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^

1 can be written as b^

1 5 1y1 2 y0 2/1x1 2 x0 2, 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).