Economics of Education Review 89 (2022) 102251 2accurate information on expectations as well as consequences (Connell &Wellborn, 1991; Downer, Stuhlman, Schweig, Martínez&Ruzek, 2015). A positive teacher-child relationship also correlates with peer acceptance, which is crucial for a warm classroom climate (Howes et al., 1994). By contrast, negative interactions (e.g., yelling, humiliation) may result in emotional distress, possibly causing distractions and behavioral challenges (Parker&Asher, 1987; Pianta, 1997). The numerous studies that suggest that teacher relationship skills, as perceived by the student, are essential for learning may be biased by students’(unobserved) preferences for a particular relationship. Recently, economists have started to use systematic classroom ob- servations to measure teacher practices that are less affected by such idiosyncrasies (e.g., Araujo et al., 2016; Kane, Taylor, Tyler&Woo- ten,2011).However,theseclassroomobservationsare resource-intensive and may fail to capture fundamental aspects of students’sentiment that ultimately drives behavior (Connell&Well- born, 1991). Moreover, there is a need to evaluate teachers and what goeson inside theclassroom using various assessments (Kane& Staiger, 2012). This study introduces and validates a new approach to measure teachers’overallcapacitytoformpositiverelationshipsandin- vestigates its effect on student learning. We use rich, high-quality data on 5830 students in 300 classes from 150 schools in Norway from the Two Teachers project (see Solheim, Rege&McTigue, 2017, for the experimental protocol), a randomized controlled trial analyzed in Haaland, Rege, and Solheim (2022). We analyze treated and non- treated children together, which we discuss in further detail in Section 2.2.3These early years lay the foundation for the productivity of future investments and are thus especially important (Cunha&Heckman, 2007). Trained and certified testers assessed the children in one-to-one assessments(inmath,literacy,andsocio-emotionalskills)atthe beginning of first grade and the end of first, second, and third grade. We matched these assessment data to class and school identifiers and registry data on the family background provided by Statistics Norway. To measure teacher relationship skills, we asked the students a broad set of questions that capture several dimensions of the teachers’ability to form positive relationships with and among the students. We use a leave-out-mean specification to account for the bias that arises from the students’preferences for a particular type of relationship. Accordingly, the contribution of our paper is twofold. We first introduce and validate a new approach to measure teachers’overall capacity to form positive relationships (at the class level), relying on student survey items previously developed and validated (at the student level) in the education literature. We denote this measure asteacher relationshipskills.Wevalidatethismeasureintwoways:(1)we demonstrate stability over time; and (2) we illustrate that there is not onlyaconsiderablevariationinteacherquality(asmeasuredby learning outcomes conditional on past achievement) but also in teacher relationship skills, even within the same school. Second, we show that children taught by teachers with better relationship skills develop more academicallyandsocially-emotionally.Theseresultsevenholdin models that carefully address selection and noise from idiosyncrasies in survey responses. Math and literacy are our primary outcome measures. Test scores may not capture all relevant aspects of development, however. Given the importance of early literacy and the growing recognition that social- emotional skills (e.g., beliefs, motivations, interests, and personality traits) are critical to school performance, labor market outcomes, and social behavior (e.g., Bettinger, Ludvigsen, Rege, Solli&Yeager, 2018; Borghans, Duckworth, Heckman&ter Weel, 2008; Heckman, Stixrud& Urzua, 2006; Jackson, 2018; Kraft, 2019), we also focus on skills closely related to motivation in reading: self-concept in reading and reading interest. The former is a measure of children’s perceived competence in reading.4 We leverage the as-good-as random class assignment in Norwegian primary schools when investigating how teachers’relationship skills affect student learning. By law, school administrators in Norway should not assign children to classes based on sex, religion, ethnicity, or ability (Kunnskapsdepartementet, 2017). Consistent with this law, our analysis demonstrates that predetermined variables and variables measured at thestartof first grade are not predictive of class, teacher, or peer group characteristics.5Furthermore, we conduct several placebo, sensitivity, and robustness analyses supporting our (identifying) assumptions. Still, as discussed carefully in our concluding section, our estimates should be interpreted with caution, as we have no source of clean exogenous variation in teacher relationship skills. We find that teacher relationship skills affect math, literacy, and students’reading motivation. A one standard deviation increase in teacher relationship skills raises math test scores by about five percent of a standard deviation and literacy test scores by about three percent of a standard deviation. Five and three percent of a standard deviation is, respectively, about 15 and 10 percent of the difference in math and literacy test scores between students of mothers with and without a college degree. Concerning a child’s motivation to read, we find that teacher relationship skills affect reading interest by about five percent of a standard deviation and self-concept in reading by about three percent of a standard deviation.6We find larger point estimates for boys and children from low socioeconomic households, but the differences are not statistically significant. Lastly, the evidence indicates that the effects of the teacher relationship skills in first grade persist in second grade and for literacy even until third grade, which suggests that the first-grade findings are not an anomaly. Our paper makes several contributions. The value-added literature referred to in the first paragraph provides ample evidence on variation in teacher value-added. The use of learning gains (conditional on prior achievement and other influences) as a measure of teacher effectiveness is ubiquitous in the literature. However, such value-added measures only allow identifying and not replicating effective teachers, as Kane et al. (2011) rightly note. In this paper, we show that the teacher’s overall capacity to form positive relationships–as measured from the students’perspective–affects student learning and relates, therefore, to effective teaching practices and provides a new perspective on teacher evaluations, which is desirable (Kane&Staiger, 2012). A growing number of studies look at objective and subjective eval- uations conducted by peers or administrators to understand how to replicate effective teachers (Araujo et al., 2016; Kane et al., 2011; Rockoff&Speroni, 2010). Such studies examine the effect of evaluated teacher practices on student learning. Araujo et al. (2016) filmed each kindergarten class for a full day and coded the videotapes using the Classroom Assessment Scoring System (CLASS: Pianta, LaParo&Hamre, 2008). CLASS categorizes teacher-child interactions into three domains: emotional support, classroom organization, and instructional support. By leveraging as-good-as random assignment to classrooms, they show that teacher quality, measured using CLASS, in yeartis a strong pre- dictor of learning outcomes in yeart+1. Kane et al. (2011) focus on the Cincinnati public school system and investigate the effect of teachers’ ability to create an environment for learning and general teaching 3We present several robustness checks that suggest our findings concerning teacher relationship skills are not due to the treatment. 4Jensen, Solheim, and Idsøe (2019) find a strong correlation between the individuallyperceived emotional support and self-concept in reading. 5Additionally, Chi-square tests of homogeneity reveal a pattern of mean differences between classes (within schools) that is consistent with as-good-as random assignment. 6When we use a control function approach to address the bias of students’ preferences for a particular type of relationship in survey responses, we find effect sizes of seven, four, nine, and six percent of a standard deviation for math, literacy, reading interest, and reading self-concept, respectively. M.W.P. Thijssen et al.
Economics of Education Review 89 (2022) 102251 7Assumption 1. (Random Assignment)Children and teachers are as- good-as randomly assigned to classes such that any systematic differences occur at the school level:φjk=φk. Importantly, Assumption 1 doesnotpreclude random assignment of unobserved teacher attributes (e.g., didactic capabilities) or teachers’ behaviors (Araujo et al., 2016). These unobserved characteristics may correlate with the teacher’s overall capacity to form positive relation- ships, affecting a child’s learning. Fortunately, we have access to a rich set of student and classroom-related covariates such as the teacher’s experience, age, sex, education, and class size. Therefore, we assume: Assumption 2. (Exogeneity)Conditional on the child, peer, teacher, and classroom observables, the teacher relationship skills, Xjk, do not correlate with the error term,εijk. A simple class average (i.e.,Xjk≡1/Ijk ∑Ijk i=1Xijk) is a noisy measure when unobserved preferences for a particular teacher correlate with the children’s level of effort and learning and shape their perceptions and hence their evaluations. For instance, as Dee (2004) pointed out, some childrenmaypreferaspecificteacheridentitybringingabouta role-model effect that increases their learning engagement and causes them to evaluate their teacher more positively. In other words, there would be an“own-observation problem”(Chetty et al., 2011, p. 1635). Formally, denoteθjkas the effect that is due to the teacher and denote ρijkas childi’s unobserved preferences such that: Xjk≡1 Ijk ∑Ijk i=1 Xijk=θjk+1 Ijk ∑Ijk i=1 ρijk(3) We assume no peer effects (i.e.,σ(θjk,ρijk) =0 andσ(ρijk,ρi′jk) =0 for i∕=i′ , whereσ(⋅)is the covariance operator). If childi, who favors the teacher for some unobserved reason, subsequently evaluates the teacher more positively,σ(Xjk,ρijk)>0, and as a result increases effort and learning,σ(YG1 ijk,ρijk)>0, then we have an upward bias inβwith finite class size (see Web Appendix D).18Therefore, the leave-out-mean ad- dresses the bias due to unobserved preferences assuming: Assumption 3. (No Peer Effects)A child’s unobserved preferences do not correlate with the teacher’s overall capacity to form positive relationships, σ(θjk,ρijk) =0, and unobserved preferences of child i do not affect the un- observed preferences of child i′ ,σ(ρijk,ρi′jk) =0for i∕=i′ . Even under Assumption 3, there is still a bias. Intuitively, childi’s unobserved preference,ρijk, still correlates withX( i)jkbecause our es- timate is relative to the school mean and, consequently,ρijkcorrelates withρk. Therefore, following Chetty et al. (2011), we also omit childi from the school mean such thatΔX( i)jk≡X( i)jkX( i)k.19We replace Xjkin (2) withΔX( i)jkand write20 YG1 ijk=ΔX( i)jkb+YG0′ ijkα+Fi ′ γ+P( i)jk ′ δ+Cjk ′ κ+τk+εijk(4) Under Assumption 1, 2, and 3, we can interpretbas the effect of how your classmates perceive the teacher relative to the classmates (and hence the teacher) you could have had if assigned to the other class in school (since we observe two classes in each school). When we investi- gate the effect of teacher relationship skills on student learning, we thus estimate (4) using a leave-out-mean instead of the mean to address the bias caused by children’s unobserved preferences. The assumption of no peer effects is strong. Peers can have positive and negative (spillover) effects, so it is difficult to characterize the magnitude of peers’(potential) effect. For example, a child may be so disruptive that he or she consumes all the teacher’s attention, precluding the teacher from building positive relationships with the other children and helping them learn (“Bad Apple”). Alternatively, a child who favors the teacher may behave in such a way that causes the teacher to direct him or herself positively to the child. Peers may respond in kind, hoping for a similar response (“Shining Light”). However, we argue that the magnitude in which peers affect the preferences and perceptions of other peers is (likely) small in the early years of schooling. In our setup, any peer effect depends on how a child can influence other children’s perceptions. Since we use the first grade of primary school, influential children are less of a concern. For most children, the transition to primary school marks a substantial change causingchildrentobepreoccupiedwiththenewenvironment.21 Moreover, children in the first grade of primary school have a natural desire to please adult figures. They are more engaged to learn because the practical application of what they learn is apparent to them (Allen, Pianta, Gregory, Mikami&Lun, 2011). These reasons suggest that children in the first grade mainly focus on themselves and what the teacher says. Lastly, children at this age can distinguish their preferences from the preferences of others (Fawcett&Markson, 2010), which sug- gests that children may not conflate their preferences with the prefer- ences of their peers. In sum, it seems reasonable to suspect that the more substantial part of the effect is due to the teacher and not from peers affecting the perceptions and hence survey response of one another. Nevertheless, we cannot be sure and hence require caution for inter- preting our results solely caused by the teacher’s overall capacity to form positive relationships. Although, one could argue that positive and negative spillover effects are both part of effective relationship man- agement strategies maintained by the teachers. One final point that requires elaboration is contemporaneity. In (4), it is not clear whether children learn more because they benefit from the teacher relationship skills or evaluate the teacher positively in their capacity to develop positive relationships because they learn more. We exploit Assumption 3 to examine such simultaneity betweenYG1 ijkand Xijk. We regress the individual measureXijkon the outcomeYG1 ijk, a vector of child and family background variables,F′ i, and a school-specific intercept. The residual of this regression,̂εijk, represents within-school variation not caused by the contemporary outcome,YG1 ijk, or the family background. We can then construct a leave-out-mean from the residual Δ̂ε( i)jkand use it as an instrument forΔX( i)jk, which is valid under Assumption 3. 3.3.Descriptive statistics Table 4 presents a Pearson correlation matrix of each of the skills at the start of first grade (G0) and the end of first grade (G1). The corre- lation coefficients reveal two patterns. First, there is a strong correlation between the same skills over time. Second, we see strong correlations amongacademicskillsandsocial-emotionalskillsandmeaningful 18In Web Appendix D, we follow Chetty et al. (2011) and use the within-class variance of the teacher relationship skill measure,Xijk, to estimate the extent of this attenuation bias at about five percent. 19 X( i)jk≡1 Ijk1 ∑Ijk i′=1,i′∕=i Xi′jkandX( i)k≡1 ∑Jk j=1Ijk1 ∑Jk j=1 ∑Ijk i′=1,i′∕=i Xi′jk. 20There is a finite sample bias in small groups due to the negative (mechan- ical) correlation betweenXijkandΔX( i)jk(Guryan, Kroft,&Notowidigdo, 2009). Intuitively, a child cannot be his or her peer (i.e., we sample without replacement). Therefore, the peers of a child who prefer the teacher comes from a group with slightly lower enthusiasm for the teacher, and vice versa. In Web Appendix F, we show results of a series of Monte Carlo simulations to examine the magnitude of this bias. The bias is negligible.21We are grateful for an anonymous teacher for pointing this out to us. M.W.P. Thijssen et al.
Economics of Education Review 89 (2022) 102251 8correlations between academic and social-emotional skills. Panel A in Table 5 summarizes the family background variables. For 16.6 percent of the children, at least one family member experiences reading difficulties. This percentage seems substantial but note that parents self-report reading disabilities.22Also, 42.4 percent of the mothers and 55 percent of the fathers have less or equivalent to a high school degree. About 21.2 percent of the families have at least one parent born in a nonwestern country. Finally, even though mothers attain more education on average, fathers earn almost double what mothers do. The average family income is 990,817 NOK. We also measure several teacher and classroom characteristics. Panel B in Table 5 summarizes these variables. As is common in lower grades, a large share of the first-grade teachers is female: 97 percent. On average, the teachers in our sample have 13–14 years of experience, and most are between 30 and 59 years of age. Roughly 42 percent of the teachers are in the distribution’s tails (below 25 or over 60). 5.8 percent of the teachers have an advanced degree (i.e., a master’s degree), while six percent do not have an undergraduate degree. On average, a class has 20 children, including about two who require special reading education. As described previously, the key identifying assumption is that, withinaschool, schooladministrators as-good-as randomly assign children and teachers to classrooms. Therefore, the availability of family background variables and skills measured at the start of first grade benefits our statistical approach in three ways: (1) we can examine if school administrators sort children into classes based on family back- ground and skills measured at the start of first grade; (2) we can con- dition in our model specification (Eq. (4)) on family background,F′ i, and skills measured at the start of first grade,YG0′ ijk, to get more precise es- timates of the effect; and (3) the availability of these variables allows us to examine the sensitivity of our results to a consecutive inclusion of relevant control variables which, under as-good-as random assignment, should be minimal.23 3.4.Assignment to classes The validity of our empirical strategy relies on the assumption of random assignment. By Norwegian law, school administrators should notgroupchildrenbasedonsex,religion,ethnicity,oracademic performance (Kunnskapsdepartementet, 2017). Despite this law, prior empirical evidence from the United States suggests that school admin- istratorsmayassignbetterteacherstobetter-performingchildren (Clotfelter, Ladd&Vigdor, 2006). Suppose the school administrators in oursamplesystematicallyassignbetter-performingchildrento higher-quality teachers. In that case, our identifying assumption is un- tenable,andwecannolongerruleoutexplanationsduetothe within-school sorting of students. Therefore, we assess the plausibility of our identifying assumption by investigating if predetermined variables and variables measured at the start of first grade are predictive of class or teacher characteristics. The former cannot predict the latter under random assignment (Rothstein, 2010). By contrast, if school adminis- trators assign better-educated teachers to academically better students, to take a case in point, we should find a relationship between teacher education and skills measured at the start of first grade. In Table 6, we regress teacher’s sex, age, experience, education, the number of children for whom the teacher thinks they require specialized Table 4 Pearson correlation coefficient matrix for skills measured at the start and the end of first grade At the start of first grade (G0)At the end of first grade (G1) (1)(2)(3)(4)(5)(6)(7)(8) VariablesMathLiteracySelf-conceptReading interestMathLiteracySelf-conceptReading interest Panel A: At the start of first grade (G0) Math1.00 Literacy0.52**1.00 Self-concept0.19**0.33**1.00 Reading interest‒0.04**‒0.03*0.26**1.00 Panel B: At the end of first grade (G1) Math0.51**0.38**0.16**‒0.001.00 Literacy0.43**0.56**0.17**‒0.02+0.50**1.00 Self-concept0.13**0.17**0.23**0.07**0.19**0.30**1.00 Reading interest0.04**0.08**0.19**0.25**0.10**0.14**0.41**1.00 Notes.This table reports Pearson correlation coefficients for each skill measure at the start of first grade (G0) and the end of first grade (G1). We use listwise deletion to handle missing values. Observations: 5,490. +p<0.10, *p<0.05, **p<0.01 (two-tailed). Table 5 Sample summary statistics (1)(2)(3) VariablesMeanSDObs. Panel A: Child and family background variables The child is female47.8%5,810 Family reading disability16.6%4,536 Siblings (no.)1.6(1.1)5,782 Non-western immigrant21.2%5,704 Education mother5,474 Not completed high school16.3%892 Only completed high school26.1%1,428 Any higher education55.8%3,055 Family income in 2015 (NOK)990,817(502,271)5,611 Panel B: Teacher and classroom variables The teacher is female96.6%5,792 Experience (in years)13.5(8.5)5,764 The teacher has an advanced degree5.6%5,810 The teacher has no undergraduate degree6.0%5,810 The teacher is over 50 years of age28.1%5,792 The teacher is under 30 years of age14.1%5,792 Class size (no.)20.1(3.8)5,810 Special education in reading (no.)1.9(1.7)5,775 Notes.This table reports the sample summary statistics. Panel A presents the child and family background variables. For“education mother,”we excluded the category any post-secondary education but not higher education from the table. This category represents 1.8% (99 obs.). For the fathers in our sample: 18.3% (991 obs.) did not complete high school; 36.7% (1,994 obs.) only completed high school; 5.1% (277 obs.) completed any post-secondary education but not higher education; 39.9% (2,166 obs.) completed any higher education. Panel B presents the teacher and classroom variables. 22Note thatexperiencedreading difficulties does not necessarily imply a diagnosed reading difficulty. 23It is well known that sex, race, relative age differences, family income, and parental education are strong predictors of performance in school (Black, Devereux,&Salvanes, 2005, 2011; Dahl&Lochner, 2012; Dee, 2004, 2007; Solli, 2017). M.W.P. Thijssen et al.
Economics of Education Review 89 (2022) 102251 9training in reading, and class size alternately on each of the pre- determined variables (Panel A) and skills measured at the start of first grade (Panel B). Each cell reports estimates of a separate OLS regression with a school-specific intercept.24We also run a series of F tests to test the joint significance of the variables that should not affect under as- good-as random assignment. Overall, the results are consistent with our identifying assumption.25The imbalances we find are not material (e.g., increasing family income by one million Norwegian Kroner in- crease class size by 0.09 children). Importantly, while the findings in Table 6 are consistent with as-good-as random assignment based on observables, school administrators may still sort children into classes based on unobservables. Since we have no source of clean exogenous variation, we cannot rule out such selection on unobservables (e.g., teachers’ability to handle children with behavioral problems). 4.Results 4.1.Teacher relationship skills and student learning As mentioned in Section 3.1, some teachers changedduringfirst grade (about 8.7 percent). It is not clear whether the children who experienced a teacher change had the old or new teacher in mind when asked about the teacher’s relationship skills. In our main analysis, we include all children. In Web Appendix E, we present results similar to those reported here but with the children who experienced a teacher change during first grade excluded. Excluding these children does not change our conclusion. Table 7 reports the teacher relationship skill estimates,b, using Eq. (4). We start by running a regression model in which we only control for mean differences between schools (Column 1). In Columns (2) through (5), we consecutively condition on: family background, skill levels measured at the start of first grade (G0), peer composition, and teacher and classroom characteristics to assess the sensitivity of our estimates. As explained above, in Column (6), we present estimates that account for simultaneity. Our preferred model specification is Column (5), as it best resembles the education production function. To provide some intuition for the effect sizes, consider that the difference in math and literacy test scores between students for whom the mother has a college degree and students from mothers without a college degree is about 30 percent of a standard deviation. The effect of teacher relationship skills on math test scores is positive Table 6 Predictability of predetermined variables and teacher and classroom characteristics (1)(2)(3)(4)(5)(6) VariablesTeacher is femaleTeacher ageTeacher experienceTeacher educationSpecial education readingClass size Panel A: Child and family background variables Child is female0.000 (0.003) [5,792] 0.020 (0.015) [5,792] 0.060 (0.104) [5,764] ‒0.007 (0.004) [5,810] ‒0.005 (0.017) [5,775] ‒0.011 (0.020) [5,810] Birth month0.000 (0.000) [5,784] 0.001 (0.003) [5,784] 0.004 (0.025) [5,756] 0.001 (0.001) [5,802] 0.002 (0.004) [5,767] 0.004 (0.005) [5,802] Siblings‒0.001 (0.001) [5,764] 0.001 (0.011) [5,764] ‒0.028 (0.072) [5,736] ‒0.003 (0.003) [5,782] 0.020+ (0.012) [5,747] 0.023 (0.015) [5,782] Family reading disability‒0.003 (0.006) [4,522] 0.025 (0.037) [4,522] 0.101 (0.289) [4,498] 0.005 (0.011) [4,536] 0.005 (0.054) [4,505] ‒0.064 (0.064) [4,536] Education mother0.000 (0.001) [5,459] ‒0.010 (0.007) [5,459] ‒0.039 (0.052) [5,431] ‒0.002 (0.002) [5,474] 0.009 (0.011) [5,440] 0.051** (0.013) [5,474] Non-western immigrant‒0.003 (0.006) [5,687] 0.024 (0.031) [5,687] 0.088 (0.216) [5,659] 0.012 (0.007) [5,704] ‒0.020 (0.034) [5,670] ‒0.073 (0.046) [5,704] Family income‒0.000 (0.004) [5,594] 0.003 (0.025) [5,594] 0.108 (0.174) [5,568] ‒0.009 (0.006) [5,611] ‒0.008 (0.031) [5,578] 0.092+ (0.048) [5,611] Panel B: Academic skills at the start of first grade (G0) Math0.001 (0.003) [5,640] ‒0.016 (0.012) [5,640] ‒0.137 (0.085) [5,612] 0.005 (0.004) [5,656] 0.007 (0.016) [5,621] ‒0.006 (0.020) [5,656] Literacy0.001 (0.002) [5,690] ‒0.001 (0.012) [5,690] 0.013 (0.087) [5,662] 0.004 (0.004) [5,708] ‒0.013 (0.015) [5,673] 0.011 (0.018) [5,708] Joint significance0.9451.4250.8480.6821.1652.471* Notes.This table reports the point estimates relating to predetermined variables to teacher and classroom characteristics. Each cell reports an estimate of a separate OLS regression, including school fixed effects and an indicator for treatment status. We regress the variables presented in the columns alternately on the child and family background variables and skills measured at the start of first grade (G0). Family income is in 1,000,000 NOKs.“Teacher age”is a categorical variable that includes five groups: under 25; between 25 and 39; between 30 and 39; between 40 and 49; between 50 and 59; and 60 or higher.“Teacher education”is also a categorical variable that includes four groups: upper secondary school, university, or college education (less than three years); bachelor’s degree (undergraduate); and master’s degree (advanced degree). Special education in reading measures the number of children the teacher believes require special education in reading. We cluster the standard errors at the school level and present them in parentheses. We report the number of observations in brackets. We use listwise deletion to handle missing values. +p<0.10, *p<0.05, **p<0.01 (two-tailed). 24Note that we do not correct the standard errors for multiple hypothesis testing Table 6. includes 54t-tests. With random sampling, one would expect to find at least two or three significant at the 5 percent significance. 25In Web Appendix E, we provide further evidence that is consistent with our identifying assumption. We examine randomization into peer groups. Finally, we borrow from Ammermueller and Pischke (2009) and Clotfelter et al. (2006), and run a series of Pearson Chi-square tests of homogeneity. All results are consistent with our identifying assumption. M.W.P. Thijssen et al.
Economics of Education Review 89 (2022) 102251 10and statistically significant (Panel A in Table 7). In our preferred model specification (Column 5), a one standard deviation increase in teacher relationship skills increases math test scores by about 4.6 percent of a standard deviation. On the other hand, the effect is only about 2.7 percent of a standard deviation for literacy.26The impact of teacher relationship skills on students’interest in reading is positive and sta- tistically significant (Panel B in Table 7). A one standard deviation in- crease in teacher relationship skills increases children’s reading interest by about 4.9 percent of a standard deviation in our preferred specifi- cation. Finally, the coefficients for self-concept likewise suggest a posi- tiveimpactonteacherrelationshipskills.A1standarddeviation increase in teacher relationship skills improves students’self-concept in reading by about 3.4 percent of a standard deviation. Note that the leave-out-mean attenuates the point estimates by about 5 percent (see Web Appendix D for details). These estimates on literacy and self-concept are consistent with Jensen, Solheim and Idsøe (2019). They also use the Two Teachers data and find that the children’sindividuallyperceived emotional support, which is one part of the teacher relationship skills, correlates with reading test scores and self-concept in reading. However, the correlation in Jensen et al. (2019) is also consistent with other mechanisms. For example, making progress in reading may increase a child’s feeling of emotional support. Alternatively, some unobserved child-level factors may result in higher individual perceived emotional support and better reading performance (e.g., a sense of belonging at school could make it easier to feel connected with the teacher and learn). Curiously, the teacher relationship skills have a more substantial effect on math than literacy. While curious, such differential effects across math and literacy are not uncommon, and several explanations have been put forth in the literature. For example, Bettinger (2012) points out that math test scores may be more elastic. Many parents read with their children even before formal schooling, while most children learn math exclusively in school. In other words, the home environment contributes to the child’s literacy skills more than to the child’s math skills. As a result, there might be more to gain in math when school starts. Although this theory seems plausible, the distributional plots in our Web Appendix A are not necessarily consistent with this story. The plots show that the distribution for literacy test scores (see, e.g., reading fluency) centers around zero, more so than math test scores. Another explanation could be that extrinsic motivation is more effective for math (Bettinger, 2012). We described above that the rela- tionship between and among the teacher and children might provide a feelingofcompetence,independence,andrelatedness,increasing motivation and effort (Connell&Wellborn, 1991). Since the teacher’s relationship skills are external causes for children’s motivation to learn, we would expect more substantial effects on math. 4.2.Assessing the plausibility of confounders To substantiate that unobserved causes are not likely driving our results, we investigate the existence of (potential) confounders. This section provides evidence supporting the exogeneity of the teacher relationship skill assumption (Assumption 2). 4.2.1.Placebo analysis We do a placebo analysis to examine if there are confounding effects that are not consistent with our identification strategy. In Table 8, we regress math and literacy measured at thestartof first grade (G0) alternately on the teacher relationship skills measured at theendof first grade (G1). As noted above, the school already started when we assessed the children. Therefore, we would not expect to find precise zeros. The Table 7 The relationship between teacher relationship skills and student learning (6) Variables(1)(2)(3)(4)(5)Simultaneity Panel A: Academic skills at the end of first grade Math0.055** (0.016) 0.044** (0.017) 0.045** (0.016) 0.045** (0.016) 0.046** (0.016) 0.042** (0.016) Adj.R20.0880.1600.3730.3730.3730.373 Observations5,6105,6105,6105,6105,6105,605 Literacy0.039* (0.016) 0.029+ (0.016) 0.025+ (0.015) 0.023 (0.015) 0.027+ (0.014) 0.027* (0.014) Adj.R20.1030.1900.4390.4400.4400.439 Observations5,6375,6375,6375,6375,6375,633 Panel B: Social-emotional skills at the end of first grade Reading interest0.056** (0.017) 0.055** (0.018) 0.052** (0.018) 0.048** (0.017) 0.049** (0.017) 0.040* (0.016) Adj.R20.0270.0420.0470.0470.0490.049 Observations5,6305,6305,6305,6305,6305,629 Self-concept0.034* (0.014) 0.035* (0.015) 0.034* (0.014) 0.030* (0.015) 0.034* (0.016) 0.039** (0.015) Adj.R20.0350.0450.0720.0720.0720.072 Observations5,6365,6365,6365,6365,6365,633 School-specific intercept✓✓✓✓✓✓ Family background✓✓✓✓✓ Initial skill level (G0)✓✓✓✓ Peer composition✓✓✓ Teacher and classroom✓✓ Notes.This table reports the point estimates from an OLS regression. Family background includes sex, birth month, birth year, the number of siblings, dummies for mother’s education, family reading disability, non-western immigrant, and family income (quartic family income polynomial). Initial skill level (G0) includes the scores for math and literacy measured at the start of first grade. Peer composition consists of all family background variables and initial skill level variables specified as leave-out-means. Teacher and classroom variables include the teacher’s sex, age, education, experience, and class size. We cluster the standard errors at the school level and present them in parentheses. All models include an indicator for treatment status and variables that predict missingness (see Web Appendix B for details). +p<0.10, *p<0.05, **p<0.01 (two-tailed). 26We also estimate our models using national assessment related to literacy as outcomes instead of the one-to-one assessments of the Two Teachers project. The results using the national assessments (not reported) present a similar story. M.W.P. Thijssen et al.