Hausman test

[Colin Reddy]

Dear stata listers

I have experienced a situation where the Hausman test points to fixed effects but the fixed effect output shows a relatively low omitted variable correlation e.g. corr(u_i, Xb) = -0.1.
I've decided to choose a maximum likelihood model instead. The mle and RE model outputs an overall model test (Prob > chi2 = 0.0000) that seems better than the FE model test (Prob > F = 0.0430).
I will appreciate any general pointers from those that might have experienced this (not looking for specific feedback to my model)

Thanks
Colin

[Carlo Lazzaro]

Colin: welcome to the list.
As always, statistical significance is not the first criterium to look at when different models are compared.
It may also be that your RE model is biased (as per -hausman- test) and the following inferece is biased accordingly.

[Jeff Wooldridge]

Colin: I'll add a bit more. There's a difference between practical and statistical significance. Are the FE and RE estimates on the variables of interest practically different? That's important. With a large cross section, small practical differences can lead to statistical significance.

One other thing: Did you use a cluster-robust version of the Hausman test? The nonrobust version could be over-rejecting.

Finally, MLE is not a "model." It is an estimation method. So you need to know the assumptions under which the estimator is consistent. In fact, the assumptions are essentially the same as for RE. They're really pretty similar. In particular, MLE does not help with correlation between the covariates and unobserved heterogeneity.

Finally, looking at p-values for joint significance cannot be used to choose among models. The FE F stat is less significant probably because of bias in the RE (and MLE) estimates.

As someone else may point out, you'll get a more informed response by showing actual Stata output.

[Carlo Lazzaro]

Colin:
if you're going to play -robust- or -cluster- standard errors, please note that you have to leave -hausman- and switch to the user-written command -xtoverid-, that you can spot and install by typing -search xtoverid- from within Stata.
If you are going to test the -fe- vs -re- specification via a robust -hausman- test (as introduced by Jeff), you can find the related code at pag 268 of the following: http://www.stata.com/bookstore/microeconometrics-stata/

[Colin Reddy]

Dear Carlo and Jeff

Thanks so much. I tried xtoverid on my unbalanced dataset after RE and cluster standard errors.

It suggested RE when I excluded my year effects:

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re robust cluster(ctry)
Sargan-Hansen statistic 10.374 Chi-sq(5) P-value = 0.0653

and,

FE when I included year effects:
Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re robust cluster(ctry)
Sargan-Hansen statistic 35.349 Chi-sq(10) P-value = 0.0001

I've included some output as below for a hausman test:

hausman fe re, sigmaless

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference S.E.
-------------+----------------------------------------------------------------
yr |
2012 | -.9531106 -.2275029 -.7256077 .2916
2013 | -3.430163 -2.392733 -1.03743 .3379679
2014 | -1.757696 -.9096575 -.8480382 .4287351
2015 | -1.575524 -.5606743 -1.01485 .4786368
2016 | -2.32344 -1.401577 -.9218637 .4679787
status | .125857 -.0600766 .1859336 .0660903
pol | 3.159571 3.295317 -.1357466 .8915864
skill | -1.486012 -.8934906 -.592521 .3863359
techwb | -15.98718 -7.134634 -8.852543 4.614103
techskill | .2777092 .180926 .0967833 .0783479
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(10) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 26.24
Prob>chi2 = 0.0034


Best
Colin

[Carlo Lazzaro]

Colin:
I would first consider whether robustified/clustered standard errors make sense in your case (that is, do you suspect heteroskedasticity and/or autocorrelation in your data?).
Besides: is the -hausman- test outcome consistent with the -xtoverid- one when you include/exclude -i.year-?

[Colin Reddy]

Dear Carlo and Jeff

Thanks so much. I tried xtoverid on my unbalanced dataset after RE and cluster standard errors.

It suggested RE when I excluded my year effects:

Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re robust cluster(ctry)
Sargan-Hansen statistic 10.374 Chi-sq(5) P-value = 0.0653

and,

FE when I included year effects:
Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re robust cluster(ctry)
Sargan-Hansen statistic 35.349 Chi-sq(10) P-value = 0.0001

I've included some output as below for a hausman test:

hausman fe re, sigmaless

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference S.E.
-------------+----------------------------------------------------------------
yr |
2012 | -.9531106 -.2275029 -.7256077 .2916
2013 | -3.430163 -2.392733 -1.03743 .3379679
2014 | -1.757696 -.9096575 -.8480382 .4287351
2015 | -1.575524 -.5606743 -1.01485 .4786368
2016 | -2.32344 -1.401577 -.9218637 .4679787
status | .125857 -.0600766 .1859336 .0660903
pol | 3.159571 3.295317 -.1357466 .8915864
skill | -1.486012 -.8934906 -.592521 .3863359
techwb | -15.98718 -7.134634 -8.852543 4.614103
techskill | .2777092 .180926 .0967833 .0783479
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(10) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 26.24
Prob>chi2 = 0.0034


Best
Colin

[Carlo Lazzaro]

Colin:
it seems that you have indvertently copied and pasted your previous #5 contribution to this thread.