I am analyzing policy diffusion using panel data, and the inclusion of temporal controls substantially influences my results. I'm wondering if it can theoretically make a difference for the estimates of my other variables if I include common time dummies for all units of observation, or if, e.g. I use separate time dummies for EU and non-EU countries. Shouldn't the common time dummies capture EU specific shocks as well?
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Yes, it can change the estimates of the other parameters. All parameters are estimated jointly. Whether you include the same time effect for all units of observation or have some different ones is a modeling choice, but if the results are highly sensitive to this choice, then you may have some deeper issues.
Suppose you are thinking about having a single time dummy or time dummies for EU and North America. And suppose, just for example, that you are interested in computing the effect of some variable on GDP. If you include a single time dummy variable, that variable will capture an average time effect across both NA and EU. It may be fine to do that. However, for example, if there were a recession that affected NA, but not EU, then the time effect would be estimated too high for NA and too low for EU. If your variable of interest is correlated with either EU or NA, then effects of the recession on GDP would be wrongly attributed to your variable of interest rather than the recession that hit NA only.
Hope that clears things up.
