Handling Heteroskedasticity and Autocorrelation in My Panel Regression Models

[RASTI WIJAYANTI]

Hello everyone,
I hope you are all doing well. I would like to ask for your guidance regarding an issue in my panel data analysis.

I am working with 219 observations (73 firms over 3 years). My variables include:

• Y (firm value),
• X1 (ESG),
• X2 (ROA),
• X3 (Size),
• and FC as a mediation variable.

Because of the mediation, I have three regression models:

1. Model 1: Y on the independent variables — selected Fixed Effects
2. Model 2: Mediator (FC) on X — estimated with OLS
3. Model 3: Y on X and the mediator — selected Fixed Effects

I conducted the classical assumption tests using Model 3 because it contains all variables. I detected heteroskedasticity and autocorrelation, so I applied vce(robust).

My questions are:

1. Is using vce(robust) in this situation appropriate?
2. When I compared vce(cluster) to vce(robust), Models 1 and 3 show no change, but Model 2 shows different standard errors (although the direction of coefficients stays the same).
3. For a thesis, what is the correct reference or justification for choosing vce(cluster) instead of vce(robust)?

Thank you very much for your assistance.

[Carlo Lazzaro]

Rasti:
you're dealing with a N>T panel dataset.
1)-3) You should go -xtreg,fe vce(cluster panelid)- or -xtreg,fe robust- (they do the very same job under -xtreg-; tha same does not hold under -regress-, though).

[RASTI WIJAYANTI]

Rasti:
you're dealing with a N>T panel dataset.
1)-3) You should go -xtreg,fe vce(cluster panelid)- or -xtreg,fe robust- (they do the very same job under -xtreg-; tha same does not hold under -regress-, though).

Previously, thank you for your explanation. May I ask about my second model, which is estimated using regress—should I apply the same approach for the standard errors, or is there a different recommendation for this case?
Also, if you have any journal references that I could cite in my thesis regarding the use of clustered standard errors in panel-data models, I would be very grateful.

Thank you very much.

[Carlo Lazzaro]

Rasti:
1) I would not consider -regress- to address your research question.
2a) see -_robust- entry and related references in Stata .pdf manual.
2b) Among many others: Hans-Jürgen Andreß , Katrin Golsch , Alexander W. Schmidt. Applied Panel Data Analysis for Economic and Social Surveys. Springer Berlin, Heidelberg, 2013:125-126.

[RASTI WIJAYANTI]

Rasti:
1) I would not consider -regress- to address your research question.
2a) see -_robust- entry and related references in Stata .pdf manual.
2b) Among many others: Hans-Jürgen Andreß , Katrin Golsch , Alexander W. Schmidt. Applied Panel Data Analysis for Economic and Social Surveys. Springer Berlin, Heidelberg, 2013:125-126.

Thank you very much, Mr. Carlo

I appreciate your clarification and the references you recommended, including the Stata manual entry on robust and the book by Andreß, Golsch, and Schmidt. Thank you for your helpful guidance.