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The cointegration hypothesis can be formulated in terms of the vector error correction model as a reduced rank test.
Vector Error Correction Model (VECM) Once the cointegration is confirmed to exist between variables, then the third step requires the construction of error correction mechanism to model the dynamic relationship.
After the long-run coefficients are identified, they are used to formulate the vector error correction model of the following generalized form: [DRLTA][y.
Vector Error Correction Model A vector error correction (VEC) model is a restricted VAR that has cointegration restrictions built into the specification, so that it is designed for use with nonstationary series that are known to be cointegrated.
Accordingly, we use vector error correction models (VECMs) to jointly estimate the long-run relationship in a cointegrating vector and short-run effects in first-difference equations, respectively: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where the lags of first-difference endogenous variables minimize the Akaike information criterion (AIC), X is a vector of exogenous factors, [[epsilon].
Their approach begins with a vector error correction model (VEC), such as the following: [Delta][X.
Granger's (1991) Representation Theorem further implies that we should specify a Vector Error Correction Model, VECM, (instead of a VAR) in which causality is detected among the variables in at least one direction.
VECTOR ERROR CORRECTION MODEL AND GRANGER CAUSALITY TEST The number of cointegrating relationships found in Table 3 will result in a corresponding number of residual series, and hence error correction terms (ECTs), to be used in the subsequent vector error correction model (VECM), results based on which appear in Table 4.