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.

Why KiwiRail losses might be a good thing

Last week in ECON110 we covered natural monopoly. One of the interesting aspects of natural monopoly is what might happen when the government owns one. Such is the case with KiwiRail, which the government purchased back from Toll Holdings in 2008, after it was originally privatised in 1993.

KiwiRail was in the news again last month, having made a loss of $248 million in the year to June 30, 2014. That follows a loss of nearly $175 million in the previous year (PDF). Now, some of those losses are writedowns and impairments, but that aside, should we really be worried about big losses from a government-owned natural monopoly?

I previously blogged about natural monopolies earlier in the year, but didn't talk specifically about government-owned natural monopolies. First some background theory - a natural monopoly arises where one producer of a product is so much more efficient (by efficient I mean they produce at lower cost) than many suppliers that new entrants into the market would find it difficult, if not impossible, to compete with them. It is this cost advantage that creates a barrier to entry for other firms, and leads to a monopoly. Natural monopolies typically arise where there are large economies of scale (when, as a firm produces more of a product, their average costs of production fall). Economies of scale are common when there is a very large up-front (fixed) cost of production, and the marginal costs (the cost of supplying an additional unit of the product) are small (the cost structure is shown in the figure below, with a simplifying assumption that the marginal cost of production is low and constant). The markets for utilities, where the up-front cost includes the cost of having all of the infrastructure in place, are good examples. Rail is another example, since you need the tracks, the rolling stock, and the associated stations and other buildings in place before you can start to provide rail services.

Now natural monopolies, like other firms, are assumed to be profit maximisers. That is, they will operate at the point where marginal revenue is equal to marginal cost. That is, they will operate at the price PM and the quantity QM in the diagram above. At that point, the producer surplus is the area PMBHPS, while the firm's profit is the area PMBKL (the difference between profit and producer surplus arises because of the large up-front fixed costs, which are subtracted from profits, but not from producer surplus). However, consumer surplus in this market is GBPM, and total welfare is GBHPS. This leaves a deadweight loss equal to the area BEH.

Now, if the government owned the natural monopoly, it doesn't necessarily have to profit maximise if it doesn't want to. Government could choose to maximise total welfare instead. It would do this by setting the price at the point where marginal social benefit is equal to marginal social cost. That is, the market will operate at the price PS and the quantity QS. At that point, producer surplus is zero (since every unit is sold for marginal cost), but the profit is negative (JDEPS) because price is below average cost. On the other hand, consumer surplus is GEPS, and total welfare is maximised at GEPS.

Having the natural monopoly make a loss (and this is an economic loss, so it includes opportunity costs, and would be greater than any accounting loss) may be a good thing because it increases total welfare. However, relative to profit maximisation, it entails a transfer of welfare from taxpayers (who ultimately end up paying the loss) to consumers of rail services (and ultimately, to consumers of stuff that is transported by rail).

Is there adverse selection in the life insurance market?

I blogged yesterday about adverse selection in the home insurance market. But does adverse selection apply in all insurance markets? What about life insurance? Adverse selection requires private information, and it requires that the informed party must be able to benefit from keeping the private information secret.

In the case of life insurance, if you have a terminal illness or have made lifestyle choices that increase your mortality risk, then that is likely to be private information. Because you are higher risk, you should pay a higher premium. However, because the life insurance company can't tell the high-risk and low-risk people apart, that leads to a pooling equilibrium. The life insurance company must assume that everyone is high risk, and raise premiums as a result.

So, if there is adverse selection in the life insurance market, we should expect to see that people with life insurance are more likely to die than people without life insurance. Which leads me to this recent paper in the journal Economics Letters (ungated here) by Timothy Harris and Aaron Yelowitz (both of University of Kentucky). Using data from the 1990 and 1991 panels of the Survey of Income and Program Participation in the U.S., combined with mortality data from the Social Security Administration's Master Beneficiary Record, Harris and Yelowitz find:

...no significant evidence of adverse selection. In virtually all specifications, those who have higher mortality are no more likely to hold life insurance.

In fact, the authors find some evidence of advantageous selection (the opposite of adverse selection - in this case, where lower risk individuals are more likely to have life insurance). But before you think this means that this proves a lack of adverse selection, consider this. Markets, particularly insurance markets (including life insurance) can be pretty adept (and often sophisticated) in mitigating the problems of adverse selection. In the case of life insurance, simply comparing those with and without a life insurance policy in terms of mortality doesn't tell the full story about adverse selection. Insurers spend some effort in screening applicants for life insurance, including questions about medical history, incidence of disease in your parents, etc. before they make a decision about offering insurance (and what the premium will be). The most risky applicants will be eliminated during this screening phase. Indeed, the authors note this themselves:

Although the empirical findings are consistent with the concept of advantageous selection, it is important to recognize the importance of underwriting in the life insurance market. All existing empirical analyses examine life insurance holdings, not applications. Insurers ask extensive questions and require medical exams prior to approval of an application. These institutional features suggest caution before claiming that applicants are advantageously selected; rather the underwriting process potentially screens out high-risk applicants who would otherwise obtain life insurance.

So, if we had no underwriting or screening processes, maybe we would observe adverse selection in the life insurance market. Or maybe not. Simply looking at mortality after an insurance contract is negotiated in the absence of screening would not be enough, because of potential moral hazard problems. Moral hazard arises when, after an agreement is made, one of the parties has an incentive to change their behaviour (usually to take advantage of the terms of the agreement) in a way that harms the other party. In the case of life insurance, once a person has life insurance their incentives change slightly - they may engage in more risky behaviour safe in the knowledge that their family will be provided for in the case of a skydiving accident, for instance. So, we might expect to see higher mortality among the insured than the non-insured not because of adverse selection, but because of moral hazard.

The authors are correct in asserting that we should look at applications for life insurance. Adverse selection is a problem of pre-contractual opportunism after all. To assess whether adverse selection exists in this market, the best approach would be to look at applications and medical histories and risk factors for life-threatening diseases of applicants, and compare with non-applicants. While looking at actual outcomes (in terms of mortality data) is somewhat appealing, it runs into issues of whether the observed difference arises because of adverse selection (the applicant was at higher risk before they obtained insurance), moral hazard (the applicant became more risky to insure after they obtained insurance), or some combination of the two.

Big trees, home insurance and adverse selection

One of the most difficult concepts we cover in ECON100 and ECON110 each semester is the problem of adverse selection. Adverse selection arises when there is information asymmetry - specifically, there is private information about some characteristics or attributes that are relevant to an agreement, that is known to one party to an agreement but not to others.

However, information asymmetry by itself is not enough for an adverse selection problem (e.g. I know whether I like the colour yellow or not, but that private information doesn't affect many market transactions I engage in - at least not to a large enough extent to cause market failure). The informed party must be able to benefit from keeping the private information secret - this is an example of pre-contractual opportunism on the part of the informed party.

An adverse selection problem arises because the uninformed party cannot tell those with 'good' attributes from those with 'bad' attributes. To minimise the risk to themselves of engaging in an unfavourable market transaction, it makes sense for the uninformed party to assume that everyone has 'bad' attributes. This leads to a pooling equilibrium - those with 'good' and 'bad' attributes are grouped together because they can't easily differentiate themselves. This creates a problem if it causes the market to fail.

In the case of insurance, the market failure may arise as follows (this explanation follows Stephen Landsburg's excellent book The Armchair Economist). Let's say you could rank every person from 1 to 10 in terms of risk (the least risky are 1's, and the most risky are 10's). The insurance company doesn't know who is high-risk or low-risk. Say that they price the premiums based on the 'average' risk ('5' perhaps). The low risk people (1's and 2's) would be paying too much for insurance relative to their risk, so they choose not to buy insurance. This raises the average risk of those who do buy insurance (to '6' perhaps). So, the insurance company has to raise premiums to compensate. This causes some of the medium risk people (3's and 4's) to drop out of the market. The average risk has gone up again, and so do the premiums. Eventually, either only high risk people (10's) buy insurance, or no one buys it at all. This is why we call the problem adverse selection - the insurance company would prefer to sell insurance to low risk people, but it's the high risk people who are most likely to buy.

Which brings me to the example of big trees and home insurance. One of my extramural ECON110 students asked me about this video for Youi insurance. It provides a good example of potential adverse selection, but one that is easily solved.

The insurance company doesn't know whether or not you have 'enormous trees that will fall and crush your house' (having big trees next to your house is private information). So, maybe they make an assumption that you do, and in order to compensate for the higher risk, they charge a higher insurance premium.

Of course, markets have developed ways of solving the adverse selection problem. If the informed party can find some way to credibly reveal the private information to the uninformed party, we call this signalling (I've previously written on signalling, in the context of wedding costs). If the uninformed party can find some was of revealing the private information, we call this screening.

In the case of the video, the screening solution to the big trees adverse selection problem is pretty simple. Just ask the person if they have big trees! [Of course, if they do have enormous trees next to their house, there is some incentive to misrepresent themselves and say 'no', but that's why you have a clause in the insurance contract that voids the contract if the insured person provides false information.]

Alternatively there is a signalling solution to the big trees adverse selection problem. The homeowner could take a photo of their house, demonstrating that there are no enormous trees next to it. Easy and credible.

[HT: Tracey from my ECON110(NET) class]