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Identification, Weak Instruments and Statistical Inference in Econometrics

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  • Jean-Marie Dufour
Abstract
We discuss statistical inference problems associated with identification and testability in econometrics, and we emphasize the common nature of the two issues. After reviewing the relevant statistical notions, we consider in turn inference in nonparametric models and recent developments on weakly identified models (or weak instruments). We point out that many hypotheses, for which test procedures are commonly proposed, are not testable at all, while some frequently used econometric methods are fundamentally inappropriate for the models considered. Such situations lead to ill-defined statistical problems and are often associated with a misguided use of asymptotic distributional results. Concerning nonparametric hypotheses, we discuss three basic problems for which such difficulties occur: (1) testing a mean (or a moment) under (too) weak distributional assumptions; (2) inference under heteroskedasticity of unknown form; (3) inference in dynamic models with an unlimited number of parameters. Concerning weakly identified models, we stress that valid inference should be based on proper pivotal functions - a condition not satisfied by standard Wald-type methods based on standard errors - and we discuss recent developments in this field, mainly from the viewpoint of building valid tests and confidence sets. The techniques discussed include alternative proposed statistics, bounds, projection, split-sampling, conditioning, Monte Carlo tests. The possibility of deriving a finite-sample distributional theory, robustness to the presence of weak instruments, and robustness to the specification of a model for endogenous explanatory variables are stressed as important criteria assessing alternative procedures. Nous analysons les problèmes d'inférence associés à l'identification et à la testabilité en économétrie, en soulignant la similarité entre les deux questions. Après une courte revue des notions statistiques requises, nous étudions tour à tour l'inférence dans les modèles non-paramétriques ainsi que les résultats récents sur les modèles structurels faiblement identifiés (ou les instruments faibles). Nous remarquons que beaucoup d'hypothèses, pour lesquelles des tests sont régulièrement proposés, ne sont pas en fait testables, tandis que plusieurs méthodes économétriques fréquemment utilisées sont fondamentalement inappropriées pour les modèles considérés. De telles situations conduisent à des problèmes statistiques mal posés et sont souvent associées à un emploi mal avisé de résultats distributionnels asymptotiques. Concernant les hypothèses non-paramétriques, nous analysons trois problèmes de base pour lesquels de telles difficultés apparaissent: (1) tester une hypothèse sur un moment avec des restrictions trop faibles sur la forme de la distribution; (2) l'inférence avec hétéroscédasticité de forme non spécifiée; (3) l'inférence dans les modèles dynamiques avec un nombre illimité de paramètres. Concernant les modèles faiblement identifiés, nous insistons sur l'importance d'utiliser des fonctions pivotales - une condition qui n'est pas satisfaite par les méthodes usuelles de type Wald basées sur l'emploi d'écart-types - et nous passons en revue les développements récents dans ce domaine, en mettant l'accent sur la construction de test et régions de confiance valides. Les techniques considérées comprennent les différentes statistiques proposées, l'emploi de bornes, la subdivision d'échantillon, les techniques de projection, le conditionnement et les tests de Monte Carlo. Parmi les critères utilisés pour évaluer les procédures, nous insistons sur la possibilité de fournir une théorie distributionnelle à distance finie, sur la robustesse par rapport à la présence d'instruments faibles ainsi que sur la robustesse par rapport la spécification d'un modèle pour les variables explicatives endogènes du modèle.

Suggested Citation

  • Jean-Marie Dufour, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," CIRANO Working Papers 2003s-49, CIRANO.
    • Handle: RePEc:cir:cirwor:2003s-49
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    More about this item

    Keywords

    hypothesis testing; confidence set; confidence interval; identification; testability; asymptotic theory; exact inference; pivotal function; nonparametric model; Bahadur-Savage; heteroskedasticity; serial dependence; unit root; simultaneous equations; structural model; instrumental variable; weak instrument; weak identification; simultaneous inference; projection; split-sample; conditional test; Monte Carlo test; bootstrap; test d'hypothèse; région de confiance; intervalle de confiance; identification; testabilité; théorie asymptotique; inférence exacte; fonction pivotale; modèle non-paramétrique; Bahadur-Savage; hétéroscédasticité; dépendance sérielle; racine unitaire; équations simultanées; modèle structurel; variable instrumentale; instrument faible; inférence simultanée; projection; subdivision d'échantillon; test conditionnel; test de Monte Carlo; bootstrap;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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