We study the invariance properties of various test criteria which have been proposed for hypothesis testing in the context of incompletely specified models, such as models which are formulated in terms of estimating functions (Godambe, 1960, Ann. Math. Stat.) or moment conditions and are estimated by generalized method of moments (GMM) procedures (Hansen, 1982, Econometrica), and models estimated by pseudo-likelihood (Gouri´eroux, Monfort and Trognon, 1984, Econometrica) and M-estimation methods. The invariance properties considered include invariance to (possibly nonlinear) hypothesis reformulations and reparameterizations. The test statistics examined include Wald-type, LR-type, LM-type, score-type, and C()−type criteria. Extending the approach used in Dagenais and Dufour (1991, Econometrica), we show first that all these test statistics except the Wald-type ones are invariant to equivalent hypothesis reformulations (under usual regularity conditions), but all five of them are not generally invariant to model reparameterizations, including measurement unit changes in nonlinear models. In other words, testing two equivalent hypotheses in the context of equivalent models may lead to completely different inferences. For example, this may occur after an apparently innocuous rescaling of some model variables. Then, in view of avoiding such undesirable properties, we study restrictions that can be imposed on the objective functions used for pseudo-likelihood (or M-estimation) as well as the structure of the test criteria used with estimating functions and GMM procedures to obtain invariant tests. In particular, we show that using linear exponential pseudo-likelihood functions allows one to obtain invariant scoretype and C()−type test criteria, while in the context of estimating function (or GMM) procedures it is possible to modify a LR-type statistic proposed by Newey and West (1987, Int. Econ. Rev.) to obtain a test statistic that is invariant to general reparameterizations. The invariance associated with linear exponential pseudo-likelihood functions is interpreted as a strong argument for using such pseudo-likelihood functions in empirical work.

Voir le document

Dernières publications

2017RP-03 RP
La surqualification professionnelle chez les diplômés des collèges et des universités : État de la situation au Québec
Brahim Boudarbat et Claude Montmarquette
Voir le document

2017s-11 CS
The social cost of contestable benefits
Arye Hillman et Ngo Van Long
Voir le document

2017s-09 CS
Fiscal Surprises at the FOMC
Dean Croushore et Simon van Norden
Voir le document

2017MO-04 MO
Méthodes avancées d’évaluation d’investissements / Advanced Methods of Investment Evaluation - Tome 2
Marcel Boyer
Voir le document

2017MO-03 MO
Méthodes avancées d’évaluation d’investissements / Advanced Methods of Investment Evaluation - Tome 1
Marcel Boyer
Voir le document


Centre interuniversitaire de recherche en analyse des organisations
1130 rue Sherbrooke Ouest, suite 1400
Montréal, Québec (Canada) H3A 2M8
(514) 985-4000
(514) 985-4039
reception@cirano.qc.ca

© 2017 CIRANO. Tous droits réservés.



Partenaire de :