Journal of the Italian Statistical Society

, Volume 2, Issue 3, pp 291–307

Encompassing and indirect inference

  • Christian Gouriéroux
  • Alain Monfort

DOI: 10.1007/BF02589066

Cite this article as:
Gouriéroux, C. & Monfort, A. J. It. Statist. Soc. (1993) 2: 291. doi:10.1007/BF02589066


In the literature on encompassing [see e.g. Mizon-Richard (1986), Hendry-Richard (1990), Florens-Hendry-Richard (1987)] there is a basic contradiction: on the one hand it is said that it is not possible to assume that the true distribution belongs to one of two competing modelM1 andM2, but, on the other hand, this assumption is made in the study of encompassing tests. In this paper we first propose a formal definition of encompassing, we then briefly examine the properties of this notion and we propose encompassing tests which do not assume that the true distribution belongs toM1 orM2; these tests are based on simulations. Finally, generalizing an idea used in the definition of an encompassing test (the GET test) we propose a new kind of inference, called indirect inference, which allows for estimation and test procedures when the model is too complicated to be treated by usual methods (for instance maximum likelihood methods); the only assumption made on the model is that it can be simulated, which seems to be a minimal requirement. This new class of inference methods can be used in a large number of domains and some examples are given. The present paper is based on Gouriéroux-Monfort (1992), and Gouriéroux-Monfort-Renault (1993), respectively GM and GMR hereafter.

Copyright information

© Societa Italiana di Statistica 1993

Authors and Affiliations

  • Christian Gouriéroux
    • 1
  • Alain Monfort
    • 2
  1. 1.ENSAE-CRESTParisFrance
  2. 2.Unité de Recherche INSEEParisFrance