Investments in Human Capital: Education and Training

“Embodying a set of skills that can be ‘rented out’ to employers”

Human Capital Physical Capital

Economic reasoning utilizes a lot of metaphors and often involves thinking by analogy.

Three major labor market investments -

1. Education and training2. Migration 3. Search for new jobs

The Concept of Present Value

In the fall of 1984, my wife and I arrived in California to teach at Pomona College for two years. My in-laws lived nearby and as a welcoming gift they gave us a checkfor $85, saying that they wanted us to use the money to buy a vanity license plate. Steve, my wife’s dad, said that vanity license plates cost $50 for the first year and then $35 each year that you renew them. Looking at the $85, I said, “You gave us too much.” If the interest rate was 5 percent, how much extra did they give us?

The Concept of Present Value𝐺0=$ 85 ,   𝐶0=$ 50 ,𝐶1=$ 35

(𝐺0 −𝐶0 )=$ 85 − $50=$ 35

(1+𝑟 ) (𝐺0 −𝐶0 )=(1.05 ) ∙ $ 35=$ 36.75

When we pay the renewal fee in the second year we will have $1.75 left over. Hence, my in-laws gave us too much!!! What they should have done was solve for where

(1+𝑟 ) (𝐺0 −𝐶0 )=$ 35

(1+𝑟 ) 𝐺0=(1+𝑟 ) 𝐶0+$ 35

𝐺0=𝐶0+$ 35

(1+𝑟 )

𝐺0=$50+$35

(1+0.05 )=$50+33.34=$ 83.34

𝑃𝑉 (𝐶0 ,𝐶1 ,𝐶2 ,⋯ ,𝐶𝑇 )=𝐶0+𝐶1

(1+𝑟 )+

𝐶1

(1+𝑟 )2+⋯+

𝐶𝑇

(1+𝑟 )𝑇

In general,

Snakehead Coyote = Human Smuggler Human Trafficker

Story of Michael Chen (“The Snakehead,” The New Yorker)

In 1991, when Michael was 18 years old, his parents paid a snakehead $5,000 and agreed to pay another $25,000 when he safely arrived in the U.S. During his journey, he “passed the remains of other Chinese who did not survive the mountains” and survived the shipwreck of the Golden Venture on Rockaway penninsula in Queens, New York. Today, he owns a “spotless” Chinese restaurant in Columbus, Ohio. Had he stayed in China, he might have been one of millions of farmers or fishermen, “working like slaves,” with little chance of changing their lives. He would have also had to abide by China’s family planning policy, better known as its one-child policy.

How did Michael (and his family) make the decision to migrate?

Benefits and Costs of the Migration Decision

• Increase in net future earnings• Greater personal freedom (psychic benefits)

Benefits

Costs• Forgone earnings during journey• Snakehead smuggling fee• Physical risk• Separation from family

Let’s initially ignore psychic benefits and costs, and physical risk,

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40Age of

Worker

Earnings(dollars)

Foregone Earnings

Snakehead Fee

Future Benefits = Δ Earnings

Cost, Outlays(dollars)

US Earnings

China Earnings

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Age of Worker

Earnings(thou. $)

Cost, Outlays(thou. $)

-15

2.5

𝐵−𝐶=−17.5 −17.5+5+10+15+20+25+30+35+40+425

5 1015

2025 30

3540 425

¿ $570 h𝑡 𝑜𝑢𝑠𝑎𝑛𝑑

5

10

15

2025

30

3540

45

2.5 2.5

15 15

=10*(45-2.5)

𝑃𝑉 (𝐵−𝐶 )=− 17.5− 17.5(1+𝑟 )

+5

(1+𝑟 )2+

10(1+𝑟 )3

+15

(1+𝑟 )4+

20(1+𝑟 )5

+25

(1+𝑟 )6

+30(1+𝑟 )7

+35

(1+𝑟 )8+

40(1+𝑟 )9

+(42.5 )( 1(1+𝑟 )10 +⋯+

1(1+𝑟 )19 )

¿−17.5 − 16.7+4.5+8.6+12.3+15.7+18.7+21.3+23.7+25.8+¿)

¿ $ 308 h𝑡 𝑜𝑢𝑠𝑎𝑛𝑑

• present value method - specify the discount rate and determine if PV(BENEFITS-COSTS) > 0

• internal rate of return method - How large of a discount rate is necessary to make migration profitable?

Two ways to determine whether it pays to migrate (or to go to college, etc)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5.394r = discount rate

PV(thousand $)

570

308

174

102 60 34

PV=0 if r*=.394

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40Age of

Worker

Earnings(current $)

Foregone Earnings

Snakehead Fee

Future Benefits = Δ Earnings

Cost, Outlays(dollars)

US Earnings

China Earnings

𝑃𝑉 ( 𝑀𝑖𝑔𝑟𝑎𝑡𝑒 )=∑𝑡=0

𝑇 (𝐵𝑡 −𝐶𝑡)

(1+𝑟 )𝑡

1. by future-oriented people, those with lower discount rates.

2. by the young and those with greater ability.3. as costs decrease (e.g, ↓ smuggling fee)4. as the earnings premium increases (e.g. ↑wUS-

wChina)

Human capital investments, such as going to college or migrating to another country, are more likely to be made

1. The Immigration Reform and Control Act of 1986 had the (unintended) effect of making it easier to get “green cards” by forging work histories.

2. President Bush signed an executive orders granting amnesty to Chinese students following 1989 Tiananmen Square Massacre.

3. President Bush signed another executive order giving “enhanced consideration” for asylum to people opposing China’s family planning policies.

Three Events 1986-1989

Result: “The largest influx of illegal Chinese in the country's history entered the United States between 1988 and 1993 (The New Yorker, 4/24/2006).

0

20

40

60

80

100

120

Earnings($ per year)

Money Earnings of Full-Time, Year-Round College Graduates, 2008

Males

Females

Earnings Gap

21 27 32 37 42 47 52

Daily Californian reporter covering Berkeley riots (1970)

Op-Ed editor of The New York Times.

Trish Hall

Trish Hall is the Op-Ed editor of The New York Times. She went to UC-Berkeley where she worked as a reporter on The Daily Californian covering student demonstrations against the Vietnam War and in favor of social and educational change. After Berkeley, she spent many years working as a reporter at small newspapers around the country and then got a job as a copy editor and reporter at The Wall Street Journal. After 6 years, she left to become a food reporter for The New York Times.

In a recent interview, Trish Hall was asked how her career would have been different if she had started college in 1963 rather than 1968.

I actually know a lot of women working at newpapers who are five or ten years older and it’s completely different. When I got to The New York Times and I was the deputy food editor, there was a woman who was like an assistant, really a secretary, and she had gone to a seven sisters college—I think she had gone to Wellesley—and she was married to a lawyer and she was smart… and she was a secretary. I mean, she could have probably done more because there were women from older generations who had done more but it wasn’t really strange for her not to have done more whereas anybody my age it would have been really strange.

Suppose Trish Hall was offered a job in 1972 as an assistant at The New York Times that would have paid her $25 thousand per year but offered no prospect of advancement, creating the flat earnings profile labeled in Figure 1. Suppose she also had an offer from a small newspaper that would pay her $10 thousand a year but would have her write and edit a lot of articles. She realized that working for the small newspaper would be an investment where she would sacrifice some earnings today for higher earnings in the future. In particular, suppose her potential earnings over the 40 years of her working life if she accepted the job at the small newspaper would be:

𝐸𝑃𝐴𝑔𝑒+1=(1+𝑟∗)∙ 𝐸𝑃

𝐴𝑔𝑒 { 𝐸𝑃21=𝐸𝑆

𝑟∗=.05 − .00125 ∙ (𝐴𝑔𝑒−21)where

The amount she would invest at every age would be

𝐸𝑃𝐴𝑔𝑒−𝐸 𝐴

𝐴𝑔𝑒= (15 − .375 ∙ ( 𝐴𝑔𝑒−21 ) )

Interviewer : How much do you think your reporting now echoes 1968 and 1969, like how… Do you think that you see events differently because of that perspective?

Trish: You know…. I have no way of knowing because… you have the life you have.

Trish is saying that she doesn’t know what to compare her experiences with—she needs some comparison group to make inferences about how her reporting was affected by being at Berkeley. Empirical economists frequently make comparisons using observational data, and need to be skeptical about the validity of their comparisons. It would be easier to make inferences if economists could more frequently conduct controlled experiments.

ln (𝐸𝑎𝑟𝑛¿¿ 𝑖)=𝛽0+𝛽1 𝑆𝐴𝑇𝐶 𝑖+𝛽2 𝑆𝐴𝑇 𝑖+𝜀𝑖¿

ln (𝐸𝑎𝑟𝑛¿¿ 𝑖)=𝛽0+𝛽1 𝑆𝐴𝑇𝐶 𝑖+𝛽2 𝑆𝐴𝑇 𝑖+𝛽3 𝐷𝑟𝑖𝑣𝑒𝑖+𝜇𝑖¿True Model:

Conventional Model:

Error term

𝜀𝑖=𝛽2 𝐷𝑟𝑖𝑣𝑒𝑖+𝜇𝑖

There is an omitted variable in the error term of the conventional equation.

is the OLS estimator of

You can show that

𝐸 ( �̂�1|𝑆𝐴𝑇𝐶 𝑖,𝑆𝐴𝑇 𝑖)=𝛽1+𝛽3∙

𝑐𝑜𝑣(𝑆𝐴𝑇𝐶 𝑖,𝐷𝑟𝑖𝑣𝑒 𝑖)

𝑣𝑎𝑟 (𝑆𝐴𝑇𝐶 𝑖)

Omitted variable bias term

𝐸 ( �̂�1|𝑆𝐴𝑇𝐶 𝑖,𝑆𝐴𝑇 𝑖)=𝛽1+𝛽3∙

𝑐𝑜𝑣(𝑆𝐴𝑇𝐶 𝑖,𝐷𝑟𝑖𝑣𝑒 𝑖)

𝑣𝑎𝑟 (𝑆𝐴𝑇𝐶 𝑖)

(+) Students with greater drive are more likely to be found at schools with high average SAT scores.

(+) Variances are always positive

(+)Students with greater drive are likely to have higher adult earnings.

Hence, is likely to be an upward biased estimate of if you don’t control for the DRIVE of students. The effect of going to prestigious colleges on adult earnings is overestimated because prestigious colleges have a greater proportion of ambitious (or driven) students and ambition (or Drive) is an important determinant of adult earnings.

Adult Earnings

College SATScore

Drive of Students

Estimated effect of College SAT Score on adult earnings is likely to be smaller when you control for the drive of the students

ln (𝐸𝑎𝑟𝑛¿¿ 𝑖)=𝛽0+𝛽1 𝑆𝐴𝑇𝐶 𝑖+𝛽2 𝑆𝐴𝑇 𝑖+𝜀𝑖¿

ln (𝐸𝑎𝑟𝑛¿¿ 𝑖)=𝛽0+𝛽1 𝑆𝐴𝑇𝐶 𝑖+𝛽2 𝑆𝐴𝑇 𝑖+𝛽3 𝐷𝑟𝑖𝑣𝑒𝑖+𝜇𝑖¿True Model:

Conventional Model:

ln (𝐸𝑎𝑟𝑛¿¿ 𝑖)=𝛽0+𝛽1 𝑆𝐴𝑇𝐶 𝑖+𝛽2 𝑆𝐴𝑇 𝑖+𝛽2 𝑆𝐴𝑇 𝐶𝐴𝑖

+𝜏 𝑖¿Dale & Krueger Model:

The average score of the colleges that the student applied to () is Dale & Krueger’s proxy for the drive of the student

𝑆𝐴𝑇 𝐶 𝑖=

𝑂𝑣𝑒𝑟𝑎𝑙𝑙𝑆𝐴𝑇 𝑆𝑐𝑜𝑟𝑒𝑜𝑓 h𝑡 𝑒𝐶𝑜𝑙𝑙𝑒𝑔𝑒100

𝑆𝐴𝑇 𝐶 𝑖=

𝑂𝑣𝑒𝑟𝑎𝑙𝑙𝑆𝐴𝑇 𝑆𝑐𝑜𝑟𝑒𝑜𝑓 h𝑡 𝑒𝐶𝑜𝑙𝑙𝑒𝑔𝑒100

An additional 100 points in the average SAT score of a college is associated with 5.6% higher adult earnings holding the SAT scores of the student constant. When you control for the average scores of the colleges that the student applied to, the estimated effect of the quality of the college they attend is no longer a statistically significant determinant of adult earnings.

Caveats to Dale and Krueger’s Results

1. Very Selective Sample of Colleges

2. Upper bound estimate is economically meaningful …

3. Evidence that peer effects are very important

4. Student Heterogeneity & matching… Which school has the best economics department? The best math department? The best computer science major?

5. Poor investment if you don’t study.