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Long-Run Structural Modelling

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  • M. Hashem Pesaran
  • Yongcheol Shin

Abstract

The paper develops a general framework for identification, estimation, and hypothesis testing in cointegrated systems when the cointegrating coefficients are subject to (possibly) non-linear and cross-equation restrictions, obtained from economic theory or other relevant a priori information. It provides a proof of the consistency of the quasi maximum likelihood estimators (QMLE), establishes the relative rates of convergence of the QMLE of the short-run and the long-run parameters, and derives their asymptotic distributions; thus generalizing the results already available in the literature for the linear case. The paper also develops tests of the over-identifying (possibly) non-linear restrictions on the cointegrating vectors. The estimation and hypothesis testing procedures are applied to an Almost Ideal Demand System estimated on U.K. quarterly observations. Unlike many other studies of consumer demand this application does not treat relative prices and real per capita expenditures as exogenously given.

Suggested Citation

  • M. Hashem Pesaran & Yongcheol Shin, 2002. "Long-Run Structural Modelling," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 49-87.
  • Handle: RePEc:taf:emetrv:v:21:y:2002:i:1:p:49-87
    DOI: 10.1081/ETC-120008724
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    References listed on IDEAS

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    1. Pesaran, M. Hashem & Shin, Yongcheol & Smith, Richard J., 2000. "Structural analysis of vector error correction models with exogenous I(1) variables," Journal of Econometrics, Elsevier, vol. 97(2), pages 293-343, August.
    2. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    3. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
    4. Pashardes, Panos, 1993. "Bias in Estimating the Almost Ideal Demand System with the Stone Index Approximation," Economic Journal, Royal Economic Society, vol. 103(419), pages 908-915, July.
    5. Saikkonen, Pentti, 1993. "Estimation of Cointegration Vectors with Linear Restrictions," Econometric Theory, Cambridge University Press, vol. 9(01), pages 19-35, January.
    6. Anthony Garratt & Kevin Lee & M. Hashem Pesaran & Yongcheol Shin, 2003. "A Long run structural macroeconometric model of the UK," Economic Journal, Royal Economic Society, vol. 113(487), pages 412-455, April.
    7. Potscher, Benedikt M. & Prucha, Ingmar R., 1994. "Generic uniform convergence and equicontinuity concepts for random functions : An exploration of the basic structure," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 23-63.
    8. Pesaran, M Hashem, 1997. "The Role of Economic Theory in Modelling the Long Run," Economic Journal, Royal Economic Society, vol. 107(440), pages 178-191, January.
    9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    10. Gordon Anderson & Richard Blundell, 1983. "Testing Restrictions in a Flexible Dynamic Demand System: An Application to Consumers' Expenditure in Canada," Review of Economic Studies, Oxford University Press, vol. 50(3), pages 397-410.
    11. Michael R. Wickens & Roberto Motto, 2001. "Estimating shocks and impulse response functions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 371-387.
    12. Saikkonen, Pentti, 1993. "Continuous Weak Convergence and Stochastic Equicontinuity Results for Integrated Processes with an Application to the Estimation of a Regression Model," Econometric Theory, Cambridge University Press, vol. 9(02), pages 155-188, April.
    13. Pesaran, M. H. & Smith, Ron P., 1998. "Structural Analysis of Cointegrating VARs," Cambridge Working Papers in Economics 9811, Faculty of Economics, University of Cambridge.
    14. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
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    16. Marcus Chambers & K. Ben Nowman, 1997. "Forecasting with the almost ideal demand system: evidence from some alternative dynamic specifications," Applied Economics, Taylor & Francis Journals, vol. 29(7), pages 935-943.
    17. M. Hashem Pesaran & Ron P. Smith, 1998. "Structural Analysis of Cointegrating VARs," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 471-505, December.
    18. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    19. Donald W.K. Andrews, 1986. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers," Cowles Foundation Discussion Papers 790, Cowles Foundation for Research in Economics, Yale University.
    20. 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.
    21. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    22. Johansen, Søren & Juselius, Katarina, 1992. "Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 211-244.
    23. Johansen, Soren, 1995. "Identifying restrictions of linear equations with applications to simultaneous equations and cointegration," Journal of Econometrics, Elsevier, vol. 69(1), pages 111-132, September.
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    25. Saikkonen, Pentti, 1995. "Problems with the Asymptotic Theory of Maximum Likelihood Estimation in Integrated and Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 11(05), pages 888-911, October.
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    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Cointegration; Identification; QMLE; Consistency; Asymptotic distribution; testing non-linear restrictions; Almost Ideal Demand Systems; JEL Classifications: C1; C3; D1; E1;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • D1 - Microeconomics - - Household Behavior
    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models

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