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Vector Autoregression and Causality: A Theoretical Overview and Simulation Study

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Abstract

This paper provides a theoretical overview of Wald tests for Granger causality in levels vector autoregressions (VAR's) and Johansen-type error correction models (ECM's) for VAR models the results for inference are not encouraging. The limit theory typically involves nonstandard distributions and nuisance parameters, and there is no sound statistical basis for testing causality in such a framework. Granger causality tests in ECM's also suffer from nuisance parameter dependencies asymptotically and nonstandard limit theory. But, in spite of these difficulties Johansen-type ECM's do offer a sound basis for empirical testing of the rank of the cointegration space and the rank of key submatrices that influence the asymptotics. In consequence, we recommend some operational procedures for conducting Granger causality tests in the important practical case of testing the causal effects of one variable on another group of variables and vice versa.

Suggested Citation

  • Hiro Y. Toda & Peter C.B. Phillips, 1991. "Vector Autoregression and Causality: A Theoretical Overview and Simulation Study," Cowles Foundation Discussion Papers 1001, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1001
    Note: CFP 890.
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d10/d1001.pdf
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    References listed on IDEAS

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    1. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    2. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
    3. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
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    Cited by:

    1. Liu Hongyu & Yun W. Park & Zheng Siqi, 2002. "The Interaction between Housing Investment and Economic Growth in China," International Real Estate Review, Global Social Science Institute, vol. 5(1), pages 40-60.
    2. Dufour, Jean-Marie & Pelletier, Denis & Renault, Eric, 2006. "Short run and long run causality in time series: inference," Journal of Econometrics, Elsevier, vol. 132(2), pages 337-362, June.
    3. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 16-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January.
    5. Elliott, Graham & Stock, James H., 1994. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 672-700, August.
    6. Greasley, David & Oxley, Les, 2007. "Patenting, intellectual property rights and sectoral outputs in Industrial Revolution Britain, 1780-1851," Journal of Econometrics, Elsevier, vol. 139(2), pages 340-354, August.
    7. Judith A. Clarke & Sadaf Mirza, 2003. "Some Finite Sample Results On Testing For Granger Noncausality," Econometrics Working Papers 0305, Department of Economics, University of Victoria.
    8. David Greasley & Les Oxley, 2010. "Cliometrics And Time Series Econometrics: Some Theory And Applications," Journal of Economic Surveys, Wiley Blackwell, vol. 24(5), pages 970-1042, December.
    9. Pierre St-Amant & David Tessier, 2000. "Résultats empiriques multi-pays relatifs à l'impact des cibles d'inflation sur la crédibilité de la politique monétaire," Canadian Public Policy, University of Toronto Press, vol. 26(3), pages 295-310, September.
    10. Les Oxley & David Greasley, 1998. "Vector autoregression, cointegration and causality: testing for causes of the British industrial revolution," Applied Economics, Taylor & Francis Journals, vol. 30(10), pages 1387-1397.
    11. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    12. Gianluca Cubadda & Domenico Mignacca, 1994. "Is Money Neutral? Some Evidence for Italy," International Finance 9410001, University Library of Munich, Germany, revised 09 Nov 1994.
    13. Peter C.B. Phillips, 1991. "Unidentified Components in Reduced Rank Regression Estimation of ECM's," Cowles Foundation Discussion Papers 1003, Cowles Foundation for Research in Economics, Yale University.
    14. Kenneth Carlaw & Les Oxley & Paul Walker & David Thorns & Michael Nuth, 2006. "Beyond The Hype: Intellectual Property And The Knowledge Society/Knowledge Economy," Journal of Economic Surveys, Wiley Blackwell, vol. 20(4), pages 633-690, September.
    15. Trecroci, Carmine & Vega, Juan Luis, 2000. "The information content of M3 for future inflation," Working Paper Series 0033, European Central Bank.

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    More about this item

    Keywords

    Error correction models; Granger causality; Wald test cointegration; vector autoregression;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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