Can refer to

" DO RISK PREFERENCES CHANGE? EVIDENCE FROM PANEL DATA BEFORE AND AFTER THE GREAT EAST JAPAN EARTHQUAKE " by Chie Hanaoka , Hitoshi Shigeoka and Yasutora Watanabe

Dear Mousumi, thank you for your response. I indeed read this article and kept this in mind, but needed further ideas on how to proceed in my case.

One way to check the changes over time is trend analysis. You can use regression models to check the trend of a continuous variable, while you can use the Cochran-Armitage test to assess the trend of a binary variable.

Building on the previous answer, I suggest including a full set of period dummies in your model (omitting the first one to avoid the dummy variables trap). This is best practice in any panel analysis, because the period dummies attenuate cross-group error correlation. (Without the period dummies, the effects of period-specific shocks enter the error terms across all of the groups and thus cause them to be correlated.) In addition, the period effects can be interpreted for their economic meaning. A time trend is usually too restrictive, because it assumes that the time effect - if any - is monotonic. However, individual period effects will give a first impression as to the presence or otherwise of structural changes over time. The next step, for a more complete analysis, is to interact the individual period dummies - or, to save degrees of freedom, the period dummies consolidated into, say, two periods - with your variables of interest. This will enable you to identify, measure and test whether the respective slope coefficients are subject to structural changes over time.

dear Geoffrey, thank you for your precious advice. As I understood correctly, I need to run FE or RE models with year dummies (i.year) and include interaction terms of control variables with those year variables to see how stability changed in each year with respect to each regressor?

Yes, exactly right. A practical consideration is that interaction between each year dummy and several variables of interest might lead to an excessive number of interactions and potential multicollinearity. However, this is a matter for trial and error rather than theory. In the event of problems with too many interactions, combine your knowledge of historical (institutional etc.) developments and the estimated effects of the year dummies to create dummies covering distinct periods (e.g. before and after the global Financial Crisis). Then interact these period dummies with your variables of interest. Finally, use Stata's "Margins" and "Marginsplot" commands to identify structural breaks (if any). One unrelated point. If you find a reply useful, then please recommend it. This is not just a matter of vanity but is helpful for new followers of the discussion.