Dynamic Panel and significance of the variable of interest

[Piku Sarkhel]

Dear All:
I am running a linear panel fixed effect model where my variable of interest (say x) is negatively related to the outcome variable. However, when I try to estimate the gmm using xtabond or xtabond2 the variable of interest becomes insignificant. The lagged value of the outcome variable now becomes significant. This is a panel where my T<N yet when I use the maximum likelihood method of estimation using xtdpdqml the same problem persists.
My questions : 1) Does it mean that the the time variant heterogeneity is crucial for the model ?2) Are there any other way I can check for the robustness ? Or can the fixed effect model stands on its if it passes the poolability test and hausman test ?
Please answer.

[Sebastian Kripfganz]

If the true data-generating process is dynamic, then estimating a static panel model without a lagged dependent variable leads to biased estimates.

Also, estimating a dynamic panel model with the traditional fixed-effects estimator leads to biased estimates when T is small.

[Piku Sarkhel]

I'm still confused whether to use the linear fixed effect model. Again if my variable of interest is significant in the linear model but turns insignificant in the dynamic model with lagged dependent variables. how do I choose among the models ? I have a panel for 156 countries and the time is 13 years. Please suggest.

[George Ford]

Some useful advice here. I wouldn't use a static model with a lag (T is short), but the static model without it may or may not be useful.

I suspect your series are persistent so the lag is eating the variable of interest.

https://www.statalist.org/forums/forum/general-stata-discussion/general/1409018-is-there-a-test-for-dynamic-panel-model-under-large-n-and-large-t

[George Ford]

https://www.researchgate.net/post/Dynamic-vs-Static-panel-data

[Piku Sarkhel]

Hi George,
Thanks a lot for the link ! I am inclined to think about my data as the one without persistence, so like mental health in period t doesn't influence the one in period t+1. However, whenver you are asked to do the robustness checks through gmm the necessity of dynamic panel wiill arise. That's where I am getting stuck. I'm trying to figure out if there are other ways of justifying the linear panel results through alternative robustness checks.

[George Ford]

mental health is often if not typically chronic.