EFFICIENT ESTIMATION OF THE COINTEGRATING VECTOR IN ERROR CORRECTION MODELS WITH STATIONARY COVARIATES

  • Published : 2005.12.01

Abstract

This paper considers the cointegrating vector estimator in the error correction model with stationary covariates, which combines the stationary vector autoregressive model and the nonstationary error correction model. The cointegrating vector estimator is shown to follow the locally asymptotically mixed normal distribution. The variance of the estimator depends on the co­variate effect of stationary regressors, and the asymptotic efficiency improves as the magnitude of the covariate effect increases. An economic application of the money demand equation is provided.

Keywords

References

  1. AHN, S. K., AND G. C. REINSEL (1988). 'Nested Reduced-Rank Autoregressive Models for Multiple Time Series', Journal of the American Statistical Association, 83, 849-856 https://doi.org/10.2307/2289316
  2. BABA, Y., D. HENDRY, AND R. STARR (1992). 'The Demand for M1 in the U. S. A.', 1960-1988, Review of Economic Studies, 59, 25-61 https://doi.org/10.2307/2297924
  3. BOSWIJK, H. P. (1995). 'Efficient Inference on Cointegration Parameters in Structural Error Correction Models', Journal of Econometrics, 69, 133-158 https://doi.org/10.1016/0304-4076(94)01665-M
  4. Box, G. E. P., AND G. C. TIAO (1977). 'A Canonical Analysis of Multiple Time Series', Biometrika, 64, 355-365 https://doi.org/10.1093/biomet/64.2.355
  5. ELLIOT, G., AND M. JANSSON (2003). 'Testing for Unit Root with Stationary Covariates', Journal of Econometrics, 115, 75-89 https://doi.org/10.1016/S0304-4076(03)00093-9
  6. ENGLE, R. F., AND C. W. J. GRANGER (1987). 'Cointegration and Error Correction Representation, Estimation, and Testing', Econometrica, 55, 251-276 https://doi.org/10.2307/1913236
  7. ENGLE, R. F., D. F. HENDRY, AND J. F. RICHARD (1983). 'Exogeneity', Econometrica, 51, 277-304 https://doi.org/10.2307/1911990
  8. ERICSSON, N. R. (1995). 'Conditional and Structural Error Correction Models', Journal of Econometrics, 69, 159-171 https://doi.org/10.1016/0304-4076(94)01666-N
  9. HANSEN, B. E. (1992). 'Convergence to Stochastic Integrals for Dependent Heterogeneous Processes', Econometric Theory, 8, 489-500 https://doi.org/10.1017/S0266466600013189
  10. HANSEN, B. E. (1995). 'Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power', Econometric Theory, 11, 1148-1171 https://doi.org/10.1017/S0266466600009993
  11. HARBO, I., S. JOHANSEN, B. NIELSON, AND A. RAHBEK (1998). 'Asymptotic Inference on Cointegration Rank in Partial Systems', Journal of Business and Economic Statistics, 16, 388-399 https://doi.org/10.2307/1392608
  12. JOHANSEN, S. (1988). 'Statistical Analysis of Cointegrating Vectors', Journal of Economic Dynamics and Control, 12, 231-254 https://doi.org/10.1016/0165-1889(88)90041-3
  13. JOHANSEN, S. (1991). 'Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models', Econometrica, 59, 1551-1580 https://doi.org/10.2307/2938278
  14. JOHANSEN, S. (1992). 'Cointegration in Partial Systems and the Efficiency of Single-Equation Analysis', Journal of Econometrics, 52, 389-402 https://doi.org/10.1016/0304-4076(92)90019-N
  15. JOHANSEN, S., AND K. JUSELIUS (1992). 'Testing Structural Hypotheses in a Multivariate Cointgeration Analysis of the PPP and the UIP for UK', Journal of Econometrics, 53, 211-244 https://doi.org/10.1016/0304-4076(92)90086-7
  16. JUSELIUS, K. (1995). 'Do Purchasing Power Parity and Uncovered Interest Parity Hold in the Long Run? An Example of Likelihood Inference in a Multivariate Time Series Model', Journal of Econometrics, 69, 211-240 https://doi.org/10.1016/0304-4076(94)01669-Q
  17. PHILLIPS, P. C. B. (1988). 'Weak Convergence of Sample Covariance Matrices to Stochastic Integrals via Martingale Approximations', Econometric Theory, 4, 528-533 https://doi.org/10.1017/S026646660001344X
  18. PHILLIPS, P.C.B. (1991). 'Optimal Inference in Cointegrated System', Econometrica, 59, 283-306 https://doi.org/10.2307/2938258
  19. PHILLIPS, P.C.B., AND S.N. DURLAUF (1986). 'Multiple Time Series with Integrated Variabies', Review of Economic Studies, 53, 473-495 https://doi.org/10.2307/2297602
  20. PHILLIPS, P.C.B., AND B.E. HANSEN (1990). 'Statistical Inference in Instrumental Variables Regression with 1(1) Process', Review of Economic Studies, 57, 99-124 https://doi.org/10.2307/2297545
  21. RAHBEK, A. AND R. MOSCONI (1999). 'Cointgeration rank inference with stationary regressors in VAR models, Econometrics Journal', 2, 76-91 https://doi.org/10.1111/1368-423X.00021
  22. SAIKKONEN, P. (1991). 'Asymptotically Efficient Estimation of Cointegration Regressions', Econometric Theory, 7, 1-21 https://doi.org/10.1017/S0266466600004217
  23. SAIKKONEN, P. (2001). 'Consistent Estimation in Cointegrated Vector Autoregressive Processes with Nonlinear Time Trends in Cointegrating Relations', Econometric Theory, 17, 296 - 326 https://doi.org/10.1017/S0266466601172026
  24. SEO, B. (1998). 'Statistical Inference on Cointegration Rank in Error Correction Models with Stationary Covariates', Journal of Econometrics, 85, 339-386 https://doi.org/10.1016/S0304-4076(97)00105-X
  25. STOCK, J. AND M. WATSON (1993). 'A Simple Estimator of Cointegrating Vectors in Highly Order Integrated Systems', Econometrica, 61, 783-820 https://doi.org/10.2307/2951763