Chapter 5 Model choice and specification analysis

This chapter discusses statistical theories of model selection and traditional problems. One important source of model-selection problems is the existence of a priori opinion that constraints are likely. Statistical testing is then designed either to determine if a set of constraints is true or to determine if a set of constraints is approximately true. The solution to these two problems that might be supposed to be essentially the same, in fact diverge in two important respects: (1) the first problem leads clearly to a significance levelthat is a decreasing function of sample size, whereas (2) the second problem selects a relatively constant significance level. The problem has a set of alternative modelsthat is determined entirely from a priori knowledge, whereas the second problem can have a data-dependent set of hypotheses. Quadratic loss functions are discussed in the chapter both with and without fixed costs. Quadratic loss does not imply a model-selection problem. The chapter also discusses problems that are not well known.