Alternative multi-way clustering routines giving different results

[Luca Uberti]

Dear Statalisters,


I would like to two-way cluster the standard errors of an OLS regression model (Cameron, Gelbach and Miller, 2011). I can think of at least four user-written programs that allow for multi-way clustering:

1) Roodman's >boottest< command (in particular, its wrapper >waldtest<)
2) >clus_nway< prefix command (by Wolfson and Kleinbaum, which is based on CGM's (2011) original >cgmreg< command)
3) >ivreg2<
4) >reghdfe<

While 1) and 2) give identical estimates of the standard errors and test statistics, those returned by 3) and 4) are different from each other and from 1) and 2).

I would like to know:

(A) Why this is the case; and

(B) Which routine is recommended.

>ivreg2<'s helpfile indicates that "ivreg2 and cgmreg [and hence clus_nway] will produce slightly different SEs" since they use different small-sample adjustments. That's all I have found in this respect.

Here's an example:

webuse nlsw88, clear
qui regress wage ttl_exp collgrad tenure, cluster(industry)
**(1) boottest's wrapper waldtest command
waldtest ttl_exp, noci cluster(industry age)
waldtest collgrad, noci cluster(industry age)
waldtest tenure, noci cluster(industry age)

**(2) clus_nway (extension of cgmreg)
clus_nway regress wage ttl_exp collgrad tenure, cluster(industry age)

**(3) ivreg2
ivreg2 wage ttl_exp collgrad tenure, cluster(industry age)

**(4) reghdfe
reghdfe wage ttl_exp collgrad tenure, noabs cluster(industry age)

Here are the estimated t-statistics for the ttl_exp regressor:

1) 5.51
2) 5.51
3) 5.84
4) 5.58

Thanks!

Luca

[George Ford]

look at the help file for ivreg2. it describes a difference between the se calculation for cgmreg (which gives you the 5.51). I suspect something similar for reghdfe.