Do Single-Sex School Advantages Exist? Evidence from a School Choice Lottery Program in Seoul*

Jungmin Lee Yoonsoo Park Seoul National University & IZA Korea Development Institute

May 2017

Abstract

We investigate the hypothesis of single-sex school advantages. Do students perform academically better in schools segregated by sex? Using Korean longitudinal data tracking individual students for 6 years from middle to high schools, we identify the types of students who prefer single-sex schools and their middle-school, individual, and household characteristics. Utilizing information on high schools they applied for in the school choice lottery system, we estimate the effects of single-sex school attendance on high-school test scores. We find little single-sex school advantages, after controlling for the gender types of the schools for which students applied. That is, the observed single-sex school advantages are mainly driven by students’ self- selection. Then, the prevailing preference for single-sex schools among parents is puzzling, for which we attempt to find some possible explanations.

Keywords: single-sex schooling, school choice lotteries, academic performance, preferences for single-sex schools. JEL codes: I21, I28.

* We would like to thank seminar participants at Yonsei University, Korea Academic Society of Industrial Organization, Korean Association of Applied Economics, and SNU Research in Economics Workshop. Lee’s work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korean (NRF-2016S1A5A01025292).

I. Introduction

It is well known that students are affected by their peers in many regards. There has been an increasing amount of empirical evidence that many student outcomes, which are of importance to policy makers as well as parents, such as students’ academic performance and behavioral problems, are influenced by surrounding peers’ behaviors, their academic performance, individual characteristics and family background. Among others, whether the gender composition of school peers matters has been studied intensively, for an obvious reason that single-sex and coeducational schools coexist and the gender type of schools is a policy variable. In particular, in the U.S., the question—whether students in single-sex schools outperform than those in coeducational schools—has received much attention in academia around the recent policy change, which relaxed the Title IX’s prohibition of sex-based discrimination and, albeit to a limited extent, allowed for single-sex education. The rationale behind this notable change is the belief that single- sex education is beneficial to students, especially in terms of academic performance. There might be various mechanisms for the “single-sex education advantage”; students of different genders have different learning styles, teachers may teach more effectively when their students are of a single gender, students might be less disruptive in single-sex classes, and so on. It is noteworthy in the literature on the single-sex school advantage that many recent studies have looked at the case of Korea (Park, Behrman, and Choi 2012; 2013; Choi, Moon, and Ridder 2014; Ku and Kwak 2013; Sohn 2016; Park 2017). The reason is not only that education is seriously taken by parents and students in Korea, but also that the Korean education institution provides a unique experimental setting for identifying the causal effect of single-sex school attendance. In Korea, under the so-called equalization policy, schools in metropolitan areas are equalized in terms of crucial school inputs including budgets, curriculum, and teacher quality, while students are randomly assigned to schools within school districts. Furthermore, students’ school transfers are not allowed within districts. Since some schools are single-sex ones and others are coeducational within districts, if students are indeed randomly assigned to schools within districts, then it is possible to estimate the causal effect of single-sex school attendance by a simple regression model with school-district fixed effects.1 In fact, all the above-mentioned studies of the Korean case relied upon the within-district random assignment for causal identification. While there are some subtle

1 There are a few papers which exploited within-district random assignment under the equalization policy in Korea to investigate other topics than single-sex school advantages. Kang (2007) estimated academic peer effects. Hahn, Wang, and Yang (2013) examined the effects of school autonomy and accountability on student performance. Both studies rely on random assignment of students to schools for causal identification. A bit differently, Kim, Lee, and Lee (2008) analyzed the effects of sorting and mixing on high-school students’ test scores by using regional variation in the adoption of the equalization policy.

1 differences among those studies, all of them found some positive evidence for single-sex school advantages. However, some concerns have been raised over the validity of the within-district random assignment assumption and the results that are based on the assumption. Lee and Kang (2015) argue that the within-district random assignment policy was rapidly eroded since the 1990s and hence a causal inference based on the within-district random assignment rule may not be valid for the data collected after the period. Han and Ryu (2016) studied high school assignment in Seoul during the early 2000s and concluded that it is essentially a distance-based rule rather than the within-district random assignment rule, although the detailed assignment rule is kept confidential. Kim and Kim (2015) argued more directly that the within-district random assignment rule in Seoul was performed only within 30-minutes commutable areas using public transportation and thus the positive single-sex schooling effect reported in the literature may be spurious. 2 Sohn (2016) found a positive within-district correlation between single-sex school attendance and academic achievement in Seoul, but when controlling for residential location of students more narrowly than school districts, the observed single-sex school premium became negligible. He interpreted these results as suggesting that there is endogenous sorting of students. To the extent that the validity of the within-district random assignment is limited, the substantial single-sex school effects reported in the previous studies may be due to spurious correlation between single- sex school attendance and unobserved student characteristics. In this paper, we attempt to re-examine the causal effect of single-sex school attendance on academic performance by explicitly controlling for potential unobserved heterogeneity between students who prefer to attend single-sex schools and those who prefer to attend coeducational schools. Specifically, we exploit a school choice lottery program – the High School Choice Program (hereafter, the Seoul lottery system) - introduced in Seoul, the capital of Korea, in 2010. An important feature of the Seoul lottery system is that it matches students with schools based on school choices of students, similarly to the Boston mechanism.3 Specifically, each student lists four schools they want to attend in a single application form, and the Seoul Metropolitan Office of Education assigns students to schools based on their choices. This feature of the lottery system allows us to observe students’ revealed preferences for school characteristics and hence estimate the single-sex school premium by explicitly controlling for the gender types of applied schools as covariates.4

2 There are 11 school districts in Seoul. Each school district typically consists of 2-3 administrative districts and 500,000-1,200,000 residents. 3 There have been a number of studies that have theoretically examined the mechanism since the seminal paper by Abdulkadiroğulu and Sönmez (2003). 4 Our empirical strategy is similar to the standard approach in lottery-based studies of school choice in the literature. To name only a few, Rouse (1998), Hoxby and Rockoff (2005), Cullen, Jacob, and Levitt (2006), Hastings, Kane, and Staiger (2008), Hoxby and Murarka (2009), Abdulkadiroŭlu et al. (2011), Deming (2011), Hastings, Neilson, and Zimmerman (2012), and Deming, Hastings, Kane, and Staiger (2014).

We apply this empirical strategy to longitudinal data that track students over six years from their 7th grade (first year in middle school) to 12th grade (third year in high school). The longitudinal feature of the data allows us to test our identification assumption by measuring correlations between single-sex school assignment and a variety of predetermined characteristics including middle-school test scores, which could not be attempted in the previous studies where the information on predetermined academic outcomes were unavailable in cross-sectional data. To summarize our results, we find that the simple OLS estimates without controlling for the gender types of applied schools yield substantial single-sex schooling advantages, even if we control for a rich set of student characteristics as well as school-district fixed effects, the latter being the key control in the previous studies. However, when we control for unobserved heterogeneity across students by controlling for the gender types of their applied schools, the estimated impact of single- sex school attendance become negligible. These results suggest that the substantial single-sex school premiums reported in the previous studies are likely to be driven by unobserved heterogeneity rather than reflecting causal effects. Another contribution of our paper is that we present direct evidence on students’ selection into single-sex and coeducational schools. Our longitudinal data allow us to investigate what types of students in terms of individual or household characteristics, among others, middle-school academic performance, prefer single-sex schools. We find that students with better academic quality and family background have stronger preferences for single-sex schools. Given our findings of no single-sex school advantages, however, the observed positive selection into single-sex schools is puzzling. To resolve the puzzle, we examine three hypotheses that potentially explain the positive self-selection into single-sex schools and empirically assess the validity of the hypotheses. The remainder of the paper proceeds as follows. Section II reviews the literature on single-sex school advantages, with a special focus on the studies of the Korean case. The section also introduces the institutional background of the school choice lottery system in Seoul that we use for identifying a causal effect of single-sex school attendance. Section III introduces the longitudinal data we use for this study. The longitudinal structure of our data allows us to examine the potential endogenous sorting of high- performing students into single-sex schools, which the previous studies mostly looking at cross-sectional correlations failed to capture. Section IV presents our empirical strategy, which is in the same line with the standard approach in the literature using school choice lotteries. Section V presents empirical results. We also present the regression-adjusted results for students’ self-selection. Section VI concludes.

II. Literature Review and Institutional Background

An ideal setting for identifying the effect of single-sex school attendance is a social experiment where students are randomly assigned to schools of different gender types. This opportunity is rarely available; in the United States in particular, where most single-sex schools are private and/or religious, students self- select into those schools (Halpern et al. 2011, Billger 2009, Lee and Marks 1992). A report of the Department of Education (Mael et al., 2005) says that “a primary criticism of previous single-sex literature has been the confounding of single-sex effects with the effects of religious values, financial privilege, selective admissions, or other advantages associated with the single-sex school being studied” (p. xi). To avoid self-selection problem, a variety of identification strategies have been tried. Some studies exploited marginal changes of gender composition, occurring across adjacent cohorts due to exogenous changes in school-age population’s gender composition (Hoxby 2000; Lavy and Schlosser 2011; Schneeweis and Zweimüller 2012). Other studies exploited exogenous variations in the gender composition of students artificially created by policy experiments (Whitmore 2005).5 These studies can only tell us the impact of the gender composition within coeducational schools, so cannot answer the impact of single-sex school attendance per se. The limitations of previous studies make Korea’s random assignment system of students attractive among researchers. To the best of our knowledge, Park et al. (2013) is the first paper that exploits Korea’s random assignment system to identify the single-sex school effect.6 Using cross-sectional data on the 2009 College Scholastic Aptitude Test (CSAT) scores in Seoul, they found a positive within-district correlation between single-sex school attendance and the CSAT scores. Assuming that students are randomly assigned to schools within school districts, they interpreted the results as reflecting a causal effect of single-sex school attendance. Choi et al. (2014), using repeated cross-sectional data on the 2008 and 2009 CSAT scores in Seoul, also estimate single-sex school advantages based on the assumption of the within-district random assignment in Seoul. They derive a school production function which allows the effect of single- sex school attendance to vary across school districts, as the effect interactively depends upon school and student characteristics, both observable and unobservable. Aggregating district-specific effects to the average partial effect, they found the single-sex school advantage is actually larger than that of Park et al. (2003).

5 Most studies in the education literature use the standard estimation method of controlling for observable characteristics. For example, see Harker (2000). Mael et al. (2005) pointed out the limitation of this approach; “the inclusion of covariates cannot control for important unobservable differences between the groups, such as motivation” (p. xi). 6 The same authors published the paper’s results in a letter at Science (2012).

Ku and Kwak (2015) distinguished the “composite” effect of single-sex school attendance and the “pure” effect of exposure to same-sex peers. The composite effect is what the previous studies focused on, and to estimate it, just like the other studies, they utilized the randomness in single-sex versus coeducational school attendance due to Seoul’s student assignment rule. As in Park et al. (2013) and Choi et al. (2014), they also used repeated cross-sectional data on the CSAT scores for students in Seoul from 1999 to 2009, prior to the introduction of the school choice system. To estimate the pure exposure effect, it is critical to control for unobservable differences in school inputs and resources between single-sex and coeducational schools, and they exploited the fact that some schools were converted from single-sex to coed schools during the sample period, assuming that, for those transition schools, other dimensions than the gender composition of students are kept the same before and after their transition to coed schools. They found that the composite effect is significantly positive for both boys and girls, which basically confirms the results of Park et al. (2013) and Choi et al. (2014). However, they also found that the pure exposure effect to same- sex peers is positive only for girls. Sohn (2016), also using the repeated cross-sectional CSAT score data in Seoul from 2002 to 2004 and from 2009 to 2012, found significant single-sex school advantages for both boys and girls after controlling for district-specific year fixed effects. However, he found the observed single-sex school advantages become smaller in magnitude and statistically insignificant when controlling for the fixed effects of administrative district, the size of which is about half of that of school district.7 He interpreted this finding as the evidence that high-performing students endogenously choose residential location within school district to increase the probability of being assigned to single-sex school. The possibility of endogenous residential location choice pointed by Sohn (2016) is also discussed in many other related studies. Lee and Kang (2015), who estimate the labor market effect of school ties using the within-district random assignment rule, mention that there were several revisions in the random assignment rule during the mid-1990s and hence they focus on students entering high schools before 1990 in which the random assignment rule was strictly implemented. Kim and Kim (2015), who estimate the effect of single-sex schooling, more directly mention that the within-district random assignment rule in Seoul was performed only within 30-minutes commutable areas using public transportation and thus the positive single-sex schooling effect reported in the literature may be spurious. Similarly, Han and Ryu (2016), who estimate the class-size effect using the CSAT score data during the early 2000s, studied the high school assignment rule in Seoul during the early 2000s and concluded that, although the detailed assignment rule is kept confidential, the distance from residential location to high school is clearly the single most important factor. Bastos et al. (2016), who estimated the effectiveness of school resources by

7 In Seoul, each school district consists of about two administrative districts.

5 exploiting the within-district random assignment rule, also excluded students in Seoul from their sample because of the possibility of non-random assignment.8 To overcome this issue, we attempt to identify the causal effect of single-sex school attendance using a novel source of random variation in high-school assignment in Seoul. In 2010, the SMOE introduced a city-wide school choice lottery program entitled as High School Choice Program (hereafter, the Seoul lottery system). All students and schools in Seoul are eligible for the lottery system. The Seoul lottery system matches students with schools through three rounds. Table 1 summarizes the assignment rule in each of the three rounds. In round 1, 20% of seats of each school (or 60% for schools in the inner city area) are allocated in the following way. Each student ranks up two different schools in order of their preferences, among all high schools in Seoul. If the school is undersubscribed (i.e. the number of students applying for the school is less than 20% of the school’s enrollment), all the applicants are offered admissions. If the school is oversubscribed, the seats are first filled by lottery among the first-choice applicants and, if seats are still available, among the second-choice applicants. In round 2, 40% of seats of each school are allocated in the following way. As in the first round, each student applies for two different schools, ranked in order of their preferences, among all high schools within their school district. Again if the school is undersubscribed, all the applicants are offered admissions. If the school is oversubscribed, the admissions are allocated by lottery after factoring in commuting time and the school’s accommodation circumstances. It is unknown exactly how those factors are taken into account because the SMOE never clarifies the details. Finally, in round 3, the SMOE assigns any remaining students (i.e. students failing to get admitted in round 1 and 2) to schools located in two adjacent school districts closest to students’ residence, considering students’ preferences revealed in the first and second rounds, religion, and commuting time. The assignment mechanism in the last round is similar to that before the lottery system, which the previous studies exploited for causal identification. The three rounds are proceeded not sequentially but simultaneously. That is, students list their favored schools up to four in the order of their preferences in rounds 1 and 2 on one single application form, and the SMOE collects all students’ applications and determines the assignments according to the above rules. Students are only notified of which school they are assigned to without

8 To check for the validity of these discussions, we searched through the digital archive for high school entrance policy at the official webpage of Seoul Metropolitan Office of Education (SMOE). Every year, the SMOE publishes a brochure explaining how they assign students to high schools. The earliest brochure available at the archive was published in August 2003. In the brochure, entitled as “Seoul High School District and Student Assignment Rule,” the SMOE explains that they assign a student to a school within the school district of residency randomly but considering commuting conveniences. In a similar brochure, published in 2007, the SMOE illustrates that they make considerable efforts to take into account students’ commuting conveniences, religions, and middle school grades in the process of the random assignment. Based on these findings, we agree with the skeptical views about the quality of random assignment discussed in Lee and Kang (2015), Kim and Kim (2015), Bastos et al. (2016) and Han and Ryu (2016) are convincing.

6 knowing how that is determined.

[INSERT TABLE 1 HERE]

III. Data and Empirical Strategy

A. Data

The data for this study are from six waves (2010-2015) of the Seoul Educational Longitudinal Survey of 2010 (hereafter, SELS 2010). The SELS 2010, administered annually by the city of Seoul, consists of three cohort panel studies: a panel study for first-year high-school students in 2010, a panel study for first-year middle-school students in 2010, and one for fourth-year elementary school students in 2010. In this paper, we choose to use the second cohort panel, which follows first-year middle-school students in 2010, because it covers the transition period from middle schools to high schools for the cohort. Students in the cohort applied for high schools in December 2012, graduated from middle schools in February 2013, and were assigned to high schools in March 2013 according to the rule described in table 1. In each wave, the SELS 2010 administered standardized tests for three high-stake subjects (mathematics, English, and Korean) for students and conducted surveys for the students and their parents, teachers, and principals.9 In the sixth wave (administered in 2015), the SELS 2010 retrospectively asked students where they lived and which high schools they chose to apply in December 2012 when they applied for high schools under the Seoul lottery system. Thus, we have very rich information about students’ educational outcomes (academic and non-academic), family backgrounds, and school environment for complete three years of middle school (2010-2012) and three years of high school (2012-2015) as well as the information about their school districts and school choices when they decided four choice high schools under the Seoul lottery system. Total 2,797 students participated in all six waves from 2010 to 2015. Among these students, we select our estimation sample in several steps. First, we limit the sample to students who were bound by the Seoul lottery system, dropping 619 students who were admitted to non-lottery (i.e. selective) high schools such as autonomous high schools and specific-purpose high schools specialized in arts, foreign language, and science.10 We also drop 705 students who have missing information on key variables such as test scores

9 The surveys and standardized tests were conducted every year in June. 10 This sample selection is not random since students are admitted on the basis of their academic records or talents. It is ambiguous how the sample selection could affect our estimates, but we should bear in mind this fact when we

(in any of all three subjects in all six years), family background, and most importantly, school choices and school districts. Additionally, we removed 165 students who we think misreported their choice schools. These students include 90 students who listed the same school twice in each round, which is not allowed technically by the Seoul lottery system,11 63 students who listed non-lottery schools for any of their four choice schools,12 and 12 students who listed schools of their opposite sex (i.e. 3 boys listing girl-only schools and 9 girls listing boy-only schools). In addition, we dropped 67 students who moved to a different high school from their original high schools assigned by the Seoul lottery system. Finally, we keep those with at least 10 observations in each cell defined by student gender, school gender type, and ranked school fixed effects, which will be defined in the empirical strategy section. Consequently, our estimation sample consists of 1,138 students, 514 boys and 624 girls. Table 2 shows summary statistics of the estimation sample. In our sample, 64% of boys and 72% of girls attend single-sex high schools. Administrative data show that 60% and 65% of enrollments for boys and girls, respectively, are from single-sex schools. Thus students attending single-sex high schools are a bit overrepresented in our sample. Comparing middle-school test scores between boys and girls, we find that girls are on average better than boys consistently for all three subjects and for all six years of middle and high school period. This is a well-known fact in Korea. 13 Regarding individual or household characteristics (predetermined as they were measured in the third year of middle school), there are little notable differences between boys and girls. Two differences are interesting. The number of siblings is slightly larger for girls. This is perhaps because of son preferences and parents’ sex-specific fertility stopping rule. The amount of private tutoring expenditure is a bit larger for boys, which might also reflect the presence of son preferences.

B. Empirical Strategy

Our estimation model is as follows:

interpret our empirical findings since they are based on the selected sample. 11 In the Seoul lottery system, students are required to list two different schools in each round. 12 Most of these students listed autonomous public high schools, which are not bound by the Seoul lottery system, for one of their four choice schools. 13 High-school test scores are the outcomes of our major interest. In addition, we examine various non-academic outcomes, such as school satisfaction and students’ attitudes. These variables are constructed based on students’ responses to questions during their first year of high school. The detailed information on how we construct these variables and related survey questions are discussed in section VI.D and Table 9.

= + + + 16 + (1)

𝐴𝐴𝑖𝑖𝑖𝑖ℎ 𝛽𝛽𝑆𝑆𝑖𝑖𝑖𝑖 𝛾𝛾𝑋𝑋𝑖𝑖𝑖𝑖 𝜃𝜃ℎ � 𝜇𝜇𝑘𝑘𝑑𝑑𝑖𝑖𝑖𝑖 𝜀𝜀𝑖𝑖𝑖𝑖ℎ 𝑘𝑘=1 where is the academic outcome of student who resides in school district h at the time of their high

14 school 𝐴𝐴lottery𝑖𝑖𝑖𝑖ℎ and is assigned to high school 𝑖𝑖under the Seoul lottery system. We measure academic outcomes of students by log of test scores of three𝑗𝑗 large-stake subjects (Math, English, and Korean) for three years of high school. is the explanatory variable of our main interest, which is the indicator for whether the student is assigned𝑆𝑆𝑖𝑖𝑖𝑖 to a single-sex school; in other words, school is a single-sex or coeducational one. Since we estimate the equation separately by gender, is the impact𝑗𝑗 of single-sex school attendance on academic outcomes for each gender. is a vector 𝛽𝛽of predetermined characteristics, measured at the third year in middle school, including 𝑋𝑋a𝑖𝑖𝑖𝑖 dummy for living with a single parent, parental income, age, and educational attainment, a dummy for disability status of a student, and a dummy for coeducational middle school attendance. represents a list of dummies for school districts or school district fixed effects. Lastly, is a stochastic𝜃𝜃ℎ error term. The key control variable𝜀𝜀𝑖𝑖𝑖𝑖ℎ for identifying the causal effect of single-sex school attendance is , which represents the gender types of ranked schools (hereafter, we will call ’s as ranked school fixed𝑑𝑑𝑖𝑖𝑖𝑖 effects). Under the Seoul lottery system, each student chooses two different 𝑑𝑑high𝑖𝑖𝑖𝑖 schools in the order of their preference in each of two rounds. Since each student has a set of four choice schools (two schools in each of two rounds) and the gender type of each school is binary (single-sex versus coeducational) for each gender of students, there are 16 possible combinations (= 2 ), each of which is indicated by where = 15 4 1, … , 16. We include the ranked school fixed effects to the list of covariates of equation (1)𝑑𝑑 𝑖𝑖to𝑖𝑖 control𝑘𝑘 for potential unobserved heterogeneity across students in terms of their preferences to the gender type of schools (single-sex vs. coeducation).16 Our empirical strategy relies on the assumption that, conditional on the ranked school fixed effects and school district fixed effects, single-sex school assignment is uncorrelated with unobservable student characteristics that might be correlated with educational outcomes. Although this assumption is fundamentally untestable, examining the correlation between single-sex school assignment and observable

14 Note that, under the Seoul lottery system, school j may or may not be located in school district h. 15 Not all the 16 possible combinations are observed in the data. For boys, 6 unique combinations are observed and, for girls, 7 combinations observed. This is partly because our sample is small and partly because the gender type of school is an important point of consideration for school choice and, therefore, the gender types of applied schools are correlated. We will discuss about preferences for schools’ gender types in more detail in Section IV.B. 16 Considering the limited sample size, we chose to only control for gender types of the four ranked schools rather than fully controlling for the exact identities of them. As a robustness check, we also present the results when controlling for the exact identities of all four ranked schools or the first-choice school in Appendix 1.

9 pre-treatment characteristics may provide useful information on the validity of the assumption. 17 Our longitudinal data are advantageous as a rich set of student characteristics prior to high-school assignment are available. Utilizing that information, we estimate the following equation:

= + + 16 + (2) 𝑚𝑚𝑚𝑚𝑚𝑚 𝐴𝐴𝑖𝑖𝑖𝑖ℎ 𝛽𝛽�𝑆𝑆𝑖𝑖𝑖𝑖 𝜃𝜃�ℎ � 𝜇𝜇�𝑘𝑘𝑑𝑑𝑖𝑖𝑖𝑖 𝜀𝜀𝑖𝑖𝑖𝑖̃ ℎ 𝑘𝑘=1 where the dependent variable ( ) represents predetermined observable characteristics of students such 𝑚𝑚𝑚𝑚𝑚𝑚 as middle-school test scores and𝐴𝐴𝑖𝑖𝑖𝑖 ℎother individual or household characteristics including those in in equation (1). = 0 for a variety of observable characteristics suggests that the potential selection of single𝑋𝑋𝑖𝑖𝑖𝑖 - sex school assignment𝛽𝛽� on unobservable characteristics is not likely to be serious. Note that estimating equation (2) without ranked school fixed effects can reveal the patterns of selection into single-sex schools. For example, if students with better academic quality self-selected into single-sex (or coed) schools, we should have > 0 (or < 0) when using predetermined characteristics that are positively correlated with academic quality𝛽𝛽� (e.g. middle𝛽𝛽� school test scores) as dependent variables.

IV. Selection into Single-Sex Schools

In this section, we present the results for equation (2). First, we present the results for middle-school test scores, which should be most directly correlated with students’ academic ability. Second, we show the results for a variety of predetermined variables which are also likely relevant for students’ performance in high schools.

[INSERT TABLE 3 HERE]

Table 3 presents the estimation results when using the log of middle-school test scores as the dependent variable. We present the results for first-, second-, and third-year middle-school scores, denoted as MS1, MS2, and MS3, for boys and girls and for three high-stake subjects; Math, English, and Korean.

17 Altonji et al. (2005) suggest that the amount of selection on observed explanatory variables in a model provides useful information on the amount of selection on unobserved variables when the number of observed explanatory variables is large enough.

We also present both estimates with and without ranked school fixed effects. Therefore, Table 3 contains the estimates from 36 different regressions. In all specifications, school district fixed effects are controlled for. The results show a very clear pattern that the estimate without ranked school fixed effects is significant and the significance is gone after controlling for the fixed effects. Out of 18 estimates without the fixed effects, 16 estimates are significant at a conventional significance level. In particular, the test scores in the last year of middle school, which is the year when they decide which high schools to apply, are significantly and positively correlated with single-sex high school assignment. The magnitude of the estimates is also quite large. For example, the estimate for boys/MS3/Math in column (1) indicates that the third-year middle-school score of those who end up attending single-sex (all-boys) high schools is on average 26.7% higher than those in coed schools. This means that better-performing middle-school students are more likely to be assigned to single-sex high schools. On the other hand, after controlling for ranked school fixed effects, we find that all the estimates turn to be statistically insignificant. The estimates become much smaller in magnitude than those without the fixed effects. In fact, it turns out that some estimates are signed negative, while those without ranked school fixed effects except one (girls/MS2/Korean) are positive. This means that single-sex school assignment is not correlated with middle-school test scores conditional on ranked school fixed effects. In other words, the fixed effects successfully control for students’ selection to single-sex schools based on middle-school test scores.

[INSERT TABLE 4 HERE]

Table 4 presents the results for non-test score pretreatment characteristics. We examine various characteristics; household income, father’s and mother’s age and education, student’s disability status, single parent, and the number of siblings. All variables are those observed at MS3. Just as in Table 3, for each variable, we present and compare the estimates without and with ranked school fixed effects. We present the results for boys and girls, separately. In total, Table 4 contains the estimates from 40 different regressions. Overall we find some evidence on students’ selection into single-sex high schools on predetermined characteristics, but controlling for ranked school fixed effects successfully addresses the selection problem. Out of 20 estimates, only one estimate, that for girls/household income, remains marginally significant even after controlling for ranked school fixed effects. We find that boys select into single-sex schools based on parents’ education. For girls, the results in column (5) show that girls select into single-sex schools based

11 on not only parents’ education but also household income and single parent status. Recall that we found in Table 3 that the patterns of selection based on middle school scores were slightly weaker for girls than for boys; the estimates for girls were a bit smaller and two estimates were insignificant, while all estimates were consistently significant for boys. The results in Tables 3 and 4 altogether suggest that both boys and girls sort themselves into single-sex and coed high schools but girls do so in more complicated ways than boys do.

V. The Impacts on High-School Test Scores

Table 5 presents the estimation results for equation (1) when first-year high school (HS1) test scores are used as the dependent variable. We consider the results for HS1 test scores as our main results because those scores are measured when students finished the first semester of their high schools and thus are likely to capture any immediate effects of their high school characteristics. Each estimate is from a separate regression; boys and girls, three subjects and four specifications. Column (1) shows the results of univariate regressions of HS1 test scores on the single-sex school indicator. Column (2) adds school district fixed effects, and (3) additionally control for predetermined student characteristics. Columns (4) and (5) add ranked school fixed effects to the list of control variables in columns (2) and (3), respectively.

[INSERT TABLE 5 HERE]

The results are very consistent across all subjects and genders. The estimates without controlling for ranked school fixed effects indicate statistically significant and positive impacts of single-sex school attendance on test scores, even after controlling for a set of control variables as well as school district fixed effects. The estimates are also large in magnitude; for example, the estimate in column (3) for boys/English indicates that single-sex school attendance increases test scores on average by 11.8 percent. This is in stark contrast to those in columns (4) and (5), which are statistically insignificant and the magnitude of the estimates is much smaller (and negatively signed) than those in columns (2) and (3). After controlling for ranked school fixed effects representing students’ preferences for single-sex and coed schools, the estimates become all insignificant. That is, there is no single-sex school advantage. The observed advantages in columns (1) to (3) are actually driven by students’ positive selection into single-sex schools, which we confirm using middle-school test scores in Table 3. The results in Table 5 show the impacts on academic test scores at the first year of high school.

One might think that the single-sex school advantages, if any, appear over time as students are more exposed to school environments including the gender composition of peers. To check this possibility, we estimate the effects of single-sex school attendance on second- and third-year high school test scores (HS2 and HS3). The estimation results are presented in Table 6. Table 6 is organized in the same way as Table 5 and presents all results (48 estimates) for HS2 and HS3. Overall the results show that our main findings are consistent across all three high school years. The estimates without controlling for ranked school fixed effects show significant and substantial advantages of single-sex school attendance. However, the advantages disappear once we control for ranked school fixed effects. For girls’ English and Korean scores in HS2, the estimates are marginally significant, but they also become insignificant and smaller in magnitude after controlling for predetermined variables. For example, for boy’s math score in HS2, the estimate in column (1) indicates that boys attending all-boys high schools score 20.4% higher than those attending coeducational schools. But the estimate in column (3) indicates that the premium is only 3.3% and it is statistically insignificant.

[INSERT TABLE 6 HERE]

The results in Tables 5 and 6, in conjunction with the results in Tables 3 and 4, suggest that single- sex school attendance does not improve academic performance of students and that the observed single-sex school premium is likely to be driven by students’ positive selection into single-sex schools based on their predetermined academic quality and other characteristics that are likely to be associated with academic performance.

VI. Who Prefer Single-Sex Schools and Why?

The results in the previous section can be summarized in two folds. First, there is little gain from attending single-sex schools in terms of academic achievement. Second, students with better academic quality tend to prefer single-sex schools, leading to positive association (but not causation) between single-sex school attendance and academic performance. These results raise another question: if there is no single-sex school premium, why better-performing students prefer attending single-sex schools? The remainder of this section tries to answer this question. We begin by examining the determinants for single-sex school preferences rather than the final school assignment and confirm the fact that students with better academic quality and socioeconomic background tend to have stronger preferences for single-sex high schools. Then, we examine three hypotheses to explain the puzzling finding that better-quality students prefer single-sex schools.

A. Preferences for Single-Sex Schools

In Section IV, we have already identified some observable predetermined characteristics which are significantly correlated with selection into single-sex schools. We found that middle-school test scores and parents’ education for both boys and girls and household income and the existence of both parents for girls, are positively correlated with preferences for single-sex schools. In this subsection, we investigate the determinants of single-sex school preferences more directly by examining the gender types of the schools for which students applied. To do so, we operationally construct an index variable quantifying the degree of single-sex school preference. For robustness, we use two alternative variables. Recall that students could rank up four different schools at maximum in their application form. Based on that information, our first variable is the indicator that a student’s first choice (i.e., the first choice in the first round) is a single-sex school. In our sample, 68% of boys and 72% of girls chose single-sex schools as their first pick. The other variable is the count of single-sex schools in each student’s application. The average count of single-sex schools is 2.6 for boys and 2.7 for girls, out of 4 ranked schools. Having defined these two variables, to find the determinants of single-sex school preferences, we run regression of one of the variables on students’ middle-school test scores (the average score of three subjects) as well as predetermined characteristics when they were 3rd year middle school students (i.e., at the time when they decided which schools to apply for).

[INSERT TABLE 7 HERE]

The results are presented in Table 7. Columns (1) and (3) present the results when using the first choice indicator as the dependent variable for boys and girls, respectively, and (2) and (4) the results when using the count of ranked single-sex schools. In all specifications, we control for school districts and cluster standard errors by school district. The results show that, for both genders, students with higher middle-school test scores and better family background have stronger preferences to single-sex high schools. We also find that students who attended coed middle schools prefer single-sex schools less. The effects are quite large. Those from coeducational middle schools applied for about 0.5 fewer single-sex schools. One explanation for this finding is that students who attended coeducational schools during middle schools or their parents are less concerned about coeducational environments. This is perhaps because they are averse to uncertainty about new school environments, which they have not experienced. Lastly, we find that, for girls, body weight is

14 positively correlated with their single-sex school preferences, although the coefficient is only marginally significant. We do not find any association for boys between body weight and single-sex school preferences.

B. Heterogeneous Effects

In the previous subsection, we found that for both boys and girls, those with higher test scores in middle schools are more likely to apply for single-sex high schools. This is quite puzzling: given no significant single-sex school advantage as we found in the previous section, it is not obvious at all why those higher- score students prefer single-sex schools. One possible explanation is that although there is no single-sex school advantage at the mean, there might be an advantage in other parts of the score distribution. That is, the single-sex school effects might be heterogeneous by students’ academic quality and, specifically, given that higher-score students select into single-sex schools, there might be a positive advantage for those higher-performing students. To check this possibility, we construct a dummy variable for students above the median in terms of MS3 (pretreatment) test score for each combination of gender, grade and subject and include the variable and its interaction with single-sex school attendance in equation (1). By doing so, we can distinguish the effect of single-sex school attendance for the two groups of students, those above or below the median at MS3. The results are summarized in Table 8. The table presents total 18 sets of estimates; 2 genders, 3 subjects, and 3 high school years. In each set, there are two estimates, one for the effect for those students above the median (inclusive) and the other for that for those below the median.

[INSERT TABLE 8 HERE]

The results show that there are little single-sex school advantages for either above-median or below-median students. Out of 36 estimates, there are only three estimates at the 10% significance level. And two of the three significant estimates are even negative, which indicates a disadvantage for single-sex school attendance. We find that boys above the median have about 16% lower score for Math at HS1 and girls below the median have 14% lower score for Math at HS2. The only positive and significant effect is found for girls above the median for English at HS2. In conclusion, the results in Table 8 do not provide a satisfactory explanation for why high-performing students select into single-sex schools.

C. Within-School Ranking Concern

So far we have examined single-sex school advantages in terms of absolute academic achievement according to standardized test scores. Another possible explanation we can think of is that students are concerned about their within-school ranking when they select high schools. This appears to be a reasonable hypothesis, especially for boys, because within-school ranking is a critical factor for college admission. For college admission in 2016, when the students in our sample applied for colleges, about 57.4% of admissions are determined based on high school records in which within-school academic ranking is a major component. Boys, except for those at the very top, could improve their within-school ranking by avoiding girls who are on average better than them. However, note that students’ within-school ranking concern does not explain why girls also prefer single-sex schools, because they could be higher ranked in coed schools. To check the hypothesis, we conducted a thought experiment to look at whether within-school ranking concern could explain boys’ selection into single-sex schools. Our thought experiment is as follow. First, for a specific boy who is assigned to an all-boys high school, we compute that boy’s ranking among all boys who are also assigned to all-boys high schools, based on the average test score at MS3.18 Second, we also compute the same boy’s counterfactual ranking among those students (both boys and girls) assigned to coed high schools if he were assigned to a coeducational school and everybody else’s assignment were held constant. Then, we compute the “return” to single-sex school attendance for the particular student by subtracting the actual ranking from the counterfactual ranking. In a similar way, we can also compute the return to single-sex school attendance for those students who are actually assigned to coeducational schools, assuming the case that they were assigned to single-sex schools.

[INSERT FIGURE 2 HERE]

Figure 2 presents the estimated returns over the MS3 average score distribution. Although the hypothesis theoretically does not make any sense for girls, for comparison with boys, we also computed the returns to single-sex school attendance for girls. In fact, the results for girls are consistent with our expectation. For almost all girls regardless of their test score at MS3, the return to single-sex high school attendance turns out to be negative. The return is actually quite substantial for middle-ranked girls. We expected that the return should be positive for some boys, but it turns out that the returns are also negative for almost all boys. This is because there is a positive selection into single-sex schools for boys as well.

18 Ideally, we should compute students’ ranking within individual schools where they are assigned. This is not feasible because there are only a few students per school in our sample.

Since higher-performing boys select into all-boys schools, boys become lower ranked in all-boys schools as well, even though they could avoid high-performing girls. The results in this subsection show that students’ within-school ranking concern does not explain why they prefer single-sex schools, either.

D. Non-Test Score Outcomes

So far we could not have explained satisfactorily why students with better academic quality and socioeconomic backgrounds, regardless of their gender, prefer single-sex schools. We have not found any evidence for single-sex school advantages in terms of academic outcomes, either standardized test scores or within-school ranking. Therefore, in this subsection, we turn our attention to non-test score outcomes such as students’ satisfaction with their assigned schools or perceived school or teacher quality, which are possibly affected by the gender type of schools. For example, it is well known that people are more easily associated with those with similar traits (homophily). This suggests that students in single-sex schools might find it easier to make friends than those in mixed-gender schools. In addition, there are many discussions that coeducation may strengthen gender stereotypes (e.g., Booth and Nolen, 2009; Beaman et al., 2006), suggesting that the gender type of a school might affect students’ attitudes, beliefs and career choice. Some students and/or parents might prefer single-sex schools for these non-test score reasons.

[INSERT TABLE 9 HERE]

The results for non-test score outcomes are presented in Table 9. Exploiting the richness of our survey data, we check a variety of non-test score outcomes, such as satisfaction with schools and teachers, friendship relationship, preferred college majors, and school violence. In total, we check 20 outcome variables. All variables, except for those regarding major preference and daily time use, are constructed using subjective-response questions where the responses are coded in the 5-point Likert scale. When there are multiple sub-questions under a category, we take the average of the responses to all the sub-questions. We modified the responses in the way that a higher point should mean a more positive response. Lastly, to facilitate the interpretation of the results, we construct a dummy variable indicating that the response score is greater than the median score of the sample. For details about how to construct the variables, please refer to Appendix X. We estimate equation (1) by replacing the dependent variable with each of the non-test score outcomes. We control for ranked school fixed effects as well as school district fixed effects. The results are presented in Table 9. First of all, the results for boys and those for girls are different. For boys, we find little significant impacts of single-sex school attendance on non-test score outcomes. The

17 only exception is satisfaction with their current schools. We find that boys in single-sex schools are more likely to be satisfied with their school. On the other hand, for girls, it turns out that more non-test score outcomes are affected by single-sex school attendance. First, we find that those girls in single-sex schools are more likely to assess their school quality and class environments higher. Second, they are more likely to think that school violence is not serious in their school. There are some negative impacts of single-sex school attendance on girls as well. They are more negative about friendship in schools and their own attitudes in classes. Interestingly, girls attending single-sex high schools are about 12% points less likely to think male-dominated fields (STEM; science, technology, engineering and mathematics) as their college majors. The results in this subsection neither reject nor strongly support the hypothesis of single-sex school advantages for non-test score outcomes. There is an indication that single-sex school attendance positively affects students, but it is ambiguous whether such positive impacts are large enough to explain substantial selection into single-sex schools, despite of no real gains in academic achievement. We are pretty confident in that there is little advantage from attending single-sex schools in terms of test scores. However, explanation for the existence of preferences for single-sex schools is far from perfect.

VII. Conclusions

Whether the gender type of schools matters for students is a question of importance for not only students and parents themselves but also educators and policy makers. Therefore, the question has long been examined in academia, for example, since Coleman et al. (1966). However, it seems that there has been no consensus so far. In this paper, we make an attempt to test whether single-sex schools matter for students. We use the data from Korea, which have recently been used frequently because of the country’s unique institutional feature of random assignment of students to schools, but exploit another source of exogenous variation that occurs by the introduction of a school choice lottery system. Our empirical strategy is to control for the gender type combination of schools that students rank up in their application form. To the best of our knowledge, our paper is the first to exploit the school choice lottery system to identify single- sex school advantages. Our findings are surprisingly consistent with regard to academic achievement, measured by standardized test scores. We find no single-sex school advantages for any of three high-stake subjects, Math, English, and Korean, in all three years of high school grades. On the other hand, the estimates without controlling for ranked school fixed effects show significant and substantial advantages. Our findings show

18 that the advantages are by and large spurious, driven by positive selection of better students into single-sex schools. We find that the observed advantages disappear totally after controlling for ranked school fixed effects. Given no advantages in academic achievement, it is puzzling why students prefer single-sex schools. Regarding this question, we are far from confident. But we attempt to explain preferences for single-sex schools by heterogeneity of single-sex school effects and within-school ranking, but basically fail to provide a satisfactory explanation. We find a few bits of evidence that there might be single-sex school advantages with respect to non-test score outcomes. However, we are not sure of whether those favorable effects on non-test score outcomes are large enough to explain the observed substantial sorting of better students into single-sex schools. Lastly, in this paper, due to the data limitation, we are not able to examine a long-term impact of single-sex school attendance. There might be some positive effects beyond high schools, at universities or in labor or marriage markets. Since most universities in Korea are coeducational, those from coeducational high schools could adapt themselves to coeducational environments at universities. On the other hand, there might be single-sex school advantages in terms of high school alumni network. Obviously, more studies are warranted.

References

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Ku, Hyejin and Do Won Kwak (2015). “Together or Separate: Disentangling the Effects of Single-Sex Schooling from the Effects of Single-Sex Schools.” mimeo. Lavy, Victor and Analía Schlosser. 2011. “Mechanisms and Impacts of Gender Peer Effects at School.” American Economic Journal: Applied Economics 3(2): 1-33. Lee, Seungjoo and Changhui Kang (2015). “Labor Market Effects of School Ties: Evidence from Graduates of Leveled High Schools in South Korea,” Korean Economic Review, 31(1): 199-237. Lee, Soohyung, Lesley J. Turner, Seokjin Woo, and Kyunghee Kim (2014). “All or Nothing? The Impact of School and Classroom Gender Composition on Effort and Academic Achievement.” NBER Working Paper No. 20722. Lee, Valerie E. and Helen M. Marks. 1992. “Who Goes Where? Choice of Single-Sex and Coeducational Independent Secondary Schools.” Sociology of Education 65(3): 226-53. Lim, Jaegeum and Jonathan Meer (forthcoming). “The Impact of Teacher-Student Gender Matches: Random Assignment Evidence from South Korea.” Journal of Human Resources. Mael, Fred A. 1998. “Single-Sex and Coeducational Schooling: Relationships to Socioemotional and Academic Development.” Review of Educational Research 68(2): 101-29. Mael, Fred, Alex Alonso, Doug Gibson, Kelly Rogers, Mark Smith (2005). “Single-Sex versus Coeducational Schooling: A Systematic Review.” U.S. Department of Education DOC No. 2005- 11. Myer, Peter. 2008. “Learning Separately: The Case for Single-Sex Schools.” Education Next Winter: 10- 21. Park, Hyunjoon, Jere R. Behrman, and Jaesung Choi (2012). “Single-sex Education: Positive Effects.” Science (New York, NY) 335(6065): 165-166. Park, Hyunjoon, Jere R. Behrman, and Jaesung Choi (2013). “Causal Effects of Single-Sex Schools on College Entrance Exams and College Attendance: Random Assignment in Seoul High Schools.” Demography 50(2): 447-469. Park, Sangyoon (2017). “The Effects of Coeducation on Academic Performance and Science Course Enrollment of High School Students: Evidence from a Quasi-Random Classroom Assignment Policy.” Working Paper, Department of Economics, The University of Hong Kong. Pahlke, Erin, Janet Shibley Hyde, and Carlie M. Allison (2014). “The Effects of Single-Sex Compared With Coeducational Schooling on Students’ Performance and Attitudes: A Meta-Analysis.” Psychological Bulletin 140(4): 1042-1072. Schneeweis, Nicole and Martina Zweimüller. 2012. “Girls, Girls, Girls: Gender Composition and Female School Choice.” Economics of Education Review 31(4): 482-500.

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Figure 1. Return to Single-Sex School Attendance

-.05

-.1

Returnto SS attendance

-.15

-.2 20 40 60 80 100 MS3 average score

Notes: For each individual student of those who attend coeducational schools, we compute his or her percentile based on the average MS3 test score among those in single-sex schools if he or she attends a single-sex school, while all the other students stay in their assigned schools. Likewise, for each of those who attend single-sex schools, we compute his or her percentile based on the average MS3 test score if he or she attends a coed school among those in coed schools, while all the other students stay in their assigned schools. Using the counterfactual percentiles, we calculate the return to single-sex school attendance as the percentile among coed school students minus that among single-sex school students. The graph shows the returns over quantiles of average MS3 score. The curves are the trends estimated by local polynomial estimation.

Table 1. The Seoul Lottery System (High School Choice Program, 2010-Present)

Rounds Application Assignment

Each student applies two different schools, ranked in 20% of seats of each high school (or 60% for Round 1 order of their preferences, among all high schools in schools in the inner city area) are allocated Seoul. by lottery. 40% of seats of each high school are Each student applies two different schools, ranked in allocated by considering students’ Round 2 order of their preferences, among all high schools within preferences, commuting conveniences, and their school district. the school’s accommodation circumstances.

Any remaining students are assigned to schools located in two adjacent school Round 3 N/A districts from students’ residence, considering students’ preferences, religions, and commuting conveniences.

Table 2. Summary Statistics

Boy sample Girl sample Std. Variable Obs Mean Std. Dev. Obs Mean Dev.

Single-sex high school (yes=1) 514 0.644 0.479 624 0.721 0.449 Test scores in HS3 Math (log) 514 3.297 0.633 624 3.375 0.652 English (log) 514 3.498 0.588 624 3.741 0.543 Korean (log) 514 3.506 0.550 624 3.781 0.465 Average (0-100) 514 56.896 17.589 624 61.811 16.486 Test scores in HS2 Math (log) 514 3.301 0.548 624 3.353 0.523 English (log) 514 3.464 0.586 624 3.694 0.527 Korean (log) 514 3.587 0.558 624 3.845 0.485 Average (0-100) 514 36.940 17.613 624 43.252 16.526 Test scores in HS1 Math (log) 514 3.498 0.638 624 3.605 0.575 English (log) 514 3.709 0.531 624 3.954 0.436 Korean (log) 514 3.571 0.553 624 3.843 0.434 Average (0-100) 514 42.365 19.335 624 50.034 18.099 Test scores in MS3 Math (log) 514 3.794 0.632 624 3.844 0.612 English (log) 514 4.031 0.521 624 4.168 0.450 Korean (log) 514 3.810 0.508 624 4.013 0.396 Average (0-100) 514 55.424 21.678 624 61.189 19.901 Test scores in MS2 Math (log) 514 3.863 0.562 624 3.909 0.529 English (log) 514 4.011 0.482 624 4.093 0.463 Korean (log) 514 3.898 0.499 624 4.088 0.391 Average (0-100) 514 56.671 20.227 624 61.579 18.837 Test scores in MS1 Math (log) 514 4.006 0.470 624 4.018 0.447 English (log) 514 4.034 0.429 624 4.136 0.368 Korean (log) 514 3.921 0.437 624 4.066 0.356 Average (0-100) 514 58.593 17.524 624 62.667 16.105 Predetermined student and family characteristics (all measured in MS3 if not specified) Family income (log) 514 6.106 0.541 624 6.015 0.606 Father younger than 50 (yes=1) 514 0.037 0.189 624 0.056 0.230 Father older than 59 (yes=1) 514 0.138 0.345 624 0.123 0.329 Mother younger than 50 (yes=1) 514 0.187 0.390 624 0.239 0.427 Mother older than 59 (yes=1) 514 0.033 0.179 624 0.042 0.200 Father college graduated (yes=1) 514 0.603 0.490 624 0.551 0.498 Mother college graduated (yes=1) 514 0.426 0.495 624 0.377 0.485 Disabled student (yes=1) 514 0.041 0.198 624 0.034 0.180 Single parent (yes=1) 514 0.041 0.198 624 0.046 0.211 Number of siblings 514 2.088 0.398 624 2.171 0.565

Graduated from coeducational MS (yes=1) 514 0.809 0.393 624 0.819 0.385 Height (cm, measured in MS1) 495 160.719 7.859 611 157.028 5.713 Weight (kg, measured in MS1) 484 51.304 10.239 566 46.216 7.892 Private tutoring expenditures (log) 437 3.148 1.532 548 2.924 1.658 Non-academic outcomes (answered by students in HS1) Satisfied with school (1-5) 511 3.027 0.828 622 2.902 0.670 School quality (1-5) 512 3.471 0.667 624 3.406 0.593 Teacher quality (1-5) 513 3.550 0.720 624 3.491 0.631 Friend relationship (1-5) 513 4.259 0.555 623 4.134 0.558 School violence (1-5) 508 2.209 0.888 624 2.090 0.822 Class environments (1-5) 505 3.562 0.503 620 3.646 0.506 My attitude in class (1-5) 511 3.450 0.737 619 3.419 0.638 Teachers in class (1-5) 492 3.952 0.598 613 3.923 0.553 Satisfied with classes (1-5) 504 3.236 0.693 620 3.259 0.699 Studying technique (1-5) 512 3.219 0.727 622 3.363 0.739 Studying effort (1-5) 513 3.428 0.728 623 3.497 0.697 Studying attitude (1-5) 514 3.160 0.723 623 3.163 0.707 Aim (1-5) 514 3.588 0.736 623 3.600 0.708 Creativity (1-5) 513 3.673 0.618 623 3.625 0.627 STEM major choice (yes=1) 504 0.389 0.488 616 0.274 0.447 Career (1-5) 513 3.857 0.670 621 3.918 0.629 Self esteem (1-5) 513 3.748 0.773 622 3.619 0.756 Television (hours per day) 367 1.718 1.110 481 1.935 1.098 Reading (hours per day) 367 0.255 0.250 462 0.220 0.196 ICT use (hours per day) 514 3.560 0.791 623 3.268 0.678

Notes: MS1, MS2, and MS3 denote first, second, and third year in middle school, respectively. Similarly, HS1, HS2, and HS3 represent first, second, and third year in high school, respectively.

Table 3. Middle School Test Scores

MS3 MS2 MS1 (1) (2) (3) (4) (5) (6) Ranked school FE No Yes No Yes No Yes A. Boys, Math Mean of dep. var. 3.794 3.863 4.006 SS high school 0.267*** 0.049 0.145** 0.122 0.110** 0.032 (0.064) (0.117) (0.059) (0.109) (0.044) (0.066) R-squared 0.063 0.081 0.057 0.062 0.066 0.074 B. Boys, English Mean of dep. var. 4.031 4.011 4.034 SS high school 0.150*** 0.064 0.169*** -0.006 0.089** 0.008 (0.052) (0.103) (0.047) (0.083) (0.041) (0.071) R-squared 0.084 0.091 0.100 0.121 0.074 0.082 C. Boys, Korean Mean of dep. var. 3.810 3.898 3.921 SS high school 0.191*** 0.072 0.115** -0.007 0.072 0.079 (0.052) (0.082) (0.051) (0.065) (0.044) (0.072) R-squared 0.065 0.072 0.083 0.092 0.024 0.033 D. Girls, Math Mean of dep. var. 3.844 3.909 4.018 SS high school 0.177*** 0.104 0.097* -0.005 0.107** 0.032 (0.060) (0.090) (0.051) (0.067) (0.042) (0.055) R-squared 0.036 0.051 0.035 0.050 0.040 0.047 E. Girls, English Mean of dep. var. 4.168 4.093 4.136 SS high school 0.088** 0.025 0.099** 0.051 0.094*** 0.018 (0.039) (0.059) (0.046) (0.061) (0.034) (0.045) R-squared 0.059 0.075 0.037 0.045 0.061 0.068 F. Girls, Korean Mean of dep. var. 4.013 4.088 4.066 SS high school 0.077** 0.047 -0.007 -0.007 0.046 0.034 (0.038) (0.055) (0.035) (0.060) (0.033) (0.046) R-squared 0.035 0.049 0.028 0.033 0.023 0.024

Notes: N=514 (boy sample), 624 (girl sample). Each estimate is obtained from a single regression model, differing by dependent variable and specification. The dependent variable is log middle-school standardized test score of each subject. MS3 represents middle school 3rd grade, MS2 2nd grade, and MS1 1st grade. All specifications control for school districts in 2012. Robust standard errors are in parentheses. *** Significance 1%; ** 5%; * 10%.

Table 4. Predetermined Characteristics of Students

Boys Girls (1) (2) (3) (4) (5) (6) Ranked school FE No Yes No Yes Household income (log) 6.106 0.054 -0.122 6.015 0.137** 0.161* (0.541) (0.036) (0.091) (0.606) (0.053) (0.074) R-squared 0.103 0.121 0.067 0.084 Father younger than 50 0.037 -0.002 0.006 0.056 -0.015 0.010 (0.189) (0.020) (0.020) (0.230) (0.012) (0.024) R-squared 0.012 0.016 0.013 0.021 Father older than 59 0.138 -0.043 -0.056 0.123 -0.010 -0.043 (0.345) (0.038) (0.038) (0.329) (0.027) (0.037) R-squared 0.031 0.041 0.017 0.022 Mother younger than 50 0.187 -0.025 -0.021 0.239 -0.033 -0.009 (0.390) (0.048) (0.075) (0.427) (0.042) (0.050) R-squared 0.015 0.018 0.034 0.044 Mother older than 59 0.033 -0.023 -0.062 0.042 -0.022 -0.044 (0.179) (0.021) (0.043) (0.200) (0.019) (0.032) R-squared 0.025 0.033 0.022 0.029 Father college educated 0.603 0.090** -0.074 0.551 0.163*** 0.067 (0.490) (0.038) (0.054) (0.498) (0.049) (0.050) R-squared 0.075 0.087 0.102 0.111 Mother college educated 0.426 0.070* 0.062 0.377 0.116* 0.102 (0.495) (0.037) (0.082) (0.485) (0.054) (0.076) R-squared 0.090 0.095 0.112 0.117 Disability 0.041 -0.019* 0.004 0.034 -0.002 -0.002 (0.198) (0.010) (0.035) (0.180) (0.014) (0.010) R-squared 0.040 0.050 0.016 0.027 Single parent 0.041 0.022 0.023 0.046 -0.030* -0.015 (0.198) (0.018) (0.021) (0.211) (0.014) (0.026) R-squared 0.014 0.016 0.028 0.035 Siblings 2.088 -0.069* -0.042 2.171 -0.048 -0.123 (0.398) (0.037) (0.068) (0.565) (0.032) (0.070) R-squared 0.023 0.034 0.010 0.019

Notes: N=514 (boy sample), 624 (girl sample). For each gender, columns (1) and (4) present sample mean and standard deviation. The other columns present the coefficient estimate for each variable in a regression where the dependent variable is the indicator for single-sex high school attendance. Each estimate is obtained from a single regression model, differing by dependent variable and specification. The specification in columns (2) and (5) controls for school districts, and those in (3) and (5) additionally controls for ranked school fixed effects. All explanatory variables are predetermined, as observed at the third year middle school (MS3). Robust standard errors, clustered by school districts of residence in 2012, are in parentheses. *** Significance 1%; ** 5%; * 10%.

Table 5. Single-Sex School Effect on High School 1st Grade Test Score by Gender and Subject

(1) (2) (3) (4) (5) School district FE No Yes Yes Yes Yes Control variables No No Yes No Yes Ranked school FE No No No Yes Yes A. Boys, Math SS high school 0.141** 0.158** 0.127** -0.057 -0.053 (0.058) (0.065) (0.064) (0.116) (0.116) R-squared 0.011 0.036 0.099 0.055 0.112 B. Boys, English SS high school 0.108** 0.141*** 0.116** -0.006 0.007 (0.049) (0.052) (0.050) (0.089) (0.087) R-squared 0.009 0.058 0.159 0.089 0.183 C. Boys, Korean SS high school 0.106** 0.140** 0.132** -0.071 -0.051 (0.049) (0.056) (0.056) (0.105) (0.101) R-squared 0.008 0.034 0.083 0.069 0.111 D. Girls, Math SS high school 0.226*** 0.223*** 0.173*** 0.047 -0.000 (0.050) (0.054) (0.053) (0.075) (0.071) R-squared 0.031 0.046 0.112 0.067 0.130 E. Girls, English SS high school 0.180*** 0.192*** 0.150*** 0.049 0.018 (0.039) (0.040) (0.039) (0.069) (0.066) R-squared 0.034 0.070 0.154 0.092 0.173 F. Girls, Korean SS high school 0.150*** 0.136*** 0.106*** 0.057 0.028 (0.040) (0.040) (0.040) (0.063) (0.061) R-squared 0.024 0.039 0.097 0.058 0.113 Notes: N=514 (boy sample), 624 (girl sample). Each estimate is obtained from a single regression model, differing by dependent variable and specification. The dependent variable is log test score. Control variables are log household income at MS3, father's age and education, mother's age and education, disability, single parent, and sibling size. All specifications except for that in column (1) control for school districts in 2012. Robust standard errors are in parentheses. *** Significance 1%; ** 5%; * 10%.

Table 6. High School 2nd and 3rd Grade Test Scores

HS2 HS3 (1) (2) (3) (4) (1) (2) (3) (4) Control variables No Yes No Yes No Yes No Yes Ranked school FE No No Yes Yes No No Yes Yes A. Boys, Math SS high school 0.204*** 0.186*** 0.033 0.031 0.165*** 0.147** -0.001 0.013 (0.054) (0.054) (0.096) (0.095) (0.062) (0.062) (0.109) (0.108) R-squared 0.063 0.098 0.079 0.111 0.043 0.080 0.055 0.087 B. Boys, English SS high school 0.170*** 0.145** 0.043 0.056 0.131** 0.122** 0.030 0.052 (0.058) (0.057) (0.088) (0.084) (0.058) (0.058) (0.095) (0.096) R-squared 0.043 0.109 0.072 0.131 0.047 0.090 0.062 0.101 C. Boys, Korean SS high school 0.209*** 0.201*** 0.104 0.113 0.167*** 0.158*** 0.064 0.078 (0.055) (0.056) (0.093) (0.093) (0.056) (0.057) (0.094) (0.093) R-squared 0.049 0.094 0.068 0.110 0.053 0.065 0.073 0.082 D. Girls, Math SS high school 0.112** 0.078 -0.006 -0.035 0.240*** 0.204*** 0.085 0.045 (0.047) (0.048) (0.073) (0.073) (0.062) (0.062) (0.099) (0.095) R-squared 0.023 0.066 0.036 0.076 0.039 0.086 0.066 0.110 E. Girls, English SS high school 0.230*** 0.184*** 0.136* 0.087 0.296*** 0.260*** 0.101 0.070 (0.048) (0.047) (0.075) (0.072) (0.050) (0.049) (0.076) (0.075) R-squared 0.080 0.150 0.092 0.161 0.074 0.115 0.105 0.142 F. Girls, Korean SS high school 0.163*** 0.149*** 0.138* 0.117 0.125*** 0.117** 0.000 -0.003 (0.044) (0.044) (0.078) (0.077) (0.046) (0.046) (0.064) (0.064) R-squared 0.044 0.086 0.057 0.097 0.041 0.060 0.069 0.085

Notes: N=514 (boy sample), 624 (girl sample). Each estimate is obtained from a single regression model, differing by dependent variable and specification. The dependent variable is log test score. HS2 represents high school 2nd grade, and HS3 represents 3rd grade. Control variables are log household income at MS3, father's age and education, mother's age and education, disability, single parent, and sibling size. All specifications control for school districts in 2012. Robust standard errors are in parentheses. *** Significance 1%; ** 5%; * 10%.

Table 7. Determinants for Single-Sex School Preferences

Boys Girls (1) (2) (3) (4) First # SS First # SS Average middle-school test score 0.004*** 0.014*** 0.002** 0.005** (0.001) (0.004) (0.001) (0.002) Household income (log) 0.059 0.400*** 0.024 0.016 (0.043) (0.120) (0.022) (0.096) Father's age -0.005 -0.179 0.054 0.120 (0.046) (0.139) (0.040) (0.105) Mother's age 0.017 0.173 0.020 0.184 (0.034) (0.129) (0.054) (0.143) Father college educated 0.067 0.195 0.106* 0.337* (0.054) (0.128) (0.057) (0.170) Mother college education -0.037 -0.117 0.014 0.145 (0.055) (0.150) (0.059) (0.206) Disability -0.058 -0.047 0.056 -0.076 (0.048) (0.116) (0.112) (0.355) Single parent 0.056 0.420 -0.112 -0.456* (0.089) (0.295) (0.087) (0.212) Siblings -0.052 -0.289* -0.002 0.001 (0.040) (0.135) (0.027) (0.101) Private tutoring (log) -0.010 -0.014 0.005 0.012 (0.014) (0.048) (0.012) (0.044) Attended coed middle school -0.090 -0.325 -0.074 -0.488** (0.086) (0.325) (0.064) (0.216) Height (cm) 0.003 0.007 -0.003 -0.017 (0.002) (0.005) (0.003) (0.009) Weight (kg) -0.005 -0.013 0.002 0.020** (0.003) (0.008) (0.003) (0.009) Constant 0.178 -1.076 0.781* 4.026** (0.455) (0.701) (0.398) (1.488) District FE Yes Yes Yes Yes Observations 411 411 498 498 R-squared 0.323 0.399 0.153 0.296

Notes: For each gender, the dependent variable is whether the student's first choice is a SS school in columns (1) and (3) and the number of SS schools in columns (2) and (4). School district fixed effects are controlled for. All explanatory variables including average test score are predetermined and obtained from the survey conducted at middle school 3rd grade. Robust standard errors, clustered by school districts in 2012, are in parentheses. *** Significance 1%; ** 5%; * 10%.

Table 8. Single-Sex School Effects Above and Below Median

Math English Korean HS1 HS2 HS3 HS1 HS2 HS3 HS1 HS2 HS3 (1) (2) (3) (4) (5) (6) (7) (8) (9) A. Boys Above median -0.156* 0.033 0.046 -0.088 0.020 0.020 -0.077 0.125 -0.007 (0.093) (0.103) (0.111) (0.090) (0.094) (0.109) (0.097) (0.103) (0.107) Below median -0.007 -0.004 -0.061 0.010 -0.004 -0.007 -0.091 0.047 0.118 (0.104) (0.096) (0.106) (0.087) (0.086) (0.099) (0.102) (0.098) (0.096) R-squared 0.338 0.205 0.179 0.351 0.273 0.227 0.274 0.218 0.158 B. Girls Above median 0.068 0.066 0.099 0.001 0.180** 0.132 0.009 0.109 -0.000 (0.079) (0.087) (0.107) (0.066) (0.084) (0.085) (0.061) (0.081) (0.075) Below median -0.081 -0.136* -0.021 0.020 0.000 0.008 0.021 0.108 -0.022 (0.075) (0.073) (0.103) (0.063) (0.069) (0.079) (0.064) (0.080) (0.071) R-squared 0.372 0.243 0.240 0.412 0.333 0.287 0.322 0.188 0.179

Notes: N=514 (boy sample), 624 (girl sample). Above median is the effect of single-sex high school attendance for students who are above the median in terms of the average test score of three subjects in MS3. Below median is the same effect for the other students at the median or below it. In each specification, the indicator for the above median group and its interaction with single-sex high school attendance indicator are included. In all specifications, school district FE, SS preference FE, and control variables are controlled for. p-values are in brackets.

Table 9. Non-Test Score Outcomes of Single-Sex School Attendance

Boys Girls Single-sex school Dependent (S.E.) Related questions variables Observations R-squared 0.115** 0.031 Satisfied with (0.045) (0.040) How much are you satisfied with your school? (1: never - 5: very school 511 622 much) 0.040 0.033 0.084 0.239*** How much do you agree with each of the following statements about your school? (1: never - 5: very much) (0.088) (0.068) - Develop academic ability well; Develop talents and aptitude well; School quality 512 624 Teach students well according to their level; Provide good individual and career counseling; Have good convenient facilities 0.027 0.081 and environments; Make effort to guarantee students' safety 0.113 -0.017 How much do you agree with each of the following statements (0.088) (0.069) about your teachers? (1: never - 5: very much) Teacher quality 513 624 - Treat students fairly; Act up own words; Make effort to teach students well; Understand students' thought and behavior well 0.016 0.040 -0.045 -0.113* How much do you agree with each of the following statements about your friendship? (1: never - 5: very much) Friend (0.084) (0.066) - Have a friend to trust and talk to; Be together with friends during relationship 513 623 rest or lunch time; Reconcile easily even after fighting; Help friends 0.021 0.031 in need -0.149 -0.301*** (0.092) (0.067) Is school violence a serious problem in your school? (1: not at all - School violence 508 624 5: very serious) 0.032 0.090 -0.004 0.142** How much do you agree with each of the following statements Class (0.091) (0.068) about your peers' attitude in class? (1: never - 5: very much) environments 505 620 - Students are not disruptive in class; Students concentrate in class 0.020 0.046 -0.004 -0.131* How much do you agree with each of the following statements My attitude in (0.091) (0.068) about your attitude in class? (1: never - 5: very much) class 511 619 - Concentrate well; Participate actively; Do not miss homework; Review class material well; Prepare class material well 0.031 0.035 0.012 0.054 How much do you agree with each of the following statements about your teachers' attitude in class? (1: never - 5: very much) (0.093) (0.070) - Do the best in class; Knowledgeable about subjects; Teach to Teachers in class 492 613 understand easily; Want students to study hard; Expect students to achieve high; Inspect homework in detail; Make sure students 0.023 0.027 follow class -0.017 0.029

(0.098) (0.069) How much do you agree with each of the following statements Satisfied with about your satisfaction with classes? (1: never - 5: very much) 504 620 classes - Classes are exciting and I look forward to them; Classes are 0.027 0.057 helpful for my study -0.081 0.131* How much do you agree with each of the following statements about your studying technique? (1: never - 5: very much) Studying (0.090) (0.068) - Think about how to link new material with existing knowledge; technique 512 622 Make summary notes or mind map; Check myself whether I 0.016 0.038 understand class materials 0.095 -0.049 How much do you agree with each of the following statements (0.089) (0.069) about your studying effort? (1: never - 5: very much) Studying effort 513 623 - Do my best to understand class materials perfectly; Stick to my study plan; Refer to books or search internet if I cannot understand 0.032 0.069 -0.013 -0.081 How much do you agree with each of the following statements (0.090) (0.067) about your studying attitude? (1: never - 5: very much) Studying attitude 514 623 - Believe that I can understand difficult stuff; Enjoy studying; Study by myself 0.020 0.048 0.067 -0.016 How much do you agree with each of the following statements about your studying motivation? (1: never - 5: very much) (0.089) (0.071) - I have an aim to have to achieve; Know what to do to achieve my Aim 514 623 aim; Do my best to achieve my aim; Studying is helpful for my aim; Teachers know my aim and think it positively; I can contribute to 0.019 0.024 the society by achieving my aim -0.052 0.033 How much do you agree with each of the following statements about yourself? (1: never - 5: very much) (0.091) (0.070) - Know things of my interests well; Search hard information I need; Creativity 513 623 Try various ways to resolve a problem; Cannot pass new things; Curious about the reason of an incidence; Ask why even about 0.021 0.036 things most people do not doubt; Want to do my own task; Want to work in a unique way; Prefer being called unique rather than smart 0.041 -0.124* STEM major (0.093) (0.067) Do you plan to choose STEM major in college preparation? (yes=1) choice 504 616 0.034 0.039 -0.130 0.069 How much do you agree with each of the following statements about yourself? (1: never - 5: very much) (0.087) (0.072) - Know what I like; Know my advantages; Have searched majors or 513 621 occupations of my interests; Thinking about what to do now to Career achieve my dream; Decide my career by myself; Want to be the best expert in my occupation; Want to be the most important decision 0.022 0.039 maker regarding my job; Will overcome any difficulties to get my dream job 0.040 0.013 How much do you agree with each of the following statements (0.088) (0.067) about yourself? (1: never - 5: very much) Self esteem 513 622 - A good person; An able person; A valuable person; Have positive attitude to myself; Satisfied with myself 0.026 0.029 0.085 0.034 Television How much time do you usually spend watching TV? (hours a day) (0.097) (0.083)

367 481 0.028 0.023 -0.057 0.216*** (0.104) (0.061) Reading How much time do you usually spend reading a book? (hours a day) 367 462 0.079 0.058 -0.016 0.012 (0.087) (0.066) How much time do you usually spend using computers or ICT use 514 623 smartphones? (hours a day) 0.022 0.027 Notes: For each of the dependent variables, the coefficient estimate for single-sex school attendance in a separate regression controlling for school district FE and ranked school FE is presented together with their robust standard errors, sample sizes, and R squared. All the dependent variables except STEM major choice are constructed by dichotomizing average values of the answers to the questions (asked in HS1) listed in the fourth column at the median. Sample sizes vary across dependent variables because of the data availability. Significance *** 1%; ** 5%; * 10%.

Appendix Tables

Appendix A. Controlling for the Exact Identities of Ranked Schools

In this Appendix, we present the results when we control for the exact identities of ranked schools. As we explained in the paper, we control for the gender type combination of ranked schools instead of their exact identities because our sample size is small. However, it should be ideal to compare, among those students who have the exactly same set of ranked schools in their application forms, those who are assigned in single- sex schools and those in coeducational schools. There are only 215 students (out of 1148) who have some other students who have the exactly identical set of ranked students but are assigned to different gender type schools. Instead of restricting those students who have others with the exactly same set of ranked schools, we may compare students in single-sex and coed schools who have the same first-choice school (the first choice in the first round). There are 534 students as such in our sample.

[INSERT TABLE A1 HERE]

The results are presented in Table A1. The results are qualitatively same as our results in the paper controlling for ranked school fixed effects. We find little single-sex school advantages in high-school test scores.

Table A1. Controlling for the Exact Identities of Ranked Schools

HS1 HS2 HS3 (1) (2) (3) (4) (5) (6) Complete First Complete First Complete First A. Boys, Math SS high school -0.091 -0.080 -0.096 -0.041 0.051 0.060 (0.215) (0.193) (0.157) (0.142) (0.217) (0.188) R-squared 0.492 0.418 0.508 0.471 0.564 0.499 B. Boys, English SS high school -0.020 -0.006 -0.111 -0.136 -0.059 -0.017 (0.154) (0.143) (0.177) (0.155) (0.202) (0.186) R-squared 0.558 0.497 0.494 0.449 0.538 0.460 C. Boys, Korean SS high school -0.202 -0.188 -0.096 -0.041 -0.031 0.019 (0.195) (0.172) (0.163) (0.145) (0.187) (0.171) R-squared 0.541 0.494 0.516 0.460 0.535 0.471 D. Girls, Math SS high school 0.138 0.118 0.058 0.046 0.345 0.360* (0.198) (0.158) (0.188) (0.145) (0.295) (0.215) R-squared 0.609 0.536 0.602 0.505 0.651 0.583 E. Girls, English SS high school 0.067 0.082 0.212 0.190 0.122 0.045 (0.137) (0.104) (0.208) (0.153) (0.147) (0.118) R-squared 0.700 0.633 0.666 0.581 0.691 0.604 F. Girls, Korean SS high school 0.129 0.067 0.112 0.153 0.004 -0.076 (0.143) (0.113) (0.136) (0.118) (0.141) (0.116) R-squared 0.655 0.589 0.717 0.652 0.644 0.570

Notes: Each estimate is obtained from a single regression model, differing by dependent variable and specification. The dependent variable is log test score. In odd-numbered columns, the exact identities of ranked schools are controlled for. In even-numbered columns, the exact identities of first-round two schools are controlled for. Robust standard errors are in parentheses. * Significance 10%.

Appendix B. Estimation Results Based on Extended Sample

To show that our main results are robust to the choice of estimation sample, we present estimation results when students with missing information on some of their test scores and family background are all included in the estimation sample. The extended sample consists of 1,433 students, 657 boys and 776 girls. The results are qualitatively same as those using the restricted data.

Table B1. Single-Sex School Effect on High School 1st Grade Test Score by Gender and Subject (Based on Extended Sample)

(1) (2) (3) (4) (5) School district FE No Yes Yes Yes Yes Control variables No No Yes No Yes Ranked school FE No No No Yes Yes A. Boys, Math SS high school 0.102* 0.133** 0.116* -0.146 -0.103 (0.056) (0.061) (0.063) (0.109) (0.112) Observations 579 575 541 575 541 R-squared 0.006 0.031 0.083 0.055 0.097 B. Boys, English SS high school 0.100** 0.131*** 0.110** -0.040 -0.009 (0.046) (0.049) (0.049) (0.084) (0.083) Observations 585 581 547 581 547 R-squared 0.008 0.054 0.158 0.085 0.181 C. Boys, Korean SS high school 0.084* 0.119** 0.131** -0.110 -0.072 (0.046) (0.052) (0.054) (0.098) (0.097) Observations 583 579 545 579 545 R-squared 0.005 0.025 0.084 0.055 0.111 D. Girls, Math SS high school 0.228*** 0.228*** 0.182*** 0.044 -0.011 (0.048) (0.051) (0.051) (0.073) (0.069) Observations 709 705 663 705 663 R-squared 0.031 0.044 0.108 0.064 0.127 E. Girls, English SS high school 0.164*** 0.168*** 0.138*** 0.042 0.005 (0.037) (0.038) (0.038) (0.065) (0.064) Observations 709 705 663 705 663 R-squared 0.028 0.063 0.147 0.083 0.164 F. Girls, Korean SS high school 0.149*** 0.137*** 0.115*** 0.076 0.046 (0.037) (0.037) (0.039) (0.059) (0.060) Observations 709 705 663 705 663 R-squared 0.024 0.039 0.091 0.053 0.102 Notes: Each estimate is obtained from a single regression model, differing by dependent variable and specification. The dependent variable is log test score. Control variables are log household income at MS3, father's age and education, mother's age and education, disability, single parent, and sibling size. All specifications except for that in column (1) control for school districts in 2012. Robust standard errors are in parentheses. *** Significance 1%; ** 5%; * 10%.

Table B2. High School 2nd and 3rd Grade Test Scores (Based on Extended Sample)

HS2 HS3 (1) (2) (3) (4) (1) (2) (3) (4) Control variables No Yes No Yes No Yes No Yes Ranked school FE No No Yes Yes No No Yes Yes A. Boys, Math SS high school 0.164*** 0.153*** -0.024 0.003 0.121** 0.123** -0.049 -0.033 (0.051) (0.053) (0.091) (0.093) (0.053) (0.060) (0.094) (0.103) Observations 584 550 584 550 647 551 647 551 R-squared 0.046 0.081 0.065 0.094 0.031 0.072 0.042 0.080 B. Boys, English SS high school 0.165*** 0.136** 0.016 0.058 0.086* 0.107* -0.039 0.048 (0.055) (0.054) (0.087) (0.085) (0.051) (0.055) (0.084) (0.094) Observations 585 551 585 551 647 551 647 551 R-squared 0.043 0.104 0.074 0.129 0.029 0.087 0.041 0.097 C. Boys, Korean SS high school 0.178*** 0.218*** 0.099 0.155 0.160*** 0.155*** 0.060 0.072 (0.052) (0.055) (0.095) (0.094) (0.051) (0.056) (0.089) (0.091) Observations 586 552 586 552 648 552 648 552 R-squared 0.039 0.094 0.057 0.111 0.039 0.062 0.052 0.075 D. Girls, Math SS high school 0.122*** 0.083* 0.019 -0.035 0.230*** 0.208*** 0.079 0.051 (0.044) (0.046) (0.069) (0.072) (0.056) (0.061) (0.084) (0.093) Observations 712 670 712 670 750 653 750 653 R-squared 0.027 0.068 0.036 0.077 0.045 0.093 0.070 0.117 E. Girls, English SS high school 0.207*** 0.166*** 0.134* 0.082 0.269*** 0.254*** 0.078 0.058 (0.044) (0.044) (0.072) (0.070) (0.045) (0.048) (0.069) (0.073) Observations 711 669 711 669 749 652 749 652 R-squared 0.071 0.136 0.082 0.147 0.070 0.116 0.106 0.144 F. Girls, Korean SS high school 0.179*** 0.138*** 0.194** 0.112 0.110*** 0.117** -0.016 -0.015 (0.043) (0.041) (0.082) (0.075) (0.042) (0.045) (0.057) (0.063) Observations 711 669 711 669 750 653 750 653 R-squared 0.046 0.080 0.057 0.088 0.039 0.057 0.066 0.081 Notes: Each estimate is obtained from a single regression model, differing by dependent variable and specification. The dependent variable is log test score. HS2 represents high school 2nd grade, and HS3 represents 3rd grade. Control variables are log household income at MS3, father's age and education, mother's age and education, disability, single parent, and sibling size. All specifications control for school districts in 2012. Robust standard errors are in parentheses. *** Significance 1%; ** 5%; * 10%.

Appendix Figure 1. Percentiles of HS1 Test Scores between Coeducational and Single-Sex Schools A. Math 60 40 HS1 Math 20 0 Coed Single Sex Coed Single Sex Girls Boys

B. English 80 60 40 HS1 English 20 0 Coed Single Sex Coed Single Sex Girls Boys

C. Korean 80 60 40 HS1 Korean 20 0 Coed Single Sex Coed Single Sex Girls Boys

Notes: For each gender and school type, three bars represent 25, 50, and 75 percentiles of first grade high school scores, respectively. The first graph show HS1 math, the second HS1 English, and the third HS1 Korean test scores.