Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T17:09:13.440Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation of Cointegration Vectors with Linear Restrictions

Published online by Cambridge University Press:  11 February 2009

Pentti Saikkonen
Pentti Saikkonen
Affiliation:
University of Helsinki
Get access Rights & Permissions [Opens in a new window]

Abstract

A general approach for the estimation of cointegration vectors with linear restrictions is described. In the special case of zero restrictions, the cointegration relations of the paper are formally similar to the structural form of a traditional simultaneous equation model. The proposed estimation procedures require a conventional rank condition of identification but no exogeneity assumption. In place of exogenous variables there are series that are not cointegrated and can therefore describe the common trends in the system. The estimators of the paper are flexible and simple to use. They can be combined with several recent estimators developed for cointegration regressions which in the present context are formally similar to the reduced form of a simultaneous equation model. After the coefficient matrix of a cointegration regression has been estimated, the estimators of the paper can be obtained by simple generalized least squares. Both single equation estimators and more efficient system estimators are developed. The asymptotic distributions of the estimators are shown to be mixed normal so that Wald tests with asymptotic chi-square distributions under the null hypothesis can be obtained in the usual way. Convenient test procedures for checking the validity of overidentification restrictions are also provided.

Type
Articles
Information
Econometric Theory , Volume 9 , Issue 1 , January 1993 , pp. 19 - 35
Copyright
Copyright © Cambridge University Press 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Anderson, T.W.The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proceedings of the American Mathematical Society 6 (1955): 170–176.CrossRefGoogle Scholar
2.Balestra, P.The indirect least square approach to structural parameter estimationA paper presented at the European Meeting of the Econometric Society inBudapest, September 1–5, 1986.Google Scholar
3.Basawa, I.V. & Scott, D.J.. Asymptotic Optimal Inference for Non-ergodic Models. New York: Springer-Verlag, 1983.CrossRefGoogle Scholar
4.Byron, R.P.Testing structural specification using the unrestricted reduced form. Econometrica 42 (1974): 869–883.CrossRefGoogle Scholar
5.Dhrymes, P.J.Introductory Econometrics. New York: Springer-Verlag, 1978.CrossRefGoogle Scholar
6.Engle, R.F. & Granger, C.W.J.. Cointegration and error correction: representation, estimation and testing. Econometrica 55 (1987): 251–276.CrossRefGoogle Scholar
7.Gourieroux, C. & Monfort, A.. A general framefork for testing a null hypothesis in a “mixed” form. Econometric Theory 5 (1989): 63–82.CrossRefGoogle Scholar
8.Hansen, B.E. & Phillips, P.C.B.. Estimation and inference in models of cointegration: a simulation study. Advances in Econometrics 8 (1990): 225–248.Google Scholar
9.Hausman, J.A. Specification and estimation of simulataneous equation models. Handbook of Econometrics, Vol. 1, Chapter 7. Amsterdam: North-Holland.Google Scholar
10.Johansen, S.Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12 (1988): 231–254.CrossRefGoogle Scholar
11.Johansen, S.Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59 (1991): 1551–1580.CrossRefGoogle Scholar
12.Judge, G.G., Griffits, W.E., Hill, R.C., Lütkepohl, H. & Lee, T.C.. The Theory and Practice of Econometrics, Second Edition. New York: Wiley, 1985.Google Scholar
13.Monfort, A. & Rabemananjara, R.. From a VAR model to a structural model, with an application to the wage-price spiral. Journal of Applied Econometrics 5 (1990): 203–227.CrossRefGoogle Scholar
14.Park, J.Y.Canonical cointegrating regressions. Econometrica 60 (1992): 119–143.CrossRefGoogle Scholar
15.Park, J.Y. Maximum likelihood estimation of simultaneous cointegrated models. Unpublished manuscript. Cornell University, 1991.Google Scholar
16.Park, J.Y. & Phillips, P.C.B.. Statistical inference in regressions with integrated processes: Part I. Econometric Theory 4 (1988): 468–497.CrossRefGoogle Scholar
17.Park, J.Y. & Phillips, P.C.B.. Statistical inference in regressions with integrated processes: Part II. Econometric Theory 5 (1989): 95–131.CrossRefGoogle Scholar
18.Phillips, P.C.B. Spectral regression for cointegrated time series. In Barnett, W.A. (ed.), Nonparametric and Semiparametric Methods in Economics and Statistics, New York: Cambridge University Press (forthcoming).Google Scholar
19.Phillips, P.C.B.Optimal inference in cointegrated systems. Econometrica 59 (1991): 283–306.CrossRefGoogle Scholar
20.Phillips, P.C.B.Error correction and long-run equilibria in continuous time. Econometrica 59 (1991): 967–980.CrossRefGoogle Scholar
21.Phillips, P.C.B.Unidentified components in reduced rank regression estimation of ECM's. Cowles Foundation Discussion Paper No. 1003, Yale University, 1991.Google Scholar
22.Phillips, P.C.B. & Durlauf, S.N.. Multiple time series regression with integrated processes. Review of Economic Studies 53 (1986): 473–496.CrossRefGoogle Scholar
23.Phillips, P.C.B. & Hansen, B.E.. Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies 57 (1990): 99–125.CrossRefGoogle Scholar
24.Phillips, P.C.B. & Loretan, M.. Estimating long-run economic equilibria. Review of Economic Studies 58 (1991): 407–436.CrossRefGoogle Scholar
25.Saikkonen, P.Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7 (1991): 1–21.CrossRefGoogle Scholar
26.Saikkonen, P.Estimation and testing of cointegrated systems by an autoregressive approximation. Econometric Theory 8 (1992): 1–27.CrossRefGoogle Scholar
27.Soms, A.P.A note on equality in Anderson's theorem. Communications in Statistics Theory and Methods 20 (1991): 141–145.Google Scholar
28.Stock, J.Asymptotic properties of least squares estimators of cointegrating vectors. Econometrica 55 (1987): 1035–1056.CrossRefGoogle Scholar
29.Stock, J. & Watson, M.. Testing for common trends. Journal of the American Statistical Association 83 (1988): 1097–1107.CrossRefGoogle Scholar
30.Stock, J. & Watson, M.. A simple MLE of cointegrating vectors in higher order integrated systems. Technical Working Paper No. 83, National Bureau of Economic Research, Inc., 1989.CrossRefGoogle Scholar
31.Sweeting, T.On estimator efficiency in stochastic processes. Stochastic Processes and their Applications 15 (1983): 93–98.CrossRefGoogle Scholar
32.Szroeter, J.Generalized Wald methods for testing nonlinear and overidentification restrictions. Econometrica 61 (1983): 335–353.CrossRefGoogle Scholar