So far, we have used a simple approach to instrumental variables (IV). We have estimated the causal effect of an IV on the treatment by weighting the effect of the IV on the treatment by the proportion of people who actually complied with the treatment. This is called the Wald (IV) estimator. However, now that we understand the Frisch-Waugh Theorem, we can take a more sophisticated approach to IV regression: two-stage least squares (2SLS). 2SLS allows us to identify the random variation in our treatment \(D\) that has been induced by the instrument \(Z\). In this lesson, you will learn how to do 2SLS.

Lecture slides.

Reading: Angrist and Pischke (2014, Ch. 3 Instrument Variables, Pages 123-146).