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Semi-Parametric Weak Instrument Regressions with an Application to the Risk-Return Trade-off

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  • Benoit Perron

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Abstract

Recent work shows that a low correlation between the instruments and the included variables leads to serious inference problems. We extend the local-to-zero analysis of models with weak instruments to models with estimated instruments and regressors and with higher-order dependence between instruments and disturbances. This framework is applicable to linear models with expectation variables that are estimated non-parametrically such as the risk-return trade-off in finance and the impact of inflation uncertainty on real economic activity. Our simulation evidence suggests that Lagrange Multiplier (LM) confidence intervals have better coverage in these models. We apply these methods to excess returns on the S&P 500 index, yen-dollar spot returns, and excess holding yields between 6-month and 3-month Treasury bills. Des recherches récentes démontrent qu'une corrélation faible entre les instruments et les variables explicatives peut mener à de sérieux problèmes d'inférence dans les régressions avec variables instrumentales. Nous étendons l'analyse locale à zéro des modèles avec instruments faibles aux modèles avec des instruments et régresseurs estimés et avec de la dépendance dans les moments supérieurs. Ainsi, cet environnement devient applicable aux modèles linéaires avec des variables anticipatoires qui sont estimées de façon non paramétrique. Deux exemples de tels modèles sont la relation entre le risque et les rendements en finance et l'impact de l'incertitude de l'inflation sur l'activité économique réelle. Nos résultats démontrent que l'inférence basée sur les tests du multiplicateur de Lagrange (LM) est plus robuste à la présence d'instruments faibles que l'inférence basée sur les tests de Wald. En utilisant des intervalles de confiance construits selon les tests de LM, nous concluons qu'il n'y a pas de prime de risque significative dans les rendements de l'indice S&P 500, les rendements excédentaires entre les Bons du Trésor de 6 mois et de 3 mois et les rendements du taux de change spot entre le yen japonais et le dollar américain.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2002s-88.

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Date of creation: 01 Nov 2002
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Handle: RePEc:cir:cirwor:2002s-88

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Keywords: Instrumental Variables; Weak Instruments; Local-to-Zero Analysis; LM Tests; Wald Tests; Risk Premium; Expectations; Semi-Parametric Models; Kernel; Variables instrumentales; instruments faibles; analyse locale à zéro; tests du multiplicateur de Lagrange; tests de Wald; prime de risque; anticipations; modèles semi-paramétriques; noyau;

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Cited by:
  1. Dufour, Jean-Marie & Taamouti, Mohamed, 2007. "Further results on projection-based inference in IV regressions with weak, collinear or missing instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.
  2. DUFOUR, Jean-Marie, 2003. "Identification, Weak Instruments and Statistical Inference in Econometrics," Cahiers de recherche 10-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.

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