Consider the simple regression modely = β0+ β1x + uand let z be a binary instrumental vari...

Consider the simple regression model

y = β0+ β1x + u

and let z be a binary instrumental variable for x. Use (15.10) to show that the IV estimator can be written as

where and are the sample averages of and over the part of the sample with = 0, and where and are the sample averages of y. and x. over the part of the sample with = 1. This estimator, known as a grouping estimator, was first suggested by Wald (1940).