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A Simple MLE of Cointegrating Vectors in Higher Order Integrated Systems

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Author Info
James H. Stock
Mark W. Watson

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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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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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Handle: RePEc:nbr:nberte:0083

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  1. John Y. Campbell & Robert J. Shiller, 1989. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," NBER Working Papers 2100, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. Hylleberg, Svend & Mizon, Grayham E, 1989. "Cointegration and Error Correction Mechanisms," Economic Journal, Royal Economic Society, vol. 99(395), pages 113-25, Supplemen. [Downloadable!] (restricted)
    Other versions:
  3. 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. [Downloadable!] (restricted)
  4. 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.
  5. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September. [Downloadable!] (restricted)
  6. King, Robert G. & Plosser, Charles I. & Stock, James H. & Watson, Mark W., 1991. "Stochastic Trends and Economic Fluctuations," American Economic Review, American Economic Association, vol. 81(4), pages 819-40, September. [Downloadable!] (restricted)
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  7. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March. [Downloadable!] (restricted)
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  8. 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, Yale University. [Downloadable!]
  9. 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. [Downloadable!] (restricted)
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  10. Campbell, John Y, 1987. "Does Saving Anticipate Declining Labor Income? An Alternative Test of the Permanent Income Hypothesis," Econometrica, Econometric Society, vol. 55(6), pages 1249-73, November. [Downloadable!] (restricted)
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  11. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-88, October. [Downloadable!] (restricted)
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  12. 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. [Downloadable!] (restricted)
  13. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation, Yale University. [Downloadable!]
  14. 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, Yale University. [Downloadable!]
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  17. 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. [Downloadable!] (restricted)
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  19. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Reinhart, Carmen & Calvo, Guillermo & Vegh, Carlos, 1994. "Targeting the real exchange rate," MPRA Paper 13765, University Library of Munich, Germany. [Downloadable!]
  2. 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, Yale University. [Downloadable!]
  3. 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. [Downloadable!] (restricted)
  4. Reinhart, Carmen, 1995. "Devaluation, Relative Prices, and International Trade: Evidence from Developing Countries," MPRA Paper 6974, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  5. 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. [Downloadable!]
  6. 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. [Downloadable!]
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  7. Karen K. Lewis & Martin D. Evans, 1992. "Do Expected Shifts in Inflation Policy Affect Real Rates?," NBER Working Papers 4134, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  8. Sharon J. Erenburg, 1993. "Productivity, Private and Public Capital, and Real Wage in the United States, 1948-1990," Economics Working Paper Archive 94, Levy Economics Institute, The. [Downloadable!]
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