Testing for multicollinearity in presence of heteroskedsticity

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pborys
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Joined: Mon Mar 09, 2020 4:34 am

Testing for multicollinearity in presence of heteroskedsticity

Postby pborys » Tue Mar 10, 2020 7:05 am

Hi everyone!

My question concerns use of VIF test for multicolinearity diagnostics when the model suffers from heteroskedasticity.

I want to use HAC correction to account for heteroskedasticity in my model. However VIF gives my starkly different results depending if I run it after estimating the model with simple OLS without error correction, compared to when I start with regression with HAC applied and then run VIF. I use Eviews 9.

For me it was surprising as in the textbooks I know (e.g. M. Verbeek, Guide to Modern Econometrics ed.5) test statistic in VIF is just an 1/(1-R^2) where R^2 is calculated for a model in which given x_i variable is regressed against the rest of X variables. This implies that the result should not depend on standard errors of the estimated parameters in our original y against X regression, and thus should not depend on whether I use robust errors or not.

However, in Eviews VIF is calculted differently and estimates of standard errors for parameters are used (tutorial, pp. 198 of the pdf). It is noted that the two approaches are not equivalent any more when robust standard errors are used.

In short, in which order should I proceed - test for multicolinearity with simple OLS model as first and then move on to model with HAC, or the other way - estimate the model with HAC and then run VIF? My guess would be the first option as only then VIF's value corresponds to the one obtained manually using standard textbook definition.

Thanks for all your help!

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