R sq and Rho

[Jihad El Yaagoubi]

Hello everybody,

What is the difference between R sq and Rho in a random effects model?

Thank you

[Carlo Lazzaro]

Jihad:
-rho-=intraclass correlation;
-R-sq means different correlations in panel language; with -re- specification, you should take at look at the between R-sq (for further details, see -xtreg- entry, Stata .pdf manual, page 443.

[Carlo Lazzaro]

Jihad:
-rho-basically tells you if there's a panel effect vs pooled estimator.
This information is obviously relevant as far as consistency is concerned.
However, some of the basic cautions that should be paid with OLS still holds: checking for possible quadratic relationships is one of them that I often consider; endogeneity, which implies a good knowledge of the data generating process,is on my post estimation list as well.

[Carlo Lazzaro]

Jihad:
let's consider -xtreg-.
The choice between -fe- and -re- specification should be made, in general, following -husman- (or the user-wriyyen programme -xtoverid- if you imposed non-default standard errors to take heteroskedasticity and/or autocorrelation into account).
The valuable textbook https://www.stata.com/bookstore/heal...s-using-stata/ covers general approaches to test for heteroskedasticity.
Another reference textbook for Stata users (https://www.stata.com/bookstore/micr...metrics-stata/) shows how to test for autocorrelation (which seldom bites in N>T panel datasets).
Quasi-extreme multicollinearity can be suspected by taking a look at -estat vce, corr-, being aware that, in panel data, it mixes up within and between correlation.

[Carlo Lazzaro]

Jihad:
the first part of my previous reply (by the way, sorry for the typos) referred to the selection between -fe-and -re-, which should be not preferred due to absence vs presence of heteroskedasticity, autocorrelation or quasi-extreme multicollinearity, but on the ground of the -hausman- test outcome (that allows default standard errors only).
That said, checking for what above should come before the -hausman- test comparison.
If you detect heteroskedastcity and/or autocorrelation via one of the available methods, you should impose clustered robust standard errors, which exclude the -hausman- test. That's when the user-written programme -xtoverid- comes in handy.
See also https://www.statalist.org/forums/for...el-regression;
https://economics.stackexchange.com/...vs-time-series.
I would also add that the so-called omitted variable bias is the first problem that should be checked and (if necessary) fixed in OLS and in panel regression.

[Carlo Lazzaro]

Jihad:
-re- estimator can be seen as a special case of pooled OLS only when the hat_theta_i parameter or the GLS transform=0.
Hence, the answer to your questions is that, in general, coefficients and standard errors of pooled OLS and -xtreg,re- differ.

[Carlo Lazzaro]

Jihad:
I thought I've already replied to your question in #11.
However, if the previous replies did not address your query, please share what you've done in Stata.
Besides, you can find a comprehensive coverage of what you're interested in at https://www.stata.com/bookstore/micr...metrics-stata/.

[Carlo Lazzaro]

Jihad:
your definition of OLS and pooled OLS are correct.
However, OLS considers one wave of data only (that is, the cross-sectional dimension of panel data only).
As panel data are by definition composed of >=2 measurements of the same variable on the same units, OLS for panel data regression is out of debate.
Hence, pooled OLS only can be considered as a possible estimator for panel data regerssion.