# Intercept in 2nd-stage Error Correction Model (ECM) regression — yes or no?

When doing a two-step ECM regression, do we add an intercept in the 2nd stage regression? I've seen course notes that add an intercept in the ECM, but some do not, so I'm confused if I should include it or not.

The inclusion of an intercept, however is important for various test statistics, like the $$R^2$$ which is, in general, not valid if the intercept is dropped from the specification. Also, as said by @1muflon1 if you run a regression without an intercept, the mean residual will usually be different from zero, which is highly undesirable.