Several estimation procedures such as the efficient method of moments
(EMM) of Gallant and Tauchen (1996,
Econometric Theory 12, 657–681) and indirect inference
procedure of Gouriéroux, Monfort, and Renault (1993, Journal of Applied Econometrics 8,
S85–S118) involve two models, an auxiliary one and a model of
interest. The role played by both models poses challenges and provides
new opportunities for hypothesis testing beyond the usual Wald-,
Lagrange multiplier–, and likelihood ratio–type tests. In
this paper we present and derive the asymptotic distribution theory for
various classes of tests for structural change. Some procedures are
extensions of standard tests, whereas others are specific to the dual model
setup and exploit its unique features.The
first author gratefully acknowledges financial support from Fonds pour la
Formation de Chercheurs et l'aide à la Recherche (FCAR). The
second author acknowledges the financial support of the Natural Sciences and
Engineering Research Council of Canada through a grant to NCM2 (Network for
Computing and Mathematical Modeling). We also thank Alastair Hall and
Éric Renault for comments on an earlier draft of the
paper.