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A Simple MLE of Cointegrating Vectors in Higher Order Integrated Systems

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  • James H. Stock
  • Mark W. Watson

Abstract

An MLE of the unknown parameters of co integrating vectors is presented for systems in which some variables exhibit higher orders of integration, in which there might be deterministic components, and in which the co integrating vector itself might involve variables of differing orders of integration. The estimator is simple to compute: it can be calculated by running GLS for standard regression equations with serially correlated errors. Alternatively, an asymptotically equivalent estimator can be computed using OLS. Usual Wald test statistics based on these MLE's (constructed using an autocorrelation robust covariance matrix in the case of the OLS estimator) have asymptotic x2 distributions.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0083.

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Date of creation: Dec 1989
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Publication status: published as Econometrica, vol 61, no 4, (July 1993), p. 783-820
Handle: RePEc:nbr:nberte:0083

Note: EFG ME
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  1. John Y. Campbell & Robert J. Shiller, 1986. "Cointegration and Tests of Present Value Models," Cowles Foundation Discussion Papers 785, Cowles Foundation for Research in Economics, Yale University.
  2. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Statistical Inference in Instrumental Variables," Cowles Foundation Discussion Papers 869R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1989.
  3. Robert J. Shiller & John Y. Campbell, 1986. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," Cowles Foundation Discussion Papers 812, Cowles Foundation for Research in Economics, Yale University.
  4. Hylleberg, Svend & Mizon, Grayham E, 1989. "Cointegration and Error Correction Mechanisms," Economic Journal, Royal Economic Society, vol. 99(395), pages 113-25, Supplemen.
  5. Hoffman, Dennis L & Rasche, Robert H, 1991. "Long-Run Income and Interest Elasticities of Money Demand in the United States," The Review of Economics and Statistics, MIT Press, vol. 73(4), pages 665-74, November.
  6. 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.
  7. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
  8. John Y. Campbell, 1986. "Does Saving Anticipate Declining Labor Income? An Alternative Test of the Permanent Income Hypothesis," NBER Working Papers 1805, National Bureau of Economic Research, Inc.
  9. 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 113-44, January.
  10. Robert G. King & Charles I. Plosser & James H. Stock & Mark W. Watson, 1991. "Stochastic trends and economic fluctuations," Working Paper Series, Macroeconomic Issues 91-4, Federal Reserve Bank of Chicago.
  11. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Estimation and Inference in Models of Cointegration: A Simulation Study," Cowles Foundation Discussion Papers 881, Cowles Foundation for Research in Economics, Yale University.
  12. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
  13. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  14. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
  15. Banerjee, Anindya, et al, 1986. "Exploring Equilibrium Relationships in Econometrics through Static Models: Some Monte Carlo Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 253-77, August.
  16. Peter C.B. Phillips & Joon Y. Park, 1986. "Asymptotic Equivalence of OLS and GLS in Regressions with Integrated Regressors," Cowles Foundation Discussion Papers 802, Cowles Foundation for Research in Economics, Yale University.
  17. Engle, Robert F & Hendry, David F & Richard, Jean-Francois, 1983. "Exogeneity," Econometrica, Econometric Society, vol. 51(2), pages 277-304, March.
  18. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
  19. Bewley, R. A., 1979. "The direct estimation of the equilibrium response in a linear dynamic model," Economics Letters, Elsevier, vol. 3(4), pages 357-361.
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Cited by:
  1. Carmen M. Reinhart, 1995. "Devaluation, Relative Prices, and International Trade: Evidence from Developing Countries," IMF Staff Papers, Palgrave Macmillan, vol. 42(2), pages 290-312, June.
  2. Reinhart, Carmen & Calvo, Guillermo & Vegh, Carlos, 1994. "Targeting the real exchange rate: Theory and evidence," MPRA Paper 13412, University Library of Munich, Germany.
  3. Martin D. Evans & Karen K. Lewis, 1992. "Do Expected Shifts in Inflation Policy Affect Real Rates?," Working Papers 92-22, New York University, Leonard N. Stern School of Business, Department of Economics.
  4. Reinhart, Carmen & Calvo, Guillermo & Vegh, Carlos, 1994. "La tasa de cambio real como meta de política: teoría y evidencia
    [Targeting the real exchange rate: Theory and evidence]
    ," MPRA Paper 13468, University Library of Munich, Germany.
  5. Carlos A. Végh Gramont & Guillermo Calvo & Carmen Reinhart, 1994. "Targeting the Real Exchange Rate," IMF Working Papers 94/22, International Monetary Fund.
  6. Pierre-Daniel G. Sarte, 1999. "An empirical investigation of fluctuations in manufacturing sales and inventory within a sticky-price framework," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 61-84.
  7. Martin D. Evans & Karen K. Lewis, 1990. "Do Stationary Risk Premia Explain It All? Evidence from the Term Struct," NBER Working Papers 3451, National Bureau of Economic Research, Inc.
  8. Peter C.B. Phillips, 1991. "The Long-Run Australian Consumption Function Reexamined: An Empirical Exercise in Bayesian Influence," Cowles Foundation Discussion Papers 1000, Cowles Foundation for Research in Economics, Yale University.
  9. Alexander W. Hoffmaister & Mahmood Pradhan & Hossein Samiei, 1996. "Have North-South Growth Linkages Changed?," IMF Working Papers 96/54, International Monetary Fund.

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