Socioeconomic differences in the long-term effects of teacher absence on student outcomes

ABSTRACT School teachers’ sickness absence has been shown to affect student achievement in the short run. However, we know little about whether socioeconomic backgrounds may compensate for reductions in instructional quality and to what extent teacher absence effects persist over time. This paper examines the socioeconomic differences in the short- and long-term effects of teacher absence. We use population-wide Norwegian register data to study the effects of certified teacher absence during lower secondary school (grades 8–10) on non-completion of upper secondary education by age 21 (i.e. school dropout) as well as academic achievement in 10th grade. In a school fixed effects model, we find that an increase in teacher absence of 5 percentage points reduces students’ examination grades by 2.3% of a standard deviation and increases the dropout probability by 0.6 percentage points. However, the teacher absence effects vary considerably by family background, with large effects for low-SES students driving the overall effects. Overall, our findings indicate that reductions in instructional quality increase social inequality in long-term educational outcomes. This result highlights that studying heterogeneous impacts of contextual exposures is needed to understand the role of schools in shaping inequality.


Online Appendix B: Robustness checks
When concluding on cause-and-effect relationships, it is crucial to account for factors that may confound the estimates.Based on the school fixed effects model, we find that teacher absence impairs students' academic achievements and subsequently increases school dropout risk.
Taking account of time-invariant school characteristics (i.e., school fixed effects) is seemingly important as the estimated effects of teacher absence without these fixed effects are considerably larger (Table 2).Still, a concern is that the within-school variation in teacher absence could be (partly) caused by variation in the share of students with behavioral and academic problems, even if we condition on time-variant student family background characteristics.This online appendix investigates this concern empirically by using a subset of the overall cohorts, for whom we have access to richer data.The smaller sample size in most of these sensitivity analyses reduces the precision of the estimated effects.For that reason, we choose to focus on the average impact of teacher absence.
We explore the robustness of the results from three complementary angles: by studying whether potential confounders influence teacher absence (i.e., with teacher absence as an outcome, Table B1), whether teacher absence influences potential confounders (Table B2), and by comparing the estimated effects of teacher absence with and without the potential confounder (Tables B3-B4).The benefit of the first two approaches is that they examine the selection mechanisms we are interested in, and we need to be less concerned about whether the confounders are adequately measured.The latter approach's advantage is that it directly suggests the size of bias in the teacher absence coefficient, but measurement error or incompleteness in the observed proxy matters.As an illustration, child delinquents' classroom behavior may influence teachers' absence, allowing us to test the concern of reverse causality.
Still, as child delinquency is rare, it is a poor proxy for general classroom behavior, and controlling for child delinquency is unlikely to influence estimates notably.Standard errors clustered at school level in parentheses.All models include school fixed effects, individual controls, and teacher controls.Measures of school environment are obtained from an annual nation-wide survey among all 10 th graders in Norway (>90% response rate), which we can match to our register data on the schoolcohort level for cohorts 2007-2012 and cohorts 2014-2015.Student-reported frequency of classroom noise is measured on a five-point scale (1=fully agree with classroom order, 5=fully disagree with classroom order), and is standardized to have a pupil-weighted mean of zero and standard deviation of 1. Student-reported school wellbeing is measured on a five-point scale (1=does not enjoy school very much, 5=enjoy school very much), and is standardized to have a pupil-weighted mean of zero and standard deviation of 1. School bullying measures the share of students that report being bullied at least 2-3 times a month, which in our sample is 7.9 percent of the students.For the cohorts 2007-2009, we do not observe the indicator classroom noise, and replace missing values with zero for these cohorts and include a dummy for missing values.* p < 0.05, ** p < 0.01, *** p < 0.001 From 2007 and onwards, every student in Norway must undergo nationwide standardized testing in reading, math, and English.The 8 th -grade test is basically an entry test since it occurs during the fall semester, shortly after the students start.Using the average of these national tests across subjects as a predictor, we do not find any indications of higher teacher absence in cohorts (within schools) with lower entry-test scores (panel A in Table B1, column 1 in Table B2).This suggests that reverse causality or simultaneity bias is not a major concern in our school fixed effects model, which aligns with previous literature using teacher fixed effects (Herrmann and Rockoff 2012).
Further, we test the concern of reverse causality and simultaneity bias more explicitly in Table B3, where we re-estimate our main results for a subset of the data (for which 8 th -grade test scores are available) using a value-added school fixed effects model.Relative to the coefficients' precision, the point estimates are similar whether entry tests are controlled for or not; the coefficient difference between columns (1) and ( 2) is about 60% of the standard error.Finally, our identifying assumption is supported by 8 th -grade test scores as a placebo outcome since there is no significant correlation between these scores and subsequent teacher absence for the same cohort (Appendix Table B5).There is a potential concern that student behavior or an unhealthy school environment causes teacher absence and poor student performance.About 1 percent of the students have received a criminal charge before entering lower secondary school (by the age of 12), which can be taken as an indicator of child behavioral problems. 1We find that the rate of teacher absence is similar for students with criminal charges by the age of 12 as for other students (Panel B in Table B1, column 2 in Table B2).It is also reassuring that we find no association between our teacher absence measure and poor marks in order and conduct in grade 10 (Panel C in Table B1, column 3 in Table B2).In our sample, 2.3% of the students obtain poor marks in order and conduct, which measures behavior such as being late to class, not doing the homework, being violent, and cheating on tests.As this is graded in the last year of lower secondary schools, any positive association could be interpreted as a combination of a causal effect of teacher absence on behavioral problems and a causal effect of behavioral problems on teacher absence.Finding no association suggests that confounding because of time-variant (unobserved) student behavioral problems is not a major issue in the school fixed effects models.Again, we test this more explicitly in Table B3, and the inclusion of behavioral problem indicators does not change the estimated effects of teacher absence (columns 5-12).
Finally, we explore the importance of an unhealthy school environment using studentreported school environment measures, available from an anonymous annual nationwide survey among all 10 th graders in Norway for cohorts after 2007.We find that more classroom noise, less school well-being, and more school bullying are associated with poorer examination grades and more dropout (Table B4).However, controlling for these variables does not change the estimated effects of teacher absence, leaving us less concerned about confounding school factors.
Besides reverse causality, another concern in the school fixed effects model is a common shock that increases teacher absence and directly affects students' learning.For some student cohorts, we can observe their visits to their general practitioner (GP) from the register of Control and Payment of Health Reimbursement (Torvik et al. 2018).Under the assumption that the variation in student GP visits within schools is a proxy variable for common health shocks, these GP visits could indicate to what extent such shocks bias our main results.Looking at the results in panel D of Table B1 and column 4 in Table B2, we see that the number of GP visits is weak but positively associated with teacher absence.However, the effect is trivial and could reflect a causal effect of teacher absence on student health: a 1SD increase in the number of GP visits increases the teacher absence rate by 0.00009 (Table B1), and a five-percentage point increase in teacher absence raises GP visits by 0.05 per year (Table B2). 2 Moreover, the estimated effects of teacher absence on standardized examination grades are nearly identical with and without student GP visits as a control (columns 3-4 in Table B3).
Since dropout rates differ by region in Norway, we are concerned about correlated trends in the outcome variables and the treatment variable that are regionally specific.Thus, we have checked whether the results are robust to including regional-specific cohort fixed effects (19 counties).Concerning short-term academic achievements, the results are largely unaffected by the inclusion of school county-specific cohort fixed effects.The effects on dropout are more affected by county-specific cohort fixed effects, with point estimates reduced by roughly 20%. 3 However, the precision is also reduced when including regional-specific cohort fixed effects, and the confidence intervals with the different specifications overlap (Appendix Figure B1).
2 Calculated as the effects of teacher absence multiplied by 5 (i.e., five percentage point increase) divided by 3 to get the annual effect: 3.1082 * .05 3 ⁄ . 3As shown in Online Appendix Figure B1, including school municipality specific cohort fixed effects for the 286 school municipalities reduces the estimated effects of teacher absence on dropout by roughly 35% and renders the coefficient significant at the 9.3% level only.Note: The coefficient in the cohort fixed effects and school county specific cohort fixed effects are also shown in Table B6.Finally, the school fixed effects only account for stable between-school differences in teacher characteristics, student characteristics, and school resources.With a long observation window, the fixed effects estimator may produce biased estimates if schools systematically change over time in a way correlated with teacher absence.To meet this concern, we re-estimate the main results with a six-year rolling average, which for the latest cohorts coincides with the period we have information on entry tests (see above).The average teacher absence effect fluctuates somewhat across the cohorts, but there is no trend (Panel A and B in Online Appendix Figure B2).In contrast, there seems to be a decline in the socioeconomic gradients in the teacher absence effects on examination grades towards the end of our observation period.
Unlike for the first nine cohorts, the parental earnings interaction coefficient is close to zero in the last six cohorts, which holds whether entry test scores are conditioned on or not (Panel C).
However, the confidence intervals overlap for all cohorts, and no strong conclusion concerning time trends can be drawn from the data.

Figure A1 :
Figure A1: Density of teacher absence by year of graduation.

Figure A2 :
Figure A2: Quantile-plot showing the fraction of data with teacher absence at a given level.

Figure A3 :
Figure A3: Non-linear effects of teacher absence on dropout and examination grades with 95% CI.Note: The teacher absence variable is grouped in 10 groups and included as dummies in a school fixed effects model.

Figure A4 :
Figure A4: Bivariate association between parental earnings rank of the student and teacher absence.

Figure A5 :
Figure A5: Effects of teacher absence on examination grades and grade point average across the outcome distributions.Note: Coefficients are estimated using RQR.Examination grades are artificially smoothed but not grade point average.

Figure A6 :
Figure A6: Effects of teacher absence on examination grades and grade point average using RQR, generalized quantile regression (GQR), and unconditional quantile regression (RIF-OLS).Note:In RIF-OLS, the kernel density estimate is oversmoothed for examination grade because of heaping, but not for grade point average.To smooth the examination grades variable in GQR and RQR, we add uniform noise to jitter the data (Machado and Silva 2005) using a uniform distribution over the interval[-0.5,0.5].The GQR model is estimated using the user-written Stata command genqreg with dummies for school ID.

Figure A8 :
Figure A8: Association between examination grades and dropout in a same-sex twin fixed effects model.Note: The predicted probability of dropout is based on a linear probability model that includes examination grades, examination grades squared, same-sex twin pair fixed effects, and cohort fixed effects.Twins are defined as individuals born in the same calendar month by the same biological mother.Standard errors clustered at mothers.See Appendix TableA8for estimated association between examination grades and dropout without twin pair fixed effects.

Figure A9 :
Figure A9: Product method to suggest how much of the teacher absence effects on dropout is explained by examination grades.Note: Panel (a) display the average marginal effects (AME) calculated based on a linear probability model of the effects of examination grades and its squared term on school dropout, using a sample of same-sex twins with a twin pair fixed effect and cohort fixed effects.Subsequently, AME is calculated at various percentiles of the grade distribution.Panel (b) includes the quantile treatment effects, and is identical to the estimates shown in Figure 2. Panel (c) display the product of the coefficients in Panel (a) and Panel (b), and shows the calculated effects of teacher absence on dropoutmediated through examination gradesfor students in different part of the grade distribution.The average of the calculated effects of teacher absence on dropout in panel (c) is 0.0399.

Figure B1 :
Figure B1: Effects of teacher absence controlling for cohort fixed effects, school county specific cohort fixed effects, and school municipality specific cohort fixed effects.

Figure B2 :
Figure B2: Socioeconomic gradients in teacher absence effects in six-year rolling averages compared to all available cohorts.

Table A1 :
Teacher absence by year

Table A3 :
Effects of teacher absence on grade point average from lower secondary school.Standard errors clustered at schools in parentheses.All models with school fixed effects, individual controls, and teacher controls.p < 0.05, ** p < 0.01, *** p < 0.001 *

Table A4 :
Effects of teacher absence on examination grades using RQR Standard errors clustered at schools in parentheses.All models with school fixed effects, individual controls, and teacher controls.The difference in coefficients shows difference between coefficients at different quantiles, along with the standard error of the difference.

Table A7 :
Teacher absence exposure by parental background of the student.

Table A8 :
Effects of examination grades on school dropout.

Table A9 :
Percent reduction in the socioeconomic dropout gap in a hypothetical setting without teacher absence.

Table A10 :
Variation in teacher absence and outcomes within and between schools.

Table B1 :
Variation in teacher absence Standard errors clustered at school level in parentheses.All models with school fixed effects, individual controls, and teacher controls.Estimates in panels are from different models.p < 0.05, ** p < 0.01, *** p < 0.001 *

Table B3 :
Robustness checks Note: Standard errors clustered at school level in parentheses.All models with school fixed effects, individual controls, and teacher controls.Sample size varies because of data availability.* p < 0.05, ** p < 0.01, *** p < 0.001