers to call them directly on the morning of an absence.13
Student Achievement and Demographic Characteristics
Our analytic data set contains detailed information on a sample of 8,631 unique students who were in the fourth grade in one or more of the 3 academic years studied. Table 4 presents descriptive statistics for these students. Our primary outcome variable, student achievement in mathematics, is based on scores obtained on state-sponsored assessments administered to fourth-grade students in early May. We also used scores on the state-sponsored English language arts (ELA) examinations as outcomes. The data set also includes students’ scores on Stanford Achievement Tests (Series-9) of mathematics and reading that the students took while they were in third grade. We treated these prior measures as covariates in our regression analyses. For the 7% of students in our sample who repeated third grade, we used the highest available score to represent their prior achievement by domain.
Our data set also contains a variety of student-level demographic and programmatic variables that we included as covariates in our analyses. Demographic controls include (a) a vector of dichotomous indicators of student race/ethnicity (African American, Asian, Hispanic, White), (b) student gender, (c) whether English was the student’s first language, (d) whether the student received special education and related services, and (e) whether a student was eligible for free or reduced price lunch. As indicated by the summary statistics presented in Table 4, our analytic sample primarily contains disadvantaged students. More than 83% of the students were eligible for a free or reduced price lunch, 34% had a first language other than English, and 13% received special education. Our sample also consisted primarily of students of color: 47% of the students were African American, 29% were Hispanic, and 9% were of Asian background.
We constructed additional student-level covariates to account for important facets of the students’ academic participation. Using information on each student’s date of enrollment in OSD, we constructed dichotomous indicators of whether students entered their fourth-grade classes after particular points in the school year. Students who entered classes late in the academic year may have differed from other students in the extent to which their fourth-grade instruction was provided by the teachers in our data set. In addition, these students may not have experienced some portion of the teacher absences that provide the focus of our inquiry. We also constructed indicators of whether students had repeated third grade and whether they were repeating fourth grade in the current year.
Finally, we acknowledge a shortcoming of our data: its lack of detailed information on student absences. Using district-level aggregated data from New York, Ehrenberg et al. (1991) found evidence that teacher absences may affect students’ attendance behavior, each additional teacher absence inducing 0.08 additional student absences. The authors did not find evidence that the arrow of causality runs the other way, although their use of district-level aggregated data might conceal this case. Detailed information on student absence, especially day-by-day information, would allow us to explore this issue. Furthermore, it would offer insights about the mechanisms through which teacher absences may affect student achievement. Specifically, we would be able to examine the extent to which the impact of teacher absences on student achievement occurs through the mechanism of increasing student absences. We return to this theme in Section VI.
IV. Method
Our investigation of the causal impact of teacher absence on student achievement was conducted in a student-teacher-year data set in which there was a single record (“row”) of information for each student, i, with each teacher, j, in each year, t. In our baseline hypothesized regression model, we specified that student mathematics achievement depended on teacher absence, as seen in Equation 1,
where Y ijkt is the mathematics achievement of student i taught by teacher j in school k in year t. The predictor of interest, A jkt , represents the count of absences for teacher j in year t. T jkt is a vector of teacher characteristics (ethnicity, gender, years of experience, licensure status, tenure status, commuting distance, classroom student turnover rate) and school characteristics (enrollment, range of grades, suspension rate, and student attendance rate). S ijkt is a vector of student characteristics (ethnicity, gender, poverty status, language status, disability status, grade repetition status, and measures of prior achievement), and the δ t represents a set of year fixed effects to account for districtwide trends in teacher absence and student achievement.14 The ɛ ijkt is a complex error term.15
Threats to Validity
Estimates of β1 obtained by ordinary least squares (OLS) estimation of Equation 1 may be biased because rates of teacher absence may be correlated with unobserved levels of teacher skill or effort. Our primary strategy for dealing with this potential problem is to fit a variant of Equation 1 in which the time-invariant teacher characteristics are replaced by dichotomous indicators representing each teacher (fixed effects), save a reference teacher. This is a powerful strategy because the teacher-specific fixed effects absorb all time-invariant teacher skills and effort levels. Of course, because this strategy involves the estimation of β1 using only year-to-year variation in absences for the same teacher, we can only fit this version of Equation 1 for teachers who appear in the data set for more than 1 academic year.
Although powerful, the teacher fixed effects strategy does not deal with potential bias that may be introduced by time-varying differences in unobserved teacher effort or skill levels that may be correlated with teacher absences. For example, a teacher with a critically ill family member during the current academic year may be absent from school more days than during the previous academic year. However, weaker performance by the teacher’s students in the current year than in the previous year may reflect not only his or her absences from school but possibly his or her low energy levels and high stress levels when the teacher is in class. To address potential bias due to unobserved, time-varying correlates of student achievement and teacher absence, we use an instrumental variables (IV) strategy.
As Ludwig and Bassi (1999) explained in an earlier issue of this journal, a successful IV must have the following properties. First, it must predict the critical question variable, in this case, teacher absences. Second, it must not be correlated with the outcome of interest (student achievement) except through its relationship with the critical question variable (teacher absences). We derived two instrumental variables from information on the daily weather conditions in the community (NCDC weather station) in which each teacher lived. The first instrument is a count by teacher and year of the number of frigid days, those on which the minimum recorded temperature was below 24 degrees Fahrenheit (M = 39, SD = 11). The second instrument is a count by teacher and year of the number of days with a snow-pack, those on which there was snow (new or old) of measurable depth on the ground (M =38, SD = 16). It is important to keep in mind that the values of these instruments vary among Ormondale teachers in a given academic year. The reason is that teachers live in different communities that experience different weather conditions. For example, teachers who live north of the city are more likely to experience frigid temperatures and snow-pack than teachers who live south of the city.
Figure 1 illustrates the intuitive appeal of these instruments. Each circle represents the annual average number of absences (on the vertical axis) in bins defined by the number of frigid days. Each diamond represents the annual average number of absences in bins defined by the number of days with snow-pack.16 Notice that the annual number of absences is particularly high for teachers who experience around 60 days of frigid weather or snow-pack. Our analyses using a data set in which a teacher day was the unit of analysis verified that teachers are particularly likely to be absent from school on days in which the weather was frigid and there was snow on the ground in the community in which he or she lived.
We estimate two equations simultaneously to implement our IV strategy. One is the structural Equation 1, in which A jkt is the endogenous predictor of interest. In the second equation, Equation 2,
A ijkt is the outcome, X is a vector representing all predictors appearing in Equation 1 other than teacher absences, the W ijkt is a vector that includes the instruments, and ν ijkt is an error term. In carrying out the IV strategy, we omitted fixed effects for years from both equations. The reason is that the instruments take on relatively few unique values owing to the relatively small number of weather stations (17) to which teachers were matched. In other words, we need the year-to-year variation in the values of the instruments as well as the more modest variation among teachers in a given academic year in fitting Equation 2 . (As discussed in the following, the OLS results are not sensitive to the inclusion of the year fixed effects, which makes us optimistic that omission of the year fixed effects does not create bias in the IV results.)
We also applied the IV strategy to the sub-sample of teachers for whom fixed effects can be estimated at both stages. As described in the following, we subjected our primary estimation strategy to a set of sensitivity tests to examine the robustness of the findings.
V. Results
Table 5 presents parameter estimates, robust standard errors, and approximate p values from fitting the model in Equation 1 using our first analytic strategy. The columns of this table are labeled 1(a) through 1(c). Column 1(a) contains OLS estimates of the parameters in Equation 1 based on information on all 285 teachers who taught fourth grade in at least 1 academic year. Column 1(b) presents OLS estimates of the parameters in the same model, but using only the sample of 125 teachers who taught fourth grade in more than 1 academic year. We provide this column of estimates to facilitate comparison with those in column 1(c), which are the estimates from fitting the version of the model that includes fixed effects for teachers. The results reported in columns 1(b) and 1(c) are based on the same sample of teachers and students.
As indicated in column 1(a) of Table 5, the OLS estimate of the impact of teacher absences on students’ mathematics achievement is negative and significantly different from zero at the .01 level. When this model is refitted using only data on the sample of 125 teachers who taught fourth grade in more than 1 year, the estimated absence parameter retains a negative sign, has a somewhat smaller magnitude, and retains statistical significance (p < .05). The teacher fixed effect estimate in column 1(c) is almost identical in magnitude to the OLS estimate for the same sample and is statistically significant (p < .05). This pattern indicates that in this sample, teachers who have relatively weak unobserved teaching skills are not more likely to be absent than teachers with stronger teaching skills.
We also fitted models in which the students’ scores on the state fourth grade English language arts examination provided the outcome measure. The estimates of interest were consistently negative but were smaller in magnitude and less precise than the estimates obtained when mathematics achievement was the outcome.17 This pattern raises the question of why teacher absences would influence students’ mathematics achievement more than their ELA achievement. Our interviews with principals provided insight into the answer to this question. They told us that in SY01, OSD had adopted a new elementary school mathematics curriculum that placed great emphasis on developing students’ mathematical problem-solving skills, their ability to make use of alternative computational algorithms, and their ability to explain their reasoning processes in writing. For most OSD elementary school teachers, teaching the new mathematics curriculum successfully required the development of new teaching skills. The district invested heavily in mathematics coaches and in summer training institutes to provide OSD’s elementary teachers with the requisite skills. The net effect of the new mathematics curriculum and the retraining of OSD’s elementary school teachers—training that was not received by OSD substitute teachers—is that the gap in instructional quality in mathematics when a fourth-grade teacher was replaced by a substitute teacher was particularly large. This explanation for the larger impact of absences on students’ math skills than on their English language arts skills is consistent with S. Nicholson et al.’s (2006) findings on other industries reported earlier.
As mentioned earlier, even though the inclusion of the teacher fixed effects controls for potential time-invariant differences among teachers in unobserved skill and effort levels, it does not control for time-varying differences other than those captured by the time-varying measure of teacher experience.18 To address this problem, we implemented the IV strategy described earlier. Table 6 displays estimates of the parameters of Equation 2 (and robust standard errors, p values, goodness-of-fit statistics, and results of an F test of the strength of the instruments).
In the two columns on the far right of Table 6, the F test results allowed us to reject the null hypothesis that the parameters associated with the instruments are simultaneously zero (p < .01 in one case, p < .05 in the other). In addition, the signs and magnitudes of the parameter estimates make sense, by and large, with respect to the anticipated relationships illustrated in Figure 1. In particular, an increase of one frigid day is associated with a larger increase in the number of absences than is an increase of one day with snow-pack. Because the instruments are positively correlated (r = .36), the net effect of these estimates supports the idea that absence increases with the wintriness of the weather.
Several results featured in Table 6 are consistent with prior research. First, tenured teachers are more likely to be absent than nontenured teachers. Second, on average, male teachers are absent between 1 and 2 fewer days than are female teachers, holding all else equal (p < .01 for each specification). Third, African American teachers are consistently absent about 3 days more often than White teachers, on average, holding all else equal (p < .01 for each specification).19
As shown in Table 7, the IV estimates of the impact of teacher absences on student achievement are substantially larger in magnitude than their OLS counterparts. For example, the IV estimate in column 3 (–0.0444) is nearly 15 times larger in magnitude than the OLS estimate (–0.0031). For each of the model specifications shown in Table 7, the associated standard errors allow us to reject the hypothesis that the parameter associated with teacher absences is zero.
Of course, a critical question is why the IV estimates are so much larger than the OLS estimates. The explanation that we favor is that unplanned teacher absences have a greater impact on student achievement than planned absences do and that the IV estimate is capturing the impact of unplanned absences. Reasons that unexpected teacher absences could be particularly detrimental to student achievement include the difficulty of finding suitable substitute teachers at the last minute and the likely low quality of the lesson plans teachers leave when they do not anticipate being absent.
The reason that the IV estimate is capturing the impact of unplanned absences is that it is these absences that are influenced by weather. In the language methodologists use, the IV estimates are local area treatment effects (see e.g., Morgan & Winship, 2007). To test this idea, we returned to the teacher day data set from which we derived the measures of absence and weather used earlier. We created two new dichotomous indicators. The first assumed a value of one for an absence due to a short-term illness, those of 1 or 2 consecutive days. The second assumed a value of one for an absence due to personal necessity (absences that teachers announce several days before they take them and that, as shown in Table 3, are the third largest category of absences). Using each of these indicators as the outcome, we fitted models to a data set in which an observation is a teacher day and the only predictors were the precursors to our instruments, minimum daily temperature and depth of snow on the ground. In the case of short-term absence, the R-squared statistic was virtually the same as when the outcome was the simple indicator of absence (.0006). In the case of personal necessity, the R-squared statistic was lower (.0000). Thus, the precursors to our instruments are more successful in predicting absences due to short-term illness than in predicting planned absences. This evidence is consistent with the notion that our IV estimates represent the marginal impact of unplanned absences as opposed to the average marginal impact of all absences.
One alternative explanation for the difference in magnitude between the IV results and the OLS results is that the IV estimates are contaminated by differences in student achievement across the 3 years used in fitting the IV model. This is possible because, as explained earlier, we need the variation in weather conditions across the 3 years to fit the first-stage equation (Equation 2) in the IV approach. To explore this possibility we fitted the OLS models using specifications that did not include the fixed effects for years. The results were not substantively different from those in which fixed effects for years were included in the models. This leads us to the conclusion that the difference in magnitude between the IV results and the OLS results does not stem from omission of the year fixed effects from the models estimated with the IV approach. Another potential explanation is rooted in potential correlation between the instruments and student absences, detailed information about which was not available to us. Correlation between either instrument and student attendance measured at the level of the school was negligible (|r| < .03 in both cases).
Threats to Validity
We conducted several sensitivity tests to examine the robustness of our primary findings. First, we assessed whether the teachers exhibiting the most extreme absence behavior drove the findings. To do this, we omitted teachers with pretest absences in excess of 63 (99th percentile) from the data set and refitted the various models. The key results for the remaining teachers were actually larger in magnitude than those presented in column 1(a) of Table 5. Surprisingly, the loss of teachers did not lead to appreciably larger estimated standard errors in columns 1(b) and 1(c) and a loss of statistical significance. This reassures us that the few teachers with the most absences are not driving the findings. Second, we omitted the 19% of students who were missing values on one or the other of our measures of prior achievement. The resulting parameter estimates were identical in sign and similar in magnitude to their analogues presented in Tables 5; standard errors were of course larger. Third, we omitted the classrooms corresponding to the 3% of teachers for whom we imputed values of teaching experience. Corresponding results were nearly identical in all respects to those presented in Tables 5. Finally, in four successive steps, we omitted from the data set students who entered their classes after January 15, December 15, November 15, and October 15, each time refitting the models embodying our analytic strategies. These results were very close to those presented in Table 5.
VI. Discussion
Contribution
Our article adds to the small amount of literature examining the causal effects of teacher absences. Our focus on a single large urban district enabled us to document important patterns of absence based on local school calendars (including snow days) and a single collective bargaining agreement. Furthermore, interviews with principals in four of the schools in our research site provided interpretations of teacher absence patterns and especially a compelling explanation for why teacher absences in OSD affected students’ mathematics achievement more than their ELA achievement. Of course, although there are many advantages of focusing on the impact of teacher absences in a single urban school district, there are disadvantages as well. In particular, it is not clear whether the patterns present in this district, one that focused intensely on professional development aimed at improving the teaching of demanding mathematics curricula, pertain to other districts.
We supplement our primary analytic strategy with an instrumental variables strategy that bolsters the case for causal interpretation. The IV results indicate that unexpected absences have a larger impact on student achievement than do anticipated absences. The complementary estimation strategies showcase a way to bring information that is routinely collected on teachers on a daily basis—whether they are absent and if so, why—to bear on an important question of educational productivity.
Nontrivial Impact
We believe that our estimate that 10 additional days of teacher absence reduce student achievement in fourth-grade mathematics by at least 3.2% of a standard deviation is large enough to be of policy relevance. This is especially the case in today’s accountability system, in which even small differences in achievement will influence whether schools satisfy the annual yearly progress requirements of the No Child Left Behind legislation. Moreover, our IV estimates indicate that 10 additional days of unexpected absences reduce student achievement in mathematics by more than 10% of a standard deviation.
Potential Policy Implications
Because our study did not examine the impact of particular policies aimed at altering the distribution of teacher absences, it cannot provide evidence on the consequences of policy changes. However, our evidence that teacher absences do affect student achievement makes it worthwhile to review briefly existing evidence on the effects of school and district policies on the distribution of teacher absences. Teachers’ rates of absence are positively associated with the generosity of leave provisions, such as the number of contractually allowed days of paid sick or personal leave (Ehrenberg et al., 1991; Winkler, 1980). Rates of absence drop when incentive schemes like buy-backs of unused sick leave or bonuses for exceptional attendance are implemented (Ehrenberg et al., 1991; Freeman & Grant, 1987; Jacobson, 1990; Skidmore, 1984; White, 1990; Winkler, 1980).
Another previously reported finding is particularly salient. Teachers who are required to report absences directly to their principal by telephone are absent less often than teachers who can report their absences indirectly via a centralized reporting center or a school-based message machine (Farrell & Stamm, 1988; Winkler, 1980). Ironically, the planned implementation of a Web-based absence reporting system in OSD will undercut the practice of two of the four principals we interviewed who require that teachers report absences directly to them by telephone.
Other possible policies reduce the detrimental impacts of unexpected teacher absences by providing better substitutes. Creating a stable pool of substitutes may reduce discontinuities in instruction. Three of the four principals we interviewed talked about explicit strategies to bolster stability and quality of substitutes in their buildings.20 Complementary policies seek to improve the quality for the lesson plans that teachers leave for substitutes.
Future Research
As mentioned earlier, our data’s lack of fine-grained information on student absences hamstrung our ability to address three important issues. First, we could not test the hypothesis that student absences stimulate teacher absences (Ehrenberg et al., 1991). Second, we could not examine the extent to which the impact of teacher absences on student achievement takes place through the mechanism of increasing student absences. Third, we were unable to test convincingly potential correlation between the weather indicators used as instruments and student absences. Our inability to bring detailed information on student absences to bear in the study reported here leaves open one direction for future research.
Advances in administrative record keeping will make it possible in the near future to improve studies of the impact of teacher absence on student achievement in two ways. First, information on the characteristics of substitute teachers matched to teacher absences will allow researchers to explore possible heterogeneity of effects due to differences in substitutes. Web-based absence reporting and substitute assignment systems promise to make such data available in the near future. Second, perhaps the greatest tool for assessing productivity costs of teacher absences will be frequent measures of student achievement. The increasing use of computer-based benchmark assessments administered throughout the school year should provide such data in the near future.
Footnotes
1
Most research on employee absence focuses on absenteeism, a term denoting the voluntary or avoidable kind of absence (Rhodes & Steers, 1990). We have intentionally avoided the term absenteeism for three reasons. First, the term has a pejorative flavor that we do not wish to impart. Second, although our data include detailed information on teachers’ reported reasons for absence, we do not observe the true motivation of particular absences. Third, student achievement may be compromised during any absence of the teacher, irrespective of motivation.
2
State policies are also relevant. For example, the California state teachers retirement system was modified in 1997 to make more teachers eligible to purchase extra retirement benefits in proportion to their accumulated, unused sick leave.
3
The effect of protected employment status on absence behavior is not surprising. It has been carefully documented in other industries (Ichino & Riphahn, 2005).
4
Absence culture, as defined by Chadwick-Jones, Nicholson, and Brown (1982), refers to the collection of the professional norms related to teacher absence by school. The salience of the culture is a measure of the strength with which these social norms affect the absence behavior of individual teachers. An absence culture with high salience could contribute to high or low rates of absence. Which situation obtains depends theoretically on the extent to which teachers feel trusted by the building administration. See Martocchio (1994) or 
for empirical work that uses this theory explicitly.
5
There are exceptions to this pattern. Studies that have not found a correlation between teacher absences and student achievement include Ehrenberg, Ehrenberg, Rees, and Ehrenberg (1991); Kirk (1998); New York City Public Schools (2000); . The Ehrenberg et al. article, for example, used data aggregated to the level of the school district.
6
In accordance with the wishes of district officials, Ormondale School District (OSD) is a pseudonym.
8
That only 125 of the 285 teachers are represented in more than 1 year in our data set troubled us. In addition to high rates of turnover, some OSD elementary schools engage in the practice of cycling, by which teachers follow cohorts of students through a sequence of two or more grades.
9
We constructed the measure of commuting distance by applying the standard formula from spherical trigonometry to the geographical coordinates (longitude, latitude) of a teacher’s school and home (centroid of the home zip code).
10
The achievement exam for English language arts takes place several weeks before the mathematics exam. Thus, to support estimates of the impact of teacher absences on English language arts achievement, we modify the measure of teacher absences by simply counting over fewer days.
11
There were 46 distinct “excuse” codes, and their names provided a reasonable basis for creating less fine-grained categories of absence.
12
Full-time OSD teachers were eligible for up to 3 days of paid leave due to personal necessity until SY05, when the new collective bargaining agreement upped the figure to 4 days. One principal noted that OSD’s budget office did not adequately anticipate the concomitant increase in school-level expenditure for substitute teachers.
13
OSD teachers are contractually bound to report their absences using a centralized telephonic system. Thus, these principals’ direct reporting requirement represents an informal, school-level policy.
14
The change in the number of days of paid leave for personal necessity, mentioned earlier, is an example of such a trend. With respect to achievement, OSD systematically strove to produce improvements in all schools during the years we studied with heavy investments in professional development, particularly around implementation of a standards-oriented mathematics curriculum. Thus, allowing for different average levels of achievement by year makes analytical sense.
15
In an analytic appendix to their 2006 article, Uribe, Murnane, Willett, and Somers explained alternative ways of specifying and fitting models to account for multilevel structures in data. Because 14% of teachers in our data set actually change schools, we check our results with a multilevel approach to fitting models (Stata’s xtmixed) that uses maximum likelihood estimation to produce point estimates and standard errors that respect this cross-nesting. We opted for a parsimonious error structure (random intercepts) because the more complex one produced similar results.
16
The 285 teachers represented in our data set were matched to a total of 17 National Climatic Data Center weather stations. This fact, combined with the integral values of the instrumental variables, leads to a sparseness of observations of teacher absence associated with particular values of the instrumental variables. We combated this sparseness by creating bins for each instrument. We experimented with weighting the size of the circles and diamonds in by the number of observations captured, but we preferred the simpler picture seen here.
17
Tables providing these results are available from the authors.
18
We rely on teaching experience as a proxy for teacher quality because our data lack any other measures of teacher quality that researchers have found useful. We note that many such measures (e.g., competitiveness of undergraduate college, National Board Certified) could probably not be treated as time-varying measures in our models, owing to a lack of variation. It would however be valuable to explore further the possibility that the effect of teacher absence varies with levels of observed teacher quality. Our explorations based on teaching experience did not yield interaction effects, perhaps because teaching experience is a weak proxy for teacher quality.
19
One possible explanation is that African American teachers are systematically assigned to schools with working conditions associated with higher rates of teacher absence. To test this hypothesis, we refit the model corresponding to column 1 including a set of fixed effects for schools. The coefficients on teacher race/ethnicity were virtually identical in the model with school fixed effects to the analogous coefficients in the model fitted without school fixed effects.
20
One principal favors the use of teaching interns (licensure candidates completing the practical portion of their program at a local university or college) in conjunction with substitutes. The interns work in coordination with the regular teacher and become acquainted with the students, thus guarding against potentially lower intensity of instruction and discontinuity of instruction during days of teacher absence. Several principals described their efforts to nurture particularly effective substitutes, whom they view as promising candidates for jobs as regular teachers.