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Human capital

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The Role of Education Quality for Economic Growth
Eric A. Hanushek and Ludger Woessmann (http://ssrn.com/abstract=960379)

The figure shows, by country, the share of students that scored very low (< 400 rough PISA equivalent, “scientifically and mathematically illiterate”) or very high (> 600) on cognitive tests administered over the last 40 years. The results give a good indication of the quality of human capital in the country’s workforce. Click for larger version.

From the paper:

…To create our measure of quality of education employed in this study, we use a simple average of the transformed mathematics and science scores over all the available international tests in which a country participated, combining data from up to nine international testing occasions and thirty individual test point observations. This procedure of averaging performance over a forty year period is meant to proxy the educational performance of the whole labor force, because the basic objective is not to measure the quality of students but to obtain an index of the quality of the workers in a country.

If the quality of schools and skills of graduates are constant over time, this averaging is appropriate and uses the available information to obtain the most reliable estimate of quality. If on the other hand there is changing performance, this averaging will introduce measurement error of varying degrees. [i.e., younger workers in developing countries probably have better skills than indicated in the data.]

More PISA fun.

Written by infoproc

September 30, 2008 at 7:52 pm

WSJ compensation survey

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The WSJ has posted some interesting compensation data which can be sorted by college and degree type. The data covers people less than 5 years out of school and more than 10 years out (“mid-career”), in all cases excluding those that earned advanced degrees — so that the outcomes are most sensitive to the undergraduate background of the respondents. Note you can click the column heading to sort by that variable (starting salary, 75 percentile mid-career salary, etc.).

There’s also an accompanying article. The author notes that schools (Ivies) at which a large fraction of students head into finance tend to have the highest starting and mid-career averages. Engineers have high starting salaries but not as much appreciation.

A social scientist can now regress the salaries on avg SAT and school / major to calculate the economic “value add” for a particular major or institution. (See UT Austin data here.) A significant confound is that people who *do* get advanced degrees would not appear in this data. (Almost half of all Caltech undergrads get PhDs and probably well over half get other advanced degrees.)

Some random results:

Caltech grads had the highest median starting salaries at $75k; by midcareer Dartmouth is number one with median compensation of $134k (MIT $126k, Caltech $123k).

Salaries by degree | starting | 10th-90th percentile midcareer range

Physics | $50k | $56k — $178k
EE | $60k | $69k — $168k
English | $38k | $33k — $136k
Economics | $50k | $50k — $210k
Philosophy | $40k | $35k — $168

• Survey respondents included two sets of U.S. bachelor’s degree graduates: Full-time workers with 5.5 years of experience or less and full-time employees with 10 or more years of experience.

• The survey excluded respondents who reported having advanced degrees, including M.B.A.s, M.D.s and J.D.s. Self-employed, project-based, and contract employees were also not included.

• Salary included annual cash compensation, including base salary or hourly wages, combined with commissions, bonuses, profit sharing and other forms of cash earnings.

Written by infoproc

July 31, 2008 at 3:18 pm

The joy of gender imbalances on campus

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The Chronicle of Higher Education reports on the social effects of gender imbalances. As we know, teenage girls are more likely than boys to have their acts together, hence make up a larger and larger percentage of those who attend college. I see this all the time in my intro classes — a majority of the most organized students are female, and a majority of the least organized are male. Many universities will have to use affirmative action for male applicants in order to preserve 50-50 gender ratios.

Math puzzle: (optional for readers who have trouble with distributions) If most of the least able students are male, and yet men and women perform equally on average (actually this may not be true anymore, but see PISA data :-), what does that imply about the most able students on campus?

Chronicle: American colleges are undergoing a striking gender shift. In 2015 the average college graduating class will be 60-percent female, according to the U.S. Education Department. Some colleges have already reached or passed that threshold, which allows anecdotal insights into how those imbalances affect the pickup culture. What can be seen so far is not encouraging: Stark gender imbalances appear to act as an accelerant on the hookup culture.

…In 2006 I visited James Madison University, a public university with 17,000 students. At the time, women made up 61 percent of the campus population.

…A senior added: “The guys see that there are a lot more girls, and they’re not interested in having a relationship longer than the next girl to come along. Men know how to take advantage of that competition. They’ll set things up at parties to get girls to do stuff, such as having a slip and slide contest,” in which girls strip to their underwear and get wet sliding through water on a plastic sheet.

As a result of the rising gender imbalances, the university has become “female centric.” But while women may run the clubs, dominate in classes, and generally define the character of the university, the law of supply and demand rules the social scene. That’s why the women are both competitive in seeking men and submissive in lowering their standards.

Men at the university don’t dispute what the women say. “Since there’s such an overwhelming number of girls, they have such competition between each other to get a guy,” a male junior admitted. “The guys here aren’t stupid. They’re plenty aware of that and know that girls have to get into a fight over them, instead of what’s normal with guys courting girls.”

I wonder what a FaceBook search on the keywords “slip and slide” brings up?

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July 22, 2008 at 6:09 pm

Higher education and human capital II

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I thought I’d also link to some interesting data from a paper by UT Austin economist Daniel Hamermesh, discussed here on the NYTimes Freakonomics blog.

Their survey covered UT Austin alumni between the ages of 23 and 43, revealing enormous variations in average earnings between different majors. Not surprisingly, the business majors and engineers tend to be high earners. However, the highest earners of all are the Plan II (honors college) alumni, who have by far the highest average SAT scores (1364). Note the huge variance within each major (SD = number in parentheses below the mean value), in particular for business, natural sciences and Plan II. For these majors the standard deviation is larger than the mean, suggesting, perhaps, that a few millionaires (startup founders, entrepreneurs?) are skewing the results.

The effect of college curriculum on earnings: …Clearly, there are large differences across major in average earnings, with the highest-earning majors (Honors Plan II, and “Hard” Business) having averages almost three times that of the lowest (Education). Much of the differences across majors must be due to differences in what the students bring to and do at the University. Students in the higher-earning majors generally have higher SAT totals upon entry, and the fractions of students taking upper-division math and science courses and doing well in them are greater too. The differences are also consistent with the results of differential effort in the labor market and male-female differences in earnings. Thus respondents in the higher-earning majors tend to state that they work longer hours than those in lower-earning majors; and except for the Honors Plan II major, the fraction of women in the higher-earning majors is lower. On the other hand, advanced degrees are more prevalent among those graduates who have majored in subjects that eventually generate lower earnings. Family incomes in the areas where the students attended high school do not differ across majors …

…Even within major, taking more upper-division science or math courses and doing better in them raise eventual earnings. While the effects are not highly significant statistically, the t-statistics generally exceed 1.28. A student who takes 15 credits of upper-division science and math courses and obtains a B average in them will earn about 10 percent more than an otherwise identical student in the same major … who takes no upper-division classes in these areas. There is clearly a return to taking these difficult courses. This holds true even after we have adjusted for differences in mathematical ability by using the total SAT score … . The importance of access to this information should not be underestimated. Estimated earnings differences across majors are substantially higher (e.g., the premium for “hard” business rises to 64 log points, that for engineering to 50 log points) when the information on science and math courses is excluded from the equation in Column (1).

Click on the figure below for a larger, more readable version.


Written by infoproc

June 29, 2008 at 8:15 pm

Higher education and human capital

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What good is higher education? The conventional view is that, in addition to producing a well-informed citizenry, it builds important human capital and raises national productivity. But what is the evidence for these assertions? In policy debates we are typically presented with faulty logic: workers in desirable, high value-added jobs (e.g., at Google or Biogen) tend to have lots of education. Therefore, if we want Americans to have such jobs we had better expand access to higher education. The counter argument, that returns to society as a whole from education diminish as access increases beyond the cognitive elite, is given below by a well-known curmudgeon and psychometric realist:

Brutal, just brutal: …There is no magic point at which a genuine college-level education becomes an option, but anything below an IQ of 110 is problematic. If you want to do well, you should have an IQ of 115 or higher. Put another way, it makes sense for only about 15% of the population, 25% if one stretches it, to get a college education. And yet more than 45% of recent high school graduates enroll in four-year colleges. Adjust that percentage to account for high-school dropouts, and more than 40% of all persons in their late teens are trying to go to a four-year college–enough people to absorb everyone down through an IQ of 104.

Note the claim is not that benefits from higher education are zero for the average student, but merely that they diminish significantly as we expand access. At some point we need to consider whether the marginal cost exceeds the marginal benefit. No amount of schooling will turn an average student into a materials engineer, tax lawyer or derivatives trader.

I’m afraid these kinds of thoughts lurk in the minds of most professors these days — I’ve heard them discussed many times. Why can’t my students write? Why can’t my students do simple math? Does the bottom half of the class really absorb anything from my lectures? Is science just too difficult for some people? If I showed you some of the emails I receive from students in my physics 101 course, you would cry at the lack of mastery of grammar and spelling, let alone physics.

Below I excerpt some depressing results from researchers at Stanford and Yale, which support the sorting and signalling model of higher ed, rather than the human capital building model.

Education and Verbal Ability over Time: Evidence from Three Multi-Time Sources

Nie, Golde and Butler

Abstract: During the 20th century, there was an unprecedented expansion in the level of educational attainment in America. Using three separate measures, this paper investigates whether there was a concurrent increase in verbal ability and skills. Changes in verbal ability in the general population as well as changes in the verbal ability of graduates of different levels of education are investigated. An additional investigation of how changes in the differences between males’ and females’ educational attainment are associated with changes in differences between their respective verbal abilities follows. The main finding is that there is little evidence that the large increase in educational attainment has resulted in an increase in any of the measures of verbal abilities and skills.

From the paper:

The results from using these three different measures of verbal ability and skills all show the same striking patterns: (1) there is no increase in scores in the overall population over time; (2) as the number of people obtaining a certain level of education increased, the verbal ability of those terminating with that degree has decreased. …

Comment for the psychometric cognoscenti: where is the Flynn effect here? I see no overall increase in verbal IQ.

See also this less technical exposition:

Nie and Golde: …Our initial hypothesis was that if amount of schooling causally affects any outcome, it would be verbal ability. The vast expansion of the American education system over the course of the 20th century served as our test bed. We expected that the huge increase in educational attainment in the U.S. across the decades would be accompanied by a substantial improvement in verbal abilities. To our initial amazement, we found no evidence for such improvement.

We started our investigation by showing that there is, indeed, a strong correlation between education and verbal ability. The data on which our analyses are based came from the General Social Survey, a program of in-person interviews that has been conducted regularly since 1972 by the National Opinion Research Center at the University of Chicago. While the samples were nationally representative, to avoid complications caused by changing demographics and questions about the validity of such tests with minority and immigrant populations, we included only the native-born, white American population 30 to 65 years of age, using information collected over the last 35 years of parallel surveys. (We used only those 30 years or older to ensure that we were dealing only with people who had completed their education; we stopped at age 65, lest we contaminate the analysis by differential mortality rates.)

Education levels and scores on a vocabulary test given to subjects are indeed correlated (see Figure 1). Over the three-plus decades studied, those with more education got better vocabulary scores, and vice versa.

Those results, however, do not necessarily imply that education causes increased verbal ability. If education did increase verbal ability, we would expect increasing levels of education over time to bring about measurably higher levels of verbal ability. During the 20th century, there was an unprecedented expansion in the levels of educational attainment in the U.S. The average American born between 1910 and 1914 received a bit more than 10 years of education. The average American born between 1970 and 1974 received 14 years of education. In 60 years, the “average American” went from being a high school dropout to having two years of college — a remarkable increase. The increase in education is across the board. A person born between 1910 and 1914 who obtained some postgraduate education was in the top 6 percent of his or her cohort in terms of education. By the 1970s, nearly 16 percent of the birth cohort had some postgraduate education. The percentage of college graduates or beyond has almost quadrupled over the same period, from just over 10 percent to almost 40 percent.

But, as Figure 2 shows, even though education has increased considerably through the decades, and even though education is correlated with verbal ability, verbal ability has stayed practically constant over time. The lack of change in the average vocabulary score of Americans, despite the large increase in the population’s average years of schooling, is an intriguing finding. …

Written by infoproc

June 28, 2008 at 2:51 pm

Asian-White IQ variance from PISA results

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The vexing question of average differences between groups of humans has been the subject of scrutiny for a very long time. Differences in variance or standard deviation (SD) are less well understood, but have important implications as well. This point was emphasized during the Larry Summers debacle, in which he posited that the variance in male intelligence might be larger than for women, even though the averages are similar (more very dumb and very bright men than women). Summers argued that this effect might explain the preponderance of males in science and engineering, even for a very small difference in SD.

Summers NBER speech:
…If one supposes, as I think is reasonable, that if one is talking about physicists at a top twenty-five research university, one is not talking about people who are two standard deviations above the mean. And perhaps it’s not even talking about somebody who is three standard deviations above the mean. But it’s talking about people who are three and a half, four standard deviations above the mean in the one in 5,000, one in 10,000 class. Even small differences in the standard deviation will translate into very large differences in the available pool substantially out [on the tail].

I did a very crude calculation, which I’m sure was wrong and certainly was unsubtle, twenty different ways. I looked at the Xie and Shauman paper-looked at the book, rather-looked at the evidence on the sex ratios in the top 5% of twelfth graders. If you look at those-they’re all over the map, depends on which test, whether it’s math, or science, and so forth-but 50% women, one woman for every two men, would be a high-end estimate from their estimates. From that, you can back out a difference in the implied standard deviations that works out to be about 20%. And from that, you can work out the difference out several standard deviations. If you do that calculation-and I have no reason to think that it couldn’t be refined in a hundred ways-you get five to one, at the high end.

I’ve occasionally heard a variant of the Summers argument applied to Europeans vs Asians (specifically, NE Asians such as Japanese, Koreans and Chinese): although NE Asians exhibit higher averages than whites in psychometric tests (SAT, IQ, etc.), some suspect a smaller variance, leading to fewer “geniuses” per capita, despite the higher mean. See, e.g., this article in National Review:

…The two populations also differ in the variability of their scores. A representative sample of Americans or Europeans will show more variability than will an East Asian sample. In the familiar bell-shaped distribution curve, the bell is much narrower for the Japanese–which is what you would expect from such a homogeneous population.

This difference is a major matter, and it is worth focusing hard on the data. Just about all Western populations report a standard deviation of 15 IQ points. (The SD, a basic measure of variability, quantifies the extent to which a series of figures deviates from its mean.) But the SD for the Japanese and other East Asian populations appears to be a shade under 13 IQ points. That difference does not sound like a big deal, and, in fact, it does not change things much in the center of the distribution. …

…but it does make a big difference at the high end, and it affects estimates of elite human capital availability in different countries.

I’ve never seen any data to back up the smaller NE Asian SD claim. Looking at SAT data shows a larger variance for the Asian-Pacific Islander category, but that is not surprising since it’s a catch-all category that includes S. Asians, SE Asians, NE Asians and Pacific Islanders. I’ve found very little analysis specific to NE Asians, so I decided to produce some myself. I took the 2006 PISA (OECD Program for International Student Assessment) data, which is painstakingly assembled every 3 years by a huge team of psychologists and educators (400k students from 57 countries tested). The samples are supposed to be statistically representative of the various countries, and the tests are carefully translated into different languages. Most studies of national IQ are quite crude, and subject to numerous methodological uncertainties, although the overall results tend to correlate with PISA results.

Below is what I obtained from the 2006 PISA mathematics exam data (overall rankings by average score here). To get the data, scroll down this page and download the chapter 6 data in .xls spreadsheet format. Level 6 is the highest achievement category listed in the data. For most OECD countries, e.g., France, Germany, UK, only a few percent of students attained this level of performance. In NE Asian countries as many as 11% of students performed at this level. Using these percentages and the country averages, one can extract the SD. (Level 6 = raw score 669, or +1.88SD for OECD, +1.28SD for NE Asians.)

OECD AVG=500 SD=90

NE Asia (HK, Korea, Taiwan) AVG=548 SD=95

The NE Asians performed about .5 SD better on average (consistent with IQ test results), and exhibited similar (somewhat higher) variance. (After doing my calculations I realized that there is actually a table of means and SDs in the spreadsheet, that more or less agree with my results. The standard error for the given SDs is only 1-2 points, so I guess a gap of 5 or 10 points is statistically significant.)

Interestingly, the Finns performed quite well on the exam, posting a very high average, but their SD is smaller. The usual arguments about a (slightly) “narrow bell curve” might apply to the Finns, but apparently not to the NE Asians.

Finland AVG=548 SD=80

Returning to Summers’ calculation, and boldly extrapolating the normal distribution to the far tail (not necessarily reliable, but let’s follow Larry a bit further), the fraction of NE Asians at +4SD (relative to the OECD avg) is about 1 in 4k, whereas the fraction of Europeans at +4SD is 1 in 33k. So the relative representation is about 8 to 1. (This assumed the same SD=90 for both populations. The Finnish numbers might be similar, although it depends crucially on whether you use the smaller SD=80.) Are these results plausible? Have a look at the pictures here of the last dozen or so US Mathematical Olympiad teams (the US Asian population percentage is about 3 percent; the most recent team seems to be about half Asians). The IMO results from 2007 are here. Of the top 15 countries, half are East Asian (including tiny Hong Kong, which outperformed Germany, India and the UK).

Incidentally, again assuming a normal distribution, there are only about 10k people in the US who perform at +4SD (and a similar number in Europe), so this is quite a select population (roughly, the top few hundred high school seniors each year in the US). If you extrapolate the NE Asian numbers to the 1.3 billion population of China you get something like 300k individuals at this level, which is pretty overwhelming.

Although it’s all there in the data set, I didn’t have time to examine the male-female variances in mathematical ability (and don’t want to deal with the abuse that might be heaped on me based on what I might find), but I encourage any interested readers to have a look. The authors of the PISA report wisely only reported that male-female averages are similar 😉

Note: as often happens with this kind of topic, a related discussion has broken out at GNXP.

Written by infoproc

June 18, 2008 at 1:08 am

Returns to elite education

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In an earlier post I discussed a survey of honors college students here at U Oregon, which revealed that very few had a good understanding of elite career choices outside of the traditional ones (law, medicine, engineering, etc.). It’s interesting that, in the past, elite education did not result in greater average earnings once SAT scores are controlled for (see below). But I doubt that will continue to be the case today: almost half the graduating class at Harvard now head into finance, while the top Oregon students don’t know what a hedge fund is.

NYTimes: …Recent research also suggests that lower-income students benefit more from an elite education than other students do. Two economists, Alan B. Krueger and Stacy Berg Dale, studied the earnings of college graduates and found that for most, the selectivity of their alma maters had little effect on their incomes once other factors, like SAT scores, were taken into account. To use a hypothetical example, a graduate of North Carolina State who scored a 1200 on the SAT makes as much, on average, as a Duke graduate with a 1200. But there was an exception: poor students. Even controlling for test scores, they made more money if they went to elite colleges. They evidently gained something like closer contact with professors, exposure to new kinds of jobs or connections that they couldn’t get elsewhere.

“Low-income children,” says Mr. Krueger, a Princeton professor, “gain the most from going to an elite school.”

I predict that, in the future, the returns to elite education for the middle and even upper middle class will resemble those in the past for poor students. Elite education will provide the exposure to new kinds of jobs or connections that they couldn’t get elsewhere. Hint: this means the USA is less and less a true meritocracy.

It’s also interesting how powerful the SAT (which correlates quite strongly with IQ, which can be roughly measured in a 12 minute test) is in predicting life outcomes: knowing that a public university grad scored 99th percentile on the SAT (or brief IQ test) tells you his or her expected income is equal to that of a Harvard grad (at least that was true in the past). I wonder why employers (other than the US military) aren’t allowed to use IQ to screen employees? 😉 I’m not an attorney, but I believe that when DE Shaw or Google ask a prospective employee to supply their SAT score, they may be in violation of the law.

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April 21, 2008 at 3:50 pm