Dear all. I need to estimate a model but sadly, my key regressor is only available in cross-section (no panel, only N observations for a given year). However, for the rest of my model I have available panel data (dependent variable and other controls for TxN). Si I did this: first I estimated the baseline model in a panel specification by not including that regressor for which panel data is not available, so I was able to calculate the fixed effects for each observation. After doing that, I turned back to my cross-section and included as an additional regressor a "new" variable containing all the calculated fixed effects, and now I included my key regressor as explanatory variable. The model performed perfectly, I now control for unobserved fixed effects in a cross section. The coefficient of the "fixed effect" variable is close to 1 and significant at 1%, then replicating what was estimated in the panel but relying on cross-section. Anybody can tell me if there is something wrong with this procedure? I am not interested in concluding about causality, just want to control for unobservables. Many thanks for your opinion.
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