Advertisement

Cointegration and VECMs

  • John D. Levendis
Chapter
Part of the Springer Texts in Business and Economics book series (STBE)

Abstract

The VARs that we looked at in the last chapter were very well suited for describing the short-run relationship between variables, especially if they are stationary. Most economic variables are not stationary, however. This required us to transform the variables, taking first differences, so that they are stationary. In this chapter, we show how to model the long-run relationship between variables in their levels, even if they are integrated. This is possible if two or more variables are “cointegrated.” If two variables are cointegrated, then, rather than taking the first difference of each variable, we can essentially model the difference between the two variables. Loosely speaking.

References

  1. Banerjee, A., Dolado, J. J., Galbraith, J. W., & Hendry, D. (1993). Co-integration, error correction, and the econometric analysis of non-stationary data. Oxford: Oxford University press.CrossRefGoogle Scholar
  2. Braun, P. A., & Mittnik, S. (1993). Misspecifications in vector autoregressions and their effects on impulse responses and variance decompositions. Journal of Econometrics, 59(3), 319–341.CrossRefGoogle Scholar
  3. Brooks, C. (2014). Introductory econometrics for finance. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  4. Campos, J., Ericsson, N. R., & Hendry, D. F. (1996). Cointegration tests in the presence of structural breaks. Journal of Econometrics, 70(1), 187–220.CrossRefGoogle Scholar
  5. Clarke, J. A., & Mirza, S. (2006). A comparison of some common methods for detecting Granger noncausality. Journal of Statistical Computation and Simulation, 76(3), 207–231.CrossRefGoogle Scholar
  6. Corbae, D., & Ouliaris, S. (1988). Cointegration and tests of purchasing power parity. The Review of Economics and Statistics, 70, 508–511.CrossRefGoogle Scholar
  7. Dwyer, G. (2014). The Johansen tests for cointegration. http://www.jerrydwyer.com/pdf/Clemson/Cointegration.pdf.Google Scholar
  8. Elliott, G. (1998). On the robustness of cointegration methods when regressors almost have unit roots. Econometrica, 66(1), 149–158.CrossRefGoogle Scholar
  9. Enders, W. (2014). Applied econometric time series (3rd edn.). New York: Wiley.Google Scholar
  10. Engle, R. F., & Granger, C. W. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica: Journal of the Econometric Society, 55, 251–276.CrossRefGoogle Scholar
  11. Engle, R. F., & Granger, C. W. (1991). Long-run economic relationships: Readings in cointegration. Oxford: Oxford University Press.Google Scholar
  12. Engle, R. F., & Yoo, B. S. (1987). Forecasting and testing in co-integrated systems. Journal of Econometrics, 35(1), 143–159.CrossRefGoogle Scholar
  13. Engle, R. F., Granger, C. W. J., Hylleberg, S., & Lee, H. S. (1993). Seasonal cointegration: The Japanese consumption function. Journal of Econometrics, 55(1–2), 275–298.CrossRefGoogle Scholar
  14. Ghysels, E., & Osborn, D. R. (2001). The Econometric Analysis of Seasonal Time Series. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  15. Gonzalo, J. (1994). Five alternative methods of estimating long-run equilibrium relationships. Journal of Econometrics, 60(1–2), 203–233.CrossRefGoogle Scholar
  16. Gonzalo, J., & Pitarakis, J.-Y. (1998). Specification via model selection in vector error correction models. Economics Letters, 60(3), 321–328.CrossRefGoogle Scholar
  17. Granger, C. W. (1988). Some recent development in a concept of causality. Journal of Econometrics, 39(1–2), 199–211.CrossRefGoogle Scholar
  18. Granger, C. W., & Newbold, P. (1974). Spurious regressions in econometrics. Journal of Econometrics, 2(2), 111–120.CrossRefGoogle Scholar
  19. Hansen, P. R., & Johansen, S. (1998). Workbook on cointegration. Oxford: Oxford University Press on Demand.Google Scholar
  20. Harris, R., & Sollis, R. (2003). Applied time series modelling and forecasting. New York: Wiley.Google Scholar
  21. Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12(2–3), 231–254.CrossRefGoogle Scholar
  22. Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica: Journal of the Econometric Society, 59(6), 1551–1580.CrossRefGoogle Scholar
  23. Johansen, S. (1994). The role of the constant and linear terms in cointegration analysis of nonstationary variables. Econometric Reviews, 13(2), 205–229.CrossRefGoogle Scholar
  24. Johansen, S. (1995a). Likelihood-based inference in cointegrated vector autoregressive models. Oxford: Oxford University Press.CrossRefGoogle Scholar
  25. Johansen, S. (1995b). A statistical analysis of cointegration for I(2) variables. Econometric Theory, 11(1), 25–59.CrossRefGoogle Scholar
  26. Juselius, K. (2006). The Cointegrated VAR Model: Methodology and Applications. Oxford: Oxford University Press.Google Scholar
  27. Juselius, K., et al. (1992). Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK. Journal of Econometrics, 53(1–3), 211–244.Google Scholar
  28. Kim, Y. (1990). Purchasing power parity in the long run: a cointegration approach. Journal of Money, Credit and Banking, 22(4), 491–503.CrossRefGoogle Scholar
  29. Lütkepohl, H. (2005). New introduction to multiple time series analysis. Berlin: Springer Science and Business Media.CrossRefGoogle Scholar
  30. Lütkepohl, H., & Saikkonen, P. (1999). Order selection in testing for the cointegrating rank of a VAR process. In R. Engle & H. White (Eds.), Cointegration, causality, and forecasting: A festschrift in honour of Clive W.J. Granger, Chapter 7 (pp. 168–199). Oxford: Oxford University Press.Google Scholar
  31. MacKinnon, J. G. (1991). Critical values for cointegration tests, Chapter 13. In R. F. Engle & C. W. J. Granger (Eds.), Long-run economic relationships: Readings in cointegration. Oxford : Oxford University Press.Google Scholar
  32. MacKinnon, J. G. (2010). Critical values for cointegration tests (Technical report), Queen’s Economics Department Working Paper.Google Scholar
  33. Murray, M. P. (1994). A drunk and her dog: An illustration of cointegration and error correction. The American Statistician, 48(1), 37–39.Google Scholar
  34. Pedroni, P. (2001). Purchasing power parity tests in cointegrated panels. The Review of Economics and Statistics, 83(4), 727–731.CrossRefGoogle Scholar
  35. Quintos, C. E., & Phillips, P. C. (1993). Parameter constancy in cointegrating regressions. Empirical Economics, 18(4), 675–706.CrossRefGoogle Scholar
  36. Rao, B. B. (2007). Cointegration for the applied economist (2nd edn.). New York: Palgrave Macmillan.Google Scholar
  37. Schaffer, M. E. (2010). EGRANGER: Engle-Granger (EG) and augmented Engle-Granger (AEG) cointegration tests and 2-step ECM estimation. http://ideas.repec.org/c/boc/bocode/s457210.html.Google Scholar
  38. Taylor, M. P. (1988). An empirical examination of long-run purchasing power parity using cointegration techniques. Applied Economics, 20(10), 1369–1381.CrossRefGoogle Scholar
  39. Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1), 225–250.CrossRefGoogle Scholar
  40. Zivot, E., & Wang, J. (2007). Modeling financial time series with S-plus® (Vol. 191). New York: Springer Science and Business Media.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • John D. Levendis
    • 1
  1. 1.Department of EconomicsLoyola University New OrleansNew OrleansUSA

Personalised recommendations