Test statistic distribution in a cointegrating regression Let's assume I have a simple cointegrating regression of the type 
$$y_t=\beta_0+\beta_1x_t+\varepsilon_t$$
$y,x$ are $I(1)$.
If testing the OLS residuals I find that $y$ and $x$ are cointegrated, how can I perform tests on the coefficients? Are the two estimators distributed as a usual t-student? Which critical values should I use?
Thank you.
 A: Charlie, I recommend two things.
First, have a read through De Boef and Keele (2008) for a really decent overview of different time series models, especially how they relate to one another.
Second, consider using a single equation generalized error correction model (described in the preceding paper, and in more detail in Banerjee, et al. 1993), which has several attractive qualities, including:


*

*estimation of instantaneous short run effects

*estimation of lagged short run effects

*estimation of long run equilibrium effects

*desirable estimation properties (see De Boef, 2001)

*model agnosticism as to the stationarity/non-stationarity of model predictors

*ready correspondence to other dynamic model forms (e.g. ADL(1)).


The basic form of the single equation generalized error correction model is:
$\Delta y_{t} = \beta_{0} + \beta_{\text{c}}\left(y_{t-1}-x_{t-1}\right) + \beta_{\Delta x}\Delta x_{t} + \beta_{x}x_{t-1} + \varepsilon$
These models can be extended to incorporate multiple predictors, more lags, random effects, etc.

References
Banerjee, A., Dolado, J. J., Galbraith, J. W., and Hendry, D. F. (1993). Co-integration, error correction, and the econometric analysis of non-stationary data. Oxford University Press, USA.
De Boef, S. (2001). Modeling equilibrium relationships: Error correction models with strongly autoregressive data. Political Analysis, 9(1):78–94.
De Boef, S. and Keele, L. (2008). Taking time seriously. American Journal of Political Science, 52(1):184–200.
