Fixed effect issue (deleting variables)

[Ammanna Azwai]

Hi,

I got a question related to my regression.In fact, I'm using merged datasets. first one is bank level and the second one is country level. my data is panel so I'm using Fixed Effect method. However, when I run my regressions using the fixed effect methods, two of my main explanatory variables are deleted by stata. Also, I would like to let u know the number of obs of country level variables is almost half of bank level jobs. Please let me know if you can provide me with any recommendations to solve this issue. Please note when I use random effect no variable got deleted. I have attached some pictures for your references. Thank alot in advance.

[Jared Greathouse]

I'm willing to bet that the two predictors are time invariant, which, as folks like Andrew Musau or Carlo Lazzaro will also explain to you, is very bad no good with FE estimation.

Well, it isn't that it's bad, it's just that the mathematical mechanics of the estimator will not allow estimators with time fixed variables to estimate, so I presume Stata drops these if it detects it (though I haven't tried and I'm not at my computer to see).

[Nick Cox]

Cross-posted at https://stackoverflow.com/questions/...ting-variables

Please note our policy on cross-posting, which is that you are asked to tell us about it. https://www.statalist.org/forums/help#crossposting

[Carlo Lazzaro]

Ammanna:
as an aside to Jared and Nick's excellent advice, it is not correct to state that Stata deleted two time-invariant predictors.
As Jared highlighted, Stata omitted them due to collinearity with the fixed effect; no wonder that it happened, as, due to the demeaning that the -fe- machinery applies, the mean of a constant is still a constant and a constants minus the very same value equals 0 (or no estimable coefficient).
Conversely, thanks to the -theta- parameter which is part of te -re- specification, Stata (or whichever other statistical package available on the market or for free) gives you back the coefficients for the time-invariant regressors, too.
Again, no wonder.
However, while the -fe- estimator is consistent event though -re- should be the way to go (say, according to the -hausman- test outcome that, unofortunately, you cannot run with non-default standard errors; see the community-contribute module -xtoverid-, instead) at the cost of a minor efficiency, if -fe- is the right specification and you go -re- , -re- is inconsistent (put differently: your estimates are unreliable).
In addition, the main (really restrictive) -re- assumption of no correlation between the u error term and the vector of regressors seldom holds in empirical researches.
Last but not least, please do not post screenshots (for reasons that are well detailed in the FAQ), buit use CODE delimiters (as per FAQ again) to share what you typed and what Stata gave you back. Thanks.

[Ammanna Azwai]

Hi @Carlo Lazzaro @Jared GreathouseI, Many thanks for your time and explanation. In fact, have doubled checked the values of these two variables and I found that it is completely true that these two variables have constant values so when Stata applies FE method the demeaning step results in zero values for these 2 variables. Hence, Stata omits them based on my understanding of your previous explanation.
(Please correct me if I’m wrong).
Based on your experience, 1)What is the best solution in this case as those two variables are (my main control variables) and I want to be able to read their impacts on my dependent variable. Kindly, is there any other way that to have an estimable coefficient for those variables. Also, I previously provided the random effect estimation just for comparison purpose to use itThank you a lot for your help and time in advance.

[Carlo Lazzaro]

Ammanna:
you may want to consider the Mundlak approach.
I'm away from my computer at the moment and cannot provide you with the link, but this topic is covered in the Stata blog.

[Clyde Schechter]

1)What is the best solution in this case as those two variables are (my main control variables) and I want to be able to read their impacts on my dependent variable.

You are contradicting yourself here.
You need to make up your mind whether these are "control" variables or whether you want to assess their impacts on the outcome. A "control variable"*, by definition, is one that is included in the model because its omission would lead to bias in the estimates of the effects of the variables you are interested in, but the effect of the "control variable" itself is of no real interest. It is a nuisance variable that is included so that its omission will not distort the important parts of the analysis.

If, in fact, these variables are "control variables," in a fixed effects model, you do not have to worry about omitted variable bias when they are time-invariant, in the fixed effects model, the fixed effects themselves carry all of this information into the analysis and any time-invariant attributes are automatically "controlled" without the need to explicitly deal with them. That is one of the attractive features of fixed-effects models: omitted variable bias for time-invariant variables is automatically eliminated.

On the other hand, if these really are variables that your research goals require you to estimate the impact of, but they are time invariant, than the conclusion is inevitable that you cannot use a fixed-effects model, because estimating the effects of such variables in such models is mathematically impossible. A random-effects model, or a Mundlak approach, as suggested by Carlo Lazzaro in #6, would be my first choices in this situation.

*I am using scarequotes around "control variable" because I hate the term with a passion. It obscures the reality that in observational data nothing is controlled. The inclusion of these variables results in adjusting the analysis in ways that reduce omitted variable bias, but it is in no way equivalent to actually controlling for those variable, as one would do in an experimental design. I realize that the term "control variable" is widely used, and it is probably a lost cause for me to try to stamp it out, but at least I want people who use it to realize that it is a very misleading term and an abuse of language.

[Ammanna Azwai]

Hi All, I would like to thank you all for your time and advices. I have taken all those recommendations into my considerations. Those advices really help to correct my results. Many thanks again.