Abstract
The paper introduces a stationary vector autoregressive (VAR) representation of the error correction model (ECM). This representation explicitly regards the cointegration error a dependent variable, making the direct implementation of standard dynamic analyses using standard VAR models possible, particularly with respect to the cointegration error. Of course, an ECM does not have an explicit VAR form, and thus, it is not convenient for conducting such dynamic analyses. In this regard, we transform the original nonstationary VAR model into a VAR model with the cointegration error and stationary variables. Finally, we employ the model to dynamically analyze the real exchange rate between the US dollar and the Japanese yen.
Highlights
The dynamic analysis of the cointegration error and stationary variables in the short run is important as the longrun equilibrium for practitioners and policy makers
Such work is possible through the classical error correction model (ECM), which was popularized by Engle and Granger (1987)
Such work may be possible if we transform the ECM into a vector autoregressive (VAR) form of the cointegration error and stationary variables, which would allow the more direct exploitation of the rich tools of VAR analyses
Summary
The dynamic analysis of the cointegration error and stationary variables in the short run is important as the longrun equilibrium for practitioners and policy makers. The persistence profiles of Pesaran and Shin (1996) and Hansen (2005) are useful alternatives for this purpose Another possible option is to follow the vector autoregressive (VAR) approach of Sims (1980), which is a standard method. Such work may be possible if we transform the ECM into a VAR form of the cointegration error and stationary variables, which would allow the more direct exploitation of the rich tools of VAR analyses (i.e., the Granger causality test, impulse response analysis, variance decomposition, and optimal forecasting). The question is whether we can transform the ECM into a finite-order VAR model of the cointegration error and stationary variables. In the VAR model, the cointegration error is regarded as a dependent variable, and VAR-type dynamic analyses may be conducted directly.
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