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Logiques et tests d'hypothèses : réflexions sur les problèmes mal posés en économétrie

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  • Jean-Marie Dufour

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Abstract

In this text, we review recent developments in econometrics from the viewpoint of statistical test theory. We first review some basic principles of philosophy of science and statistical theory, emphasizing parsimony and falsifiability as criteria for evaluating models, test theory as a formalization of the falsification principle for probabilistic models, and the logical foundation of basic notions in test theory (such as the level of a test). We then show that some of the most frequently used statistical and econometric methods are fundamentally inappropriate for the problems and models considered, while several hypotheses, for which test procedures are commonly proposed, are not testable at all. Such situations lead to ill-defined statistical problems. We analyze several cases of such problems: (1) building confidence intervals in structural models where identification problems may be present; (2) the construction of tests for nonparametric hypotheses, including procedures robust to heteroskedasticity, non-normality or dynamic specification. We point out that these difficulties often originate from the ambition to weaken regularity conditions typically required by statistical analysis, and from an inappropriate use of asymptotic distributional theory. Finally, we underscore the importance of formulating testable hypotheses and models, and of developing econometric methods with provable finite-sample properties. Dans ce texte, nous analysons les développements récents de l'économétrie à la lumière de la théorie des tests statistiques. Nous revoyons d'abord quelques principes fondamentaux de philosophie des sciences et de théorie statistique, en mettant l'accent sur la parcimonie et la falsifiabilité comme critères d'évaluation des modèles, sur le rôle de la théorie des tests comme formalisation du principe de falsification de modèles probabilistes, ainsi que sur la justification logique des notions de base de la théorie des tests (telles que le niveau d'un test). Nous montrons ensuite que certaines des méthodes statistiques et économétriques les plus utilisées sont fondamentalement inappropriées pour les problèmes et modèles considérés, tandis que de nombreuses hypothèses, pour lesquelles des procédures de test sont communément proposées, ne sont en fait pas du tout testables. De telles situations conduisent à des problèmes statistiques mal posés. Nous analysons quelques cas particuliers de tels problèmes: (1) la construction d'intervalles de confiance dans le cadre de modèles structurels qui posent des problèmes d'identification; (2) la construction de tests pour des hypothèses non paramétriques, incluant la construction de procédures robustes à l'hétéroscédasticité, à la non-normalité ou à la spécification dynamique. Nous indiquons que ces difficultés proviennent souvent de l'ambition d'affaiblir les conditions de régularité nécessaires à toute analyse statistique ainsi que d'une utilisation inappropriée de résultats de théorie distributionnelle asymptotique. Enfin, nous soulignons l'importance de formuler des hypothèses et modèles testables, et de proposer des techniques économétriques dont les propriétés sont démontrables dans les échantillons finis.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2001s-40.

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Date of creation: 01 May 2001
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Handle: RePEc:cir:cirwor:2001s-40

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Keywords: Econometrics; statistics; testing. philosophy of science; falsifiability; Popper; parsimony; identification; weak instruments; nonparametric model; time series; autoregressive model; heteroskedasticity; unit root; robust method; non-normality; ill-defined problem; Économétrie; statistique; théorie des tests; philosophie des sciences; falsifiabilité; Popper; parcimonie; identification; instruments faibles; modèle non paramétrique; séries chronologiques; modèle autorégressif; hétéroscédasticité; racine unitaire; méthode robuste; non-normalité; problème mal posé;

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Cited by:
  1. DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 2003-12, Universite de Montreal, Departement de sciences economiques.
  2. Abdelhamid El Bouhadi, 2003. "Conditional Volatility Of Most Active Shares Of Casablanca Stock Exchange," Finance 0305007, EconWPA, revised 10 Oct 2003.

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