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 a sub-relationship among fewer variables without introducing any specification error to correct misspecifications in a small area level model. Second, we then 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.