I derive the exact distribution of the exact determined instrumental variable estimator using a geometric approach. The approach provides a decomposition of the exact estimator. The results show that by geometric reasoning one may efficiently derive the distribution of the estimation error. The...

Nonlinear relationships are common in economic theory, and such relationships are also frequently tested empirically. We argue that the usual test of nonlinear relationships is flawed and derive the appropriate test for a U-shaped relationship. Our test gives the exact necessary and sufficient...