Negative coefficient on the error correction term in an ECM Why should $\beta_2$ in the error correction model, $(Y_t – Y_{t−1}) = \beta_0 + \beta_1(X_{t−1} – X_{t−2}) + \beta_2(Y_{t−1} + (–\beta_3)X_{t−1}) + u_t$, be negative? I cannot locate any clear explanations in textbooks or presentation. All simply mention that it is negative.

It is indicating failure on stationarity around the mean, so some changes on your specification may be needed
