Mundlak's Approach and clustering standard errors

[Maarten Loomans]

Hi all,

I am doing an analysis of the effect of sovereign ESG scores on total factor productivity. Originally, I wanted to use a fixed effects model as the Hausman test indicated I should. however, after reading Bell, A., & Jones, K. (2015). Explaining Fixed Effects: Random Effects Modeling of Time-Series Cross-Sectional and Panel Data. Political Science Research And Methods, 3(1), 133–153. https://doi.org/10.1017/psrm.2014.7 I decided to go for the adjusted Mundlak's approach (within-between) which should the same as a fixed effects model and more. What I am now wondering is: should I cluster my standard errors? I cannot seem to find literature on clustering standard errors in random effects models, and most of the literature is on fixed effects models. A Breusch Pagan LM test indicated the rejection of homoskedastic standard errors. I used Drukker's (2003) test for serial correlation and confirmed the presence of it. and in general, when there is serial correlation, clustering standard errors will help.

Looking forward to your insights.
Kind regards,
Maarten

[Andrew Musau]

The choice of correlated random/ random effects (CRE/RE) or fixed effects (FE) estimation methods does not change the need to consider clustering standard errors.Clustering addresses issues of correlated errors within groups, while the RE and FE methods address unobserved heterogeneity across groups. With panel data, it is difficult to argue that observations of firm \(i\) at time \(t\) are uncorrelated with observations of firm \(i\) at time \(t-1\). What may be open to discussion is at what level to cluster. Abadie, Athey, Imbens and Wooldridge address this question here.

[Maarten Loomans]

Thank you Andrew! I was not able to formulate it myself!!

[Erik Ruzek]

You can also account for the time-dependent residual correlation in the CRE/RE (Mundlak) model if you are using mixed (but not xtreg, re),

*I assumed AR1, but there are many other options for the residual specification
help mixed##restype               // for all the options
mixed out pred1 mn_pred1 time || id: , residuals(ar 1, t(time))