Handbook of Econometrics Vols1-5 _ Chapter 44

Chapter 44 TESTING NON-NESTED HYPOTHESES The comparison of different hypotheses, . of competing models, is the basis of model specification. It may be performed along two main lines. The first one consists in associating with each model a loss function and in retaining the specification | Chapter 44 TESTING NON-NESTED HYPOTHESES C. GOURIEROUX CREST-CEPREMAP A. MONFORT CREST-1NSEE Contents 1. Introduction 2585 2. Non-nested hypotheses 2587 . Definitions 2587 . Pseudo-true values 2589 . Semi-parametric hypotheses 2590 . Examples 2591 . Symmetry of the problem 2596 3. Testing procedures 2597 . Maximum likelihood estimator under misspecification 2597 . The extended Wald test 2598 . The extended score test 2600 . The Cox procedure 2602 . Application to the choice of regressors in linear models 2605 . Applications to qualitative models 2608 4. Artificial nesting models 2610 . Examples 2610 . Local expansions of artificial nesting models 2614 . A score test based on a modified Atkinson s compound model 2618 . The partially modified Atkinson s compound model 2621 5. Comparison of testing procedures 2621 . Asymptotic equivalence of test statistics 2622 . Asymptotic comparisons of power functions 2622 . Exact finite sample results 2624 Handbook of Econometrics Volume IV Edited by . Engle and . McFadden 1994 Elsevier Science . All rights reserved 2584 C. Gourieroux and A. Monfort . Monte Carlo studies 6. Encompassing . The encompassing principle . The encompassing tests References 2625 2626 2626 2628 2633 Ch. 44 Testing Non-Nested Hypotheses 2585 1. Introduction The comparison of different hypotheses . of competing models is the basis of model specification. It may be performed along two main lines. The first one consists in associating with each model a loss function and in retaining the specification implying the smallest estimated loss. In practice the loss function is defined either by updating some a priori knowledge on the models given the available observations the Bayesian point of view or by introducing some criterion taking into account the trade-off between the goodness of fit and the complexity of the model for instance the usual adjusted R2 or the Akaike information .