st: RE: Re: IVREG2 and Multi-way Clustering

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Jessie,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jessie C
> Sent: 29 January 2012 21:42
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Re: IVREG2 and Multi-way Clustering
> 
> Mark,
> 
> Thank you very much for your response and for taking the time 
> to help out.  I greatly appreciate it.
> 
> 1. Your example makes sense of the 2 X 2.  z_1 has 2 
> clusters.  z_2 has 2 clusters.  The union of z_1 and z_2 is 4 
> clusters but also 4 observations.
> 
> I don't quite understand then the 2-way clustering formula in 
> terms of 1-way clusters.
> 
> Cameron, Gelbach, and Miller say:
> 
> 1. OLS regression of y on X with variance matrix estimate 
> computed using clustering on g in the set of {1, 2, ...G}; 2. 
> OLS regression of y on X with variance matrix estimate 
> computed using clustering on h  in the set of {1, 2, ...H}; 
> 3. OLS regression of y on X with variance matrix estimate 
> computed using clustering on (g, h)  in the set of {(1, 1), 
> ..., (G, H)};
> 
> Given these three components, V[beta] is computed as the sum 
> of the ...first and second components, minus the third component.
> 
> I thought that would correspond with:
> i. reg y x, cluster(g)
> ii. reg y x, cluster(h)
> iii. reg y x, cluster(i) where egen i = group(g h) and the 
> standard error is se(i) + se(ii) - se(iii) or
> sqrt(se(i)^2 + se(ii)^2 - se(iii)^2)
> 
> I tried an example in Stata and it worked out using the sqrt formula.
> Not sure if that's just a coincidence.

A coincidence, I think.  To do it properly in the K-regressor case you
need to work with the meat of the cluster-robust sandwich formulation.
In the slides you point to below, see slides 10 and 22.  The meat of the
sandwich in the 2-way cluster case is B_hat on slide 22.

> 2. If I'm understanding correctly, the correction to ivreg2 
> is an adjustment based on finite samples?

The finite-sample adjustment we use in -ivreg2- is one of those
recommended by Cameron-Gelbach-Miller; see their paper.

> I am wondering whether you have any response to using the 
> t-statistic of G-L as suggested in:
> http://www.stata.com/meeting/mexico11/materials/cameron.pdf
> Section 4, slide 17

No, sorry.

--Mark

> 
> Thank you so much for everything!!
> 
> On Sun, Jan 29, 2012 at 11:54 AM, Jessie C 
> <jessiecoh@gmail.com> wrote:
> > I have 2 questions about two-way clustering using ivreg2.
> >
> > 1. What would be the 1-way cluster equivalent of the 
> following 2-way clustering?
> >
> > ivreg2 y x, cluster(z_1, z_2)
> >
> > I thought it would be
> > a. ivreg2 y x, cluster(z_1)
> > b. ivreg2 y x, cluster(z_2)
> > c. ivreg2 y x, cluster(z) where egen z = group(z_1 z_2) and the 
> > two-way standard error on x would be the standard error in a + the 
> > standard error in b - the standard error in c or would it be 
> > sqrt(se(a)^2 + se(b)^2 - se(c)^2)
> >
> > Note. That is not the full model, but I thought would be 
> illustrative 
> > to get at the main issue.
> >
> 
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