pooled OLS, random effects or fixed effects

[David Planiol Sierra]

Hi guys,

I have several questions regarding the proper use of model for my data. I have panel data with 4 observations per panel-ID. I want to observe what the effect is of the variable 'chosen' on the variable 'r2_rank" additionally I would like to know the effects of 'treatmentgroup' 'discounted' and 'type'.
However, I am not entirely sure what my prefered model would be. I don't know whether I should use pooled OLS, random effects or fixed effects and whether I should include clustered standard errors.
I included the pooled OLS, the random effects, the fixed effects and a hausman test (between RE and FE) below.

This is the code I used:
xtset panelid t

*Pooled OLS
reg r2_rank chosen i.treatment_group discounted type, vce(cluster panelid)

*Random effects with clustered standard errors
xtreg r2_rank chosen i.treatment_group discounted type, re vce(cluster panelid)

*RE and FE and hausman test
xtreg r2_rank chosen i.treatment_group discounted type, fe
estimates store fe
xtreg r2_rank chosen i.treatment_group discounted type, re
estimates store re

hausman fe re

Let me know what you think!

David

[Carlo Lazzaro]

David:
the first issue here seems to rest on the lack of panel-wise effect (as the -rho- is really low).
This is confirmed by the lack of statistical significance of the F-test that appears as a footnote of the -xtreg,fe- outcome table.
Running -xttest0- after -xtreg.re-, would probably confirm the lack of panel-wise effect.
In addition, both your R-sq between (relevant for -re-) and within (relevant for -fe-) are really low.
Hence, the first concern relates to the your model specification (ie, are you sure that all the predictors and interactions necessary to give a fair and true view of the datagenerating process were plugged in?).
If there's no way to revise/improve the specification of your regression model, you shoud switch to pooled OLS (with -vce(cluster clusterid)- standard errors, as your observations arte not independent).
However, due to the high number of panels, non-default standard errors are wisely invoked under -xtreg,fe- and -xtreg,re-, too, as autocorrelation is to be expected.

[David Planiol Sierra]

Hi Carlo,

Thank you for you reply! I added control variables and ran the Breusch pagan test (on re with clustered standard errors) and the h0 cannot be rejected.
Does this then mean that there is no reason to suggest the variance of the unobserved fixed effects is different from zero OR that OLS residuals contain individual specific error components (which one is a better conclusion here?)
And hence a random effects model would be inappropriate?

Thanks!
David

[Carlo Lazzaro]

David:
as you surmised, the -xttest0- outcome does not reject the null.
Hence, given the (confirmed) lack of evidence of a panel-wise effect (I think this is the simplest take-home message), you shoudl switch to pooled OLS (with vce(cluster clusterid) standard errors, as your observations are not independent)..
In addition, as per your previous post, -fe- points you toward the same direction,