industrt-region fixed effect with firm observations

[Min Zhu]

Dear all,
I have a firm-level panel data which I estimate how much regional institution quality contributing to firm-level TFP. In other words, my dependent variable is firm-level TFP, my regressor including firm-level controls such as size and age of the firm, regional institutional quality and year fixed effect. I use firm fixed effect and cluster at regional level.
I do not including region and industry dummy as they will wiped out by firm fixed effect. The result is 1 unit increase in non-state
share in gross output increases firm TFP about 2.6%, even is marginal, which is not that bad.

But I was wondering that the firm fixed effect is too narrow that I basically kills lots of variations. So I decided use region-industry fixed effect. My code is:egen region_indus=group(region industry), then I xtset region_indus. The problem is if I writing xtset region_indus year. it reports repeated time values within panel error. But if I only write xtset region_indus. I am actually able to proceed my regression. So I did not declare my tsset year in STATA. At this setting, my dependent variable is still firm TFP, my regressor is size, age, export dummy, ownership dummy, regional institutional quality, time fixed effect, and industry-regional fixed effect, clustering at regional level. Because the ownership and export dummy can't be wiped out when I use industry-regional fixed effect, so i added them in the regression. My question is how much I can trust this regression result when I have the repeated time values within panel error. I don't really understand why I can do the regression with this error. My regression result is:

lnb is the size of firm, Dev_lab_m~4c measures regional institution quality, exp_dum is export dummy, type01 is the ownership dummy. The number of group is correct. But I really don't know whether this is correctly regressed. Because I have firms nested in regional level and my region_indus is not uniquely identified. But why write xtset region_indus the regression can continue. But when I write xtset region_indus year, the regression can't proceed.
Another issue which way is making mores sense? In my opinion, firm fixed effect is too narrow, because firms located at the same place and within the same industry can be very similar. So I prefer region-industry level fixed effect, as I subtract the average of all firms within the same industry at the same province. But i feel really puzzling. Therefore, I sincerely need the suggestions to clear my cloud.

The attachment is a small sample from my data.

[Clyde Schechter]

First, about -xtset-. When you specify -xtset panelvar timevar-, Stata requires that the combination of panelvar and timevar uniquely identify observations in your data. When you use region_indus as the panel var, this is no longer true, because for any combination of region_indus and year there are several observations corresponding to each firm. If you specify only -xtset panelvar-, then you can have as many observations per level of panelvar as you like. For -xtreg, fe-, the time variable in -xtset- plays no role, in the analysis, so setting the time variable is not necessary.

Now, the question remains whether it is appropriate to use -xtset region_indus- for your modeling. I would argue that the answer is no. The most important thing that using -xtreg- does, in my opinion, is that it can correctly overcome the problem created by the lack of independence of observations. But for that to work, you must -xtset- your data at the lowest level of clustering. By going up to the level of region_indus, you have ignored the clustering of observations within firms; you are treating them as if they are independent. That is incorrect.

I don't really understand your firm effect is "too narrow" or that it "kills to many" sources of variation. Using -xtset firm- with -xtreg, fe- automatically adjusts for any time-invariant firm-levvel attributes and thereby eliminates many potential sources of observed and unobserved missing variable bias. If what you mean is that you are actually interested in estimating some of these effects, that they are of interest in their own right, then the solution is not to do an incorrect and distorted version of -xtreg, fe- clustered at the wrong level, but to do a between-effects analysis with -xtreg, be-, or a random-effects regression (-xtreg, re-, or perhaps in your case a 3-level model using -mixed-.)

So, to summarize. Don't worry about the warning from -xtset-; it doesn't matter for your purposes. But I wouldn't run -xtreg, fe- with -xtset region_indus- because the results will be invalid. If you want to study the effects of time-invariant firm-attributes, you need a different model altogether: -xtreg, be- or -xtreg, re-, or -mixed-.)

Finally, a few asides about posting. Attaching data sets is discouraged. To show example data, use the -dataex- command. See FAQ#12 for details, and also for advice on the best ways to show output.

[Min Zhu]

Dear Clyde,
Thank you very much for your prompt reply. It really helps me clear the cloud. I will read the FAQ right now to understand the best ways of showing output.