In time-series analysis we were taught that one can test for cointegration by estimating an error correction model and testing whether the coefficient estimated to the deviation of the equilibrium level is significantly smaller than zero.
Consider two explanatory variables ($x_{t}^{a}$, and $x_{t}^{b}$) and dependent variable $y_{t}$. Testing the null hypothesis of no cointegration can be done by testing the significance of the error correction term in an ECM-model. More specifically, if $\alpha$ in the following model is significantly smaller than zero this is evidence in favour of cointegration.
$$\Delta y_{t}=\beta_{1}+\alpha(y_{t-1}-\gamma_{a} x_{t-1}^{a}-\gamma_{b} x_{t-1}^{b})+\beta_{2}\Delta x_{t}^{a} + F$$
In this model $F$ contains ADL-terms in first differences needed to complement the ECM-model. The cointegrating vector $\gamma=(1 -\gamma_{a} -\gamma_{b})$ is estimated within the ECM (instead of using the residuals of a first stage estimation of the equilibrium relationship). The significance of $\alpha$ should be tested using McKinnon critical values, since under the null hypothesis of no cointegration the term $y_{t-1}-\gamma_{a} x_{t-1}^{a}-\gamma_{b} x_{t-1}^{b}$ is nonstationary.
My question: can cointegration be tested for panel-data in a similar way? If so, what critical values should be used to evaluate the significance of $\alpha$?
