[R] Hausman Test

[Achim Zeileis]

On Mon, 12 Sep 2016, Ding, Jie Ding (NIH/NIA/ERP) [F] wrote:

> Dear Achim,
>
> Sorry to have disturbed you. I have encountered a problem  when computing Hausman test statistics (i.e. p values)  in R to compare OLS and 2SLS models.
>
> The problem is a discrepancy between the two p-value outputs from the "manual approach (by hand)" and the " diagnostics argument" in the "AER" library, respectively.
>
> With respect to manual approach, I used the following codes:
>
> cf_diff<-coef(ivreg)-coef(olsreg)
> vc_diff<-vcov(ivreg)-vcov(olsreg)
> x2_diff<-as.vector(t(cf_diff)%*% solve(vc_diff)%*%cf_diff)
> pchisq(x2_diff,df=2,lower.tail=FALSE)
>
>
> For diagnostic approach, I applied the following:
>
> summary(ivreg, vcov = sandwich, df = Inf, diagnostics = TRUE)
>
>
> However, p-value from the manual approach is always much larger than the 
> diagnostic approach, e.g.  0.329 vs. 0.138
>
> I would expect the values should be the same. Your advice would be 
> highly appreciated.

The Wu-Hausman test in ivreg() follows the auugmented regression approach 
that is also used by Stata. This regresses the endogenous variable on the 
instruments and includes the fitted values in an OLS regression. The test 
is then a simple Wald test, see:
http://www.stata.com/support/faqs/statistics/durbin-wu-hausman-test/

> With very best wishes,
> Jennifer
>
>
>
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>
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