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

  • Jean-Marie Dufour

    (CRDE)

  • Joanna Jasiak

    (York University)

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. 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).
  2. 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.
  3. 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.
  4. 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.
  5. Nelson, C. & Startz, R., 1988. "The Distribution Of The Instrumental Variables Estimator And Its T-Ratio When The Instrument Is A Poor One," Discussion Papers in Economics at the University of Washington 88-07, Department of Economics at the University of Washington.
  6. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-80, 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. Alastair R. Hall & Glenn D. Rudebusch & David W. Wilcox, 1994. "Judging instrument relevance in instrumental variables estimation," Finance and Economics Discussion Series 94-3, Board of Governors of the Federal Reserve System (U.S.).
  9. Joshua D. Angrist & Alan B. Krueger, 1995. "Split Sample Instrumental Variables," NBER Technical Working Papers 0150, National Bureau of Economic Research, Inc.
  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. 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.
  12. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  13. 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.
  14. Dagenais, M.G. & Dufour, J.M., 1987. "Invariance, Nonlinear Models and Asymptotic Tests," Cahiers de recherche 8738, Universite de Montreal, Departement de sciences economiques.
  15. 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.
  16. 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.
  17. 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.
  18. Murphy, Kevin M & Topel, Robert H, 2002. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 88-97, January.
  19. 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.
  20. Hayashi, Fumio, 1982. "Tobin's Marginal q and Average q: A Neoclassical Interpretation," Econometrica, Econometric Society, vol. 50(1), pages 213-24, January.
  21. 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.
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