3 Consider the simple regression model y 5 b0 1 b1x 1 u and let z be a binary instrumental variable for x. Use (15.10) to show that the IV estimator b ˆ 1 can be written as bˆ 1 5 ( - y1 2 - y0)/(- x1 2 - x0), where - y0 and - x0 are the sample averages of yi and xi over the part of the sample with zi 5 0, and where - y1 and - x1 are the sample averages of yi and xi over the part of the sample with zi 5 1. This estimator, known as a grouping estimator, was first suggested by Wald (1940).