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

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Author Info
Jean-Marie Dufour (CRDE)
Joanna Jasiak (York University)

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Abstract

We propose finite sample tests and confidence sets for models with unobserved and generated regressors as well as various models estimated by instrumental variables method. 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 generated 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. A distributional theory is obtained under the assumptions of Gaussian errors and strictly 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.

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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1536.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1536

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, vol. 80(2), pages 325-353, October. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Dufour, Jean-Marie, 1989. "Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions," Econometrica, Econometric Society, vol. 57(2), pages 335-55, March. [Downloadable!] (restricted)
  6. Nelson, Charles R & Startz, Richard, 1990. "The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One," Journal of Business, University of Chicago Press, vol. 63(1), pages S125-40, January. [Downloadable!] (restricted)
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  7. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
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  8. 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.
  9. Andrew B. Abel & Janice C. Eberly, . "A Unified Model of Investment Under Uncertainty," Rodney L. White Center for Financial Research Working Papers 14-93, Wharton School Rodney L. White Center for Financial Research.
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  10. 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. [Downloadable!] (restricted)
  11. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-80, January. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
  13. Barro, Robert J, 1977. "Unanticipated Money Growth and Unemployment in the United States," American Economic Review, American Economic Association, vol. 67(2), pages 101-15, March.
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  14. Oxley, Les & McAleer, Michael, 1993. " Econometric Issues in Macroeconomic Models with Generated Regressors," Journal of Economic Surveys, Blackwell Publishing, vol. 7(1), pages 1-40.
  15. 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. [Downloadable!] (restricted)
  16. Joshua D. Angrist & Alan B. Krueger, 1995. "Split Sample Instrumental Variables," NBER Technical Working Papers 0150, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  17. Abel, Andrew B & Blanchard, Olivier J, 1986. "The Present Value of Profits and Cyclical Movements in Investment," Econometrica, Econometric Society, vol. 54(2), pages 249-73, March. [Downloadable!] (restricted)
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  18. 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.
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  19. Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-15, November. [Downloadable!] (restricted)
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  20. 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 370-79, October.
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  21. Hayashi, Fumio, 1982. "Tobin's Marginal q and Average q: A Neoclassical Interpretation," Econometrica, Econometric Society, vol. 50(1), pages 213-24, January. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Benoit Perron, 2000. "Semi-Parametric Weak Instrument Regressions with an Application to the Risk-return Trade-off," Econometric Society World Congress 2000 Contributed Papers 1576, Econometric Society. [Downloadable!]
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  2. Eric Zivot & Saraswata Chaudhuri, 2008. "A Comment on Weak Instrument Robust Tests in GMM and the New Keynesian Phillips Curve," Working Papers UWEC-2008-23, University of Washington, Department of Economics. [Downloadable!]
  3. Jean-Marie Dufour, 2001. "Logiques et tests d'hypothèses : réflexions sur les problèmes mal posés en économétrie," CIRANO Working Papers 2001s-40, CIRANO. [Downloadable!]
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