Question

Problem 4: Instrumental Variables 4a. What are the two requirements for a valid instrument? We're interested in estimating B, in Wage, BoBEducation,+ u but we have a problem with omitted-variable bias. Instrumental variables can potentially help. 4b. As we've discussed, we need an instrument for (endogenous) education. Do you think the number of children would be a valid instrument? Explain why it passes/fails ech of the two requirements for a valid instrument 4c. Which estimates would you trust more-OLS or IV, where number-of-children is your instrument? Explain

Answer 1

(a) If Z is an instrument variable, then it must be the case that-

i. Cov(Z,u) = 0 i.e. Instrument Z is exogenous - It is also called instrument exogeneity
ii. Cov(Z,X) ≠ 0 i.e. instrument Z and variable X are correlated to each other - It is also called instrument relevance.

(b) Let us check for both conditions:

i. Cov( Education, Number of children) ≠ 0 i.e. Instrument is relevant. This is satisfied because educated people are expected to have lesser number of children.

ii. Cov( u, Number of children) = 0 i.e. instrument is exogenous. This is because the disturbance term captures ability (that is unobserved) which is correlated with education. Number of children and ability will be uncorrelated as individual's ability (IQ) won't affect number of children.

(c) I would trust IV estimates since these estimates are expected to be consistent and unbiased over large samples.