regressions with Fixed Effect and CCEMG/CCEP give different results

[Zahrina Adani]

Dear all,

I want to ask you about results of fixed effect and CCEP/CCEMG.

I regressed my variables using FE two way (with command xtreg) and found that my variable of interest and control variables significant.
However, I did the test of cross-sectional dependence for every variable and found them to be cross-sectional dependent.

For that reason, I decided to regress again using CCEP and CCEMG. However, I ended up with all my variables become insignificant.
Can someone help me if it's actually normal?

Thanks a lot

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex. You are also asked to provide the source of any routines not provided by Stata.

I don't find any ccep or ccemg routines when I do findit from the command window. Without knowing what these procedures are or how you implemented them, it is pretty hard to help you.

It looks like this is a lot like what xthybrid does and it will give you precisely the same results as xtreg, fe for the within estimates.

[JanDitzen]

Zahrina, I agree with Phil and there are a few more important things. First of all what are the dimensions of your dataset? Depending on the dimension and your underlying model you need to decide which estimator to choose. This has implications whether you can estimate heterogeneous slopes (CCEMG) or if a pooled estimator is preferable.

In a nutshell, there are the following possibilities:

• large N, fixed T: then you can use the standard fixed effects estimator such as xtreg. If you sample is large enough, then you might be able to use xtmg or xtdcce2. If you use xtdcce2 and pooled coefficient, then I encourage to use the fixed T standard error correction. There are plenty of discussions in this forum.
• fixed N, large T: commands such as xtpcse are the choice (see https://www.statalist.org/forums/for...xpcse-vs-xtreg)
• In the case of large N and large T (or assuming that these are the dimensions going jointly to infinity), you can use CCEP and CCEMG estimators and thus xtmg or xtdcce2. This is usually the standard case when cross-sectional dependence really becomes a problem.

[Zahrina Adani]

Zahrina, I agree with Phil and there are a few more important things. First of all what are the dimensions of your dataset? Depending on the dimension and your underlying model you need to decide which estimator to choose. This has implications whether you can estimate heterogeneous slopes (CCEMG) or if a pooled estimator is preferable.

In a nutshell, there are the following possibilities:

• large N, fixed T: then you can use the standard fixed effects estimator such as xtreg. If you sample is large enough, then you might be able to use xtmg or xtdcce2. If you use xtdcce2 and pooled coefficient, then I encourage to use the fixed T standard error correction. There are plenty of discussions in this forum.
• fixed N, large T: commands such as xtpcse are the choice (see https://www.statalist.org/forums/for...xpcse-vs-xtreg)
• In the case of large N and large T (or assuming that these are the dimensions going jointly to infinity), you can use CCEP and CCEMG estimators and thus xtmg or xtdcce2. This is usually the standard case when cross-sectional dependence really becomes a problem.

Dear Sir,

Thank you for your reply. My observation is N=70 T=38 and N=44 T=37, what do you suggest me to chose then?
Also my question is, 'large N' or 'large T' corresponds to what number exactly?

Thank you in advance

[Carlo Lazzaro]

Zahrina:
I think that in your case Jan's point #3 is the way to go.

[JanDitzen]

I agree with Carlo.

From a applied perspective, both of your dimensions should be sufficient to use a large N, large T estimation method. From a theoretical perspective the question is if both dimensions go jointly to infinity, or at least with constant speed.

[Zahrina Adani]

Zahrina:
I think that in your case Jan's point #3 is the way to go.

Yes thank you very much, gentlemen.
I tried with xtdcce2 for the static model of pooled and mean group, the results remained. Everything is insignificant. My FE results using xtreg show that my variable of interest is significant and some control variables are too. Do you think I should rely on the results of xdcce2 still?

[Carlo Lazzaro]

Zahrina:
if the structure of your panel dataset still resembles the one described in Jan's point #3, you should stick with -xdcce2-.

[JanDitzen]

Let me elaborate a bit on Carlo's last post. First of all, heterogeneous slop coefficients and cross-sectional dependence are two different things. Models with heterogeneous slope coefficients require datasets with large N and large T. In this type of datasets cross-sectional dependence is likely to be found. On the other hand this means that if you have pooled model with a large dataset, you might have problems with cross-sectional dependence as well.

So what is cross-sectional dependence then. It means that the series you are using (or variables) contains a common factor and this factor does not disappear even if the number of observations, with respect to cross-sectional units and time, reaches infinity. You can think of it differently in terms of correlations. Your series is correlated across cross-sectional units and it does not disappear even if your dimensions increase.
Why is this a problem? You are interested in the causal effect of X on Y and not on the effect of (X + common factor) on Y. In practice this means that you have an omitted variable bias (the common factor) and/or a endogeneity problem if the factors become a part of the error term and are correlated with the explanatory variables. Finally, in the presence of cross-sectional dependence in the residuals, the residuals are not iid anymore. This is why commands such as xtdcce2 automatically test for cross-sectional dependence in the residuals. What does cross-sectional dependence imply? It implies results from a simple OLS regression are inconsistent and biased. Therefore point estimates and standard errors are unreliable.

For your results this means that FE regressions results can be significant, CCE regression results can be insignificant. Remember that even if you use a pooled model, calculation of standard errors obtained by xtdcce2 differ from those by xtreg! You found cross-sectional dependence in your variables, so you should use a estimation method which controls for this. As a side note, do you find cross-sectional dependence in the residuals of the FE regression?

What you need to do is to specify the type of your model, i.e. mean group or pooled, static or dynamic, short-run or long run coefficients. Then you adjust the options of xtdcce2 (i.e. cross-sectional averages, lags of those if model is dynamic, pooled coefficients or not, etc.) to your model and run the regression. The obtained results should be then consistent.

[Saberia Sadeq]

Dear JanDitzen

How we can estimate CCEP in stata ?????

[JanDitzen]

Hi Saberia,
there are several resources available how to estimate CCEP models using xtdcce2. Please see the helpfile for xtdcce2 and the Stata Journal Article explaining the command: https://journals.sagepub.com/doi/10....867X1801800306

Hope this helps.

Best,

Jan

[S. M. Woahid Murad]

Hi Jan,
Does xtdcce2 command automatically correct endogeneity problem along with cross-sectional dependence and heterogeneity problems? If the answer is 'no', how can I eliminate the potential endogeneity problem threat in the CCEMG model? In my case, N = 154 and T = 80. Thank you so much in advance for your response.

Kind Regards,
Woahid

[JanDitzen]

Dear S. M. Woahid Murad, xtdcce2 does not automatically correct endogeneity (in the "classical" sense, i.e. reversed causality etc.). It has a function which integrates ivreg2, please see the helpfile and the SJ article (https://journals.sagepub.com/doi/10....867X1801800306). However there is no good theoretical foundation on how to deal with endogeneity in panels with cross-section dependence and large N and large T. The closest is Sebastian Kripfganz's xtivdfreg (http://www.kripfganz.de/research/Kripfganz_Sarafidis_xtivdfreg.html)

Best,
Jan

[Trevor Lee]

Dear JanDitzen - thank you very much for your Stata packages and lucid explanations, they've been incredibly helpful! I just had a follow-up question along the above lines. I imagine that CCE-ARDL/CCE-DL approaches per se cannot deal with endogeneity from omitted variable bias or reverse causality, so we should still include variables that might cause OVB as controls, even if we're not concerned about their marginal impact. This seems logical, but I've read quite a few papers saying things like the ARDL approach is a magic bullet for all types of endogeneity, meaning one doesn't have to find an IV or include covariates.
If this is not the case, would you a priori expect the results of your xtdcce2 package with an external IV to be similar to xtivdfreg, and are there any theoretical considerations in choosing between the two? Early into a Master's program so don't yet have the technical skills to differentiate between the approaches.
Thanks again!

[JanDitzen]

ARDL does not account endogeneity issues. I believe the idea is that OLS is super consistent when there is cointegration. However you might have a small sample and therefore biases do not disappear. Therefore if you expect OMVB or reversed causality I would definitely account for those using the appropriate methods.