Multiple Linear Regression vs OLS Pooled Regression

[Ben Cunningham]

Am I right in thinking that Pooled OLS is just a multiple linear regression applied to panel data? Therefore using regress in Stata after I've used xtset to declare a panel variable and time variable using the regress command is Pooled OLS?

And finally that using

regress Y X, i.panelVariable

Is also therefore Pooled OLS?

[Nick Cox]

That syntax is strictly illegal, as the comma is out of place.

Also, xtset doesn't enable and the lack of xtset doesn't prohibit your using factor variable notation.

But more to the point: whoever talks about pooled OLS should give a definition, and if not you can supply your own. I don't think I've ever heard the term. It may be one of those terms utterly standard in some sub-fields, but by no means all.

[Ben Cunningham]

My apologies, I accidentally added the comma.

I'm not sure if it's entirely standard but I've encountered it a few times while attempting to create a model. I think perhaps it's an econometric specific term, as that's what I'm currently doing and it usually seems brought up by people on researchgate etc. who work in finance or economic related positions. A few people on stats.stackexchange do say that Pooled OLS is just OLS on panel data, so I guess I'll trust their consensus.

I guess my final question then is whether the same sort of data analysis applies to

regress Y X

As it does to

regress Y X i.panelVariable

Thank you again by the way, first you help me with my scatter plots and now you're helping me with my actual model.

[Ben Cunningham]

Okay so I think

regress Y X i.panelVariable

Is what actually makes it a Pooled OLS/Multiple Linear Regression

regress Y X

Is just a regular OLS on the data

Originally I had thought that xtset was what declared it as panel data for the regression, but having opened a fresh Stata window and tried each regression before and after using xtset panelVariable timeVariable I get the same results for each.

[Nick Cox]

Yes and no is the annoying answer.

Once you have a panel structure declared then there is all kinds of extra scope for modelling systematic structure and error structure.

[Andrew Musau]

But more to the point: whoever talks about pooled OLS should give a definition, and if not you can supply your own. I don't think I've ever heard the term. It may be one of those terms utterly standard in some sub-fields, but by no means all.

To address Nick's point and answer Ben's question in #1, pooled OLS is standard terminology in empirical economics and refers to running OLS on panel data. You can do this is there is no heterogeneity in the data (hence you pool the data).

regress Y X

Once you include panel dummies, you acknowledge that there is heterogeneity, and the model now becomes fixed effects.

regress Y X i.panelvar
*/ or

xtset panelvar timevar
xtreg Y X, fe