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Co-integration and error correction: Representation, estimation, and testing

Listed author(s):
  • Engle, Robert

    ()

    (New York University Stern School of Business)

  • Granger, Clive

The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples. If each element of a vector of time series x, first achieves stationarity after differencing, but a linear combination a’x_t is already stationary, the time series x, are said to be co-integrated with co-integrating vector a. There may be several such co-integrating vectors so that a becomes a matrix. Interpreting a’x_t = 0 as a long run equilibrium, co-integration implies that deviations from equilibrium are stationary, with finite variance, even though the series themselves are nonstationary and have infinite variance. The paper presents a representation theorem based on Granger (1983), which connects the moving average, autoregressive, and error correction representations for co-integrated systems. A vector autoregression in differenced variables is incompatible with these representations. Estimation of these models is discussed and a simple but asymptotically efficient two-step estimator is proposed. Testing for co-integration combines the problems of unit root tests and tests with parameters unidentified under the null. Seven statistics are formulated and analyzed. The critical values of these statistics are calculated based on a Monte Carlo simulation. Using these critical values, the power properties of the tests are examined and one test procedure is recommended for application. In a veries of examples it is found that consumption and income are co-integrated, wages and prices are not, short and long interest rates are, and nominal GNP is co-integrated with M2, but not M1, M3, or aggregate liquid assets. (in Russian)

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File URL: http://pe.cemi.rssi.ru/pe_2015_3_106-135.pdf
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Article provided by Publishing House "SINERGIA PRESS" in its journal Applied Econometrics.

Volume (Year): 39 (2015)
Issue (Month): 3 ()
Pages: 106-135

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Handle: RePEc:ris:apltrx:0274
Contact details of provider: Web page: http://appliedeconometrics.cemi.rssi.ru/

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  1. Salmon, Mark H, 1982. "Error Correction Mechanisms," Economic Journal, Royal Economic Society, vol. 92(367), pages 615-629, September.
  2. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-174, January.
  3. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
  4. Campbell, John Y & Shiller, Robert J, 1984. "A Simple Account of the Behavior of Long-Term Interest Rates," American Economic Review, American Economic Association, vol. 74(2), pages 44-48, May.
  5. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
  6. Currie, David A, 1981. "Some Long Run Features of Dynamic Time Series Models," Economic Journal, Royal Economic Society, vol. 91(363), pages 704-715, September.
  7. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  8. Davidson, James E H, et al, 1978. "Econometric Modelling of the Aggregate Time-Series Relationship between Consumers' Expenditure and Income in the United Kingdom," Economic Journal, Royal Economic Society, vol. 88(352), pages 661-692, December.
  9. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-779, May.
  10. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  11. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-247, February.
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