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st: heteroskedasticity questions

From   Richard Williams <>
Subject   st: heteroskedasticity questions
Date   Sat, 24 Feb 2007 10:15:51 -0500

Here are a few questions that will betray my ignorance in some areas of statistics...

-estat hettest- tests for a specific type of heteroskedasticity, i.e. it tests whether the residual variances go up as yhat goes up. However, there are other possible forms of hetero, e.g. error variances go up as x gets more extreme in either direction, producing an hourglass shape. This can be simulated via

set seed 123
set obs 200
corr2data x e
gen y = x + 2*abs(x)*e
scatter y x
reg y x

If you now type -estat hettest-, as expected, the test stat is insignificant. However, how should you formally test for hetero in this case? -estat imtest- does produce a significant chi-square; is that just happy coincidence or is this a good all purpose test for hetero? (Basically, what i am saying is I don't understand what -estat imtest- does! I'm thinking it is a more general test than hettest, but the generality can also cost it some power compared to tests that are more specific.) Also, would it be appropriate to do something like

gen xabs = abs(x)
estat hettest xabs

i.e. based on visual inspection (with data I had not made up) could I try to construct a var that I thought reflected the hetero?

Finally, Goldfeldt-Quant and -estat hettest- seem to be testing similar hypotheses. Goldfeldt-Quant is a little clunky to estimate, though, so is there any reason I would prefer it over -hettest-? (I actually asked this question 3 years ago, but I don't think I got a definitive answer, or if I did I can't find it anymore).

Thanks for any ideas.

Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME: (574)289-5227
EMAIL: Richard.A.Williams.5@ND.Edu

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