2b.

Question 1

What does this graph show?

Answer 1

Ace has a discount rate of r, and given his MRR he would choose 11 years of schooling.

(This means he does not finish high school and drops out, earning Wdrop)

Question 2

Why does Bob face a MRR that is higher for every year of education?

Answer 2

BECAUSE HE IS MORE ABLE!

So his wage returns from schooling will also be higher for all levels of schooling.

Question 3

Imagine both Bob and Ace have the same discount rate (r), what happens?

Answer 3

Bob has the same discount rate (r) but chooses an extra year of schooling simply because he is more able and thus faces a higher MRR for all schooling levels.

Earning him Wgrad (remember = he is more able to his wage returns are higher for all levels of schooling)

Question 4

How does the wage-differential between Bob and Ace arise?

Answer 4

WATCH OUT!!!

It arises BOTH because Bob attends 1 more year or school, and ALSO because Bob is more ABLE

Question 5

Show the Ability bias / True return to schooling in the diagram

Answer 5

Question 6

Explain the “True return to schooling” in the diagram:

Answer 6

The blue bracket shows the true return to schooling

This is because Bob attended one more year of school, so, if Ace were to have done the same, he would have earned Wace. So that part of the wage differential is attributed to schooling.

Question 7

Explain the “ability bias” in the diagram:

Answer 7

The red bracket is the extra wage difference coming from Bob having higher ability than Ace (Bob’s wage-schooling locus is greater than Ace’s).

Question 8

What is the ability bias formally?

Answer 8

Key assumption in OLS: the error term is not correlated with schooling.

But if more able people tend to get more schooling,
schooling is correlated with the error…

That BREAKS the OLS assumption.
​
Result: OLS tends to overestimate β, because some of the wage advantage from ability gets incorrectly credited to schooling.

Question 9

Why does this equation overestime Beta?

Answer 9

Because it doesn’t account for ability

Question 9

What does each element in the generalised equation mean?

Answer 9

Question 10

What variable would be added to account for ability in this equation?

Answer 10

Question 11

What are the three ways in which economists have attempted to estimate Beta more credibly?

Answer 11

1. Proxy for ability
2. Instrumental Variables
3. Twins/ sibling differences

Question 12

What is a “proxy for ability”?

Answer 12

Use something observable that’s related to ability (test scores, grades, IQ, etc.). Not perfect, but helps.

Question 13

What are “Instrumental Variables (IV)”?

Answer 13

Find a variable that affects schooling but (ideally) doesn’t directly affect wages except through schooling (e.g., changes in compulsory schooling laws, distance to college). This can remove ability bias.

Question 14

What are “Twins / sibling differences”?

Answer 14

Compare twins (especially identical twins): ability is assumed very similar, so differences in wages are more plausibly due to differences in schooling.

Question 15

What are problems with twin studies?

Answer 15

• Many UK and US studies are based on small sample sizes make estimates less reliable (and unable to test between estimation methods – no large sample properties).
• Returns to schooling are assumed linear. Every extra year of schooling has the same return– unlikely!
• Do not compare the return to specific `qualifications’ only schooling. Some degrees are worth more than others – heterogeneous returns!
• Based on the assumption that twins have the same ability

Question 16

Why is the standard error for Instrumental Variables always greater?

Answer 16

IVs uses only the variation in schooling that’s explained by the instrument(s). That “usable” variation is typically smaller than the total variation OLS uses, so the estimate is less precise → bigger standard errors (especially with weak instruments).

Question 17

What is an example of an “Instrumental Variable” study?

Answer 17

Esther Duflo uses Indonesia’s INPRES primary-school construction as an instrument for schooling. Some regions got many new schools while others got few, and only younger cohorts could benefit. This created plausibly exogenous variation in years of education. She estimates returns by using school-building intensity (often × being young enough) to predict schooling (first stage), then using predicted schooling to explain wages (second stage). This reduces ability/selection bias because schooling changes come from policy-driven school access, not individual ability.

Question 18

Which job has seen large wage increases? (1994-2011)

Answer 18

Tech/ Engineering (0.066 log points)

Question 19

What does this show?

Answer 19

Greater variance in wages!
-> Especially within subjects

People with econ degrees in 1990 were all kind of earning the same, but since then variance exploded

Question 20

Did variance of log wages by suject degree increase?

Answer 20

YES - for basically every subject (1994-2011)

Question 21

Why is the dispersion of wages within degree subjects increasing?

Answer 21

1. Supply Side: As more individuals are accepted onto degree courses, a wider range of ability will be observed amongst graduates.
2. Demand Side: Employers have increased their demand for graduates of some subjects more than others, so some graduates find themselves in lower paid jobs.

! MISMATCHES !

Question 22

How do demand/supply mismatches contribute to the increasing variance in log wages?

Answer 22

Mismatches refers to people studying something but working in something else (usually do to a demand/supply mismatch). This result in greater variance in log wages!

Question 23

What does this show?

Answer 23

VARIANCE plotted!

But if you control for test scores (proxy of ability?) - the curve flattens greatly…

This means most of the inequality in wages is driven by the inequality of the abilities of people entering these professions.

Question 24

Import summary notes:

Answer 24

- Most of the increase in graduate wage inequality has been within subjects (mostly Non-STEM). (mainly due to an increasingly wider range of ability of students within subjects) - Graduate wage inequality growth would have been flat if it were not for the increase in the variance of cognitive skill.

Question 25

How would you solve this mock question?

Answer 25

Calculate the NPV's !

Question 26

Ability bias ________ the true returns to education

Answer 26

Ability bias OVERESTIMATES the true returns to education

Question 27

Measurement error ____________ the true returns to education

Answer 27

Measurement error UNDERESTIMATES the true returns to education