Bryan Caplan  

Regressions By Popular Demand: Black Education Pays Extra

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In my critique of Harford's chapter on statistical discrimination, I wrote:

But is it really true that the market fails to reward blacks for getting more education? Is it even true that the market rewards them less? I tested these claims using one of the world's best labor data sets, the NLSY. The results directly contradict Tim's self-fulfilling prophesy story. Blacks actually get a substantially larger return to education than non-blacks! The same goes for experience, though the result is not statistically significant. The real lesson of the data is that if you are young, gifted, and black, you should get a ton of education, because it has an exceptionally large pay-off.
Here's an introduction to the kinds of regressions I ran using the NLSY. (The data comes from 1992, the most recent year on my CD-ROM that asks everyone about their annual labor income).

I start out with a simple benchmark regression of the logarithm of annual labor income on Black (=1 if the respondent is black, and 0 otherwise), AFQT (percentile on an IQ-type test), and Grade (number of years of education completed). The results are pretty standard: Blacks earn about 13% less than comparable non-blacks, and each year of education raises income by about 8%. (You can make the black-white gap completely disappear if you add family status control variables, but that's not the focus here).

harfordreg1.jpg

Note that the baseline specification assumes that blacks and non-blacks get the same payoff for each year of education. Harford's chapter predicts that blacks get less. To adjudicate between these two views, all we have to do is add Grade*Black as a control variable. If Grade*Black=0, blacks and whites get the same percentage increase in earnings from a year of education. If Grade*Black<0, education pays blacks less; if Grade*Black>0, education actually pays blacks more.

The results are striking:

harfordreg2.jpg

Yes, in this specification, education pays blacks more than twice as much as it pays non-blacks. At the same time, adding this control variable makes the coefficient on Black much more negative. The upshot is that at low levels of education, blacks earn much less than non-blacks; but at high levels of education, they earn more. This result remains even if you add a lot of other control variables, but I suspect that two regressions have already tried most readers' patience.

Incidentally, the cut-point in this equation is roughly at 15 years of education. This means that blacks with fewer than 15 years earn less than comparable non-blacks; blacks with more than 15 earn more than comparable non-blacks. (Adding more control variables pushes the cut-point down to 13 years).

If this were a journal article, I'd look for a more recent version of the NLSY, and run more robustness checks. But still, it's striking that one of the best labor data sets in the world decisively rejects the view that statistical discrimination reduces blacks' incentive to try to better their lot. Instead, the data strongly support the diametrically opposed view that acquiring education is a great way for a black worker to credibly tell employers, "No matter what you think about the average black, I've got the right stuff."


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COMMENTS (14 to date)
mgroves writes:

You aren't trying my patience at all--this is fascinating stuff. I really don't understand your interpretation of the grade coefficient from the first regression, though. Are you saying that blacks are essentially equal to whites after the 2nd grade (in terms of salary outcome)? Or are we talking years in college? I'm slightly confused...

Bryan Caplan writes:
mgroves writes:

You aren't trying my patience at all--this is fascinating stuff. I really don't understand your interpretation of the grade coefficient from the first regression, though. Are you saying that blacks are essentially equal to whites after the 2nd grade (in terms of salary outcome)? Or are we talking years in college? I'm slightly confused...

I assume you're talking about the first regression. What it says is that if a black and a non-black have the same AFQT score and the same total number of years of education, the average black will earn about 13% less.
Gorgasal writes:
Yes, in this specification, education pays blacks more than twice as much as it pays non-blacks.

The coefficient on GRADE is .065, on GRADE*BLACK .074. That is a difference, but I don't really see a factor of two there.

Looking at the SE of GRADE*BLACK, it does not appear that the difference between the coefficients of GRADE and GRADE*BLACK is statistically significant, or is it? Would be interesting.

One final point: given that you are working with log wages, the coefficient of -.13 for BLACK does not mean that blacks earn 13% less than whites, it's more like 1-exp(-.131135)=12.3% less...

But overall, a very nice post! I like it!

Bob Knaus writes:

The cutpoint is 15 years of education = 12 years primary/secondary + 3 years college. So the cutpoint is in the 3rd year of college, not the 3rd year of primary school.

It seems to me that education is just one of many successful signaling strategies. Yes, "I am educated" works, but I'll bet "I am a Jehovah's Witness" or "I am an Army sergeant" would be equally successful signals.

Socially, of course, it's easier to gain a consensus around promoting education as compared to promoting religious beliefs or military careers. And it's a lot easier to include education in a database of labor statistics.

At one time, "I'm a Bahamian" was a successful signalling strategy for blacks. I was the first white guy to live in a historic black Miami neighborhood, and that's the first thing my next-door neighbor told me, to let me know she was better than the others around her. By then (1993) there were only a few old Bahamians left. They had settled there over a period of several decades to provide labor as Miami grew. Both they, and the firms that hired them, considered Bahamian blacks to be better workers than American blacks.

My point is not to dredge up old stereotypes, but simply to point out that there are many more factors than education which can make one stand out from the pack.

John writes:
Instead, the data strongly support the diametrically opposed view that acquiring education is a great way for a black worker to credibly tell employers, "No matter what you think about the average black, I've got the right stuff."

I agree with this. The ones that stay in school might have some other qualities that are not showing up in your regressions which can explain the coefficient. If possible you should add in an i.v. regression by adding mother's education. I think that might change the results further and be interesting to look at. (if you have the data)

spencer writes:

Actually, better data to directly test the thesis exist at Census.

Census provides data on money income by race and education at;
http://pubdb3.census.gov/macro/032007/hhinc/new01_005.ht

The following is one set of calculation for 2006
that shows the median income of white versus blacks as a % of the average of whites or blacks.


(% of total)
............................................white....black......ratio
Total, 25 yrs & over..........
Less than 9th grade..................... 42.0....43.2.....102.70
9th to 12th grade, no diploma........... 54.1....50.8....93.87
High School graduate
(includes equivalency).................. 80.2....83.6....104.25
Some college, no degree................. 98.5....118.3....120.14
Associate Degree........................ .114.2....121.4....106.31
Bachelor's Degree or more........... 161.0....189.4....117.68
Bachelor's Degree.......................
150.1....177.5....118.28
Master's Degree......................... 173.0....205.0....118.50
Professional Degree..................... 193.3....300.0....155.20
Doctorate Degree........................ 193.3....228.5....118.21

The column is white- black income at that educational level as a % of white-black average.

the ratio data shows how much better black income
then white income.

for example, for a professional degree a white earns 193% of the average white income and a black
earns 300% of the average white income.

the ratio shows that the return for a black obtaining a professional degree is 15% higher for a black then for a white relative to the average black or white income.

At all levels except not finishing high school the ratio is greater then 100, implying that the returns to a black for education or greater then returns to a white.

You can do the stat tests if you are so inclined.

blejkrajli writes:

Gorgasal,

The black return on education is not just the coefficient of GRADE*BLACK. That is the return for blacks in addition to the overall return. So, each year of education raises the wage of whites by ~6.5%, but the wages of blacks raise by (6.5%+7.5%)=14%.

omalley writes:

Bryan,

You may be right but there is another point that your regression doesn't rule out. It is possibly true that an additional year of education increase income for blacks relative to whites - but just because that effect is there does not rule out the possibility that statistical discrimination depresses incentives to get more education. It could be that there is a highly non-linear effect of the interaction between education and being black. Your linear regression makes it impossible to rule that out.

And also more fundamentally, the example that Hartford talks about (black and white-sounding names) - that was an experiment where everything was virtually controlled for but for differences in "black" and "white" names (they achieved that by equating virtually every observable variables among the 'candidates' except for the names). I know it's not feasible to control for "everything" in a typical regression but controlling for only 2 variables is way short of controlling many observable factors that explain variations in wages.

You may be right but I don't think your regression exercise settled anything.

Buzzcut writes:

With an R squared much less than .2, aren't you reading a lot into those regression coefficients?

DJ writes:

Wouldn't age drive a lot of the variation in earnings and be worth adding (as a proxy for experience)? Depending on the age distribution of the black and white populations, I would imagine that adding an age variable or dummies could make a difference to the educational results (or running your educational regression for different cohorts)? All interesting stuff and comments - thanks.

burger flipper writes:

How much of a difference would it make to remove the AFQT component and just compare by education?

Matt writes:

Bryan,

I am not sure that you have really addressed the incentive effects. I am going to guess that fewer African-Americans finish college. Possibly dramatically fewer.

If you are a poor African-American then you are likely surrounded by people who are African-American, have not finished college, and receive lower compensation for their education levels compared to whites. Thus the signal that you are getting is that education does not pay as much as it does for whites.

Unless you are also interacting with lots of college educated African-Americans you are unlikely to get the signal that education pays. If there are relatively few college educated African-Americans then you are probably not receiving that signal.

Floccina writes:

An interesting thing in this debate is that some people seem to think that giving a job is like giving a gift. I hire people to make me money or to give me time, I do not even have to like them as long as they do the job. Consider Margie Scott (sp?)(from baseball), she did not seem to like blacks but she liked to hire them becuase they did the job.

steve writes:

Correct me if Im wrong but this data seems to be looking at the effect of education assuming one gets a job. Harford seemed to be looking more at the likelihood of getting a job to begin with. Am I misreading this data?

Steve

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