ECON323 Lecture Notes - Lecture 2: Ziz, Heteroscedasticity, Instrumental Variable

• School: University of Waterloo
• Department: Economics
• Course: ECON323
• Professor: Emmanuelle Pierard

Document Summary

Using iv, we can still estimate the relationship. Let y = + x + where cov(x, ) 6= 0. We have variable z, an instrumental variable, such that (1) cov(z, )=0 and (2) cov(x, z) 6= 0 athese notes are based on wooldridge, 2016. Cov(z, )=0 implies that z should have no e ect on y after x has been controlled for: we call this instrument exogeneity. Cov(x, z) 6= 0 implies that the endogenous regressor has to be related to the instrument: we call this instrument relevance. X = + z + where = cov(x,z) we can reject h0: =0 using a t-test. : good ivs do not make good proxies and vice versa. Cov(z, y ) = cov(z, x) + cov(z, ) which can be solved for b = cov(z,y ) : when z=x, we obtain the ols estimator of : this makes sense as if x is exogenous, it can be used as its own instrument.