I am an applied economist; not an econometrician. So I hesitate to say that published papers in good journals are not adhering to good practice. However, having made this gesture towards humility, this is what I am about to argue. The key to determining the model specification that best conforms to the underlying process or mechanism that generates your data (the data generating mechanism) is diagnostic testing. In the case of distinguishing between a static or a dynamic model - hence, making a judgement about the underlying data generating mechanism - a simple procedure is to estimate a static panel FE model and then test the within-group residuals for serial correlation. (In Stata, this may be done by the user-written xtserial package, which implements a test devised by Jeffrey Wooldridge.) If the null of no serial correlation in the residuals is not rejected, then it is reasonable to conclude that your model does not suffer from unmodelled dynamics. In this case, estimate a static model. However, if the null is rejected, then your model has not captured the dynamics in the data. In this case, estimate a dynamic model. In effect, estimating a dynamic model is to displace the dynamics in the data from the error term (where serial correlation violates the assumptions of the estimator) into the estimated part of the model (where the dynamics are explicitly modelled and thus yield useful information - e.g. enabling long-run and short-run effects to be distinguished). If this reasoning is correct, then it is not helpful (to say the least) to report both static and dynamic models. They cannot both be well specified. Indeed, it is my observation that researchers who report both do not undertake diagnostic tests. I suspect that if diagnostic testing were to be undertaken then it would reveal the static models to be misspecified and thus - by their construction - yielding biased and inconsistent estimates . (In my experience, time-series data usually exhibit serial dependence, which needs to be taken into account in specifying econometric models). To summarise: (I) test for serial correlation; and (ii) if you find it, explain to your readers why you specify and report only a dynamic model.

By the way, the GMM is a general approach to estimation. As such, it is often applied to dynamic models but is not restricted to dynamic modelling (e.g. the GMM approach can be used to estimate static models).

Your assumption makes sense on economic grounds. However, if the time-series depth of your data permits, I suggest that you also investigate longer lags between R&D and firm performance.

Your decision to report both static and dynamic models is OK as long as you explain to your readers which of these is your preferred model. However, in the case that your preferred model is dynamic (i.e. including one or more lags of the dependent variable among the regressors), do not make the (common) mistake of reporting static models as "robustness checks". They are not. Please allow me to explain.

If your investigation - guided by diagnostic testing - leads you to specify a dynamic model, then static models are (by definition) not robustness checks. A robustness check would be to estimate the same model but with, say, one or more different variable definitions (where theory does not precisely guide the precise choice of variable or definition), sample periods, sample countries, and choice of estimator (where all available estimators involve different trade offs such that there is no clear universally preferred approach to estimation). The point is that a robustness check must be a genuinely plausible alternative to your chosen strategy. A clearly misspecified model - e.g. static FE in the presence of residual autocorrelation - is not a robustness check, because it has already been rejected by your diagnostic testing. It is "tennis with the net down"! Having said this, if space permits, it can be useful to report, say, a static FE model along with appropriate diagnostic tests - especially for serial correlation - so that readers can see the difference made by dynamic specification. But this is to report a baseline model; it is not a robustness check.

.ice of estimator (where all available estimators involve different trade offs such that there is no clear universally preferred approach to estimation). The point is that a robustness check must be a genuinely plausible alternative to your chosen strategy. A clearly misspecified model - e.g. static FE in the presence of residual autocorrelation - is not a robustness check, because it has already been rejected by your diagnostic testing. It is "tennis with the net down"! Having said this, if space permits, it can be useful to report, say, a static FE model along with appropriate diagnostic tests - especially for serial correlation - so that readers can see the difference made by dynamic specification. But this is to report a baseline model; it is not a robustness check.

As to your decision to report both static and dynamic models, this is OK as long as you are clear about your preferred model (and explain this to your readers). However, if your preferred model is dynamic (i.e. including one or more lags of the dependent variable) then do not make the (common) mistake of reporting static models as "robustness" checks. They are not. Please allow me to explain.ice of estimator (where all available estimators involve different trade offs such that there is no clear universally preferred approach to estimation). The point is that a robustness check must be a genuinely plausible alternative to your chosen strategy. A clearly misspecified model - e.g. static FE in the presence of residual autocorrelation - is not a robustness check, because it has already been rejected by your diagnostic testing. It is "tennis with the net down"! Having said this, if space permits, it can be useful to report, say, a static FE model along with appropriate diagnostic tests - especially for serial correlation - so that readers can see the difference made by dynamic specification. But this is to report a baseline model; it is not a robustness check.

Manali Chatterjee I recommand for you to read Wintoki et al., (2012), I'm currently working on something similair of yours, comparing static and dynamic results helps alot in confirming the existence of endogeneity especially in research traiting firms performance

Chapter PANEL VERİ MODELLERİNDE SAPMALARA KARŞI ALTERNATİF YAKLAŞIML...

You can reach your answer up link.