Instrumental Variables

Question 1

What are the three experimental paths to create other things equal?

Answer 1

instrumental variables

regression discontinuity design

difference in difference

Question 2

What does λ denote?

Answer 2

causal effect of interest
it is the causal effect

same as beta but different letter to distinguish it- this is the parameter of interest

Question 3

What is an instrumental variable?

Answer 3

Variable that has to be satisfied by two conditions - these are at the vore of the instrumental variables

Covariance between instrumental variable and treatment variable
but
instrumental variable cannot be correlated with the error term
if both of these conditions are satisfied aids in the reduction of selection bias

Question 4

What is the equation to work out λIV?

Answer 4

φ= first stage
ρ= reduce form
so λIV= reduced form/first stage

E[Yi|Zi =1] - E[Yi|Zi=0] = φ
divided by
E[Di|Zi=1] - E[Di|Zi = 0] =ρ

Question 5

What are some examples of non-experimental IV?

Answer 5

China’s one child policy
- quantity-quality trade off - family size and living standard

Question 6

What makes a good IV?

Answer 6

1. First stage - the IV affects the causal channel of interest
2. Independence assumption: IV is as good as randomly assigned - no difference in the unobservables
3. Exclusion restriction: IV affects the outcome only through a single causal channel - the treatment

Question 7

Is IV valid?

Answer 7

Internal validity
- effect on compliers
-doesnt say anything about the never or always takers
ie. people whos decisions are not impacted by the instrument eg. the lottery ticket

Externally
- when treatment status is not determined through the IV mechanisms in other context
- have to think if external people are similar to our scompliers - might not be the same

Question 8

What are the two regressions used by IV?

Answer 8

Reduced form
Yi = α + ρZi + εi

First stage
Di = α + φZi + μi

λIV= reduced form/1st stage

Question 9

what is the equation for the first stage?

Answer 9

Di= a + OZi + ui

Question 10

What is the equation for the reduced stage

Answer 10

Yi = a + pZi + ei

Question 11

What does the first stage do?

Answer 11

the IV affects the causal channel of interest

Question 12

Does Di have to randomly assigned?

Answer 12

No does not require it to be as good as randomly assigned - assumption in a ranodmised control trial

we argue that Zi is as good as randomly assigned - use it to predict Di in the first stage

Question 13

What is the relationship betwen the independence assumption and the exclusion restriction

Answer 13

as long as you satisfy the indepdence assumption the exclusion restriction is automatically satisfied

Question 14

What is challenging about this method?

Answer 14

the indepdent assumption is a strong assumption therefore it has to be convincing