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Computing Numerical Distribution Functions in Econometrics

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  • James G. MacKinnon

    ()
    (Queen's University)

Abstract

Many test statistics in econometrics have asymptotic distributions that cannot be evaluated analytically. In order to conduct asymptotic inference, it is therefore necessary to resort to simulation. Techniques that have commonly been used yield only a small number of critical values, which can be seriously inaccurate. In contrast, the techniques discussed in this paper yield enough information to plot the distributions of the test statistics or to calculate P values, and they can yield highly accurate results. These techniques are used to obtain asymptotic critical values for a test recently proposed by Kiefer, Vogelsang, and Bunzel (2000) for testing linear restrictions in linear regression models. A program to compute P values for this test is available from the author's web site.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1037.pdf
File Function: First version 2001
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1037.

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Length: 15 pages
Date of creation: Dec 2001
Date of revision:
Publication status: Published in A. Pollard, D. Mewhort, and D. Weaver, High Performance Computing Systems and Applications, Kluwer, 2000
Handle: RePEc:qed:wpaper:1037

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Related research

Keywords: unit root test; cointegration test; simulation; critical values; distribution functions; numerical distribution;

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References

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  1. Kiefer, Nicholas M. & Bunzel, Helle & Vogelsang, Timothy & Vogelsang, Timothy & Bunzel, Helle, 2000. "Simple Robust Testing of Regression Hypotheses," Staff General Research Papers 1832, Iowa State University, Department of Economics.
  2. James G. MacKinnon, 1992. "Approximate Asymptotic Distribution Functions for Unit Roots and Cointegration Tests," Working Papers 861, Queen's University, Department of Economics.
  3. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  4. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  5. MacKinnon, James G & Haug, Alfred A & Michelis, Leo, 1999. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 563-77, Sept.-Oct.
  6. Neil R. Ericsson & James G. MacKinnon, 1999. "Distributions of error correction tests for cointegration," International Finance Discussion Papers 655, Board of Governors of the Federal Reserve System (U.S.).
  7. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  8. MacKinnon, James G, 1996. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 601-18, Nov.-Dec..
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Cited by:
  1. Gencay, Ramazan & Fan, Yanqin, 2007. "Unit Root Tests with Wavelets," MPRA Paper 9832, University Library of Munich, Germany.
  2. Peter Sephton, 2008. "Critical values of the augmented fractional Dickey–Fuller test," Empirical Economics, Springer, vol. 35(3), pages 437-450, November.

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