Encompassing: Concepts and Implementation

30 Pages Posted: 2 Dec 2008

See all articles by Christophe Bontemps

Christophe Bontemps


Grayham E. Mizon

University of Southampton - Division of Economics


The encompassing principle has been carefully and precisely defined in various contexts, since its first appearance in the 1980s literature in numerous papers by Hendry, Mizon and Richard. Since then, several distinct notions of encompassing have been proposed and still coexist in the literature. We describe, illustrate and connect these notions in this paper. We start with the intuitive properties of exact encompassing between estimated models and compare it with its testable counterpart, approximate encompassing. We examine these notions and their main properties within static and dynamic, parametric and non-parametric, classical and Bayesian models and estimators. Encompassing or the lack of encompassing, is also studied via the concepts of parsimonious and partial encompassing. Pseudo-true values, which are central elements in measuring and testing approximate encompassing, are defined in line with the concept of specificity between models. We also examine the role played by the data generating process in the different approaches in the literature.

Suggested Citation

Bontemps, Christophe and Mizon, Grayham E., Encompassing: Concepts and Implementation. Oxford Bulletin of Economics and Statistics, Vol. 70, Issue s1, pp. 721-750, December 2008, Available at SSRN: https://ssrn.com/abstract=1307310 or http://dx.doi.org/10.1111/j.1468-0084.2008.00528.x

Christophe Bontemps (Contact Author)

ESR-INRA ( email )

Chemin de Borde-Rouge
Auzeville B.P. 27
Castanet-Tolosan Cedex, 31326

Grayham E. Mizon

University of Southampton - Division of Economics ( email )

Southampton, SO17 1BJ
United Kingdom
+44 (0)23 80 592519 (Phone)
+44 (0)23 8059 3858 (Fax)

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