zbMATH — the first resource for mathematics

Weak exogeneity in \(I(2)\) VAR systems. (English) Zbl 0946.62085
Summary: This paper defines parametric conditions under which a subset of variables is weakly exogenous with respect to the (multi)-cointegration parameters in I(2) VAR systems. The weak exogeneity conditions can be interpreted in terms of common trends, corresponding to the cumulation of the errors from the marginal equations into the I(2) trends, or in terms of ‘no levels and difference feedback’ into the marginal model equations. A modified version of the two-stage procedure proposed by S. Johansen [Econ. Theory 11, 25-59 (1995)] is adopted for conditional statistical inference. Corresponding tests for the above restrictions are derived and discussed. Asymptotic properties of the tests and of the conditional estimators are analyzed.
It is shown that if the conditions of weak exogeneity do not apply, the conditional estimators of the long-run parameters can be inconsistent and/or present limit distributions with nuisance parameters, according to which part of the conditions fails to hold. A test for weak exogeneity restrictions as a routine check before any analysis of conditional models is strongly recommended.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F05 Asymptotic properties of parametric tests
62P20 Applications of statistics to economics
62F12 Asymptotic properties of parametric estimators
Full Text: DOI
[1] Barndorff–Nielsen, O.E., 1978. Information and Exponential Families in Statistical Theory. Wiley, New York. · Zbl 0387.62011
[2] Boswijk, H.P., 1992. Cointegration, identification and exogeneity: Inference in structural error correction models. Thesis, Publisher Tinbergen Institute, Amsterdam.
[3] Boswijk, H. P.: Efficient inference on cointegration parameters in structural error correction models. Journal of econometrics 69(1), 133-158 (1995) · Zbl 0832.62098
[4] Engle, R. F.; Hendry, D. F.; Richard, J. F.: Exogeneity. Econometrica 51, 277-304 (1983) · Zbl 0528.62093
[5] Engle, R.F., Yoo, B.S., 1991. Cointegrated economic time series: An overview with new results. In: Engle, R.F., Granger, C.W.J. (Eds.), Long-Run Economic Relationships, Advanced Texts in Econometrics. Oxford University Press, Oxford.
[6] Granger, G. W. J.; Lee, T. -H.: Multicointegration. Advances in econometrics 8, 71-84 (1989)
[7] Gregoir, S.; Laroque, G.: Multivariate integrated time series: A polynomial error correction representation theorem. Econometric theory 9, 329-342 (1993)
[8] Hansen, B. E.: Convergence to stochastic integrals for dependent heterogeneous processes. Econometric theory 8, 489-500 (1992)
[9] Harbo, I., Johansen, S., Nielsen, B., Rahbek, A., 1998. Test for cointegrating rank in partial systems. Journal of Business and Economic Statistics 16, 388–399.
[10] Hendry, D.F., 1995. Dynamic econometrics. Advanced Texts in Econometrics. Oxford University Press, Oxford. · Zbl 0897.62127
[11] Hendry, D. F.; Ericsson, N. R.: Modeling the demand for narrow money in the united kingdom and the united states. European economic review 35, 833-881 (1991)
[12] Johansen, S.: Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551-1580 (1991) · Zbl 0755.62087
[13] Johansen, S.: Testing weak exogeneity and the order of cointegration in the UK money demand data. Journal of policy modeling 14, 313-334 (1992)
[14] Johansen, S.: A representation of vector autoregressive processes integrated of order 2. Econometric theory 8, 188-202 (1992)
[15] Johansen, S.: Cointegration analysis in partial systems and the efficiency of single-equation analysis. Journal of econometrics 52, 389-402 (1992) · Zbl 0747.62115
[16] Johansen, S.: A statistical analysis of cointegration for \(I(2)\) variables. Econometric theory 11, 25-59 (1995) · Zbl 1274.62597
[17] Johansen, S., 1996. Likelihood-Based Inference in Cointegrated Vector Autoregressive Models, second ed. Oxford University Press, Oxford. · Zbl 0928.62069
[18] Johansen, S.: Likelihood analysis of the \(I(2)\) model. Scandinavian journal of statistics 24, 433-462 (1997) · Zbl 0923.62094
[19] Johansen, S.; Juselius, K.: Maximum likelihood estimation and inference on cointegration – with applications to the demand for money. Oxford bulletin of economics and statistics 52, 169-210 (1990)
[20] Paruolo, P., 1994. The role of the drift in I(2) systems. Journal of the Italian Statistical Society 3, Correction vol. 61 65–96. · Zbl 1446.62247
[21] Paruolo, P.: On the determination of integration indices in \(I(2)\) systems. Journal of econometrics 72, 313-356 (1996) · Zbl 0844.62096
[22] Paruolo, P., 1998. On the effects of mis-specification in cointegrated VAR models. Paper presented at the 53rd ESEM meeting, Berlin, 1998, Department of Statistics, University of Bologna.
[23] Paruolo, P., 1999. Asymptotic efficiency of the 2 stage estimator in I(2) VAR systems. Econometric Theory, forthcoming. · Zbl 0946.62085
[24] Paruolo, P., Rahbek, A., 1996. Weak exogeneity in I(2) systems. Preprint 1996. 4, Department of Theoretical Statistics, University of Copenhagen. · Zbl 0946.62085
[25] Phillips, P. C. B.: Optimal inference in cointegrated time series. Econometrica 59, 283-306 (1990) · Zbl 0729.62104
[26] Rahbek, A., Kongsted, H.C., Jørgensen, C., 1999. Trend-stationarity in the I(2) cointegration model, Journal of Econometrics, forthcoming. · Zbl 1041.62522
[27] Salmon, M.: Error correction mechanisms. The economic journal 92, 615-629 (1982)
[28] Srivastava, M.S., Kathri, C.G., 1979. An Introduction to Multivariate Statistics. North-Holland, Amsterdam.
[29] Stock, J. H.; Watson, M. W.: A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica 61, 783-820 (1993) · Zbl 0801.62097
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.