Random effects is the same as OLS

[Kenulina Schneider]

HI,

when Im trying to differentiate between FE and REs , Hausman test is highly insignificant, but when i use -xtoverid- option to account for heterosk. problem, then i get the following message:
Error - saved RE estimates are degenerate (sigma_u=0) and equivalent to pooled OLS I compared both results from RE and OLS, they are exactly the same. This happens when i use first differences and lagged regressors. (Please don't advice me to use GMM). The model is static. Could u tell me if something wrong with the model? My superviser recommended me to use first differences, and to run Hausman test for FE and REs. But I have problems with REs.

here is output:

[Phil Bromiley]

What is happening is that when you force the panel effects to be orthogonal to the included variables, you get no explained variance from the panel effect (i.e., in the random effect estimator, the sigma u is zero). This means that the xtreg re is identical to normal regression (which is exactly what your results show - the parameter values in xtreg re are exactly the same as reg. Apparently, this also messes up xtoverid.

Substantively, you get very similar results from the FE and RE. That is what the Hausman is telling you. I would just go with the Hausman which says regression is OK. Alternatively, report both FE and RE/regression - you get almost identical results with the two.

[Phil Bromiley]

As you pose the question, 1) includes dummies for each panel and year while 2) only includes dummies for years. Both use clustered standard errors.

Whether you include time dummies is independent of a Hausman test. The Hausman should be done on the model you intend to interpret. No one can tell you whether to include year dummies - this depends on the substance of your project.

As I said before, I don't see why you don't just take the Hausman results as correct, and move forward with random effects which in this case means straight regression, or, alternatively, report both fixed effects and random effects. Since you get the same results with both, I wouldn't spend a lot of time choosing between the two.

[Andrew Musau]

Just to add onto Phil, it's good practice not to start by running a Hausman test to choose between FE and RE. You should first verify whether pooled OLS is rejected in favor of FE, then you can proceed to the Hausman test. Secondly, the RE estimator (which is Generalized Least Squares) is a weighted average of the within estimator and the between estimator, and equals OLS if equal weights are given to the within- and between-variation. Finally, it's a matter of preference whether you choose FE or first differences (FD), although note that you lose a cross-section in the latter, so your T dimension needs to be sufficiently large.

[Jeff Wooldridge]

The reason the RE and OLS estimates are the same is because the estimate of the variance of the unobserved effect is negative, in which case Stata sets it to zero, and then GLS = OLS. That's because you first differenced the data before applying RE, so there is likely a lot of negative serial correlation (which leads to the negative estimate of the error components variance). It is a bit strange to apply RE to first differences.

With N = 11 and T = 10, you shouldn't be doing anything other than basic OLS, anyway. Conceptually, random effects doesn't make much sense with aggregated data, anyway.

Perhaps most importantly: Given that the OLS and FE estimates are so similar -- which I expect when you have already differenced -- why would you compute a Hausman test, anyway? You should use OLS and then note that adding fixed effects changes little. The end.

[Carlo Lazzaro]

Kenulina:
according to Paul Allison's http://www.stata.com/bookstore/fixed...els/index.html, page 8:

...dummy variables can be treated like any other variables in this regard...

[amira elshal]

Dear Sirs,

To test for random effects, I ran the Breusch and Pagan Lagrangian multiplier test for random effects. I got the results below although I did not difference my data. Prob > chibar2 = 1.0000 because u = 0. Please advise on how I shall proceed.

Breusch and Pagan Lagrangian multiplier test for random effects

childmort[id,t] = Xb + u[id] + e[id,t]

Estimated results:
Var sd = sqrt(Var)
---------+-----------------------------
childmort 17.83105 4.222683
e 17.64855 4.201018
u 0 0

Test: Var(u) = 0
chibar2(01) = 0.00
Prob > chibar2 = 1.0000

Thank you.

Kind regards,
Amira