I'm not sure "using a combination of the AIC and general-to-specific" for estimating an ECM model is appropriate. You may rely on G-T-S or AIC to estimate your ECM model and make sure that the model passes the diagnostic checking. Alternatively, you may estimate 2 ECM models; the first one using G-T-S and the second one using AIC. If the results are similar that ensure the accuracy of your estimation or can be considered as a robustness or a sensitivity analysis.

Don't feel compelled to automatically drop a lagged term because its t-stat prob is above your preferred significance level, especially if the discrepency is marginal.

You say that you are principally interested in cointegration results. As Abdalla suggests, you can estimate several variants of the ECM with different lag structures and note whether the cointegration conclusions are robust with respect to the details of the lag structure.

Dear Mads, note that while the choice of information criteria to be used is entirely the author's as no information criteria is superior to the other, AIC is preferable when dealing with very large sample and SIC is ideal for relatively small sample size. For ARDL model, the starting point is to determine the optimal lag of the dependent variable by conducting a regression on both the first differences and lag of level variables and then using lag structure to determine. In constructing the ARDL-based ECM, it is rather more scientific to consider either AIC or SIC when applying general to specific method. For instance, as you remove the insignificant variables, you also keep a close watch on AIC or SIC as they decrease in value, until they reach a threshold and start increasing in value, then you have attained the optimal lag. The lag order doesn't follow chronological process as a variable may appear in its 2nd lag whereas its first lag has been removed. If you have difficulty implementing the general to specific ARDL-based ECM, I suggest you consider using EVIEWS version 9 or 10 as ARDL is easier and follows automatic process. However, if you insist on using other eviews versions lower than 9, you should be mindful of mis-specification error as you remove variables.

I would expect that log(Y) (output variable) and u are I(1). If this is the case their first difference is I(0) and I do not see how Okun's Law can be an ecm. If you find that the first differences are I(1) then you should probably use a VECM as it is likely that neither variable is weakly exogenous and you should jointly model both variables and test for cointegration in a Johansen framework. You can test for weak exogeneity within this framework . and proceed with your single equation analysis if you find weak exogeneity.

I´m using the ARDL bounds-approch to estimate my ECM. I haven´t tested if my independent variable is weakly exog. I have a single equation bivariate model, where both of my variables are I(0). Does any of you know how I can test if my independent variable for the weakly exogeneity assumption?

Mette Marit Johansen

If you have only two variables and they are I(0) you have no need for an ecm. You can still use the ARDL methodology to estimate a dynamic bivariate model in the levels of the variables. This will enable you to estimate the short-run (from the regression coefficients0 and the long-run (by assuming that all variables are at a steady-state) multipliers. See Pesaran (2015), Time series and Panel Data Econometrics, CUP.

One way of testing for exogeneity in a bivariate context uses the Durbin-Wu-Hausmann procedure. The model is estimated by OLS and 2SLS and the two estimates compared. For details check your software manual and your text book. There is a very good but advanced treatment of these matters in Wooldridge (2010), Econometric Analysis of Cross Section and Panel Data.

John C Frain

Thank you very much for answering! :)

I´m a bit confused about the difference between the use of an ecm when the variables are both I(0) compared to when they are both I(1). If you have time, can you give me a quick explanation?

Let y(t) be some economic variable. The path of y(t) may be subject to random shocks over time,

None of 2 to 6 applies to stationary variables. If x and y are stationary you can work with the variables in levels (and possible lags of the variables). I presume that you have an appropriate economic model in mind and that you do not have relevant missing variables.

I understand. That´s clarifying.

I have read some other comments, among yours, on the ARDL bound testing approach, and it seems like Im not able to use that approach when my dependent variable also is I(0). Is that correct?

Im modeling one single equation between the mortgage rate and the money market and, one single equation between the money market rate and the Norwegian policy rate. I though it was possible to use the above mentioned approach, but now I´m not so sure anymore... :)

I have ordered the Pesaran (2015) from the library and will check it out in a few days.