Choosing between static and dynamic panel data analysis

[Jovana Ju]

Hello everyone!

I’m seeking help with my problem regarding the choice between static and dynamic analysis of panel data. I am examining the impact of ESG variables (2 variables) on financial performance indicators (ROA, ROE, ROS), with N=60 (companies) and T=6 years. In the literature, both models that include lagged dependent variables among the independent variables and those that do not are used. What method can I use to methodologically determine whether I need to use a lagged dependent variable as a regressor? I started with static analysis, using independent variables with lags, and the analysis led me to apply a fixed effects model. However, the question arose whether I should switch to dynamic analysis. Intuitively, I understand that I should test whether Yt-n is statistically significant, but I assume it’s not correct to simply include it in the fixed effects model?

Thank you all so much in adance!

[Sebastian Kripfganz]

The first question should be whether there are theoretical arguments for considering a dynamic panel model. This seems to be the case given that dynamic models are indeed estimated in the related literature. Models with lagged dependent variables can be regarded as partial-adjustment or equilibrium-correction models. There is some persistence in the dependent variable that lets it react only partially to a change in its predictors, and therefore it takes more time until a new equilibrium is reached.

If the true data-generating process is indeed dynamic, a static model will yield biased estimates of the immediate short-run effects. A dynamic model instead allows to compute both long-run and short-run effects.

Assuming that the dynamic model is consistently estimated, you can indeed simply test whether the coefficients of the lagged dependent variables are statistically significant. If they are not, then a static model might be sufficient.

You can also test for the presence of serially correlated errors in the static model; see xtdpdserial. If there is evidence of such serial correlation, then a dynamic model might be more appropriate. However, serially correlated errors could also be caused by other types of model misspecification, not just omitted lagged dependent variables.

Estimating a dynamic model is more challenging than estimating a static model. With such a small T, the fixed-effects estimator can be severely biased. The most popular alternative are GMM estimators, which also allow treating the other regressors to be potentially endogenous or predetermined; see xtdpdgmm. If you are confident with your assumption of strictly exogenous regressors (other than the lagged dependent variable) - which is also an underlying assumption of the static fixed-effects estimator - then bias-corrected or maximum-likelihood estimators can be very good alternatives that tend to be (much) more precise than GMM estimators; see xtdpdbc and xtdpdqml.