QE 5/6 - applied micro

Question 1

Describe 4 groups in world of imperfect compliance in terms

Answer 1

Compliers: Di(1) = 1, Di(0) = 0

Always-takers: Di(1) = 1, Di(0) = 1

Never-takers: Di(1) = 0, Di(0) = 0

Defiers: Di(1) = 0, Di(0) = 1

Question 2

Given LATE theorem, what are the causal effects for each of the 4 groups?

Answer 2

1. Compliers: Yi(1,1) – Yi(0,0) = Yi(1) – Yi(0)
2. Always-takers = 0 (exclusion restriction)
3. Never-takers = 0 (exclusion restriction)
4. Defiers don’t exist (monotonicity assumption)

Question 3

1. How does ITT relate to the LATE?
2. When would LATE = ITT
3. Explain intuition

Answer 3

1. ITT = lower bound for LATE
2. If compliers were 100% of population, then LATE = ITT

3a. LATE = scaled-up version of ITT (by % of compliers)
3b. Whereas ITT includes everyone (even non-compliers who weren’t actually treated), so treatment effect diluted among non-treated

Question 4

In education example, how do we obtain ability bias if we can only observe the ‘short regression’ without ability?

Answer 4

1. Start with short regression
2. Write out coefficient on schooling
3. Sub into this from the long regression

Question 5

Features of classical measurement error

Answer 5

1. Expected value of zero

2. Not correlated with anything

Question 6

What is attenuation bias?

Answer 6

Measurement error causes coefficient to be biased towards zero (this bias = attenuation bias)

Question 7

Why is adding additional regressors potentially bad if there is measurement error?

Answer 7

Worsens attenuation bias

Question 8

How does a ‘regression in differences’ using twins help control for (unobservable) omitted variable ability?

Answer 8

1. Ability plausibly the same within pairs of twins

2. So regression in differences allows us to remove effect of ability (control for it) without directly observing it

Question 9

Why use 2SLS regression for IV?

Answer 9

1. Can use multiple instruments (e.g. 3 QOB dummies)
2. Can add control variables (e.g. 9 year of birth dummies to control for fact that average schooling levels increased over time)

Question 10

Why does 2SLS/IV regression only give the LATE?

Answer 10

Only gives effect for those for whom the instrument changed their decision (e.g. stayed in school due to birth quarter, but otherwise would have dropped out)