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Finite Sample Inference Methods for Simultaneous Equations and Models with Unobserved and Generated Regressors

  • Jean-Marie Dufour
  • Joanna Jasiak

We propose finite sample tests and confidence sets for models with unobserved and generated regressors as well as various models estimated by instrumental variables methods. The validity of the procedures is unaffected by the presence of identification problems or weak instruments, so no detection of such problems is required. We study two distinct approaches for various models considered by Pagan (1984). The first one is an instrument substitution method which generalizes an approach proposed by Anderson and Rubin (1949) and Fuller (1987) for different (although related) problems, while the second one is based on splitting the sample. The instrument substitution method uses the instruments directly, instead of generating regressors, in order to test hypotheses about the structural parameters of interest and build confidence sets. The second approach relies on generated regressors, which allows a gain in degrees of freedom, and a sample split technique. For inference about general possibly nonlinear transformations of model parameters, projection techniques are proposed. A distributional theory is obtained under the assumptions of Gaussian errors and stricly exogenous regressors. We show that the various tests and confidence sets proposed are (locally) asymptotically valid under much weaker assumptions. The properties of the tests proposed are examined in simulation experiments. In general, they outperform the usual asymptotic inference methods in terms of both reliability and power. Finally, the techniques suggested are applied to a model of Tobin's q and to a model of academic performance. Nous proposons des tests et régions de confiance exacts pour des modèles comportant des variables inobservées ou des régresseurs estimés de même que pour divers modèles estimés par la méthode des variables instrumentales. La validité des procédures proposées n'est pas influencée par la présence de problèmes d'identification ou d'instruments faibles, de sorte que la détection de tels problèmes n'est pas requise pour les appliquer. De façon plus spécifique, nous étudions deux approches différentes pour divers modèles considérés par Pagan (1984). La première est une méthode de substitution d'instruments qui généralise des techniques proposées par Anderson et Rubin (1949) et Fuller (1984) pour des problèmes différents, tandis que la seconde méthode est fondée sur une subdivision de l'échantillon. La méthode de substitution d'instruments utilise directement les instruments disponibles, plutôt que des régresseurs estimés, afin de tester des hypothèses et de construire des régions de confiance sur les paramètres structuraux du modèle. La seconde méthode s'appuie sur des régresseurs estimés, ce qui permet un gain de degrés de liberté, ainsi que sur une technique de subdivision de l'échantillon. Pour faire de l'inférence sur des transformations générales, possiblement non-linéaires, des paramètres du modèle, nous proposons l'utilisation de techniques de projection. Nous fournissons une théorie distributionnelle exacte sous une hypothèse de normalité des perturbations et de régresseurs strictement exogènes. Nous montrons que les tests et régions de confiance ainsi obtenus sont aussi (localement) asymptotiquement valides sous des hypothèses distributionnelles beaucoup plus faibles. Nous étudions les propriétés des tests proposés dans le cadre d'une expérience de simulation. En général, celles-ci sont plus fiables et ont une meilleure puissance que les techniques traditionnelles. Finalement, les techniques proposées sont appliquées à un modèle du q de Tobin et à un modèle de performance scolaire.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2000s-13.

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Length: 38 pages
Date of creation: 01 Apr 2000
Handle: RePEc:cir:cirwor:2000s-13
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  1. Andrew B. Abel & Olivier J. Blanchard, 1983. "The Present Value of Profits and Cyclical Movements in Investment," NBER Working Papers 1122, National Bureau of Economic Research, Inc.
  2. Abel, Andrew B & Eberly, Janice C, 1994. "A Unified Model of Investment under Uncertainty," American Economic Review, American Economic Association, vol. 84(5), pages 1369-84, December.
  3. Jiahui Wang & Eric Zivot, 1998. "Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 66(6), pages 1389-1404, November.
  4. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  5. Maddala, G S, 1974. "Some Small Sample Evidence on Tests of Significance in Simultaneous Equations Models," Econometrica, Econometric Society, vol. 42(5), pages 841-51, September.
  6. Charles R. Nelson & Richard Startz, 1988. "The Distribution of the Instrumental Variables Estimator and Its t-RatioWhen the Instrument is a Poor One," NBER Technical Working Papers 0069, National Bureau of Economic Research, Inc.
  7. Dagenais, M.G. & Dufour, J.M., 1987. "Invariance, Nonlinear Models and Asymptotic Tests," Cahiers de recherche 8738, Universite de Montreal, Departement de sciences economiques.
  8. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-47, February.
  9. Hall, Alastair R & Rudebusch, Glenn D & Wilcox, David W, 1996. "Judging Instrument Relevance in Instrumental Variables Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 283-98, May.
  10. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Tests in Single Equation Autoregressive Distributed Lag Models," Cahiers de recherche 9549, Universite de Montreal, Departement de sciences economiques.
  11. Oxley, Les & McAleer, Michael, 1993. " Econometric Issues in Macroeconomic Models with Generated Regressors," Journal of Economic Surveys, Wiley Blackwell, vol. 7(1), pages 1-40.
  12. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  13. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January.
  14. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-80, January.
  15. Joshua D. Angrist & Alan B. Krueger, 1993. "Split Sample Instrumental Variables," Working Papers 699, Princeton University, Department of Economics, Industrial Relations Section..
  16. Dufour, J.-M., 1986. "Nonlinear hypotheses, inequality restrictions and non-nested hypotheses: Exact simultaneous tests in linear regressions," CORE Discussion Papers 1986016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. Montmarquette, Claude & Mahseredjian, Sophie, 1989. "Could teacher grading practices account for unexplained variation in school achievements?," Economics of Education Review, Elsevier, vol. 8(4), pages 335-343, August.
  18. Murphy, Kevin M & Topel, Robert H, 1985. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(4), pages 370-379, October.
  19. Robert J. Barro, 1976. "Unanticipated Money Growth and Unemployment in the United States," Working Papers 234, Queen's University, Department of Economics.
  20. Savin, N.E., 1984. "Multiple hypothesis testing," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 14, pages 827-879 Elsevier.
  21. Maddala, G S & Jeong, Jinook, 1992. "On the Exact Small Sample Distribution of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 60(1), pages 181-83, January.
  22. Tobin, James, 1969. "A General Equilibrium Approach to Monetary Theory," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 1(1), pages 15-29, February.
  23. Hayashi, Fumio, 1982. "Tobin's Marginal q and Average q: A Neoclassical Interpretation," Econometrica, Econometric Society, vol. 50(1), pages 213-24, January.
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