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]

Housing policy: Subsidy vs. Supply

National and Labour are proposing quite different approaches to solving the 'housing affordability crisis'. I'm a bit late coming to this because these policies were announced over the last few weeks, and others have looked at this already (see for example Eric Crampton on the effect on tenants here).

In this post, I'm going to use some fairly simple comparative statics to look at the probably effects of the two policy approaches. I'm putting aside the issue of whether there is a 'housing affordability crisis' at all (incidentally, I have an MBA student looking at that question at the moment - my take is that it depends on how you define 'crisis', hence the quotation marks), and let's assume that there is a crisis and it needs to be 'solved' somehow.

The policies

The National government is proposing that "grants for first-home buyers will be increased from $10,000 to $20,000 for a couple buying a newly built home". This approach is a straight out subsidy, effectively being paid to the buyers (but which, of course, will be passed onto the firm selling the newly-constructed home). Subsidies are a market-based solution, because the government isn't intervening directly in the market but simply changing the incentives for buyers and sellers.

In contrast, the Labour opposition is proposing to "build 100,000 new, affordable homes over ten years and sell them at cost to new home buyers". This approach is a more direct intervention in the market for new housing, since the government would be constructing houses itself (or presumably, through some intermediary - likely drawn from the same set of large firms that would benefit most from the subsidy offered by National).

The effects

Let's start with National's housing subsidy, and for simplicity let's ignore that there is already a subsidy in place for new home buyers, and that this policy simply increases the existing subsidy. Before we lay out the comparative static results, we need to recognise an important feature of the market for housing. That feature is that the supply of housing is relatively less elastic than the demand for housing, especially in the short run. In other words, if the price of housing increases supply will not respond quickly and the number of new homes will not increase by a lot. This is because it takes a long time to develop new housing, get building permits, complete construction, etc. In contrast, the number of buyers wanting to purchases will decrease almost immediately if price rises (or increase immediately if price falls).

The effect of the (increased) housing subsidy is shown in Figure 1 below. Demand for new housing is initially D0, and the subsidy induces increased demand for housing - this isn't a 'true' increase in demand since it would not exist without the subsidy, so we show this with the new curve D+subsidy. The price of new housing is initially P0, but once the subsidy is implemented the price for sellers increases to PP, and the effective price for buyers (after subtracting the subsidy) falls to PC. The higher price for sellers induces them to provide more new housing, while the lower effective price for buyers encourages them to buy more new housing. Everyone wins!

Everyone, that is, except the taxpayer. When we consider the welfare effects of the policy, the consumer surplus has increased from GEP0 to GBC (so buyers are better off), and the producer surplus has increased from P0EH to FDH (so sellers are better off), but the area of the subsidy (FDBC) is being provided into this market by taxpayers (which makes them worse off). Total welfare has decreased as a result of the subsidy (from GEH to GEH-EDB). That is, there is a deadweight loss of EDB.

Figure 1:

So, the policy results in a transfer from taxpayers to new home buyers and new home sellers. But even worse than that, because the supply curve is much less elastic in the short run than the demand curve, the sellers gain most of the benefit from the subsidy. You can see this from the relative change in prices - the price for sellers increases by relatively more than the price for buyers decreases. You can also see this in the change in welfare - the consumer surplus increases by just P0EBC, whereas the producer surplus increases by FDEP0 (of course, I have exaggerated the difference in elasticity between demand and supply, but the difference is still likely to be large). This policy makes home construction firms much better off. Little wonder then that builders are hugely in favour of it.

So, what about Labour's policy alternative? Building more houses directly increases the supply of new housing. This should lower the price of new housing, and increase the number of new houses. Housing affordability is solved and everyone's a winner, right? Not so fast - if it was that easy, both parties would be advocating this solution, and it would already have been done.

What this policy is describing isn't an increase in supply of new housing though - it is an increase in quantity of new housing supplied. This might seem like a semantic difference, but the difference is critical. There is no increase in capacity for constructing new houses and no new construction firms entering the market, so the supply curve remains unchanged. The effect is shown in Figure 2 below. The quantity of new houses being sold increases from Q0 to QD (which is Q0 plus 100,000 additional new homes). In order to induce buyers to buy the additional homes, the price must fall from P0 to P1. (Note: as above, the price only needs to fall a small amount in order to increase quantity demanded by a lot, as potential buyers are prepared to move into the market). At this lower price though, construction firms want to produce fewer homes, so the quantity of new homes supplied falls to QS. The difference between QD and QS is excess supply, but this excess supply is met by the government. Notice that the government would need to build much more than 100,000 new homes in order to increase quantity supplied by 100,000 - because they would need to also make up for the fewer homes that the construction firms want to produce at the lower price.

What about the welfare effects? The consumer surplus increases from GEP0 to GBP1, but the producer surplus decreases from P0EH to P1JH, which is why builders are much less in favour of this policy. The government is intervening in the market, and all houses between QS and QD are actually being sold at a price below the marginal cost of production. The taxpayer loses the area JDB. Total welfare decreases from GEH to GEH-EDB. That is, there is a deadweight loss of EDB.

Figure 2:

Now, I've had to make an additional assumption here, and that is that the houses cannot be sold 'at cost'. At least, not as economists interpret 'at cost', which includes all of the implicit (opportunity) costs of production (in addition to all the direct monetary costs). Otherwise, the marginal cost of the last house is much higher than the current market price - besides which, the market operating at equilibrium already delivers the marginal house 'at cost'.

Comparing the policies

Now, if you compare Figure 1 and Figure 2, you will notice that the areas of deadweight loss are very similar. In fact, if the HomeStart subsidy increased the number of new houses constructed by exactly 100,000 then the size of the deadweight loss would likely be identical for both policies.

And the second-order effects of the policies would be the same if the number of additional homes constructed was the same. That is, increased construction increases the demand for construction materials, and raises their prices. Lower prices for buyers of new housing decreases the demand for existing housing and lowers the price there. And so on.

So, how to choose between the policies?

If both policies induce the same deadweight loss for the same increase in housing (which seems plausible given the simple comparative statics above), and both have the same second-order effects (again plausible if they increase housing by the same amount), then any difference must come down to the costs of administering the policies. If Labour actually intends to build houses themselves (through some subcontracting arrangement), it seems clear to me that the administrative costs of increasing the HomeStart subsidy would be lower. After all, not much in the way of additional bureaucracy would be required since the market is providing the services. Whereas with Labour's approach, new bureaucratic processes would be required (in order to pay subcontractors, sell the newly constructed homes, etc.).

So, if there is a 'crisis' to be solved here, and these are the two options on the table, I would be more in favour of the subsidy approach. Of course, simply lowering the costs of supplying new housing through freeing up land and easing development restrictions, would probably be even more effective.

Try this: "The Economy", the new e-book beta by INET CORE

INET CORE has just released their long-awaited e-book beta on economics principles, The Economy. You can register to read the e-book free here.

The INET CORE project is pretty exciting, and I've been following it closely since its inception. It's headed by Wendy Carlin at University College London, Sam Bowles at the Santa Fe Institute, and Oscar Landerretche at the University of Chile. The stated aim is to teach economics "as if the last three decades had happened". You can read more about the project here, and here is their blog.

Chapter 1 of the e-book is entitled "The Capitalist Revolution" and gives a good flavour for what's ahead. Here's the outline of the chapter:

You will learn:

• That capitalism is an economic system in which goods are produced by employees and are sold on markets for a profit.

• That capitalism has changed living standards, the ways in which people interact, and the natural environment.

• The conditions that enabled capitalist economies to take off.

• How the Industrial Revolution also transformed the economy.

• That there are different ways to organise a capitalist economy.

• That economics is the study of how people interact with each other, and with the natural environment, in producing their livelihoods.

Students who have been in my first-year class (especially ECON110) will know that economic history is important in my teaching, and so is understanding economic theory in context. Chapter 4 is "Strategy, Altruism and Cooperation", and Chapter 5 is "Property, Contract and Power". So, there's lots of interesting bits in this book, and lots of things that make it very different from your run-of-the-mill economics principles text (not least that it's a free online book which will be supported by lots of learning resources for students).

I look forward to reading through this text carefully over the next month or so, and hopefully we can use it (or parts of it) in teaching at Waikato next year.