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st: Panel data Hausman test questions

From   Brett William Parris <>
Subject   st: Panel data Hausman test questions
Date   Thu, 31 Jul 2003 07:06:20 +0000

Dear Statalisters,

I am using Stata 8 on a panel dataset of 84 developing countries over 5 periods covering a range of economic and social indicators. I have been using random (RE) and fixed effects (FE) panel models (-xtreg, re/fe- and -xtregar, re/fe-) allowing for autocorrelation effects with -xtregar- when the new Wooldridge test command -xtserial- suggests a problem with autocorrelation. I have two questions. (I am fairly new to panel regressions and to Stata so my apologies if these are a bit naive).

1. Sometimes a Hausman specification test between the 'consistent' estimator (FE) and the 'efficient under the null' estimator (RE) yields a negative chi-squared result, a message that the model "fails to meet the asymptotic assumptions of the test", and a recommendation
to use suest. But suest requires models with the score() option which I gather the xtreg/xtregar models don't support.

Is there a way of deciding between the RE and FE xt-models if the Hausman test fails in this way? The manual [R, Hausman, p. 57] says "We might interpret this [a negative chi-squared] as strong evidence that we cannot reject the null hypothesis." Does this mean,
in a test between RE and FE regressions that a negative chi-squared should be interpreted as a failure to reject the null and therefore as evidence in favour of the RE regression?

If not, would choosing the regression whose residuals are closest to a normal distribution and with the least autocorrelation (using -xtserial- on the residuals) be a legitimate approach?

2. Sometimes with the Hausman test I get a message saying: 
(V_b-V_B is not positive definite) 
The manual [R, Hausman, p. 58] says that a Moore-Penrose generalized inverse is used in this case. I'd be grateful if someone could tell me whether this affects the reliability or interpretation of the Hausman test at all. 

Thanks for any light anyone can shed on these questions.

Brett Parris
Monash University
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