Instrumental Variables Estimation

Question 1

What is instrumental variables estimation (IV)?

Answer 1

Instrumental variables estimation is used to address endogeneity in regression models. Endogeneity is a situation where a predictor variable (x) is correlated with the error term (u), leading to biased and inconsistent estimates of the model parameters. Violating OLS assumptions.

Question 2

Problem Setup & Derivation for simple regression

Answer 2

y = B0+B1x+u, with Cov(x,u) does not equal 0.

Question 2

Instrumental Variable (z) must satisfy what two conditions?

Answer 2

Relevance: Cov(z,x) must not equal 0.

Exogeneity: Cov(z,u) = 0

z is correlated with endogenous regressor, z is uncorrelated with u

Question 3

Multiple regression IV (2SLS)

Answer 3

For a multiple linear regression model: y=B0+B1x1+B2x2+u

First stage: Regress x1 on all instruments z and exogenous variables.

Second stage: Regress y on predicted a1 and a2.

Question 4

What is a weak instrument?

Answer 4

If the correlation between z and x is small, estimates are biased and imprecise. We want to avoid instruments with low explanatory power.