Do single-sex schools make girls more competitive?

It is often argued that single sex schools are good in the sense that they reduce gender gaps (see here for a rundown of recent evidence). This recent paper in the journal Economics Letters (ungated here) by Soohyung Lee (University of Maryland), Muriel Niederle (Stanford University), and Namwook Kang (Hoseo University, Korea) caught my attention because it looks at whether the gender gap in competitiveness is narrowed by single-sex schooling.

The general problem with trying to estimate the effects of single-sex schooling on any outcomes is that students (or rather, their parents) self-select into single-sex or coed schools. So, its not generally possible to separate the effect of single-sex schooling from the unobserved student or family characteristics that are related to the choice of school. On top of that, single sex schools in many countries (like New Zealand) are more likely to be private schools that can be more selective about the students they admit.

Lee et al. exploit a unique feature of the South Korean education system - that students are randomly assigned to middle schools. From the study:

The key challenges to estimating the effect of single-sex schooling are two-fold: first, coeducational and single-sex schools often have different qualities, and second, students often select which type of school they attend. We address these challenges by examining middle school students (grades 7 to 9) in Seoul, South Korea. This experimental group is well-suited for the purpose of our study because a student is randomly assigned to a single-sex or coeducational school within a school district and all school districts have both single-sex and coeducational schools...

Therefore,  we identify the causal effect of single-sex schooling on competitiveness by estimating simple regression models controlling for school-district fixed effects and individual characteristics.

Participants in the study were asked to solve as many simple addition problems as they could in three minutes. They could then choose to participate in a tournament where they would be paid only if they were the top performer in a randomly-selected group of four students. Those who are more competitive will more likely choose the tournament (the study also includes controls for risk aversion, and for students who want to avoid denying others the chance to win the tournament). The experiment is run twice - first at the beginning of the second term of the 2011-12 academic year (August 2011), and second near the end of the academic year (February 2012).

The authors find:

...girls are less likely than boys to choose tournament: 29.9% of boys select tournament in Task 3, while 22.3 girls do (p-value of testing no gender gap: 0.032). This difference remains even after we control for students’ characteristics.

The results contrast with earlier and widely cited work in the U.K. (earlier ungated version here) by Alison Booth and Patrick Nolen (both at the University of Essex and Australian National University). However, Booth and Nolen's sample were not randomised by school type.

There are a couple of reasons that make me worry about the robustness of the results in Lee et al.'s paper. First, it is essentially an impact evaluation - what is the impact of school type on competitiveness? Given that there are three variables of interest (gender, school type, and before/after), I would have expected them to use difference-in-difference-in-differences (aka DDD - see here for a quick, but somewhat technical, description of DDD). Their simple regression controls lacks the appropriate controls for the direct effect of gender (although this might have been included in student characteristics, which weren't reported), school type interacted with before/after (in case different schools have different general effects over time), gender interacted with before/after, and the triple-interaction (which is the variable of interest in DDD). While this doesn't necessarily invalidate their results, it would be interesting to see what their results look like in a DDD analysis.

Second, the timing of the two rounds of data collection is an issue. Given that the first round occurred after the students had already commenced middle school, the results likely underestimate any impact of single-sex schooling on competitiveness. So, demonstrating a statistically insignificant effect of single-sex schooling on narrowing the gender gap doesn't demonstrate that there is no effect, because perhaps most of the effect occurs in the first term of middle school. We don't know.

I have to agree with the authors when they conclude.:

...whether policies expanding single-sex schools will promote gender equality is a question that requires more thorough empirical investigation.

For me, this paper just doesn't answer the question on whether single-sex schooling narrows gender gaps or not.