Hi! I would like to have an opinion on something, rather than a straight-out answer, so to speak. In time-series econometrics, it is common to present both long-term coefficients from the cointegrating equation, as well as the short-term coefficients from the error correction model. Since I have a lot of specifications, and since I'm really only interested in the long-term, I only present the long-term coefficients from a cointegrating equation in a paper I'm writing. Would you say that is feasible? I'm using the Phillips-Oularis singe-equation approach to cointegration.
General principle: present what's relevant. Maybe archive the full results in case you get questions later.
ECMs are a (restricted) form of VAR and VAR champions are of the opinion that the short run cannot be modelled. From this perspective, presenting only the long run coefficients is sensible.
The Phillips-Oularis approach is a TEST for the presence of cointegration. It might not be an efficient estimator of the long run coefficients. If the coefficient values are important to you then maybe read around to get an opinion on what is a good estimation method (e.g. Stock & Watson DOLS ?)
Concerning your specific question, there is no convention about what to focus either on an error correction model and/or long term regression. The focus is determined by the objective of the research.
Anyway, consider other forms of testing long run relationships and their coefficient. Phillips Oularis is residual-based test and assumes that there is only one long run relationship, where there can be more (endogeneity between variables). In that sense, consider other alternatives, may be Johansen cointegration test is preferable as it admites more than one possible vector for long run associations between variables.
Thanks for good input. For the Phillips-Oularis approach, I present both FMOLS and DOLS estimates.
If you are interested in the long -run estimates, you should state that as an objective of the paper. Then, present JJ, ARDL, FMOLS and DOLS. That is, what will make sense. and at least look exhaustive.
http://www.ecostat.unical.it/Algieri/Didattica/Financial%20Markets/Tutorials/LIBRO%20Asterious_Applied-Econometrics-387-392.pdf