Prof. Bryan Caplan

Econ 321


Weeks 6-7: Human Capital

I.             Present Discounted Value (PDV)

A.           What determines the sale value today of a future payment - positive or negative?

1.            Ex: If you issue a certificate that pays $1, 10 years in the future, what could you sell it for today? 

2.            Clearly the answer is not $1!  No one would pay $1, because they are foregoing 10 years worth of interest.

B.           But how much less?  Just figure: "How much money would I have to put in the bank today in order to have $1, 10 years from now?"  With a constant interest rate, that comes out to: $1/(1+n)10.  If e.g. the interest rate is 10%, then you would need $1/(1.1)10= $1/2.59= $.386.  $.386 is what economists call this asset's present discounted value (PDV).

C.           Similarly, a future cost is less harmful than it seems on its face.  If you learn you will need a $1000 operation 30 years from now, ask: "How much money must I put in the bank today in order to have $1000 three decades from now?"  If the interest rate is 5%, then the answer is $1000/(1.05)30=$231.38.

D.           One step harder: What is the total amount people will pay for a whole set, or "bundle," of future benefits and costs?  Just add up what they would pay for each item separately.  That sum is the income stream's PDV.

E.           In the real world, people have to make educated guesses about both future payments and future interest rates.  We can think of something's current market price as its expected PDV.

1.            Important: When economists say people "maximize profits," what they actually mean is that they are maximizing PDV.  (For 1 period, they are equivalent).

F.            You can apply the PDV formula to virtually anything: houses, land, buildings, stock, bonds, animals, etc.  E.g. what is the PDV of a chicken?

G.           General rule: The lower the interest rate, the more the future counts.

II.            Rate of Return on Investment

A.           Once you know an asset's PDV, you can calculate your rate of return on this investment.

B.           Ex: If you get $100 in dividends from a stock worth $10,000, and the stock's value doesn't change, what was your rate of return?  1%.  If you get $100 in dividends from a stock worth $10, what would you rate of return be then?  1000%.

C.           Ex: If you get no dividends from a stock but it rises in price from $400 to $500, what was your rate of return?  25%.

D.           In general, the rate of return for a year is:

E.           Basic economic logic suggests that equally risky assets must have the same expected rate of return.  Otherwise, people would sell the asset with the lower rate of return and buy the asset with the higher rate of return, until their rates of return are equal. 

F.            Of course, two gambles can have the same expected return, even though one turns out to pay much more than the other.  For example, it is not surprising that some people win at blackjack and others lose.  But if there are two casinos next to each other, and one gives better odds, something strange is going on.

III.          Slaves As Investments

A.           What slave-owners like about owning slaves is that the slave can't easily say "no."  The owner can threaten violence or death to make the slave do as he is told.

B.           But the slave owner still can't give the slave nothing.  In order to take advantage of the slave, it is still necessary to provide the slave with his "subsistence" (food, shelter, etc.).

C.           They must also pay some costs of “enforcement” - guarding and monitoring the slave.

D.           So what is the most a slave-owner would pay to buy a slave?  The logic of PDV directly applies: The sale price will equal the PDV of the slave's lifetime earnings, minus the PDV of his subsistence, minus the PDV of enforcement.

E.           Similarly, suppose a slave-owner is weighing whether to train his slave to be a metal smith.  This means foregone earnings - the slave could have been working instead of training.  But it also means higher earnings for the master in the future.  The profit-maximizing slave-owner will pick the level of training that maximizes the slave's PDV.

F.            Or suppose that a slave-owner is deciding whether to allow his slaves to have children (who are also legally slaves).  If a slave has a child, the mother will bring in less income for a while, and the enslaved child will have little productive value for many years; but eventually the master will have two slaves instead of one.  The profit-maximizing slave-owner picks whichever PDV is higher. 

G.           What is the rate of return on a slave?  If a slave sells for $3000, produces $300 in net income, and falls to $2850 in value, the rate of return is (300-150)/3000=5%.

H.           In an economy with slavery, you would expect investments in slaves would earn the same typical return as anything else.

IV.          You As An Investment: Human Capital Theory

A.           Putting aside the moral repugnance of slavery, the same logic applies to your management of the person you own - yourself!  This insight is known as human capital theory.

B.           There are various things you can do with your time.  Which is the best investment?  Compare PDV!

C.           Ex: Should you get another year of school?  Add up the PDV of your foregone earnings during school and the extra income you expect to get after you've completed the schooling.

1.            Note: Since you forego earnings first, and get a raise afterwards, education makes less and less sense as interest rates rise.

D.           What else can you do for your career, and how do you decide if they are good investments?

1.            Plastic surgery

2.            Speech classes

3.            An Armani suit

4.            A fancy car to impress clients

V.           Application: The Rate of Return on Education

A.           Are you wasting your time in college?  Let's do PDV calculations to find out.

B.           Assumption 1: One additional year of school will raise your average salary by $2500/year during your working life; finishing four years of college gives you $10,000 during your working life.

C.           Assumption 2: You forego $15,000 worth of labor income for each year of college.

D.           Assumption 3: You have to pay $10,000 for school and extra school-related expenses.

E.           Assumption 4:  The interest rate will be 8% during your lifetime.

F.            Assumption 5:  You are 18 years old now and will work until you are 68.

G.           Conclusion: Putting all this into Excel, we find that going to college has a PDV of $7136 more than the alternative.

H.           What if:

1.            The interest rate rose to 9%?  PDV falls to -$3978.  You'd be better off quitting school and putting your earnings and tuition in the stock market.

2.            Your wage without college rises to $17,000 (but the marginal benefit of college stays the same)?  PDV falls to -$18.

3.            The benefit of college were $10,000 for your first 20 years of work, but $30,000 for all remaining years?  PDV rises to $41,241.

VI.          General Versus Firm-Specific Training

A.           People get experience on-the-job, but there are two basic kinds:

1.            General

2.            Firm-specific

B.           General skills are skills that you can use in other firms or even other industries.  Typing is a good example.

C.           Firm-specific training, in contrast, really only has value in a specific firm.  A good example is learning the names of your co-workers.  You're more productive on that job, but if you quit this knowledge is valueless.

D.           Will employers invest in general skills?  At first glance, there seems to be little point.  After they invest in you, you will be more productive in both your current and alternative jobs.  They will have to give you a suitable raise to retain you.

E.           On second thought, though, this only means that if you want general training from your firm, you will have to pay for it by working for less.  Internships are a standard example.

F.            What about firm-specific training?  By definition, such skills won't help you get a better offer elsewhere.  So if a firm gives you some firm-specific training, your productivity rises, but market forces don't force them to give you a corresponding raise.  You are more likely to get firm-specific training without a dock in your pay.

G.           However, the difference between general and firm-specific training may be weaker than it seems.  Why?  Firms have reputations for giving raises, and often even have formal pay scales.  If one firm pays employees the full value of their firm-specific training, and another doesn't, the latter will not be able to attract employees in the first place. 

1.            If this argument is right, then employees will have to accept lower pay for all costly training, but receive their full MVP wherever they work.

H.           In the real world, firms often seem to initially overpay (you get your full salary even during the first few weeks or months when you are using up other employee's time by asking questions).  Ideas?

VII.        Application: Understanding the Life Cycle

A.           Most people have a standard life pattern: get school when you're young, then work until retirement.  (Alternate pattern involves taking breaks from the labor force to have children).

B.           Human capital theory sheds considerable light on this pattern.  Why don't people work for 20 years, then go to college, then go back to work for 20 more years? 

1.            Because then they would only get to reap the benefits of education for 20 years instead of 40.

2.            Opportunity cost of time is lower when you're younger, so you give up less income.

C.           Why retire?  After a point, you become a less and less productive worker, and your wage will reflect that.  It makes more sense to work doing your most productive years, and enjoy leisure when it's cheaper.

D.           Work-hour patterns fit this story too.  People work the most hours during their peak-earning years (mid-40's to early 50's).

VIII.       Accounting for Compensating Differentials

A.           But isn't there any difference between how you regard yourself and how a slave-owner regards a slave?  Yes!  As discussed earlier, a free worker can factor "fun" and discomfort into their calculations.

B.           How can you quantify this?  Simple.  Ask yourself, "How much extra would someone have to pay me to do this unpleasant task rather than something else?"  Or, "How much would I be willing to give up for the extra fun of this other job?"

C.           Then, when you calculate PDV, add or subtract these numbers from your income in the appropriate time period. 

D.           For example, suppose you expect to suffer in an Internet start-up for five years.  You figure it would take $30,000/year to compensate your for your suffering.  Afterwards, you earn $10,000 extra for the next 20 years in an atmosphere with a normal fun level.  With a 10% interest rate, the PDV is -$39,627!

E.           Or suppose you are considering relocating from Rochester, NY to Fairfax, VA.  You figure that you would be willing to pay $7000 to live in Fairfax rather than Rochester.  If it costs $10,000 to move, and you have to take a $6000 pay cut for 10 years, should you move?  No, sorry, the PDV of the move is -$2855.

F.            In sum, human capital theory does not say that workers care only about money income.  Rather, it provides an accounting framework for managing your life.

G.           Something to consider: Do you actively dislike school compared to work?  Then you should count your "pain and suffering" as one of the costs of attending school.

IX.          Education Subsidies: The Failure of Externality Arguments

A.           Externalities are non-excludable benefits and costs.  The basic logic of selfishness then goes:

1.            If benefits are non-excludable, then each individual beneficiary gets them whether or not he pays for them.

2.            If beneficiaries get the benefits whether or not they pay for them, then they won't pay for them.

3.            If providers receive no pay for providing benefits, they won't provide them.

4.            Thus, due to non-excludability, potential social benefits don't materialize.

B.           Even if a good is partly excludable, less than 100% of the potential social benefits will normally be realized.

1.            Caveat: Inframarginal externalities

C.           It is easy to see why people see externalities of pollution clean-up.  But where are the externalities of education?

D.           Most externalities arguments for education amount to the absurdity that anything beneficial is an externality.  "We all benefit from education."  How is that different from "We all benefit from steel."  Yes, there's a benefit, but doesn't the market pay people to provide that benefit?!

E.           The sophisticated externality arguments focus on non-job-related aspects: crime ("Uneducated youth turn to crime,") and political culture ("An educated electorate votes better,") are probably the leading contenders.

F.            The crime argument is again weak.  We could just as easily increase the severity of punishment.  (More on this later!)

G.           The political education argument is stronger; there is no clear way to pay people for being smart voters.  But you certainly could just restrict the franchise to people with a certain education level!  Same effect, and no subsidy needed.

X.           Education Subsidies and Credit Market Imperfections

A.           A quite different argument concedes that education is a private good, but focuses on "credit market imperfections."  In essence, the problem is that it is difficult to credibly promise to repay an educational loan.  With a house, they can repossess the house if you default.  But they can't repossess your brain if you default on a student loan.

B.           Still, the problem is less serious than it sounds.  The IRS doesn't take excuses for failure to pay taxes; why couldn't lenders be given a comparable level of legal authority to attach your wages if you default? 

C.           Even under the current legal regime, your parents or other relatives or an employer could cosign for you.  Or schools might loan you money themselves, and refuse to release transcripts for former students who default.

D.           Economists who take credit market perfections seriously normally point to the measured rate of return to education.  They say that it is unusually large, indicating a failure of credit markets to equalize rates of return on different investments.

E.           If you assume that foregone earnings are the only cost of education, then on NLSY data the rate of return to education is 12.6% (controlling for no other variables).

F.            But this number is surely too high:

1.            It costs resources to educate people.  Counting these costs would definitely reduce the rate of return.

2.            This is an estimate of the average, not the marginal rate of return.  (The marginal rate would be lower.  Can you explain why?)

3.            It does not control for intelligence, which is highly correlated with education.

G.           (There's another big problem with return-to-education estimates we'll deal with after the midterm).

XI.          Intelligence and Human Capital

A.           We all have an intuitive notion of what is means to be "intelligent."  Empirical research on intelligence is one of the best-developed areas of psychology.

B.           In practical terms, researchers usually measure intelligence with IQ (Intelligence Quotient) or related tests.  These tests have come under angry attack on a number of grounds.  We'll briefly consider each in turn:

1.            Cultural bias

2.            "There is no one thing that constitutes 'intelligence.'"

3.            Imperfection

C.           Complaint #1: "Cultural bias."  There are large group differences in performance on IQ tests.  Jews do about 1 SD better than average, blacks about 1.2 SDs worse.  Critics blame this on cultural bias - supposedly, the tests measure familiarity with middle-class lifestyles rather than ability.  Unfortunately for this argument, it has been carefully tested and shown to be wrong.  If you use IQ tests to predict performance on practical tasks – like ability to drive a tank through an obstacle course – IQ tests actually overstate the performance of members of groups with low average IQs.   

D.           Complaint #2: "There is no one thing that constitutes 'intelligence.'"  Everyone is good at some things and bad at others, or so the claim goes.  Still, the fact is that for a wide range of mental problems, people who are good at some are usually (not always) good at all of them, and vice versa.  Think about the SAT Verbal versus Math scores.  There are some people who are great at Verbal and terrible at Math, but there are a lot more who are great at both or terrible at both.

E.           Complaint #3: Imperfection.  There are several varieties of this complaint.  One is that the same person has received very different test scores at different times.  Another is that world-renowned geniuses (Feynman is a common example) got low IQ scores.  All this may be true, but it's irrelevant.  IQ scores are more reliable than anything else, and if you tested 100 geniuses their average score would be very high.

F.            Intelligence is a lot like "strength."  There is some ambiguity, but at root we know what we mean, we know there are real differences, and we know that people who are strong by one measure are usually strong by other measures, too.

G.           There is a second debate about the extent to which IQ is hereditary or environmental.  There is no time to resolve this here, but evidence from carefully-constructed twin and adoption studies finds that the variance is about 80% genetic.  Unclear where the remaining 20% comes from - it doesn't seem to be family environment.

H.           Why do I bring all this up?  Because controlling for IQ sharply reduces the measured return to education to a mere 7.5%.  (1 extra percentile of IQ bumps you up .7%; a year of education is thus worth about as much as 11 percentiles of IQ).

I.             This is actually the central argument of the much-maligned book The Bell Curve by Charles Murray and Richard Herrnstein: The market pays a lot for intelligence.  Intelligence isn't the whole story, but it is on par with education in explanatory power.

XII.        Personality, Culture, and Human Capital

A.           Another well-developed field in psychology is the study of personality.  To my knowledge, unfortunately, there is little cross-over between this literature and labor economics.

B.           My hypothesis: What the main personality tests call Conscientiousness is probably another important determinant of income.  Ignoring it probably leads us to over-state the effect of education.  (In contrast, IQ and Conscientiousness are roughly unrelated).

1.            Note for the curious: In the popular Myers-Briggs personality test, Conscientiousness is captured by the Judging-Perceiving axis.

C.           Curious about your personality?  You can take the Myers-Briggs test at: and the Five-Factor test at:

D.           Sowell presents a great deal of historical evidence on the economic importance of culture.  This is a complicated issue, though, because culture is hard to measure.  Many leap to the conclusion that unexplained group differences must stem from "discrimination."

E.           We'll deal with discrimination later.  But: Let us suppose, as I guess most Americans do, that religious discrimination is no longer important in the U.S.

F.            What are the labor income differences for different religions, controlling for education, experience, and intelligence?


Religious Background

Earnings Residual















Roman Catholic







G.           Maybe this reveals massive discrimination in favor of Jews, mild discrimination in favor of Episcopalians and Catholics, and mild discrimination against Presbyterians and Methodists, but I doubt it.  Rather, I'd say that much of this represents various cultural differences that have made some denominations more economically prosperous than others.