Female Labor Force Participation

Keith Chen and Judith Chevalier have a provocative paper on value of education to women:

We examine whether investing in becoming a physician is a positive net present value project for women who do so. We sidestep some selection issues associated with measuring the returns to education by comparing physicians to physician assistants, a similar profession with lower wages but much lower up front training costs. We find that the median female (but not male) primary-care physician would have been financially better off becoming a physician assistant in a primary-care field. This is partially due to a gender wage gap in medicine. However, our result is mostly driven by the fact that the median female physician simply doesn’t work enough hours to amortize her up-front investment in medical school. In contrast, male physicians work substantially more hours on average and the median male physician easily works enough hours to amortize his up-front investment. [emphasis added]

Once you account for the fact that women will generally spend less time in the workforce than men due to time spent childrearing, all sorts of puzzles come up. For instance — how is is that women now outnumber men in a variety of education outcome measures — such as graduating College — and are at parity with men in others — like Medical School attendance? Again, from Chen and Chavalier, we have that women’s lesser time in the workforce lowers the financial return to education -- to the point that med school seems a bad deal in financial terms on average for women.

It would seem likely that non-monetary returns play a large role. What is the relative premium that higher education brings men and women in the marriage market? In the past, higher education was if anything a liability for women’s marriage prospects. This seems less likely to be the case today. As Betsey Stevenson and Justin Wolfers have argued, marriage has gone from an institution encouraging complementarity in production to one of complementarity in consumption. This has encouraged levels of similarity between men and women along a number of different criteria in marriage.

That generates a number of positive spillovers from education for women, which are especially stark when considering the number of co-movements in social and economic trends over the years. For instance, women’s education is hugely predictive of future children’s success — in several studies, I believe, more important than the father’s education. College-educated and above households are substantially less likely to divorce or face other negative events than even high school-educated households — and that divergence is growing. High school-educated families increasingly resemble high school dropouts rather than College educated families. Divergences in job markets — in which College-educated jobs receive high and growing premiums, while jobs requiring a high school degree see stagnating incomes — encourage these trends.

So while Chen and Chevalier phrase their paper through the question, “Are women over-educating themselves?” I’d instead look at the empirical evidence that people are pursuing more education, and then think about what sort of incentives drive them to do that. The financial incentives are only a part of the picture. The non-financial incentives — marriage on average with a more stable, higher educated person, kids that will be better off as well, general transformations of life views — may be substantial.

There are all sorts of other social consequences resulting from a lower female workforce rate. For instance, Social Security and pension plans are typically gender-neutral in the sense that they require equal savings per dollar earned from men and women. This may make sense for families that do not anticipate divorce, in which total earnings are pooled and split to finance joint consumption. It doesn’t necessarily make sense for divorced families or single women. Given that women can also expect a greater life expectancy, the average women can anticipate lower savings to finance a longer retirement period. That doesn’t seem right. Women should probably be saving at far higher rates than men.

This also means that it doesn’t make too much sense to put men and women in a lab, observe that women take fewer risks than women, and then conclude that we need to put women in charge of banks because they're safer people. Laboratory experiments on men and women may reflect nature/nurture effects on fundamental risk preferences. But as long as men and women specialize differently in child rearing/time in the workforce/occupational structure; there’s no good reason to expect them to have identical risk preferences. In fact it would be nonsense to expect them to have identical risk preferences — yet that’s what pension plans do.

You also have the usual taxation questions. Marginal tax rates carry far higher deadweight losses on women than men, because women are more often on the margin between working or not. Progressive taxation produces additional burdens, as the wives of high-earning men can expect to keep much less of their earned income, and so more often choose to opt-out of the workforce entirely. The obvious solution would be to handle child subsidies in the form of reducing the entire marginal tax rate schedule for families with children; and tax households as two single individuals. If feminists got together with the tea party to make this happen, it would probably do more to encourage female labor force participation than any other act of public policy in fifty years. India already has a different tax rate system for men and women, so don't tell me this is impossible to think about.

There are also thorny issues related to admissions policy — as raised for instance by Posner on his blog. If Universities are aiming to maximize the success and income of future graduates to raise their own prestige; they will not be indifferent to the amount they want their graduates to work, and they will not be indifferent in choosing between two applicants, one of which plans on working much less in the future than another. Taxpayers, in general, will also not be indifferent between subsidizing the education of two people, one of whom plans on spending much less time in the job market than another (though that taxpayer might also be concerned about the human capital of others children as well). This presents obvious issues that I’ll leave to Posner to discuss.

There’s also a medicine-specific issue relating to this study. The authors mention that women represent 24% of first year medical students in 1976, but 48% in 2006. What does that imply in terms of the labor supply of doctor? The authors write:

Specifically, the median male doctor in our data has accumulated 37,594 hours of experience by 15 years post-residency, while the female doctor does not achieve that number of cumulative hours until year 19.

Roughly, that suggests that female doctor labor supply is 75% that of male doctors. The cumulative impact of achieving gender parity in medical school has reduced doctor supply by something like 6% since 1976 — or roughly 12-13% since women began attending medical schools in any numbers. That estimate could be higher if women also tend to retire earlier than men. And it doesn’t take into account any “learning-by-doing” effects that might leave women less qualified than an otherwise identical man due to their less time in the workforce.

In most other fields, this wouldn’t be a huge issue. The fact that women work less than men would be balanced by the fact that they’re entering the workforce to begin with.

But medicine is different given that the AMA operates a cartel regulating tightly the number of medical school seats. The role of this cartel in limiting the supply of doctors and raising medical costs is strongly under-covered.

And has the AMA thought about this issue? One imagines that they have not. If we assume that the AMA was optimizing medical school seats so as to maximize monopoly profits but didn’t consider the impact of greater female participation on overall doctor labor supply — than we have too few doctors relative to the optimal number doctors a monopoly would prefer. I can’t think of another case where a monopoly has irrationally undersupplied its product. Ironically, alleviating gender inequality in medical school admissions may have inadvertently raised income inequality, assuming I’m right in thinking that medical school slots are indeed fixed in this manner, given that the resulting lower supply of doctors surely raised medical costs on everyone, hurting proportionally more the poor.

To clarify — I’m not taking any stances on the desirability of greater female employment, or the labor decisions within households, or anything like that. One can draw many conclusions from this depending on ideological proclivities. For instance, one could say that the real problem is that men spend too much time in the workforce, and should spend equal time in home production. Or the real problem might be the cartel powers of the AMA. But certainly this is a real issue deserving greater attention.

The Value of Marginal Education

There’s an ongoing debate at EconLog, Marginal Revolution, the New York Times and elsewhere over the value of additional education. No one doubts that education appears to be a valuable investment for students who pursue it. But it valuable for the marginal individual? Do we need public policy to steer more students through high school, College, and degrees beyond? Given the centrality of cognitive ability and human capital to economic output and general wellbeing, this has to rank as one of the more important economic questions out there.

Tyler Cowen refers us to some studies:

How much do returns to education differ across different natural experiment methods? To test this, we estimate the rate of return to schooling in Australia using two different instruments for schooling: month of birth and changes in compulsory schooling laws. With annual pre-tax income as our measure of income, we find that the naıve ordinary least squares (OLS) returns to an additional year of schooling is 13%. The month of birth IV approach gives an 8% rate of return to schooling, while using changes in compulsory schooling laws as an IV produces a 12% rate of return. We then compare our results with a third natural experiment: studies of Australian twins that have been conducted by other researchers. While these studies have tended to estimate a lower return to education than ours, we believe that this is primarily due to the better measurement of income and schooling in our data set. Australian twins studies are consistent with our findings insofar as they find little evidence of ability bias in the OLS rate of return to schooling. Together, the estimates suggest that between one-tenth and two-fifths of the OLS return to schooling is due to ability bias. The rate of return to education in Australia, corrected for ability bias, is around 10%, which is similar to the rate in Britain, Canada, the Netherlands, Norway and the United States.

These are all basically examples of an Instrumental Variable (IV) approach. Let’s take these one at a time. First, we have the month of birth evidence. Yet this is the classic example of a weak instrument, an issue which is well discussed elsewhere. The month or quarter of birth has a very weak impact on final educational outcomes, and parents with children born in different months are not identical either.

Next, there is the compulsory schooling evidence, that Arnold Kling actually takes on as well, though only in the US context. He observes that the variation across states in terms of when a student can legally graduate doesn’t seem to predict their actual graduation habits. This is basically also a weak instrument; at least in the case of the US.

Finally, we have the twins evidence. The idea here is to observe one twin going to College and compare her with her sister twin who did not go to College. The assumption is that these two individuals shared identical environmental background factors, and so any resulting differences can be causally attributed to the College attendance of one twin. While this is a clever trick, it requires you to believe that twins are interchangeable humans. What if a family can only afford to send one twin to College, and so they send their more able child? What about all sorts of cognitive and non-cognitive differences that come up between children growing up in the same house? What about the possibility of twin interactions? Though interesting and suggestive, I don’t believe this evidence to be causally definitive.

It’s easy enough to knock holes in any body of literature, even one (as here) which does purport to establish identification. So here’s some evidence that points in the other direction.

1. Cognitive abilities have limited scope for educational intervention in developed economies beyond age ~5.

The evidence of this actually comes from James Heckman. He argues that we simply do not have access to any educational treatment that can reliably boost IQ over an extended period of time. Even the lauded Head Start/Perry Preschool programs can't do that. And if spending tens of thousands of dollars per pupil on a pilot program can’t produce results, it’s difficult to imagine what would.

An education proponent could now say something like, “Fine, but cognitive skills aren’t everything. Heckman supports Head Start — because it boosts noncognitive skills like impulse control.” Suppose I even grant that point — though I note that these noncognitive skills are something like a black box. There’s defined entirely as a residual of what can’t be a cognitive skill, and are inferred largely on the basis of lower crime rates among treated populations.

But think about what that would mean. Everything we do in schools — the teaching, the homework, etc. — has limited value when it comes to actually improving mental functions. Rather, it may or may not be effective in domesticating children to functioning in a modern post-industrial economy. At the very least, that would suggest that education ought radically change its focus away from cognitive tasks towards those aspects of behavior modification. Maybe we’d get the same results as school from a program forcing children to dig holes every day and fill them back up. Also note that Heckman’s results on the payoffs of education based on these noncognitive skills is rapidly declining in age. Are Head Start, prenatal care, or child nutrition policies worthwhile? Very likely. What about pushing unprepared children to attend College? Less clear.

2. Other estimates of the marginal return to education are low.

Heckman has another paper with coauthors where he attempts more rigorously to estimate the marginal impact of more education — in particular, of more College. Even the Instrumental Variable estimates discussed above may be biased — as they measure the impact on individuals induced to have the treatment (ie, more education). This need not be the same population as those induced to have more education in response to some arbitrary policy change.

Instead, Heckman creates an estimate designed to get exactly at the impact of more College on outcomes. The basic logic of his approach is to find individuals who had a low ex ante likelihood of attending College, but who went anyway. These are a proxy of the individuals targeted by, say, a program to induce more people to attend College.

He argues:

For a sample of white males from the NLSY, we establish that marginal expansions in college attendance attract students with lower returns than those enjoyed by persons currently attending college. The contrast between what conventional IV measures and the marginal return to a policy can be stark. For example, while the conventional IV estimate is 0.0951, the estimated marginal return to a policy that expands each individual’s probability of attending college by the same proportion is only 0.0148. This policy induces students who should not attend college to attend it. Too many people go to college. [Emphasis added]

Note in particular that his estimates are consistent with high “IV” estimates — based on a set of instruments that he was able to use here. So even if the “identified” estimates based on the IV literature are correct, they do not necessarily serve as useful diagnostics on whether College expansion programs are worthwhile.

I’ll acknowledge that there’s substantial uncertainty about this question and much that we don’t know. I’m not particularly on one “side” in this debate. But this is such a difficult question to answer because people who seek more education would likely have done well anyway.

What I can say is that the most effective policy interventions here have little to do with simply broadening the access to education. All sorts of early child intervention techniques seem to yield positive results. A number of charter school/school choice/voucher experiments have resulted in institutional improvements in the quality of education while lowering the cost.

Prometheus and Education

Via Sanjoy Mahojan's excellent TED(ish) talk, here is a good quote:

The goal [of teaching] should be, not to implant in the student's mind every fact that the teacher knows now; but rather to implant a way of thinking that will enable the student, in the future, to learn in one year what the teacher learned in two years. Only in that way can we continue to advance from one generation to the next.
-Edwin T Jaynes

Yet this is a goal that's completely absent from any education reform movement of any flavor. Generally, the reformers try to change some aspect of schools or teachers in order to improve proficiency levels variously measured, ie smaller class sizes or merit pay.

What the quote illustrates is a broader point about education: that the process by which we teach must become efficient in time as we gain knowledge, or else our ability to advance the frontier of education necessarily slows down. Otherwise, people will take so long to advance to the frontier of knowledge that they have less time for active discovery, resulting in a Great Stagnation in research.

These teaching efficiencies have somehow happened anyway, at least in the math/science areas, without us being too aware of it. Calculus is now routinely taught in High Schools, while it was once at the frontier of knowledge. I'm not sure what advances in math education have allowed that to happen, but certainly students are being exposed to "deeper" knowledge at younger and younger ages.

I think this points to the importance of figuring out how to develop meta-cognitive tools that allow people to learn more in less time. ie, improvements in teaching pedagogy that really focus on reducing the actual time involved to learn a skill. I think this particular goal -- which aims for a steady reduction in the age at which students master given skills -- isn't really on the radar for any particular group, but it should be.

There are a couple of other creative ways to get at this idea. We can try more tracking-based systems, so children have more time to focus on learning in a particular direction. We can extend the hours that children spent learning, perhaps by using video games. Alternatively, we should be actively pruning the set of things taught in school as various forms of knowledge become less useful. Geometry and trigonometry seem to be widely taught, yet this is due largely to the importance of those tools to practical engineering applications in the 19th century, as well as reflecting the legacy of a particular mathematical tradition dating back to Euclid and beyond. Seems to me they ought be pruned to make way for mathematical tools of greater practical importance today, like statistics or street fighting math. In general, we should focus away from empirical facts (which are growing like kudzu) towards general reasoning; and in particular innovations that allow for rapid growth in the rate of general reasoning skills.

Teacher Incentives Don't Work

From Roland Fryer's new paper:

Financial incentives for teachers to increase student performance is an increasingly popular education policy around the world. This paper describes a school-based randomized trial in over two-hundred New York City public schools designed to better understand the impact of teacher incentives on student achievement. I find no evidence that teacher incentives increase student performance, attendance, or graduation, nor do I find any evidence that the incentives change student or teacher behavior. If anything, teacher incentives may decrease student achievement, especially in larger schools. The paper concludes with a speculative discussion of theories that may explain these stark results.

There really don't seem to be very many scalable ways to boost student performance at this point. Smaller class sizes or schools, early childhood education, even some school choice measures; all don't seem to improve test scores in a systematic way. Add to that now merit pay -- which, if anything, reduces scores.

If anything, this points to the edu-nihilist point that what goes in classrooms doesn't seem to impact what children know very much. Perhaps peer effects or family background are more important, or else variation across teachers just isn't very informative. One logical strategy in response to this information would be to forget about trying to raise test scores, and settle for providing schooling services at minimum cost.

Lies my Teacher Told Me

I was always told that getting a liberal arts degree would pay off in the long run in both psychic and monetary rewards.  Who knows about the psychic/intellectual rewards.  But I've always been skeptical about the monetary rewards.  Most data that's available shows that the quant fields--math, finance, econ--do much better than the soft disciplines for the first job (some of the skills premium for postgraduates was probably mispriced because of asset bubbles, excessive leverage, and poor risk models on the finance side--more on this later).  Again, the liberal arts partisans claim that this is unique to your first job, and that the liberal arts majors dominate over time.  This would actually be somewhat odd to see, as most people receive a similar, small annual increase every year regardless of major.  

Well, this is easy enough to check.  The government collects stats on the profile of around 8k graduates 10 years out of graduation.  As the chart shows, the math/quant/sciences dominate the liberal arts guys income-wise.   

Some weird stuff does happen in the distribution of income separated by major, shown left.  Engineers aren't as well represented as you might think at the top bracket given their high mean.  But the social and biological scientists dominate the humanities.  Psychology does abysmally, trailing even Education with .31% claiming an income in excess of $150,000 (2003 Dollars).  At the very least, this is good evidence that the liberal arts are not a great path to riches.  

The better question is whether this reflects knowledge learned in school, or whether majors serve to filter students along measures of intelligence and career preference.  Unfortunately, I can't correct for all potential problems as they don't release the full data, but I can look at some things anyway.  

First-I checked SAT/ACT grade variation by gender.  There's not too much resolution--I only have scored by quartiles, and many are missing---but this data would suggest a higher mean score for males as well as lower variance.  However, this group has already been preselected, so data at the bottom tail is unlikely to be perfectly representative.  Interestingly, this pattern is reversed for GPA: Females dominate the top end of GPA.  However, GPA is not as directly comparable between people, especially given the stark differnences in major choices by gender, and the differences in average GPA by major. Interestingly, given this difference, undergraduate GPA and test scores correlate.  The top quartile on the SAT/ACT had a 3.45 while the bottom received a 3.13. 

I also have SAT/ACT quartile by College Major.  Business majors don't do so great on standardized tests, but obviously make plenty of money.  The quant majors disproportionately pull in the top scorers.  But the Humanities, History, and Psychology do well enough test-wise.  But given another result from this data--that SAT/ACT predicts future income--it's clear that the liberal arts are underperformers in future earnings, taking intellectual ability before College into account.  

This isn't entirely definitive, and I'd like to run some real regressions here.  A big issue is personal preference for career--how much you make is a function of how much you want to work, and what you want to do as much as raw ability before or after College.  And obviously, there's more to college than becoming employable.  I really don't even know how much I could say from this data.  It's not clear what is contribution of a major to earnings outside of personal initiative and intellgience, or even to what degree College gives people skills or labels people as belong to various levels of quality.