# Question regarding cointegration and superconsistency

https://warwick.ac.uk/fac/soc/economics/staff/gboero/personal/hand2_cointeg.pdf

where on pages 4 and 5 it says that if the residuals are stationary, the OLS regression is superconsistent even if the Y and X variables are non-stationary.

My question then is why is it necessary to estimate the Error Correction Model (Second step)? Isn't the stationarity of residuals a sufficient condition?

Why negative $$\alpha$$? Suppose the error-correction equation is $$\Delta y_t=\alpha(y_{t-1}-\beta x_{t-1})+e_t$$. When $$y_{t-1}-\beta x_{t-1}>0$$, it means that the lagged value $$y_{t-1}$$ is "too large" relative to the cointegrating relationship, so that if $$y_t$$ is to contribute to restoring the equilibrium relationship, its change in $$t$$ must be negative, whence $$\alpha<0$$ is required.