I am using STATA to estimate some models. I have an unbalanced data panel of 6,610 companies over 16 years.
I would like to include dummy variables about the country of origin and the sector of the companies, but, since they are time-invariant, they generate collinearity problems and they are omitted in the fixed effects model.
Could I use a random effects model although I know about the collinearity problems? (Hausman test for the models without the dummy variables tells me that the right model is the fixed effects one).
If not, what kind of model should I estimate to be able to include those dummy variables?
One option would be to try some interaction terms between your time invariant variables and one of the other variables. In this manner you can induce time variance via your interaction term and can retain the desired variables it in your fixed effects model. Besides, you may capture some nice moderating effects that can be discussed further in your conclusions.
Dear Elena,
If you are familiar with R packages, there is a nice package to analyze panel data. Here is
https://cran.r-project.org/web/packages/plm/plm.pdf
Hi Maite,
I had a similar problem. Collinearity means you can't estmate the model with FE and dummy terms, and a random effects estimate will likely be biased due to ommitted variable bias. One solution to this problem is to do a Mundlak decomposition, where you seperate each of your variables into a part that varies within and one that varies between. This has the same properties as an FE model, but has the grest advantage that you can include time-invariate variables (such as dummies). See here for details: https://www.cambridge.org/core/journals/political-science-research-and-methods/article/explaining-fixed-effects-random-effects-modeling-of-timeseries-crosssectional-and-panel-data/0334A27557D15848549120FE8ECD8D63
Hope that helped.
Tim
Thank you everybody for your answers.
I tried using R for panel data estimations for another paper and got to the conclusion that STATA was way easier to use (and also had functions I never found in R), so I will try and stick with STATA for the moment.
Tim, I will definitely take a look at the document you referenced. After posting the question I have continued researching on options to solve my problem and I have found the two-step estimation of fixed effects (https://www.stata.com/meeting/germany17/slides/Germany17_Kripfganz.pdf). Have you heard about it or used it?
Hi Maite,
no, I didn't know about this 2SLS approach, but it seems pretty clever. I would try to find some peer reviewed work checking it's properties though before completely trusting it. As the slides mention, the well established Mundlak approach is already implemented in STATA with xthybrid, so you might just want to compare the results to see whether their newer approach makes a difference.
Tim
Hi Tim,
I finally decided on using the hybrid model you suggested. Now that I am starting to do the estimations (there are quite a few I want to do), I have encountered the issue that I cannot get a goodness of fit measure easily (at least, as much as I have searched in the Internet, I have not found any feasible solution so far). I know I can compare the goodness of fit of the models using Akaike's and Schwartz's Information criteria, but I want a figure (or a couple of them) that shows how well my model is explaining the dependent variable (like a traditional R^2 would do).
Do you know which measure I should use? I have calculated McFadden's Pseudo R^2 before, but I suspect it is not applicable to these estimations, since the dependent variable is either gaussian or negative binomial (overdispersed count data).
I have found that Dr. Christopher K Baum and colleagues calculated within and between R^2 for this paper (http://fmwww.bc.edu/EC-P/wp963.pdf), but I have not found the way to calculate them in STATA after performing xthybrid.
Any suggestions?
Thank you very much.
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