Instrumental Variables

Question 1

How does IV solve the problem of omitted variables?

Answer 1

If you find a good IV no omitted variables are present as there is no correlation to the other factors and it also solves reverse causality

Question 2

Explain the steps in IV estimation

Answer 2

1. Isolate the exogenous variation in the variable of interest due to the instrument (first stage): regressions where T is dependent and Z is independent variable
2. Estimate the impact of the instrument on the outcome (reduced form): regression with Y as dependent and Z is independent variable
3. Divide reduced form by first stage

Effect of Z on Y = Effect Z on T * Effect T on Y
Effect T on Y = Effect Z on Y / Effect Z on T

Question 3

Why does IV estimate a Local Average Treatment Effect (LATE) on basis of compliers?

Answer 3

Compliers are people that change their treatment due to the instrument. IV does not measure the ATT because this also includes always-takers.

Question 4

Assumptions of IV (whether and how they can be tested)

Answer 4

1. Instrument must causal effect on T: F-stat should be > 10
2. Instrument should be uncorrelated with (other determinant of) Y (= independence assumption): cannot be tested
3. The instrument has no direct effect on Y, only through T (= exclusion restriction): cannot be tested

Question 5

Limitations of IV, trade-off between internal and external validity

Answer 5

Effect only applies to those who changed treatment status due to the instrument - estimate is a Local Average Treatment Effect (LATE) and extrapolation to other groups is not possible
Independence assumption and exclusion restriction cannot be verified
LATE is internally valid but not very externally valid because not generalizable to whole population