Different models for different hypotheses?

[Amina Sagittaire]

Dear all, I have been testing the hypotheses for my master thesis and I have run into a problem. For hypotheses 1-3, Stata tells me to use the fixed effects model. However for hypotheses 4 , I get the following error "Error - saved RE estimates are degenerate (sigma_u=0) and equivalent to pooled OLS r(198)". Why is that and what does it mean? So I use the fixed effects model for hypotheses 1-3 and the pooled OLS for hypotheses 4?

Please find my code below:

**Hypothesis 1: 

* Pooled OLS
reg CAR ESG_score Firm_size Firm_performance Firm_leverage RD_intensity i.Layoff_Reason_New i.Industry i.Year, vce(robust) 

* Fixed effects 
xtreg CAR ESG_score Firm_size Firm_performance Firm_leverage RD_intensity i.Layoff_Reason_New i.Industry i.Year, fe vce(robust) 

* Random effects
xtreg CAR ESG_score Firm_size Firm_performance Firm_leverage RD_intensity Layoff_reason1-Layoff_reason7 Industry1-Industry8 Year2002-Year2020, re vce(robust) 

xtoverid // o. operator not allowed -> remove omitted variables from model

xtreg CAR ESG_score Firm_size Firm_performance Firm_leverage RD_intensity Layoff_reason1-Layoff_reason6 Industry1-Industry3 Industry5 Industry7-Industry8 Year2002-Year2019, re vce(robust)

xtoverid // Rejection of null-hypothesis -> fixed effects 

**Hypothesis 2: 

* Pooled OLS
reg CAR ESG_score c.ESG_score##industry_wave_dummy Firm_size Firm_performance Firm_leverage RD_intensity i.Layoff_Reason_New i.Industry i.Year, vce(robust) 

* Fixed effects 
xtreg CAR ESG_score c.ESG_score##industry_wave_dummy Firm_size Firm_performance Firm_leverage RD_intensity i.Layoff_Reason_New i.Industry i.Year, fe vce(robust) 

* Random effects
xtreg CAR ESG_score industry_wave_dummy moderation1 Firm_size Firm_performance Firm_leverage RD_intensity Layoff_reason1-Layoff_reason7 Industry1-Industry8 Year2002-Year2020, re vce(robust) 

xtoverid // o. operator not allowed -> remove omitted variables from model

xtreg CAR ESG_score industry_wave_dummy moderation1 Firm_size Firm_performance Firm_leverage RD_intensity Layoff_reason1-Layoff_reason6 Industry1-Industry3 Industry5 Industry7-Industry8 Year2002-Year2019, re vce(robust)

xtoverid // Rejection of null-hypothesis -> fixed effects 

**Hypothesis 3:

* Pooled OLS
reg CAR ESG_score c.ESG_score##c.Layoff_Size_in_Percent Firm_size Firm_performance Firm_leverage RD_intensity i.Layoff_Reason_New i.Industry i.Year, vce(robust) 

* Fixed effects 
xtreg CAR ESG_score c.ESG_score##c.Layoff_Size_in_Percent Firm_size Firm_performance Firm_leverage RD_intensity i.Layoff_Reason_New i.Industry i.Year, fe vce(robust) 

* Random effects
xtreg CAR ESG_score Layoff_Size_in_Percent moderation2 Firm_size Firm_performance Firm_leverage RD_intensity Layoff_reason1-Layoff_reason7 Industry1-Industry8 Year2002-Year2020, re vce(robust) 

xtoverid // o. operator not allowed -> remove omitted variables from model

xtreg CAR ESG_score Layoff_Size_in_Percent moderation2 Firm_size Firm_performance Firm_leverage RD_intensity Layoff_reason1-Layoff_reason6 Industry1-Industry3 Industry5 Industry7-Industry8 Year2002-Year2019, re vce(robust)

xtoverid // Rejection of null-hypothesis -> fixed effects 

** Hypothesis 4:

* Pooled OLS
reg CAR ESG_score c.ESG_score##c.ESG_disclosure_score Firm_size Firm_performance Firm_leverage RD_intensity i.Layoff_Reason_New i.Industry i.Year, vce(robust) 

* Fixed effects 
xtreg CAR ESG_score c.ESG_score##c.ESG_disclosure_score Firm_size Firm_performance Firm_leverage RD_intensity i.Layoff_Reason_New i.Industry i.Year, fe vce(robust) 

* Random effects
xtreg CAR ESG_score ESG_disclosure_score moderation3 Firm_size Firm_performance Firm_leverage RD_intensity Layoff_reason1-Layoff_reason7 Industry1-Industry8 Year2002-Year2020, re vce(robust) 

xtoverid // o. operator not allowed -> remove omitted variables from model

xtreg CAR ESG_score ESG_disclosure_score moderation3 Firm_size Firm_performance Firm_leverage RD_intensity Layoff_reason1-Layoff_reason6 Industry1-Industry2 Industry5 Industry7-Industry8 Year2005-Year2019, re vce(robust)

xtoverid // -> error?

Thank you very much in advance!

[Carlo Lazzaro]

Amina:
let's focus on your last question.
The outcome of the community-contributed module -xtoverid- is simply telling you that it is not able to support evidence of a panel-wise effect.
You can also double-check it via -xttest0- after -xtreg,re-.
As an aside, please note that, while -robust- annd -vce(cluster clusterid)- options do the very same job under -xtreg- (as they take heteroskedasticity and/or autocorrelation into account), it does not hold for -regress-. Hence, in your pooled OLS you should use -vce(cluster panelid)- instead of -robust- (as the latter takes heteroskedasticity only into acccount under -regress-, whereas your standard errors should consider the autocorrelation of the residuals, as your observations are not independent within panels).

[Amina Sagittaire]

Hi Carlo,
thanks for your answer!

I double checked with -xttest0- after -xtreg, re- which indicates the Null-hypothesis cannot be rejected and I should therefore use pooled OLS.
I did this for all hypotheses (1-4) and the result remains the same. Hence, I am wondering now - how do I decide between the fixed effects and pooled OLS model?

Thanks in advance!

[Carlo Lazzaro]

Amina:
1) go -fe- for hypotheses 1-3;
4) go pooled OLS (with -vce(cluster panelid)- standard errors) for hypothesis 4.

[Amina Sagittaire]

Thanks Carlo!