Estimating Long Run Economic Equilibria
Our subject is econometric estimation and inference concerning long-run economic equilibria in models with stochastic trends. Our interest is focused on single equation specifications such as those employed in the Error Correction Model (ECM) methodology of David Hendry (1987, 1989 inter alia) and the semiparametric modified least squares method of Phillips and Hansen (1989). We start by reviewing the prescriptions for empirical time series research that are presently available. We argue that the diversity of choices is confusing to practitioners and obscures the fact that statistical theory is clear about optimal inference procedures. Part of the difficulty arises from the many alternative time series representations of cointegrated systems. We present a detailed analysis of these various representations, the links between them, and the estimator choices to which they lead. An asymptotic theory is provided for a wide menu of econometric estimators and system specifications, accommodating different levels of prior information about the presence of unit roots and the nature of short-run dynamic adjustments. The single equation ECM approach is studied in detail and our results lead to certain recommendations. Weak exogeneity and data coherence are generally insufficient for valid conditioning on the regressors in this approach. Strong exogeneity and data coherency are sufficient to validate conditioning. But the requirement of strong exogeneity rules out most cases of interest because long-run economic equilibrium typically relates interdependent variables for which there is substantial time series feedback. One antidote for this problem in practice is the inclusion of leads as well as lags in the differences of the regressors. The simulations that we report, as well as the asymptotic theory support the use of this procedure in practice. Our results also support the use of dynamic specifications that involve lagged long-run equilibrium relations rather than lagged differences in the dependent variable. Finally, our simulations point to problems of overfitting in single equation ECM's. These appear to have important implications for empirical research in terms of size distortions that are produced in significance tests that utilize nominal critical values delivered by conventional asymptotic theory. In sum, our results indicate that the single equation ECM methodology has good potential for further development and improvement. But in comparison with the semi parametric modified least squares method of Phillips and Hansen (1989) the latter method seems superior for inferential purposes in most cases.
|Date of creation:||Oct 1989|
|Date of revision:|
|Publication status:||Published in Review of Economic Studies (1991), 58: 407-436|
|Contact details of provider:|| Postal: |
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
|Order Information:|| Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA|
When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:928. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.