Two Applications of the Random Coefficient Procedure: Correcting for Misspecifications in a Small Area Level Model and Resolving Simpson's Paradox

We apply a random-coefficient framework to deal with two problems frequently encountered in applied work. First, we use a real-world relationship to derive from it a sub-relationship among fewer variables without introducing a single specification error to correct misspecifications in a small area level model. Second, we use this framework to resolve Simpson’s paradox. We show that this paradox does not arise if a statistical relationship between a pair of variables is derived from the corresponding real-world relationship involving all relevant variables including the original pair without introducing a single specification error.