So, what do you understand by vector error correction model (VECM)?

You may say any of the following: that it is a system having a ** vector** of two or more variables;

that all the variables in a VECM are endogenous; there are no exogenous variables;

VECM is constructed only if the variables are cointegrated; cointegration implies evidence of a long-run relationship among the variables;

it is a restricted VAR model with cointegrating restrictions built into the specification;

constructed to examine long- and short-run dynamics of the cointegrated series;

restricts the long-run behaviour of endogenous variables to converge to their cointegrating relationships;

that the cointegrating term is known as the error correction term;

it is a representation of cointegrated VAR (courtesy of Granger’s representation theorem) and that the resulting VAR from VECM representation has more efficient coefficient estimates.

Also, note that VAR specified in differences is a mis-specification while VECM is obtained by differencing a VAR, hence losing a lag. So, you construct a VECM with a (*p-1*) lag lengths for all the variables in the system.

These are the basic steps required to estimating a VECM. (1) series must be stationary (integrated of same order); (2) determine optimal lag length for the model; (3) perform Johansen cointegration test; (4) if there is no cointegration, estimate the unrestricted VAR model; (5) but if there is cointegration, then specify the restricted VAR model (i.e. VECM).

[Here is the video clip for the tutorial]

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I must say, your youtube videos got me through my MSc Dissertation on the use of VECM in my study. Thanks. However, there’s still an elephant in the room which is the issue of losing a lag when specifying a VECM especially when the lag criteria has revealed a particular number. If you could she’d more light on this. Amazing work you’re doing.