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st: RE: Hausman Test when the RE OLS model includes time-constant variables

From   "Rodrigo Alfaro A." <>
To   <>
Subject   st: RE: Hausman Test when the RE OLS model includes time-constant variables
Date   Thu, 17 Apr 2008 10:27:56 -0400


When you run (FE versus RE+industry_dummies) or (FE versus RE) the Hausman-Test (HT) shows FE>RE. In addition running (FE+cross_dummies versus RE+cross_dummies), HT shows RE>FE. 

It seems that you have a model like: y(i,t) = b*x(i,t) + a(i,t) + e(i,t), where a(i,t) is unobservable. FE seems to capture many of the variation of a(i,t) with b(i), at least more than RE or RE+dummies. Up to here, I would prefer the FE over the RE model. The realizations of b(i) are not "purely" random, or the random component is correlated with x(i,t).

In your second round, your RE seems more appropiate than FE with these pseudo a(i,t)... but note that FE is also "adding" other b(i) in the estimation. There is a competition between [pseudo a(i,t) minus the firm_mean] and other b(i). I am not convinced that you are estimating similar models here. It seems that a more close comparison between RE and FE can be computed with RE+ind_dummies+cross_dummies versus FE+cross_dummies. Anyway, I tend to prefer FE over RE in most of the cases. If you have a good HT supporting that RE>FE, then I would like to know how much variance is the random component adding to the model. My guess is the random component is not adding much to the explained-variance and there is a highly probability that it is not uncorrelated with x(i,t). 

Best, Rodrigo.


-----Mensaje original-----
De: [] En nombre de Pavlos C. Symeou
Enviado el: Miércoles, 16 de Abril de 2008 08:24 p.m.
Asunto: st: Hausman Test when the RE OLS model includes time-constant variables

Dear Statalisters,

I have a question regarding the Hausman specification test. I want to include in my OLS model 7 time-constant variables which depict the industry classification of a firm. In order to use the Hausman test, I first estimate the FE model, I store the estimation results, then run the RE model and finally ask Stata for the estimation of the Hausman test. As it is expected, the time-constant variables are dropped from the FE model but not from the RE. This implies that the Hausman test compares two different models; one with time-constant variables and one without. The Hausman test rejects the RE model. If I omit the time-constant variables from the two models, then the Hausman test compares comparable models and still rejects the RE model. Yet, inclusion of the time-constant variables in the OLS model is important for its correct specification so I interact these variables with year dummies and include the interaction variables (and exclude the original time-constant variables) !
 in both FE and RE models. I rerun the Hausman test which now rejects the FE in favor of the RE model. I am confronted here with a dilemma where I can only perform the Hausman test if I interact my time-constant variables with year dummies, but what I actually need from my final model is the inclusion of the original time-constant variables, which however leads to the wrong estimation of the Hausman test.

I would appreciate if you could advise on this. Should I arbitrarily choose the RE model that can involve the time-constant variables in its estimation? Otherwise?


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