Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 10

Refer to equations and . Assume that ?u = ?x, so that the population variation in the error term is the same as it is in x. Suppose that the instrumental variable, z, is slightly correlated with u: Corr(z,u) = .1. Suppose also that z and x have a somewhat stronger correlation: Corr(z,x) = .2.

(i) What is the asymptotic bias in the IV estimator?

(ii) How much correlation would have to exist between x and u before OLS has more asymptotic bias than 2SLS?

Step 1 of 2

(i)

Given that

When,

This implies,

Hence, the asymptotic bias in the IV estimator is 0.5