Individual and country fixed effects

[Christian Elmar]

Hi,

I have a groups of individuals coming from differnt countries. Those individuals change their behavior over time and put effort depending on the incentives provided. I regress effort on salaries and put individual dummies as salaries changed from year one to two. If my reasoning is correct, then individual dummies help to capture personal unobservables.

When I replicate a regression from a publication, They do a similar regression of effort on salaries with individual and country dummies at the same time. Is that actually possible/necessary? Since the unobservables are already captured by the individual dummies what should the country dummies capture? (Notice, individuals do not change the country).

The regression is the following:
reg Effort Salaries i.individual i.year i.country, vce(clustering country)

Thanks,
Christian

[Carlo Lazzaro]

Christian:
probably, in the example you quoted, authors considered country (not individuals) as the cross-sectional part of their panel and performed a pooled OLS (as they clustered the standard errors on that independent variable). it would be interesting to see the results of their regression and, especially, if any predictor was dropped due to collinearity.
Eventually just out of curiosity, did you rely on the-xt- suites available in Stata for your analysis?

[Christian Elmar]

Thanks for your reply.
The variation in salaries is indeed at the country level, why country clustering would make sense. However, when I checked the authors cluster at the individual level. Unfortunately, I do not have the authors stata output, but since the study was published, I guess there will be no remaining issues of multicollinearity.

My questions still remains, what are the country dummies good for, when there are already individual dummies? Thanks.

[Carlo Lazzaro]

Christian:
I'm a bit puzzled by the fact that authors seem to have clustered standard errors in two different ways; i would e-mail them up to get some explanation and, possibly, Stata code and output.
As far as I can understand their approach, they might have investigated whether or not, other things being equal, country had some effect in predicting variation in mean conditional salary. Again, it would be interesting to take a look at their regression machinery.
Anyway, I find quite unsusual that they did not log the dependent variable -salary-, as a log-linear model makes more sense in this instance.

[Phil Bromiley]

The discussion seems to be mixing country/individual dummies (fixed effects) and clustering of the remaining error term. If individuals do not change country, then you cannot have individual dummies (fixed effects) and country dummies in the same model - the country dummies are redundant. You could estimate a similar model that assumes country effects are orthogonal to the rest of the variables (see xthtaylor). In your regression example, you should not get estimates on many of the dummies.

However, the dummy variable issue is separate from the clustering of the remaining errors. You could do a more complex error structure allowing the remaining errors to correlate in lots of different ways.

[Roman Mostazir]

Could you cite the paper please? May be we could have a look, if get the access, to understand their approach.

[Christian Elmar]

Of course, http://onlinelibrary.wiley.com/doi/1...coj.12056/full page 1144, table 5, specification 4.

[Roman Mostazir]

To be honest, I didn't have the time to get through all the details of this large article. However, as I skimmed through, I didn't find any explicit description of the models. Though it is unrealistic to comment specifically without seeing the data structure, by looking at the output I think they used fixed effect (within subject) model. They even didn't mention what software has been used for analysis (unless I missed!!). In Stata, command for such model will be "xtreg ..,fe" You don't need 'i.individual' in the model, as 'fe' does the necessary thing for you. But again confusion remains about country because if country does not vary within subject it will be dropped from the model and I can't think of how a parliamentarian from i.e. Poland can be from Germany in next session !!!! You can always email the authors for further clarification.

[Carlo Lazzaro]

Christian:
as an aside to Roman's informal review of the article (on which I do agree, especially about the quite scant methods section), it seems that Authors clustered standard errors at the parliamentarian level and include both individual and country fixed effect (as you reported). Although I am not clear about the difference between parliamentarian and individual level, I find interesting that Authors included a squared term for age (and that may be a valuable input for your model, too), which turned out to be significant (i.e., identified a turning point) in some of the reported regressions.

[Christian Elmar]

Thanks for your answers.
@Roman: yes, I guess they use STATA, but do not explicitely mention it. Furhtermore, I agree this is a fixed effect (within subject) model. "xtreg ...,fe" should be the same as "xi: reg .... i.individual". However, how individual and country fixed effects can go together in one specification still remains unsolved. (Could it be the case that a country dummiey just sums up the individual dummies from those individuals in this specific country?)

@Carlo: I think parliamentarian and individual level is the same. The squared term of age is indeed a nice finding.

@all: Given that the authors include country fixed effects, shouldn't country control variables (such as GDP or the HHI) be redundant? In the case of individual fixed effects, age gender and PhD-MD are also excluded.

Best,
Christian

[Carlo Lazzaro]

Christian:
reading around the first third from above of page 1137, it seems that parliamentarian and individual fixed effects are not the same thing; however, I still fail to get a clear difference between these two terms.
If your interest in this article is still high, I would e-mail the Authors asking for clarifications on the same list of remarks as per your last post.