"If the education premium is 100% signaling, then if a non-smart person gets a degree, they will still get the full labor market bonus for possessing the degree. Similarly, if a smart person fails to get a degree, they will get none of the labor market bonus for possessing a degree."
Yup, yup.
"In a simple model where education is the sole way to signal intelligence, the 100% signaling assumption implies that intelligence has zero independent reward; you only get credit for your IQ if you “launder” it through the education system."
Also true, but I don't understand how "education is the sole way to signal intelligence" is implied from the question. The question asks us to assume the *education premium* is 100% due to signaling. This tells me education gives workers no increase in human capital. That doesn't tell me anything about the relationship between earnings and intelligence.
Yeah to give an example. Let’s say Person A is born being able to perform all tasks 50% faster than Person B because they’re more intelligent.
Now education premium=100% signaling doesn’t mean job market doesn’t reward that intelligence. It could also mean you don’t learn anything (this might be where the holdup is. If education premium=100%, that could also mean jobs don’t reward intelligence).
That means if people who get educated are also Person A, and those who aren’t are Person B, then controlling for intelligence would matter given that jobs reward people who perform 50% faster.
That seems to be a fairly concrete proof by counterexample
Except your counterexample directly contradicts what Bryan pointed out: if the return to education is 100% signaling, it's 0% ability bias. Thus, either Person A and Person B have the same amount of education, or employers don't reward intelligence.
I think Caplan is the one who's confused, not you. Your statement is completely correct. Signaling only requires employers to change their beliefs about workers' types based on their attainment, not that employers have no other way to gather information about types. Realistically, the existence of self-employed people is already enough to guarantee that the coefficient on intelligence would be nonzero.
I think that if there is an "intelligence premium", it means colleges will pick up on it and use it as part of admissions, which will increase the relative portion of smarter people in college, effectively creating an ability bias. In this scenario, part of the education premium is due to college selecting smarter people, which contradicts the "100% signaling" assumption. In other words, the "100% signaling" assumption implies there can't be an intelligence premium. Does that make sense?
I thought one of the things that finishing college is supposed to signal is that you're more intelligent than average? It's a cheap way for employers to figure that out because university admissions does the hard work for them. The 100% signaling model just means that the entire income premium one gets from education comes from that signaling, and nothing comes from increasing skills while in university, or networking, or anything else that universities are supposed to provide.
This, by itself, does not imply that there isn't an independent intelligence premium and if you hold all else equal more intelligent people will make more money.
If intelligence only has value insofar as education signals its presence, and has no value in terms of its ability to improve work performance, then it has no economic value at all.
Smells like a hocus pocus thought experiment of a question that requires terms be redefined to something meaningless in order to make sense of it. You have to ask 'what concept are the professors trying to test me on' with this sort of question, not 'what's a genuine answer to the damn question'. Don't like that. Not even a bit.
Even if "the observed education premium is 100% due to signaling", it seems to me that it fails to preclude intelligence and education from being correlated.
For example, if we imagine a world where college teaches *absolutely nothing* but colleges still admit smarter students -- in this case, controlling for intelligence will have an impact.
It seems like your question takes it as an unspecified assumption that the signal is a "fake" signal of intelligence, rather than a true signal. (Perhaps your definition of "signal" only counts fake signals?) Or perhaps I am missing something.
During labor shortages, employers are given greater incentive to go through the effort of finding the diamonds in the rough rather than increasing salaries; immigration actually fuels this sheepskin effect by making the degree premium more affordable for employers. https://apnews.com/article/cb2739df66fea98e4e017f25e114dfb6
The effect of immigration is to make wages cheap enough that employers would rather save on testing materials and rely more on university degrees rather than raising wages or finding the diamonds in the rough.
I'm still not convinced the statement is true in any arbitrary finite sample. You need a restriction that controls how *noise* is correlated with income *in the sample*, which is definitely not present in any explicit sense.
Saying that the *observed* education premium is entirely due to signaling might get you far enough, although I'm unsure. One could define the observed education premium in a way that includes noise (in a simple model, where you only have education havers and education not havers, the observed premium is defined as the average wage of education havers minus the average wage of education not havers, so it includes noise on both sidse), but I don't think that actually solves anything. Instead it puts you in a setting where there's no reason to expect that the *estimated* education premium will equal the observed one.
For the statement to be true in general, I still think you'd need to specify that there is no noise in the DGP that generates income.
“If the education premium is 100% signaling, then if a non-smart person gets a degree, they will still get the full labor market bonus for possessing the degree,” the answer says.
In a field, such as Google software engineer, that (generally) only accepts applications from college grads, but does its own rigorous testing, the “full labor market bonus” consists only of the opportunity to apply.
The non-smart person is getting nothing of value to him.
The concepts might be easier to grasp if you use the simpler vocabulary of *selection* and *treatment* -- standard terminology across the social sciences -- to establish the framework:
Step 1) College grads earn more than do similar dropouts. (Empirical premise.)
Step 2) The extra earnings are caused either by *selection effects* or by *treatment effects*.
Step 3) *Selection effects* cover the permanent traits of college students, prior to matriculation. Note: *Selection* may be self-selection; for example, most applicants to Harvard are very intelligent. Or *selection* may occur by a filter; for example, tests, procedural hurdles, criteria, or clinical judgment by admissions officers, employers, etc. (Presumably, the filters focus partly on indicators of permanent psychological traits.) Self-selection occurs in the shadow of selection-by-filter.
Step 3a) Bryan Caplan highlights three psychological traits -- intelligence, grit, and ability to intuit and follow social expectations -- in his book, The Case against Education. Employers want to hire people who have these traits. BTW, conformity, the 3rd psychological trait, has its own forms of excellence; for example, 'anticipation is the essence of service.'
Step 3b) A subset of dropouts, too, have these traits (intelligence, grit, conformity); but employers usually find it too troublesome to sort the wheat from the chaff (i.e., to try and discern these traits) among dropouts.
Step 4) *Treatment effects* cover the difference that college completion makes for students.
Step 4a) One *treatment effect* of college is education (human-capital formation). Most economists emphasize this. Bryan makes a case that it plays a relatively minor role -- except maybe in STEM -- partly because there is broad mismatch between curriculum/pedagogy and job knowledge/skills.
Step 4b) Another *treatment effect* of college is *signaling:* The degree signals that the grad is smart, hard-working, and willing and able to jump through many hoops (i.e., to conform flexibly and durably). By the time a student graduates, she has performed reasonably well under numerous, somewhat arbitrary, occasionally exigent bosses (called professors). The signal/degree greatly eases the challenge of sorting wheat from chaff; i.e., of discerning who has the 3 key psychological traits (intelligence, grit, conformity).
Back to Bryan's exam question:
"If the observed education premium is 100% due to signaling, controlling for intelligence will NOT reduce estimates of the effect of education on earnings."
We may rephrase:
"If the observed education premium is 100% due to a treatment effect (say, for example, signaling), then controlling for a selection effect (say, for example, intelligence) -- i.e., for an underlying psychological trait -- will NOT reduce estimates of the effect of college completion (the degree) on earnings."
BTW, Tyler Cowen, contra Bryan, seems to argue that conformity (and perhaps also grit) is not so much a selection effect (an underlying psychological trait), but is instead mainly a treatment effect of school/college. See Tyler's blogpost, "Why education is productive — a parable of men and beasts:"
Why do you write: “In a simple model where education is the sole way to signal intelligence, the 100% signaling assumption implies that intelligence has zero independent reward; you only get credit for your IQ if you ‘launder’ it through the education system.” This “simple” model was not specified in the setting of the question.
The education bonus need not be the same for each person; there may be interaction with other factors that affect salary. For example, stupid people who get a degree may get less of a bonus than intelligent people who get a degree . . . or they may get more of a bonus, depending on how the education signal interacts with the other factors that determine salary.
But that's not quite the question you asked. You asked about *estimates* of the effect of education on earnings while the answer you gave seems to be about what effect intelligence will actually have (a reasonable interp that gives other answer is to imagine conducting a study controlling for something like SAT scores if you assume employers have access to them).
I know it's a bit pedantic but I'd like to suggest asking instead: does conditioning on intelligence affect expected earnings.
At least in my mind controlling is an imperfect technique used in statistical estimation while you wanted to know about the effect of conditioning on the probability distribution. But maybe that's why I do math and don't work in an applied field.
I don't understand what the functional form of "the education premium is 100% signaling" looks like. Since it doesn't matter whether we use logistic or linear regression for the answer here, let's just make it linear with no loss of generality. So the regression equation to estimate is:
(1) earnings = a + b*Educ + c*IQ
and the corresponding estimate *without* controlling for intelligence is:
(2) earnings = a + b*Educ
My interpretation of the corresponding (linear) causal model implied by "the education premium is 100% ability bias" is:
(3) earnings = a + c*IQ + noise
with
(4) Educ = d*IQ + other stuff
and clearly if (3) and (4) represent the true model, then the estimate of "b" in (1) is going to be lower than the estimate of (b) in (2). In fact, "b" should be 0 in expectation in (1) and some intermediate value in (2) (depending on the size of "noise" and "other stuff").
So what are the corresponding versions of (3) and (4) in the "education premium is 100% due to signaling" case. Because clearly I (and many others) *did* confuse this for ability bias, and still, even after two posts, don't see what the alternative model actually is. So if Bryan or anyone could clarify by writing out a simple linear model for "education premium is 100% due to signaling", that would really help (and might help out students who think in terms of math/stats but not Caplanisms).
I’d still answer false to this question but reading through the whole thread made me appreciate how difficult the question is so I will try to give a comprehensive counter example that’s very niche but does technically show a situation where (1) education premium 100% due to signalling and (2) controlling for intelligence matters:
There is one employer: Company X. Company X hires by giving all employees an IQ test and by giving each potential a score of 100 if they went to college and 0 if they didn’t. They add these scores together and hire/give salaries based on the index. We will assume that college does absolutely nothing to improve IQ. Thus, the signalling premium is 100% of the benefit of education.
Now, there are 2 types of people. Type A has IQ of 115 and makes up 70% of college population and 30% of non-college population. Type B has IQ of 100 and makes up 30% of college population and 70% of non-college population. Now, I’m not gonna do the math because I’ll screw it up, but controlling for IQ will reduce the perceived value of education.
Yeah, not sure I agree with your answer. Even if the education premium is 100% due to signaling, that doesn't mean that education is the sole way to signal Intelligence.
For example, say a random 50% of people are intelligent and a random 50% of people go to college. And that independently, being intelligent and/or going to college each provide a $25k wage premium. Outcomes would look something like this:
- No College / Not Smart: 25% of people. Average Income $50k
- College / Not Smart: 25% of people. Average Income: $75k
- No College / Smart: 25% of people. Average Income: $75k
- College / Smart: 25% of people. Average Income: $100k
^The college wage premium may be 100% due to signaling, but that doesn't mean intelligence can't have an impact on wages independent of college.
ln(Labor Earnings) = a' + b'*SignalingValueofDegree + c'*RealEducationalValueofDegree+ d'*IQ
The hypothetical true world you have posited has b'>0 and c'=0.
The model that a social scientist would test is ln(Labor Earnings) = a + b*Degree in which b is allegedly a combination of b' and c' (which we will assume collapses to just b' as c'=0). But IQ predicts Degree (even if it doesn't affect the signaling value), so b will be an upwardly biased estimate of b' as long as d'>0 (likely!). So if we're talking about *observed* premia and *estimates*, covarying will have an effect. The answer is FALSE.
Oh wait, in the answer you snuck in that education is the sole method through which intelligence affects earnings (different from signaling is the sole method through which education affects earnings!). That wasn't in the question and is a very important assumption that sets d'=0. Now the answer is TRUE.
I think to be fair to Bryan, he’s not adding an extra assumption, so much as he’s arguing “if b’>0 and c’=0, then d’=0.”
The best I can follow his argument (forgive the conventions and variables. I only have formal math training, not economics) is that 1) Labor Earnings (LE) is a function of Intelligence (I) and SignallingValueOfEducation (S) (and some set of other things that are not relevant); 2) Intelligence is a function of RealValueOfEducation (R) and IQ (Q); 3) 100% value of education=singalong means dLE/dR=0 (derivative of Labor Earnings with respect to R); 4) dLE/dR=dLE/dI*dI/dR (bastardized version of chain rule); 5) (3) and (4) imply dLE/dI=0; that means IQ has no effect or d’=0.
The main issue with this is step (5). dI/dR=0 is also entirely possible. If education doesn’t teach you anything, then your Intelligence isn’t determined by your education. There might also be other problems with this chain of logic but I think this response is sufficient.
That was a long winded way of saying I think you’re right but you didn’t properly identify Bryan’s mistake.
Still confused.
"If the education premium is 100% signaling, then if a non-smart person gets a degree, they will still get the full labor market bonus for possessing the degree. Similarly, if a smart person fails to get a degree, they will get none of the labor market bonus for possessing a degree."
Yup, yup.
"In a simple model where education is the sole way to signal intelligence, the 100% signaling assumption implies that intelligence has zero independent reward; you only get credit for your IQ if you “launder” it through the education system."
Also true, but I don't understand how "education is the sole way to signal intelligence" is implied from the question. The question asks us to assume the *education premium* is 100% due to signaling. This tells me education gives workers no increase in human capital. That doesn't tell me anything about the relationship between earnings and intelligence.
Pretty much exactly this. Why can't there be an education premium and an intelligence premium?
Yeah to give an example. Let’s say Person A is born being able to perform all tasks 50% faster than Person B because they’re more intelligent.
Now education premium=100% signaling doesn’t mean job market doesn’t reward that intelligence. It could also mean you don’t learn anything (this might be where the holdup is. If education premium=100%, that could also mean jobs don’t reward intelligence).
That means if people who get educated are also Person A, and those who aren’t are Person B, then controlling for intelligence would matter given that jobs reward people who perform 50% faster.
That seems to be a fairly concrete proof by counterexample
Except your counterexample directly contradicts what Bryan pointed out: if the return to education is 100% signaling, it's 0% ability bias. Thus, either Person A and Person B have the same amount of education, or employers don't reward intelligence.
I agree. I’m saying Person A and Person B have the same amount of education because college does absolutely nothing in terms of teaching you.
That’s how we can have employers rewarding intelligence.
I think Caplan is the one who's confused, not you. Your statement is completely correct. Signaling only requires employers to change their beliefs about workers' types based on their attainment, not that employers have no other way to gather information about types. Realistically, the existence of self-employed people is already enough to guarantee that the coefficient on intelligence would be nonzero.
I think that if there is an "intelligence premium", it means colleges will pick up on it and use it as part of admissions, which will increase the relative portion of smarter people in college, effectively creating an ability bias. In this scenario, part of the education premium is due to college selecting smarter people, which contradicts the "100% signaling" assumption. In other words, the "100% signaling" assumption implies there can't be an intelligence premium. Does that make sense?
I thought one of the things that finishing college is supposed to signal is that you're more intelligent than average? It's a cheap way for employers to figure that out because university admissions does the hard work for them. The 100% signaling model just means that the entire income premium one gets from education comes from that signaling, and nothing comes from increasing skills while in university, or networking, or anything else that universities are supposed to provide.
This, by itself, does not imply that there isn't an independent intelligence premium and if you hold all else equal more intelligent people will make more money.
Exactly my confusion as well. Was coming to write this exact comment (but not as lucidly!)
Do more of these Bryan. They really engage readers.
If intelligence only has value insofar as education signals its presence, and has no value in terms of its ability to improve work performance, then it has no economic value at all.
Smells like a hocus pocus thought experiment of a question that requires terms be redefined to something meaningless in order to make sense of it. You have to ask 'what concept are the professors trying to test me on' with this sort of question, not 'what's a genuine answer to the damn question'. Don't like that. Not even a bit.
Even if "the observed education premium is 100% due to signaling", it seems to me that it fails to preclude intelligence and education from being correlated.
For example, if we imagine a world where college teaches *absolutely nothing* but colleges still admit smarter students -- in this case, controlling for intelligence will have an impact.
It seems like your question takes it as an unspecified assumption that the signal is a "fake" signal of intelligence, rather than a true signal. (Perhaps your definition of "signal" only counts fake signals?) Or perhaps I am missing something.
Hey Caplan, guess what?
During labor shortages, employers are given greater incentive to go through the effort of finding the diamonds in the rough rather than increasing salaries; immigration actually fuels this sheepskin effect by making the degree premium more affordable for employers. https://apnews.com/article/cb2739df66fea98e4e017f25e114dfb6
The effect of immigration is to make wages cheap enough that employers would rather save on testing materials and rely more on university degrees rather than raising wages or finding the diamonds in the rough.
I'm still not convinced the statement is true in any arbitrary finite sample. You need a restriction that controls how *noise* is correlated with income *in the sample*, which is definitely not present in any explicit sense.
Saying that the *observed* education premium is entirely due to signaling might get you far enough, although I'm unsure. One could define the observed education premium in a way that includes noise (in a simple model, where you only have education havers and education not havers, the observed premium is defined as the average wage of education havers minus the average wage of education not havers, so it includes noise on both sidse), but I don't think that actually solves anything. Instead it puts you in a setting where there's no reason to expect that the *estimated* education premium will equal the observed one.
For the statement to be true in general, I still think you'd need to specify that there is no noise in the DGP that generates income.
“If the education premium is 100% signaling, then if a non-smart person gets a degree, they will still get the full labor market bonus for possessing the degree,” the answer says.
In a field, such as Google software engineer, that (generally) only accepts applications from college grads, but does its own rigorous testing, the “full labor market bonus” consists only of the opportunity to apply.
The non-smart person is getting nothing of value to him.
The concepts might be easier to grasp if you use the simpler vocabulary of *selection* and *treatment* -- standard terminology across the social sciences -- to establish the framework:
Step 1) College grads earn more than do similar dropouts. (Empirical premise.)
Step 2) The extra earnings are caused either by *selection effects* or by *treatment effects*.
Step 3) *Selection effects* cover the permanent traits of college students, prior to matriculation. Note: *Selection* may be self-selection; for example, most applicants to Harvard are very intelligent. Or *selection* may occur by a filter; for example, tests, procedural hurdles, criteria, or clinical judgment by admissions officers, employers, etc. (Presumably, the filters focus partly on indicators of permanent psychological traits.) Self-selection occurs in the shadow of selection-by-filter.
Step 3a) Bryan Caplan highlights three psychological traits -- intelligence, grit, and ability to intuit and follow social expectations -- in his book, The Case against Education. Employers want to hire people who have these traits. BTW, conformity, the 3rd psychological trait, has its own forms of excellence; for example, 'anticipation is the essence of service.'
Step 3b) A subset of dropouts, too, have these traits (intelligence, grit, conformity); but employers usually find it too troublesome to sort the wheat from the chaff (i.e., to try and discern these traits) among dropouts.
Step 4) *Treatment effects* cover the difference that college completion makes for students.
Step 4a) One *treatment effect* of college is education (human-capital formation). Most economists emphasize this. Bryan makes a case that it plays a relatively minor role -- except maybe in STEM -- partly because there is broad mismatch between curriculum/pedagogy and job knowledge/skills.
Step 4b) Another *treatment effect* of college is *signaling:* The degree signals that the grad is smart, hard-working, and willing and able to jump through many hoops (i.e., to conform flexibly and durably). By the time a student graduates, she has performed reasonably well under numerous, somewhat arbitrary, occasionally exigent bosses (called professors). The signal/degree greatly eases the challenge of sorting wheat from chaff; i.e., of discerning who has the 3 key psychological traits (intelligence, grit, conformity).
Back to Bryan's exam question:
"If the observed education premium is 100% due to signaling, controlling for intelligence will NOT reduce estimates of the effect of education on earnings."
We may rephrase:
"If the observed education premium is 100% due to a treatment effect (say, for example, signaling), then controlling for a selection effect (say, for example, intelligence) -- i.e., for an underlying psychological trait -- will NOT reduce estimates of the effect of college completion (the degree) on earnings."
BTW, Tyler Cowen, contra Bryan, seems to argue that conformity (and perhaps also grit) is not so much a selection effect (an underlying psychological trait), but is instead mainly a treatment effect of school/college. See Tyler's blogpost, "Why education is productive — a parable of men and beasts:"
https://marginalrevolution.com/marginalrevolution/2006/02/why_education_i.html
More of such puzzles!
Why do you write: “In a simple model where education is the sole way to signal intelligence, the 100% signaling assumption implies that intelligence has zero independent reward; you only get credit for your IQ if you ‘launder’ it through the education system.” This “simple” model was not specified in the setting of the question.
The education bonus need not be the same for each person; there may be interaction with other factors that affect salary. For example, stupid people who get a degree may get less of a bonus than intelligent people who get a degree . . . or they may get more of a bonus, depending on how the education signal interacts with the other factors that determine salary.
But that's not quite the question you asked. You asked about *estimates* of the effect of education on earnings while the answer you gave seems to be about what effect intelligence will actually have (a reasonable interp that gives other answer is to imagine conducting a study controlling for something like SAT scores if you assume employers have access to them).
I know it's a bit pedantic but I'd like to suggest asking instead: does conditioning on intelligence affect expected earnings.
At least in my mind controlling is an imperfect technique used in statistical estimation while you wanted to know about the effect of conditioning on the probability distribution. But maybe that's why I do math and don't work in an applied field.
I don't understand what the functional form of "the education premium is 100% signaling" looks like. Since it doesn't matter whether we use logistic or linear regression for the answer here, let's just make it linear with no loss of generality. So the regression equation to estimate is:
(1) earnings = a + b*Educ + c*IQ
and the corresponding estimate *without* controlling for intelligence is:
(2) earnings = a + b*Educ
My interpretation of the corresponding (linear) causal model implied by "the education premium is 100% ability bias" is:
(3) earnings = a + c*IQ + noise
with
(4) Educ = d*IQ + other stuff
and clearly if (3) and (4) represent the true model, then the estimate of "b" in (1) is going to be lower than the estimate of (b) in (2). In fact, "b" should be 0 in expectation in (1) and some intermediate value in (2) (depending on the size of "noise" and "other stuff").
So what are the corresponding versions of (3) and (4) in the "education premium is 100% due to signaling" case. Because clearly I (and many others) *did* confuse this for ability bias, and still, even after two posts, don't see what the alternative model actually is. So if Bryan or anyone could clarify by writing out a simple linear model for "education premium is 100% due to signaling", that would really help (and might help out students who think in terms of math/stats but not Caplanisms).
I’d still answer false to this question but reading through the whole thread made me appreciate how difficult the question is so I will try to give a comprehensive counter example that’s very niche but does technically show a situation where (1) education premium 100% due to signalling and (2) controlling for intelligence matters:
There is one employer: Company X. Company X hires by giving all employees an IQ test and by giving each potential a score of 100 if they went to college and 0 if they didn’t. They add these scores together and hire/give salaries based on the index. We will assume that college does absolutely nothing to improve IQ. Thus, the signalling premium is 100% of the benefit of education.
Now, there are 2 types of people. Type A has IQ of 115 and makes up 70% of college population and 30% of non-college population. Type B has IQ of 100 and makes up 30% of college population and 70% of non-college population. Now, I’m not gonna do the math because I’ll screw it up, but controlling for IQ will reduce the perceived value of education.
Yeah, not sure I agree with your answer. Even if the education premium is 100% due to signaling, that doesn't mean that education is the sole way to signal Intelligence.
For example, say a random 50% of people are intelligent and a random 50% of people go to college. And that independently, being intelligent and/or going to college each provide a $25k wage premium. Outcomes would look something like this:
- No College / Not Smart: 25% of people. Average Income $50k
- College / Not Smart: 25% of people. Average Income: $75k
- No College / Smart: 25% of people. Average Income: $75k
- College / Smart: 25% of people. Average Income: $100k
^The college wage premium may be 100% due to signaling, but that doesn't mean intelligence can't have an impact on wages independent of college.
ln(Labor Earnings) = a' + b'*SignalingValueofDegree + c'*RealEducationalValueofDegree+ d'*IQ
The hypothetical true world you have posited has b'>0 and c'=0.
The model that a social scientist would test is ln(Labor Earnings) = a + b*Degree in which b is allegedly a combination of b' and c' (which we will assume collapses to just b' as c'=0). But IQ predicts Degree (even if it doesn't affect the signaling value), so b will be an upwardly biased estimate of b' as long as d'>0 (likely!). So if we're talking about *observed* premia and *estimates*, covarying will have an effect. The answer is FALSE.
Oh wait, in the answer you snuck in that education is the sole method through which intelligence affects earnings (different from signaling is the sole method through which education affects earnings!). That wasn't in the question and is a very important assumption that sets d'=0. Now the answer is TRUE.
I think to be fair to Bryan, he’s not adding an extra assumption, so much as he’s arguing “if b’>0 and c’=0, then d’=0.”
The best I can follow his argument (forgive the conventions and variables. I only have formal math training, not economics) is that 1) Labor Earnings (LE) is a function of Intelligence (I) and SignallingValueOfEducation (S) (and some set of other things that are not relevant); 2) Intelligence is a function of RealValueOfEducation (R) and IQ (Q); 3) 100% value of education=singalong means dLE/dR=0 (derivative of Labor Earnings with respect to R); 4) dLE/dR=dLE/dI*dI/dR (bastardized version of chain rule); 5) (3) and (4) imply dLE/dI=0; that means IQ has no effect or d’=0.
The main issue with this is step (5). dI/dR=0 is also entirely possible. If education doesn’t teach you anything, then your Intelligence isn’t determined by your education. There might also be other problems with this chain of logic but I think this response is sufficient.
That was a long winded way of saying I think you’re right but you didn’t properly identify Bryan’s mistake.