Consider the linear regression model y = X + u, u IID(0, 2 In), where y and u are n 1, X is n k and non-random, and is k 1.

Let W be an n l non-random matrix of instruments with l > k.

The test of overidentifying restrictions in this model can be derived from the test regression

u = Wb + error term, where u = yX IV are the IV residuals, as n times the uncentered R2 from the test regression.

Show that this test statistic is equal to the Sargan test statistic, that is, the minimized IV criterion function for the model divided by the IV estimate of the error variance for the model.