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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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Bibliographic Info

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. 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.
  2. 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.
  3. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-80, January.
  4. 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.
  5. 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.
  6. Hayashi, Fumio, 1982. "Tobin's Marginal q and Average q: A Neoclassical Interpretation," Econometrica, Econometric Society, vol. 50(1), pages 213-24, January.
  7. 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.
  8. Nelson, Charles R & Startz, Richard, 1990. "The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One," The Journal of Business, University of Chicago Press, vol. 63(1), pages S125-40, January.
  9. 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.
  10. 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.
  11. Dagenais, M.G. & Dufour, J.M., 1987. "Invariance, Nonlinear Models and Asymptotic Tests," Cahiers de recherche 8738, Universite de Montreal, Departement de sciences economiques.
  12. Joshua Angrist & Alan Krueger, 1993. "Split Sample Instrumental Variables," Working Papers 699, Princeton University, Department of Economics, Industrial Relations Section..
  13. 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.
  14. 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.
  15. 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.
  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. 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.
  18. 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.
  19. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  20. 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.
  21. 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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Cited by:
  1. Jean-Marie Dufour, 2001. "Logiques et tests d'hypothèses : réflexions sur les problèmes mal posés en économétrie," CIRANO Working Papers 2001s-40, CIRANO.
  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. 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.
  4. Dufour, Jean-Marie, 2001. "Logique et tests d’hypothèses," L'Actualité Economique, Société Canadienne de Science Economique, vol. 77(2), pages 171-190, juin.

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