How the (Econometric) Sausage is Made

Guest post by Jonathan Roth Many interesting questions in economics involve the causal effect of a treatment that was not randomly assigned. Luckily, empirical researchers often find creative ways to circumvent endogeneity issues.  One way to get creative is to use an instrumental variable (IV). Consider the following example: we want to know the causal effect of attending a private school (X) on test scores (Y). Define the potential outcomes of a student attending (X=1) and not attending (X=0) a private school as Y(1) and Y(0), respectively. The individual-level causal effect of attending versus not attending is the difference in potential outcomes, Y(1)-Y(0). With heterogeneity in the treatment effects, this difference will vary across all students.  If we suspect that choice of school is endogenous, we can instrument for X using information on whether you were offered a voucher that reduces the cost of private school (Z). For Z to be a valid instrument, it must obey certain properti