This question is pretty tough to translate to English.
So: we're trying to estimate the effect of education on earnings. We have a scenario where the education premium is exclusively created by signaling. What exactly is our education signaling though? Does it signal that I have some set of character traits (ie: commitment and work ethic sufficient to complete a degree), that I have special knowledge (ie: knowledge of my field), or that I have a certain degree of intelligence (ie: more because I went to Brown instead of Arizona State)? Does it signal all of the above?
If the value of my education is due to the fact that it signals I am intelligent, then controlling for intelligence when seeking the effect of that observed education premium on income would certainly reduce the estimate -since it would mitigate the signaling effect, given the well-established connection between IQ and income- making this statement FALSE.
It seems that even in normal circumstances, where even a part of the observed education premium is determined by signaling (which includes signaling of one's intelligence), that controlling for intelligence WOULD reduce the estimate of the effect of education on earnings. I don't see why things would be different in a scenario where 100% of that observed premium is due to signaling -not unless 'signaling' doesn't include 'signaling intelligence', which isn't specified in the question.
I'm obviously not an economist. Does the statement '100% due to signaling' mean something very specific in economics, such that these students would have been expected to know ahead of time? Maybe I'm misunderstanding what exactly the 'observed' education premium is?
The key is to distinguish between ability bias and signaling. Controlling for ability bias (where it is present) will reduce the estimated effect of education on earnings because a high ability student would have earned more than a low ability non-student even without education.
Assuming 100% signaling implies no ability bias and also that education does not increase human capital. Thus the signal directly explains higher earnings and is unaffected by controlling for intelligence.
I guess my question would be 'signaling what?'. The concept that there's a signal suggest *something* is being signaled. What is that thing? It seems like a big part of educational signaling is intelligence, kind of by definition. If I say 'I graduated magna cum laude from Harvard', that's basically proxy for saying 'I'm super smart and I have a piece of paper that says so' -regardless of whether my graduating from Harvard gave me special knowledge, skills, or ability of any kind.
Controlling for intelligence may control for ability bias, but it also controls for part of the signaling value of education at the same time. I assume that economists use some definition of signaling in this context that doesn't include intelligence signaling? I don't see that as an intuitive decision to make when creating a useful definition of the term, but I'm curious as to what their definition even is, since I don't see how the answer to the posed question can be 'TRUE' given my understanding of the terminology.
*Disclaimer: I'm an electrician and a building manager, not an economist or data scientist.
I don't think you have understood what the word "signaling" means in this context. Signaling is in contrast to providing actual evidence of the thing. When I say that an action is "all signaling", I mean that doing the action is not at all a product of the thing you want people to infer (intelligence in the case of education). This is, I believe, how the word "signaling" is standardly used in a behavioral/economic context, though it is somewhat different from how the word is used in an engineering context.
> I don't think you have understood what the word "signaling" means in this context. Signaling is in contrast to providing actual evidence of the thing.
That is not correct; signaling is providing actual evidence. The concepts are one and the same.
A signal may be falsified, but that doesn't matter to the concept. A signal that is easily falsified is a low-value signal; a signal that is not easily falsified is a high-value signal.
So, to signal that you have intelligence is to provide a cue that you have it, without actually providing evidence? For example, you could attend Harvard, which would be a cue for your intelligence, but not take, say, a set of standardized tests that would definitively show your intelligence.
There seems to be a very fine line in that definition between what actually constitutes evidence for a thing, and what constitutes a 'signal' or a 'cue'. There also seems to be a subjective element to such an understanding of the term. The same thing might be a signal to some people, and definitive evidence for others -ie: going to Harvard as a signal for intelligence.
I think you must be right though: unless economists are drawing a definitive line to determine what constitutes actual evidence and what constitutes a signal, then the question that GMU posed to their PhD students would be absurdly subjective and unfair -and would probably cause most students to follow a line of thinking not too different than my own, ultimately getting the question wrong.
I'm not sure what you mean by "cue", apart from "weak evidence".
A degree in can be strong evidence of a skill set whether signaling is 100% or 0%. Just like knowing that a highly reputable contractor built a pool, and knowing that a highly reputable inspector certified the pool, are both good evidence of the pool's quality.
In reality (the question is obviously a counterfactual hypothetical), going to Harvard is almost certainly some mix of signaling intelligence and evidence of intelligence. Rational people can disagree and debate about what that mix is, and people can be mistaken about what that mix is, but I wouldn't say that the answer is different for different people.
Eh. I'm a big fan of Thomas Sowell, and I think he'd disagree. He's a Harvard grad, and he doesn't consider degrees from the institutions to be useful markers for intelligence at all. My father was of a similar mind -and he had an MIT PhD.
Ivy League degrees can easily be a marker for work ethic, pedantry, and a profound ability to think in a systematized academic box, while being nothing especially intelligent when it comes to real world problem solving and learning. This butts up against the eternally sticky problem of 'what exactly do we mean by intelligence', but yeah.
I'd say you certainly can't graduate from an Ivy League institution and be a moron, but I also certainly wouldn't say that graduating from such an institution is a clear form of evidence that you are particularly intelligent (given a common understanding of the term: able to think on one's feet, solve problems, and learn quickly). Maybe I'm wrong? I'm not even American/ European, so to be honest, I haven't ever met more than two or three Ivy-league graduates. I'm definitely not the best person to get a well-rounded opinion on the topic from.
If the education premium is 100% due to signaling, then the signal is perfectly correlated with higher levels of productivity (thus income in a competitive labor market), no matter what factors contribute to productivity. That means that controlling for *any* factor, intelligence or otherwise, will not reduce the estimate of the effect of education on earnings.
I think you snuck in the assumption that wages and productivity are perfectly correlated as well. That needn't be true, even in a competitive labor market.
This makes sense to me if "the observed education premium" is synonymous with "estimates of the (positive) effect of education on earnings". When I read the question, I did not think these two phrases were synonymous. However, after reading Handle's answer, I now think that the author of the question may have intended for these phrases to be synonymous.
I had thought "the observed education premium" referred to something like "How much more people are willing to pay for a (university) education compared to some baseline (e.g. how much they were willing to pay in the past)".
Does "perfectly correlated" necessarily imply a linear relationship (I'm assuming that's what you're assuming)? It seems to me that it would only imply that a function from one to the other is strictly monotonically increasing.
Let there be 10 young people: 3 are intelligent and have degrees. They earn $200. 2 are intelligent and do not have degrees. They earn $100. So do the 5 who are dull and have no degree. ("Dull with degree" would violate the signaling model, at least in a strong form.)
First, you compare the 3 with the 7. The averages are $200 vs. $100.
Then you "control for intelligence." Does that mean you compare the 5 intelligent with the 5 dull? You would reduce the effect of education on earnings by doing so, but I don't think that is what "control for intelligence" means.
I think that "control for intelligence" means you compare the 3 with the 2. The averages are $200 vs. $100 again. So you don't reduce the effect.
Under a strong version of the signaling hypothesis. the intelligent without a degree have no way of proving that they are worth more. That may seem unrealistic, but I am responding to the question as posed.
It looks like “everyone in Smith family is tall but not all tall people are from Smith family” situation to me. Education allows smart people to signal their intelligence and 100% of education value is signalling but intelligence can improve your income even if you can’t signal it. Question doesn’t even say “wages”, “earnings” can be from being employer businessman, or from inheritance.
The signaling theory does not deny that there are other ways of providing evidence of your productivity besides graduating from college. Your 3 who graduated from college took four years (or more) to signal their productivity; meanwhile your 7 who did not graduate were doing something else--say, working--and the bright 2 were making employment records superior to those of the dull 5. So after four years the 3 earn $200, the 5 $100, and *the 3 $125*. (But this does not help me answer the question, because I still do not know what "controlling for intelligence" means in this context.)
The observed education premium being 100% due to signaling means all the effect of education on income is mediated by observable education variables (years of schooling, credentials, grade performance, etc). In other words, there is no direct effect of intelligence on income (and no omitted variable bias).*
Imagine a simple model where income is a function of both intelligence and education (plus some residual shock), and that education is a function of intelligence (again, leaving some residual exogenous shock). In this model, if we regress income on education, the estimates will be biased because education will capture some of the direct effects of intelligence on income (a canonical case of omitted variable bias). Controlling for intelligence will solve the problem.
But this supposes part of the observable education premium is spurious. It is not purely the signal education gives to employers, but the fact that education signals correlate with other skills.
*We could think of a model where intelligence has no effect on observed education and still have a direct effect on income. In this case, controlling for education would also have no effect on the estimates of observed education since both variables are uncorrelated.
Here is the argument for False. Even in a 100% signaling world, intelligence is positively correlated with the decision to attend and the probability of admission. Controlling for variable positively correlated with the covariates reduces the estimated correlation.
BY DEFINITION IN THE QUESTION 100% of the premium is from signaling (not from intelligence or anything else).
Therefore 100% of the effect of education is due to signaling, and not intelligence. (Yes, I know I just said the same thing twice.) And therefore controlling for intelligence won't change anything at all, *because intelligence doesn't have any effect* (100% - 100% == 0%). By definition in the question.
> BY DEFINITION IN THE QUESTION 100% of the premium is from signaling (not from intelligence or anything else).
So, in our "it's all signaling" model, we postulate that (1) employees with degrees are paid more than employees without degrees, and that (2) the degree does not affect the value of the employee to the employer.
Instead, it must be the case that the average value of the pool "employees with degrees" is higher than the average value of the pool "employees without degrees". This is due to some average difference in the trait being signaled, presumably intelligence. (If there were no such difference, a signal would not exist and signaling would explain 0% of the premium.)
In a normal model of the world, different employees belonging to the same broadly-defined class will be paid differing amounts. If we assume that more-valuable employees tend to receive upward adjustments to their income (by any of a variety of methods: promotions ahead of schedule, raises, more frequent or larger bonuses...), while less-valuable employees tend to receive downward adjustments to their income, then we will get the result that Caplan says is incorrect: controlling for intelligence will reduce the computed effect of education on earnings. We will observe that some (unintelligent) graduates have income which is shifted from the graduate average toward the dropout average, and some (intelligent) dropouts have income which is shifted from the dropout average toward the graduate average. We will not see that the difference in average income between 120 IQ graduates and 120 IQ dropouts is equal to the difference in average income between all graduates and all dropouts.
. I interpret the question to ask, “If in reality 100% of the education premium is caused by signaling, what answer will conventional statics give when you estimate the influence of intelligence on this effect?” In reality, the effect is zero, by assumption, unless signaling somehow incorporates intelligence. The question is about the estimate, though, and this could conceivably be a case where careless use of statistics leads us astray and gives a mistaken answer. I would not want to bet that no one could sincerely come up with a regression that shows a significant correlation between intelligence and education premium, even given good data. It sounds like Caplan thinks they could only do so by making a fundamental mistake in their calculations. But I have forgotten all my stats, so I should not make bets on that sort of thing anyhow.
There are two major phenomena of interest when we say a premium is due to signaling:
A. Imagine that every employee has a particular value to their employer. Our hypothesis tells us that possessing or lacking a degree does not affect this value.
B. We could form a model in which everyone is paid according to their value, and we compute an education premium solely due to the fact that educated people have higher value (and always did, even before they were educated). In this model, controlling for value would reduce the computed education premium to 0. It is open to argument whether intelligence contributes to value, but if it does, then controlling for intelligence should reduce the computed education premium (but not necessarily all the way to zero).
C. It seems like Caplan is ruling that model out. We could form a different model like so:
C-1. Every employee has an inherent value to their employer.
C-2. Education does not affect this value.
C-3. But it's difficult for employers to measure employee value.
C-4. Measurement error when the employer assesses employee value means that the income of degreed employees gets adjusted toward the average value of all degreed employees, while the income of degreeless employees gets adjusted toward the average value of all degreeless employees. (Conceptually, this adjustment happens in the other direction: high-value degreeless employees have their income adjusted upward from the average of all degreeless employees. But because their value is measured imperfectly, the adjustment will be, on average, too small. This gives the described result: high-value degreeless employees have income which is too low for their actual value.)
C-5. Thus, we observe that, at a given level of value, degreed employees enjoy higher income than degreeless employees. We may assume that two employees of equal value "should" have the same income, but the income of the degreed employee gets regressed toward the mean value of degreed employees, and the income of the degreeless employee gets regressed toward the (lower) mean value of degreeless employees.
C-6. We could call the observation in C-5 "the education premium".
Let's make some assumptions:
The average income of the degreeless is $60,000, and their average value is 95. The average income of the degreed is $75,000, and their average value is 110. There is no measurement error in the average values; $75,000 is the true income that an employee of value 110 should enjoy.
Income should, when value is perfectly measured, correspond to it linearly. An employee of value 125 should enjoy an income of $90,000.
Regression to the mean is 70%.
Now let's calculate some education premia:
First, the value of a degree appears to be $15,000, because that's the difference in income between having a degree and not having a degree. (And the difference in value between 95 and 110.)
Second, what if a hypothetical employee has a true value of 100?
In this case, the employee's ideal income would be 1/3 of the way between the two group averages, $65,000. This would be adjusted based on his status: if he has a degree, he is 10 points below average, but he will be paid as if he's only 7 points below average. This will reduce his income by $15,000*(7/15) or $7,000, leaving him with an income of $68,000. If he doesn't have a degree, he is 5 points above average and he'll be paid as if he's 3.5 points above average; he's getting $63,500. So the education premium at value 100 has been reduced from $15,000 to $4,500. This is a reduction of 70%, which by a stunning non-coincidence is the value we gave for regression to the mean in employer assessment of value.
Third, what if a superstar employee has a value of 160?
This employee should be making $125,000. If he has a degree, he is 50 points above average and gets paid like he's 35 points above average, giving him an income of $110,000. If he doesn't have a degree, he's 65 points above average and gets paid like he's 45.5 points above average, giving him $105,500. The gap is $4,500 again. It seems safe to assume that this will be true at all value levels.
This clearly shows that controlling for employee value will reduce the education premium we compute. We would need to lay down some other assumptions in order to say that controlling for employee intelligence won't do the same thing.
> I interpret the question to ask, “If in reality 100% of the education premium is caused by signaling, what answer will conventional statics give when you estimate the influence of intelligence on this effect?” In reality, the effect is zero, by assumption, unless signaling somehow incorporates intelligence.
This is not true. The question doesn't assume that the influence of intelligence on the education premium is zero. All it assumes is that the value of a worker to an employer is unaffected by that worker's education.
I provided some conflicting interpretations of what a premium "due to signaling" might mean, but both of those interpretations clearly show that controlling for intelligence will reduce the education premium. (Under the assumption that worker intelligence influences worker value, which I did not take to be in question.) So the conclusion we're left is that Bryan Caplan has something very strange in mind when he poses his question, and he's not telling us what it is.
“ Under the assumption that worker intelligence influences worker value, which I did not take to be in question”
But worker value is not the dependent variable, education premium is. I think Caplan is saying that if the premium is due entirely to signaling, then the premium is constant for persons of different intelligence. It is possible for the premium to be the same in spite of different worker values, though it seems counterintuitive. My best guess is that Caplan has some nice statistical flourish that I have lost or never quite grasped.
I'm treating worker value as the independent variable.
I fleshed out a model in which educated workers are paid more than uneducated workers -- even at the same level of worker value. The model has the following properties:
1. Education has zero effect on worker value. (I take this to be equivalent to the statement "100% of the education premium is due to signaling".)
2. Educated workers make $15,000 more than uneducated workers. (Without controlling for anything.)
3. Controlling for worker value, an educated worker makes $4,500 more than an uneducated worker. This number is indeed constant over different value levels.
We can see that controlling for worker value sharply reduces our estimate of the effect of education on earnings. Our model tightly constrains the relationship between worker value and worker income, but the relationship between worker intelligence and worker income is less constrained. However, as long as we're willing to assume a positive relationship between worker intelligence and worker value, we will also see that controlling for worker intelligence reduces the estimate of the effect of education on earnings.
Our model obeys the only constraint Caplan has specified ("the observed education premium is 100% due to signaling"), so we know the answer can't be TRUE. If TRUE and FALSE are the only options, then the answer is FALSE. But that isn't right either; other people in this same thread have presented other models that obey the constraint without falsifying the claim of the problem.
So again, all we can say is that the problem is underspecified, and if Caplan wants an answer he's going to have to pose the problem better.
Assume everyone born either smart or dumb and this only trait employers care about. Graduating from college proves you are smart, but some smart people are incapable of going to college. Smart non-college grads end up proving themselves through something more costly than college, but eventually do prove themselves and eventually end up with the same wage as college grads. Adjusting for intelligence will reduce estimates of effect on education on earnings since lifetime wage difference between smart college grads and smart non-grads will be less than that between smart college grads and dumb people. What am I missing?
OTOH, the non-college whiz gets a four year head start. Why isn’t 4 years of experience in the field as good a signal to their actual employer as 4 years of college?
Because then you wouldn't need college as a signal. Also, observation is costly and imperfect plus the job wouldn't be as optimized for signaling as college is.
When you’re hiring, observation is costly, and so is actual measurement. When the guy is working for you, at least some degree of observation comes for free. Do you know which workers didn’t show up today? I think so.
I could make an alternate story, where employers would be as happy or happier hiring a bunch of highschool grads (or homeschoolers?) and firing the lemons after a month or so (or even getting them to work free as apprentices or “interns”), except other factors interfere. Those might include the legal climate, which makes hiring and firing expensive and internships or apprenticeships difficult. Maybe it would also hurt the morale of the novice workers.
Speaking of observation and it’s difficulties, do we know whether using the signal actually works, compared to some alternative? Or is that just the way everyone does it, and to the extent that anyone gets ahead by modifying that approach, could it be that it is just too difficult to estimate the effectiveness of alternatives? That sees it as a culture trap, a local rather than a global equilibrium. I would think that society would hop out of the local equilibrium just by accident, if there was a huge disparity between it and the alternatives. It's bad for everyone who has to signal, but it’s not obvious what the alternative is. Even if a kid wants to become an entrepreneur and hire himself without signaling, he has to signal the people who lend him the capital. That brings it down to “start your own business with $100 and a good attitude.”
If there was an obviously better signal or measurement, it seems like it could spread easily. Maybe I am misperceving that. I know people are groaning about student debt, but are people groaning about the difficulty of hiring good workers, or patting themselves on the back?
Not a question, it is a statement. Even if it were a question, it is worded confusingly. No wonder most students got it “wrong”. I guess the GMU PhD program is pure sheepskin.
It's a True/False question; those always imply "Is this statement true or false" by their very structure. Being able to understand the question is pretty much half the battle.
It needs a "True or false:" preamble, which I presume it had but Bryan neglected to include when copying over. Including "NOT" in a true/false question invokes the uncommon way the English language treats double negatives mathematically -- as positives. But I'm sure all GMU PhD candidates were native English speakers with perfect ability to read the minds of their professors, so much useful signal was extracted by having them answer it as worded.
The preamble would probably be in the heading of the section declaring the questions as True/False. You will also note that Caplan specified that 90% of the students gave the wrong answer of FALSE, which strongly implies that it is a True/False question in this context.
You would be quite incorrect as to the demographics, too: many GMU PhD candidates are not native speakers. Something like 1/4 of my cohort were non-native speakers as I recall.
And double negatives have nothing to do with it. The statement to be evaluated is as it is, a single negative. This is no more uncommon than saying "It is not raining outside currently. True or False?" In what language is that misleading or confusing? It makes perfect sense in German and Chinese, I am sure.
I think your reading comprehension is perhaps to blame for your confusion. Lack of recognition of context clues often causes people difficulties on standardized tests.
You have failed to comprehend the sarcasm in my statements and failed to address the real critiques. Recommend more humanities classes — the real valuable degree.
If you are estimating the effect specifically of *education*, don't you have to control for *everything else* (except factors you know *a priori* are irrelevant)?
No, not only do you not have to do that, you must not do it. Controlling for a large number of variables means you will overfit the data and produce a completely worthless result.
But don’t you at least have to control for the factors that are known to be important in generating the result? Who would pay any attention to a claim about the effect of education on earnings that did not control for intelligence?
If the observed education premium is 100% due to signalling, that means that the education premium is 0% due to education improving the skills of students.
This means that the education premium is caused by potential-employees-with-a-degree differing from potential-employees-without-a-degree in characteristics that would be unchanged by education, such as intelligence, Big-5 personality trait conscientiousness, and class background. However, since it is a noisy signal (those traits cannot be legally measured directly in many cases), this means that people who get a degree will be grouped together, to some degree.
[TRUE] This suggests that controlling for intelligence will NOT reduce the estimates of the effect of education on earnings, and will in fact increase them, because education serves to lump in dumb students with smart students, raising the wages of dumb students more than it raises the wages of smart students.
Interestingly, the smart students will still benefit from education both individually *and in aggregate* because the existence of education as a reliable quality-signalling mechanism will raise employers's confidence in the intelligence of their prospective employees relative to the counterfactual where education did not exist [holding all else about reality constant; alternate realities exist where intelligence is divined more accurately during the hiring process using methods that are currently illegal].
Alternate answer: It depends on what "effect of education" means. The first answer I gave above was assuming that "effect of education" means "comparing those with a degree to those without a degree, and taking the difference as the effect of education". If instead you take the definition of "effect" as "something education does to change the individual's actual characteristics, rather than how they are perceived", then by definition if the education premium is 100% signalling it is 0% real skills benefit. If it is 0% real skills benefit, then the effect of education on earnings is always zero and controlling for intelligence will not change this [unless for some strange reason education is 100% due to signalling *in aggregate* but for dumb students it is 90% signalling 10% real and for smart students it is 110% signalling -10% real {makes smart students actually worse}].
The issue is one of voluntarily submitting yourself to educational sorting. The less intelligent will not submit themselves to the educational test, and will thus bias the returns to education upward.
Self-selection. If this worked perfectly, then everyone who was a good prospect would attend and graduate from college, and no one else would. How would the stats work then? It seems like intelligence, or whatever they use to self-select, would be doing all the work, and correcting for intelligence would explain everything (assuming intelligence is the thing employers want, or a good proxy), leaving n9thing for education to explain. Or Ed explains everything, since in that scenario, a degree is just a binary measure of intelligence. How do you explain intelligence in terms of intelligence? This is why I am confused.
Ahhh. Good point. If Ed is nothing but a signal for intelligence, then controlling for intelligence turns the signal into nothing but noise. *face palm*
If outcome A is 100% dependent upon input S, then only changes in S can affect A. No other variable is important. So the statement is not only TRUE, but would also be true if you infinitely changed "intelligence" for other characteristics such as race, gender, age, productivity, hours worked, etc.).
This question is just a fancy re-working of "If I jumped hard enough could I land on the moon ?"
If the observed education premium is 100% due to signaling, controlling for intelligence will NOT reduce estimates of the effect of education on earnings.
If the education premium is 100% signaling then there is no ability bias in that observed premium; i.e. there are no returns to ability that are being mistakenly attributed to education. There may be returns to ability, but they're separate from the returns to education and are not captured by the observed returns to education. In Chapter 3 (I think) of CAE Caplan quotes Heckman saying something very close to the following: "Ability and education are distinct. Ability has its returns and education has its returns."
This sets up a view where the observed education premium is split 3 ways: 1. the human capital formation that is caused by education, 2. the signal that education gives about a prospective worker, and 3. the premium that is not attributable to education at all, but ability. If it's 100% #2 then it's 0% #1 and 0% #3. Controlling for #3 doesn't reduce the observed premium.
This is hard for most people to wrap their heads around because to the extent they consider signaling an explanation they believe that education signals ability, but there are arguments for why it (mostly) does not. The sheepskin effect is one challenge for this view. If education signals ability there should be little difference in the average lifetime earnings of people with 17 years of education, including 120 credit hours and a diploma and those with 17 years of education, including 119 credit hours and no diploma. But there is a significant difference, one that takes up a big chunk of the observed premium.
The obvious correlation between education and ability works in the following way: those with more ability find education to be easier and/or more enjoyable than those with less ability, so they consume more of it. Education is not an investment to prove how smart you are, it's an investment in a signal that you are able to endure mundane and apparently pointless tasks because someone with a small amount of authority told you to, for many years. People with more ability can simply have a lower cost when making that investment. Higher ability *distorts* the signal. The 150 IQ guy with, say, a business degree may be (likely is?) far lazier than the one with a 100 IQ.
That's the strong version. I personally tend to think that education might signal some ability, although imperfectly. If someone has a mechanical engineering degree I take that as a signal that they're pretty smart. But I still run into the sheepskin problem. How would I, as an employer, evaluate one candidate with a perfect GPA, 119 credits and no degree vs. one with a 3.5 GPA and a degree? The former sends a signal that he's smart but there's something wrong with him, whereas the latter sends the signal that he's smart enough and enough of a conformist to finish a degree and fill out the paperwork. And what if I meet someone who is an engineer but does not have a degree? That also signals ability, perhaps moreso.
Assuming that smarter people are better at creditably faking credentials, and that sociopaths earn more, you might see a negative correlation between actual schooling and earnings among the highly intelligent that doesn't emerge at intelligence levels where sociopaths lie and fake less successfully.
Half-joke aside, it occurs to me that "education" being 100% signaling presumably refers to the entire university experience, and is therefore incompatible with personal networking at e.g. Ivy League schools having a positive effect on earnings. Am I mistaken in that assumption? After all, a successfully faked Harvard degree won't make you Harvard friends.
> it occurs to me that "education" being 100% signaling presumably refers to the entire university experience, and is therefore incompatible with personal networking at e.g. Ivy League schools having a positive effect on earnings.
That's correct; personal connections you make while at school are tangible assets that would be excluded by a 100% signaling model. Such a model would allow for the existence of those connections, but it would require their effect on your income to be zero.
This question is pretty tough to translate to English.
So: we're trying to estimate the effect of education on earnings. We have a scenario where the education premium is exclusively created by signaling. What exactly is our education signaling though? Does it signal that I have some set of character traits (ie: commitment and work ethic sufficient to complete a degree), that I have special knowledge (ie: knowledge of my field), or that I have a certain degree of intelligence (ie: more because I went to Brown instead of Arizona State)? Does it signal all of the above?
If the value of my education is due to the fact that it signals I am intelligent, then controlling for intelligence when seeking the effect of that observed education premium on income would certainly reduce the estimate -since it would mitigate the signaling effect, given the well-established connection between IQ and income- making this statement FALSE.
It seems that even in normal circumstances, where even a part of the observed education premium is determined by signaling (which includes signaling of one's intelligence), that controlling for intelligence WOULD reduce the estimate of the effect of education on earnings. I don't see why things would be different in a scenario where 100% of that observed premium is due to signaling -not unless 'signaling' doesn't include 'signaling intelligence', which isn't specified in the question.
I'm obviously not an economist. Does the statement '100% due to signaling' mean something very specific in economics, such that these students would have been expected to know ahead of time? Maybe I'm misunderstanding what exactly the 'observed' education premium is?
The key is to distinguish between ability bias and signaling. Controlling for ability bias (where it is present) will reduce the estimated effect of education on earnings because a high ability student would have earned more than a low ability non-student even without education.
Assuming 100% signaling implies no ability bias and also that education does not increase human capital. Thus the signal directly explains higher earnings and is unaffected by controlling for intelligence.
I guess my question would be 'signaling what?'. The concept that there's a signal suggest *something* is being signaled. What is that thing? It seems like a big part of educational signaling is intelligence, kind of by definition. If I say 'I graduated magna cum laude from Harvard', that's basically proxy for saying 'I'm super smart and I have a piece of paper that says so' -regardless of whether my graduating from Harvard gave me special knowledge, skills, or ability of any kind.
Controlling for intelligence may control for ability bias, but it also controls for part of the signaling value of education at the same time. I assume that economists use some definition of signaling in this context that doesn't include intelligence signaling? I don't see that as an intuitive decision to make when creating a useful definition of the term, but I'm curious as to what their definition even is, since I don't see how the answer to the posed question can be 'TRUE' given my understanding of the terminology.
*Disclaimer: I'm an electrician and a building manager, not an economist or data scientist.
I don't think you have understood what the word "signaling" means in this context. Signaling is in contrast to providing actual evidence of the thing. When I say that an action is "all signaling", I mean that doing the action is not at all a product of the thing you want people to infer (intelligence in the case of education). This is, I believe, how the word "signaling" is standardly used in a behavioral/economic context, though it is somewhat different from how the word is used in an engineering context.
> I don't think you have understood what the word "signaling" means in this context. Signaling is in contrast to providing actual evidence of the thing.
That is not correct; signaling is providing actual evidence. The concepts are one and the same.
A signal may be falsified, but that doesn't matter to the concept. A signal that is easily falsified is a low-value signal; a signal that is not easily falsified is a high-value signal.
So, to signal that you have intelligence is to provide a cue that you have it, without actually providing evidence? For example, you could attend Harvard, which would be a cue for your intelligence, but not take, say, a set of standardized tests that would definitively show your intelligence.
There seems to be a very fine line in that definition between what actually constitutes evidence for a thing, and what constitutes a 'signal' or a 'cue'. There also seems to be a subjective element to such an understanding of the term. The same thing might be a signal to some people, and definitive evidence for others -ie: going to Harvard as a signal for intelligence.
I think you must be right though: unless economists are drawing a definitive line to determine what constitutes actual evidence and what constitutes a signal, then the question that GMU posed to their PhD students would be absurdly subjective and unfair -and would probably cause most students to follow a line of thinking not too different than my own, ultimately getting the question wrong.
I'm not sure what you mean by "cue", apart from "weak evidence".
A degree in can be strong evidence of a skill set whether signaling is 100% or 0%. Just like knowing that a highly reputable contractor built a pool, and knowing that a highly reputable inspector certified the pool, are both good evidence of the pool's quality.
In reality (the question is obviously a counterfactual hypothetical), going to Harvard is almost certainly some mix of signaling intelligence and evidence of intelligence. Rational people can disagree and debate about what that mix is, and people can be mistaken about what that mix is, but I wouldn't say that the answer is different for different people.
Eh. I'm a big fan of Thomas Sowell, and I think he'd disagree. He's a Harvard grad, and he doesn't consider degrees from the institutions to be useful markers for intelligence at all. My father was of a similar mind -and he had an MIT PhD.
Ivy League degrees can easily be a marker for work ethic, pedantry, and a profound ability to think in a systematized academic box, while being nothing especially intelligent when it comes to real world problem solving and learning. This butts up against the eternally sticky problem of 'what exactly do we mean by intelligence', but yeah.
I'd say you certainly can't graduate from an Ivy League institution and be a moron, but I also certainly wouldn't say that graduating from such an institution is a clear form of evidence that you are particularly intelligent (given a common understanding of the term: able to think on one's feet, solve problems, and learn quickly). Maybe I'm wrong? I'm not even American/ European, so to be honest, I haven't ever met more than two or three Ivy-league graduates. I'm definitely not the best person to get a well-rounded opinion on the topic from.
If the education premium is 100% due to signaling, then the signal is perfectly correlated with higher levels of productivity (thus income in a competitive labor market), no matter what factors contribute to productivity. That means that controlling for *any* factor, intelligence or otherwise, will not reduce the estimate of the effect of education on earnings.
I think you snuck in the assumption that wages and productivity are perfectly correlated as well. That needn't be true, even in a competitive labor market.
This makes sense to me if "the observed education premium" is synonymous with "estimates of the (positive) effect of education on earnings". When I read the question, I did not think these two phrases were synonymous. However, after reading Handle's answer, I now think that the author of the question may have intended for these phrases to be synonymous.
I had thought "the observed education premium" referred to something like "How much more people are willing to pay for a (university) education compared to some baseline (e.g. how much they were willing to pay in the past)".
Does "perfectly correlated" necessarily imply a linear relationship (I'm assuming that's what you're assuming)? It seems to me that it would only imply that a function from one to the other is strictly monotonically increasing.
Let there be 10 young people: 3 are intelligent and have degrees. They earn $200. 2 are intelligent and do not have degrees. They earn $100. So do the 5 who are dull and have no degree. ("Dull with degree" would violate the signaling model, at least in a strong form.)
First, you compare the 3 with the 7. The averages are $200 vs. $100.
Then you "control for intelligence." Does that mean you compare the 5 intelligent with the 5 dull? You would reduce the effect of education on earnings by doing so, but I don't think that is what "control for intelligence" means.
I think that "control for intelligence" means you compare the 3 with the 2. The averages are $200 vs. $100 again. So you don't reduce the effect.
Why would dull and intelligent without degree earn the same? Seems like wrong assumption.
Under a strong version of the signaling hypothesis. the intelligent without a degree have no way of proving that they are worth more. That may seem unrealistic, but I am responding to the question as posed.
It looks like “everyone in Smith family is tall but not all tall people are from Smith family” situation to me. Education allows smart people to signal their intelligence and 100% of education value is signalling but intelligence can improve your income even if you can’t signal it. Question doesn’t even say “wages”, “earnings” can be from being employer businessman, or from inheritance.
The signaling theory does not deny that there are other ways of providing evidence of your productivity besides graduating from college. Your 3 who graduated from college took four years (or more) to signal their productivity; meanwhile your 7 who did not graduate were doing something else--say, working--and the bright 2 were making employment records superior to those of the dull 5. So after four years the 3 earn $200, the 5 $100, and *the 3 $125*. (But this does not help me answer the question, because I still do not know what "controlling for intelligence" means in this context.)
The observed education premium being 100% due to signaling means all the effect of education on income is mediated by observable education variables (years of schooling, credentials, grade performance, etc). In other words, there is no direct effect of intelligence on income (and no omitted variable bias).*
Imagine a simple model where income is a function of both intelligence and education (plus some residual shock), and that education is a function of intelligence (again, leaving some residual exogenous shock). In this model, if we regress income on education, the estimates will be biased because education will capture some of the direct effects of intelligence on income (a canonical case of omitted variable bias). Controlling for intelligence will solve the problem.
But this supposes part of the observable education premium is spurious. It is not purely the signal education gives to employers, but the fact that education signals correlate with other skills.
*We could think of a model where intelligence has no effect on observed education and still have a direct effect on income. In this case, controlling for education would also have no effect on the estimates of observed education since both variables are uncorrelated.
Here is the argument for False. Even in a 100% signaling world, intelligence is positively correlated with the decision to attend and the probability of admission. Controlling for variable positively correlated with the covariates reduces the estimated correlation.
BY DEFINITION IN THE QUESTION 100% of the premium is from signaling (not from intelligence or anything else).
Therefore 100% of the effect of education is due to signaling, and not intelligence. (Yes, I know I just said the same thing twice.) And therefore controlling for intelligence won't change anything at all, *because intelligence doesn't have any effect* (100% - 100% == 0%). By definition in the question.
This is a tautology.
> BY DEFINITION IN THE QUESTION 100% of the premium is from signaling (not from intelligence or anything else).
So, in our "it's all signaling" model, we postulate that (1) employees with degrees are paid more than employees without degrees, and that (2) the degree does not affect the value of the employee to the employer.
Instead, it must be the case that the average value of the pool "employees with degrees" is higher than the average value of the pool "employees without degrees". This is due to some average difference in the trait being signaled, presumably intelligence. (If there were no such difference, a signal would not exist and signaling would explain 0% of the premium.)
In a normal model of the world, different employees belonging to the same broadly-defined class will be paid differing amounts. If we assume that more-valuable employees tend to receive upward adjustments to their income (by any of a variety of methods: promotions ahead of schedule, raises, more frequent or larger bonuses...), while less-valuable employees tend to receive downward adjustments to their income, then we will get the result that Caplan says is incorrect: controlling for intelligence will reduce the computed effect of education on earnings. We will observe that some (unintelligent) graduates have income which is shifted from the graduate average toward the dropout average, and some (intelligent) dropouts have income which is shifted from the dropout average toward the graduate average. We will not see that the difference in average income between 120 IQ graduates and 120 IQ dropouts is equal to the difference in average income between all graduates and all dropouts.
The question is underspecified.
You seem to be answering a different question.
. I interpret the question to ask, “If in reality 100% of the education premium is caused by signaling, what answer will conventional statics give when you estimate the influence of intelligence on this effect?” In reality, the effect is zero, by assumption, unless signaling somehow incorporates intelligence. The question is about the estimate, though, and this could conceivably be a case where careless use of statistics leads us astray and gives a mistaken answer. I would not want to bet that no one could sincerely come up with a regression that shows a significant correlation between intelligence and education premium, even given good data. It sounds like Caplan thinks they could only do so by making a fundamental mistake in their calculations. But I have forgotten all my stats, so I should not make bets on that sort of thing anyhow.
There are two major phenomena of interest when we say a premium is due to signaling:
A. Imagine that every employee has a particular value to their employer. Our hypothesis tells us that possessing or lacking a degree does not affect this value.
B. We could form a model in which everyone is paid according to their value, and we compute an education premium solely due to the fact that educated people have higher value (and always did, even before they were educated). In this model, controlling for value would reduce the computed education premium to 0. It is open to argument whether intelligence contributes to value, but if it does, then controlling for intelligence should reduce the computed education premium (but not necessarily all the way to zero).
C. It seems like Caplan is ruling that model out. We could form a different model like so:
C-1. Every employee has an inherent value to their employer.
C-2. Education does not affect this value.
C-3. But it's difficult for employers to measure employee value.
C-4. Measurement error when the employer assesses employee value means that the income of degreed employees gets adjusted toward the average value of all degreed employees, while the income of degreeless employees gets adjusted toward the average value of all degreeless employees. (Conceptually, this adjustment happens in the other direction: high-value degreeless employees have their income adjusted upward from the average of all degreeless employees. But because their value is measured imperfectly, the adjustment will be, on average, too small. This gives the described result: high-value degreeless employees have income which is too low for their actual value.)
C-5. Thus, we observe that, at a given level of value, degreed employees enjoy higher income than degreeless employees. We may assume that two employees of equal value "should" have the same income, but the income of the degreed employee gets regressed toward the mean value of degreed employees, and the income of the degreeless employee gets regressed toward the (lower) mean value of degreeless employees.
C-6. We could call the observation in C-5 "the education premium".
Let's make some assumptions:
The average income of the degreeless is $60,000, and their average value is 95. The average income of the degreed is $75,000, and their average value is 110. There is no measurement error in the average values; $75,000 is the true income that an employee of value 110 should enjoy.
Income should, when value is perfectly measured, correspond to it linearly. An employee of value 125 should enjoy an income of $90,000.
Regression to the mean is 70%.
Now let's calculate some education premia:
First, the value of a degree appears to be $15,000, because that's the difference in income between having a degree and not having a degree. (And the difference in value between 95 and 110.)
Second, what if a hypothetical employee has a true value of 100?
In this case, the employee's ideal income would be 1/3 of the way between the two group averages, $65,000. This would be adjusted based on his status: if he has a degree, he is 10 points below average, but he will be paid as if he's only 7 points below average. This will reduce his income by $15,000*(7/15) or $7,000, leaving him with an income of $68,000. If he doesn't have a degree, he is 5 points above average and he'll be paid as if he's 3.5 points above average; he's getting $63,500. So the education premium at value 100 has been reduced from $15,000 to $4,500. This is a reduction of 70%, which by a stunning non-coincidence is the value we gave for regression to the mean in employer assessment of value.
Third, what if a superstar employee has a value of 160?
This employee should be making $125,000. If he has a degree, he is 50 points above average and gets paid like he's 35 points above average, giving him an income of $110,000. If he doesn't have a degree, he's 65 points above average and gets paid like he's 45.5 points above average, giving him $105,500. The gap is $4,500 again. It seems safe to assume that this will be true at all value levels.
This clearly shows that controlling for employee value will reduce the education premium we compute. We would need to lay down some other assumptions in order to say that controlling for employee intelligence won't do the same thing.
You totally lost me.
> I interpret the question to ask, “If in reality 100% of the education premium is caused by signaling, what answer will conventional statics give when you estimate the influence of intelligence on this effect?” In reality, the effect is zero, by assumption, unless signaling somehow incorporates intelligence.
This is not true. The question doesn't assume that the influence of intelligence on the education premium is zero. All it assumes is that the value of a worker to an employer is unaffected by that worker's education.
I provided some conflicting interpretations of what a premium "due to signaling" might mean, but both of those interpretations clearly show that controlling for intelligence will reduce the education premium. (Under the assumption that worker intelligence influences worker value, which I did not take to be in question.) So the conclusion we're left is that Bryan Caplan has something very strange in mind when he poses his question, and he's not telling us what it is.
“ Under the assumption that worker intelligence influences worker value, which I did not take to be in question”
But worker value is not the dependent variable, education premium is. I think Caplan is saying that if the premium is due entirely to signaling, then the premium is constant for persons of different intelligence. It is possible for the premium to be the same in spite of different worker values, though it seems counterintuitive. My best guess is that Caplan has some nice statistical flourish that I have lost or never quite grasped.
I'm treating worker value as the independent variable.
I fleshed out a model in which educated workers are paid more than uneducated workers -- even at the same level of worker value. The model has the following properties:
1. Education has zero effect on worker value. (I take this to be equivalent to the statement "100% of the education premium is due to signaling".)
2. Educated workers make $15,000 more than uneducated workers. (Without controlling for anything.)
3. Controlling for worker value, an educated worker makes $4,500 more than an uneducated worker. This number is indeed constant over different value levels.
We can see that controlling for worker value sharply reduces our estimate of the effect of education on earnings. Our model tightly constrains the relationship between worker value and worker income, but the relationship between worker intelligence and worker income is less constrained. However, as long as we're willing to assume a positive relationship between worker intelligence and worker value, we will also see that controlling for worker intelligence reduces the estimate of the effect of education on earnings.
Our model obeys the only constraint Caplan has specified ("the observed education premium is 100% due to signaling"), so we know the answer can't be TRUE. If TRUE and FALSE are the only options, then the answer is FALSE. But that isn't right either; other people in this same thread have presented other models that obey the constraint without falsifying the claim of the problem.
So again, all we can say is that the problem is underspecified, and if Caplan wants an answer he's going to have to pose the problem better.
Assume everyone born either smart or dumb and this only trait employers care about. Graduating from college proves you are smart, but some smart people are incapable of going to college. Smart non-college grads end up proving themselves through something more costly than college, but eventually do prove themselves and eventually end up with the same wage as college grads. Adjusting for intelligence will reduce estimates of effect on education on earnings since lifetime wage difference between smart college grads and smart non-grads will be less than that between smart college grads and dumb people. What am I missing?
“ eventually end up with the same wage as college grads. “
This is simply a denial of the existence of an education premium.
No because lifetime earnings will be lower, and wages will be lower until the smart non-grad has proved herself.
Oops, my bad. Wages != lifetime earnings
OTOH, the non-college whiz gets a four year head start. Why isn’t 4 years of experience in the field as good a signal to their actual employer as 4 years of college?
Because then you wouldn't need college as a signal. Also, observation is costly and imperfect plus the job wouldn't be as optimized for signaling as college is.
When you’re hiring, observation is costly, and so is actual measurement. When the guy is working for you, at least some degree of observation comes for free. Do you know which workers didn’t show up today? I think so.
I could make an alternate story, where employers would be as happy or happier hiring a bunch of highschool grads (or homeschoolers?) and firing the lemons after a month or so (or even getting them to work free as apprentices or “interns”), except other factors interfere. Those might include the legal climate, which makes hiring and firing expensive and internships or apprenticeships difficult. Maybe it would also hurt the morale of the novice workers.
Speaking of observation and it’s difficulties, do we know whether using the signal actually works, compared to some alternative? Or is that just the way everyone does it, and to the extent that anyone gets ahead by modifying that approach, could it be that it is just too difficult to estimate the effectiveness of alternatives? That sees it as a culture trap, a local rather than a global equilibrium. I would think that society would hop out of the local equilibrium just by accident, if there was a huge disparity between it and the alternatives. It's bad for everyone who has to signal, but it’s not obvious what the alternative is. Even if a kid wants to become an entrepreneur and hire himself without signaling, he has to signal the people who lend him the capital. That brings it down to “start your own business with $100 and a good attitude.”
If there was an obviously better signal or measurement, it seems like it could spread easily. Maybe I am misperceving that. I know people are groaning about student debt, but are people groaning about the difficulty of hiring good workers, or patting themselves on the back?
More costly than four to eight years of your life and potentially a hundred thousand dollars of debt, or more?
Yes because college is also fun for lots of students.
TRUE.
Can I have a PhD please?
Not a question, it is a statement. Even if it were a question, it is worded confusingly. No wonder most students got it “wrong”. I guess the GMU PhD program is pure sheepskin.
It's a True/False question; those always imply "Is this statement true or false" by their very structure. Being able to understand the question is pretty much half the battle.
It needs a "True or false:" preamble, which I presume it had but Bryan neglected to include when copying over. Including "NOT" in a true/false question invokes the uncommon way the English language treats double negatives mathematically -- as positives. But I'm sure all GMU PhD candidates were native English speakers with perfect ability to read the minds of their professors, so much useful signal was extracted by having them answer it as worded.
The preamble would probably be in the heading of the section declaring the questions as True/False. You will also note that Caplan specified that 90% of the students gave the wrong answer of FALSE, which strongly implies that it is a True/False question in this context.
You would be quite incorrect as to the demographics, too: many GMU PhD candidates are not native speakers. Something like 1/4 of my cohort were non-native speakers as I recall.
And double negatives have nothing to do with it. The statement to be evaluated is as it is, a single negative. This is no more uncommon than saying "It is not raining outside currently. True or False?" In what language is that misleading or confusing? It makes perfect sense in German and Chinese, I am sure.
I think your reading comprehension is perhaps to blame for your confusion. Lack of recognition of context clues often causes people difficulties on standardized tests.
You have failed to comprehend the sarcasm in my statements and failed to address the real critiques. Recommend more humanities classes — the real valuable degree.
Controlling WHAT for intelligence? Question seems vague.
Controlling estimates of the effect of education on earnings.
If you are estimating the effect specifically of *education*, don't you have to control for *everything else* (except factors you know *a priori* are irrelevant)?
No, not only do you not have to do that, you must not do it. Controlling for a large number of variables means you will overfit the data and produce a completely worthless result.
But don’t you at least have to control for the factors that are known to be important in generating the result? Who would pay any attention to a claim about the effect of education on earnings that did not control for intelligence?
If the observed education premium is 100% due to signalling, that means that the education premium is 0% due to education improving the skills of students.
This means that the education premium is caused by potential-employees-with-a-degree differing from potential-employees-without-a-degree in characteristics that would be unchanged by education, such as intelligence, Big-5 personality trait conscientiousness, and class background. However, since it is a noisy signal (those traits cannot be legally measured directly in many cases), this means that people who get a degree will be grouped together, to some degree.
[TRUE] This suggests that controlling for intelligence will NOT reduce the estimates of the effect of education on earnings, and will in fact increase them, because education serves to lump in dumb students with smart students, raising the wages of dumb students more than it raises the wages of smart students.
Interestingly, the smart students will still benefit from education both individually *and in aggregate* because the existence of education as a reliable quality-signalling mechanism will raise employers's confidence in the intelligence of their prospective employees relative to the counterfactual where education did not exist [holding all else about reality constant; alternate realities exist where intelligence is divined more accurately during the hiring process using methods that are currently illegal].
Alternate answer: It depends on what "effect of education" means. The first answer I gave above was assuming that "effect of education" means "comparing those with a degree to those without a degree, and taking the difference as the effect of education". If instead you take the definition of "effect" as "something education does to change the individual's actual characteristics, rather than how they are perceived", then by definition if the education premium is 100% signalling it is 0% real skills benefit. If it is 0% real skills benefit, then the effect of education on earnings is always zero and controlling for intelligence will not change this [unless for some strange reason education is 100% due to signalling *in aggregate* but for dumb students it is 90% signalling 10% real and for smart students it is 110% signalling -10% real {makes smart students actually worse}].
The issue is one of voluntarily submitting yourself to educational sorting. The less intelligent will not submit themselves to the educational test, and will thus bias the returns to education upward.
Self-selection. If this worked perfectly, then everyone who was a good prospect would attend and graduate from college, and no one else would. How would the stats work then? It seems like intelligence, or whatever they use to self-select, would be doing all the work, and correcting for intelligence would explain everything (assuming intelligence is the thing employers want, or a good proxy), leaving n9thing for education to explain. Or Ed explains everything, since in that scenario, a degree is just a binary measure of intelligence. How do you explain intelligence in terms of intelligence? This is why I am confused.
Ahhh. Good point. If Ed is nothing but a signal for intelligence, then controlling for intelligence turns the signal into nothing but noise. *face palm*
If outcome A is 100% dependent upon input S, then only changes in S can affect A. No other variable is important. So the statement is not only TRUE, but would also be true if you infinitely changed "intelligence" for other characteristics such as race, gender, age, productivity, hours worked, etc.).
This question is just a fancy re-working of "If I jumped hard enough could I land on the moon ?"
That's what 100% means.
The double negative is annoying. Eliminate the "NOT" so that the correct answer is "True".
There is no double negative.
"NOT" is the first negative, "False" is the second.
The question, to recap, was:
If the observed education premium is 100% due to signaling, controlling for intelligence will NOT reduce estimates of the effect of education on earnings.
That's right, you read well.
👓
If the education premium is 100% signaling then there is no ability bias in that observed premium; i.e. there are no returns to ability that are being mistakenly attributed to education. There may be returns to ability, but they're separate from the returns to education and are not captured by the observed returns to education. In Chapter 3 (I think) of CAE Caplan quotes Heckman saying something very close to the following: "Ability and education are distinct. Ability has its returns and education has its returns."
This sets up a view where the observed education premium is split 3 ways: 1. the human capital formation that is caused by education, 2. the signal that education gives about a prospective worker, and 3. the premium that is not attributable to education at all, but ability. If it's 100% #2 then it's 0% #1 and 0% #3. Controlling for #3 doesn't reduce the observed premium.
This is hard for most people to wrap their heads around because to the extent they consider signaling an explanation they believe that education signals ability, but there are arguments for why it (mostly) does not. The sheepskin effect is one challenge for this view. If education signals ability there should be little difference in the average lifetime earnings of people with 17 years of education, including 120 credit hours and a diploma and those with 17 years of education, including 119 credit hours and no diploma. But there is a significant difference, one that takes up a big chunk of the observed premium.
The obvious correlation between education and ability works in the following way: those with more ability find education to be easier and/or more enjoyable than those with less ability, so they consume more of it. Education is not an investment to prove how smart you are, it's an investment in a signal that you are able to endure mundane and apparently pointless tasks because someone with a small amount of authority told you to, for many years. People with more ability can simply have a lower cost when making that investment. Higher ability *distorts* the signal. The 150 IQ guy with, say, a business degree may be (likely is?) far lazier than the one with a 100 IQ.
That's the strong version. I personally tend to think that education might signal some ability, although imperfectly. If someone has a mechanical engineering degree I take that as a signal that they're pretty smart. But I still run into the sheepskin problem. How would I, as an employer, evaluate one candidate with a perfect GPA, 119 credits and no degree vs. one with a 3.5 GPA and a degree? The former sends a signal that he's smart but there's something wrong with him, whereas the latter sends the signal that he's smart enough and enough of a conformist to finish a degree and fill out the paperwork. And what if I meet someone who is an engineer but does not have a degree? That also signals ability, perhaps moreso.
Assuming that smarter people are better at creditably faking credentials, and that sociopaths earn more, you might see a negative correlation between actual schooling and earnings among the highly intelligent that doesn't emerge at intelligence levels where sociopaths lie and fake less successfully.
Half-joke aside, it occurs to me that "education" being 100% signaling presumably refers to the entire university experience, and is therefore incompatible with personal networking at e.g. Ivy League schools having a positive effect on earnings. Am I mistaken in that assumption? After all, a successfully faked Harvard degree won't make you Harvard friends.
> it occurs to me that "education" being 100% signaling presumably refers to the entire university experience, and is therefore incompatible with personal networking at e.g. Ivy League schools having a positive effect on earnings.
That's correct; personal connections you make while at school are tangible assets that would be excluded by a 100% signaling model. Such a model would allow for the existence of those connections, but it would require their effect on your income to be zero.