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

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  • Jean-Marie Dufour

    (CRDE)

  • Joanna Jasiak

    (York University)

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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  1. Robert J. Barro, 1976. "Unanticipated Money Growth and Unemployment in the United States," Working Papers, Queen's University, Department of Economics 234, Queen's University, Department of Economics.
  2. Joshua Angrist & Alan Krueger, 1993. "Split Sample Instrumental Variables," Working Papers, Princeton University, Department of Economics, Industrial Relations Section. 699, Princeton University, Department of Economics, Industrial Relations Section..
  3. Maddala, G S, 1974. "Some Small Sample Evidence on Tests of Significance in Simultaneous Equations Models," Econometrica, Econometric Society, Econometric Society, vol. 42(5), pages 841-51, September.
  4. Maddala, G S & Jeong, Jinook, 1992. "On the Exact Small Sample Distribution of the Instrumental Variable Estimator," Econometrica, Econometric Society, Econometric Society, vol. 60(1), pages 181-83, January.
  5. Hayashi, Fumio, 1982. "Tobin's Marginal q and Average q: A Neoclassical Interpretation," Econometrica, Econometric Society, Econometric Society, vol. 50(1), pages 213-24, January.
  6. Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, Elsevier, vol. 80(2), pages 325-353, October.
  7. Nelson, C. & Startz, R., 1988. "The Distribution Of The Instrumental Variables Estimator And Its T-Ratio When The Instrument Is A Poor One," Working Papers, University of Washington, Department of Economics 88-07, University of Washington, Department of Economics.
  8. Andrew B. Abel & Janice C. Eberly, . "A Unified Model of Investment Under Uncertainty," Rodney L. White Center for Financial Research Working Papers, Wharton School Rodney L. White Center for Financial Research 14-93, Wharton School Rodney L. White Center for Financial Research.
  9. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-47, February.
  10. Alastair R. Hall & Glenn D. Rudebusch & David W. Wilcox, 1994. "Judging instrument relevance in instrumental variables estimation," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 94-3, Board of Governors of the Federal Reserve System (U.S.).
  11. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  12. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, Econometric Society, vol. 65(6), pages 1365-1388, November.
  13. Dufour, Jean-Marie, 1989. "Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions," Econometrica, Econometric Society, Econometric Society, vol. 57(2), pages 335-55, March.
  14. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, Econometric Society, vol. 60(1), pages 173-80, January.
  15. Savin, N.E., 1984. "Multiple hypothesis testing," Handbook of Econometrics, Elsevier, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 14, pages 827-879 Elsevier.
  16. Montmarquette, Claude & Mahseredjian, Sophie, 1989. "Could teacher grading practices account for unexplained variation in school achievements?," Economics of Education Review, Elsevier, Elsevier, vol. 8(4), pages 335-343, August.
  17. Abel, Andrew B & Blanchard, Olivier J, 1986. "The Present Value of Profits and Cyclical Movements in Investment," Econometrica, Econometric Society, Econometric Society, vol. 54(2), pages 249-73, March.
  18. Oxley, Les & McAleer, Michael, 1993. " Econometric Issues in Macroeconomic Models with Generated Regressors," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 7(1), pages 1-40.
  19. Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, Econometric Society, vol. 59(6), pages 1601-15, November.
  20. Murphy, Kevin M & Topel, Robert H, 2002. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(1), pages 88-97, January.
  21. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, Elsevier, vol. 70(1), pages 39-68, January.
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Cited by:
  1. Dufour, J.M., 2001. "Logique et tests d'hypotheses: reflexions sur les problemes mal poses en econometrie," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 2001-15, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Benoit Perron, 2003. "Semiparametric Weak-Instrument Regressions with an Application to the Risk-Return Tradeoff," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 424-443, May.
  3. Dufour, Jean-Marie, 2001. "Logique et tests d’hypothèses," L'Actualité Economique, Société Canadienne de Science Economique, Société Canadienne de Science Economique, vol. 77(2), pages 171-190, juin.
  4. Debdulal Mallick, 2007. "The Role of Elasticity of Substitution in Economic Growth: A Cross-Country Test of the La Grandville Hypothesis," Economics Series 2007_04, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.

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