st: IVREG2 and Multi-way Clustering

[Jessie C <jessiecoh@gmail.com>]

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.

2. Does ivreg2 adjust standard errors in anyway if 1 of the clusters
if small in number (e.g. 12 clusters in z_2)?  Should there be any
adjustment made or does there not need to be if z_1 is sufficiently
large in size (e.g. 1000 clusters)?

I would be very grateful for any help you could provide.
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