Re: st: How does xtreg calculate clustered standard error?

[Steve Samuels <sjsamuels@gmail.com>]

In the -xtreg- help is a section on the vce() option. This has a link to
the -help- for "vce_option" which, in turn, contains links to the Manual
entry for "Obtaining robust variance estimates". P. 313  of the Stata 13 U
Manual shows the formulas for the robust independent-data and
cluster-data variance-covariance matrices.

Steve
sjsamuels@gmail.com


On Mar 12, 2014, at 7:59 AM, Ting JIANG <econjiang@gmail.com> wrote:

Thanks, Austin. I checked xtreg and _robust, but didn't find relevant
answers to my questions. Would you kindly offer more specific advice?
Thanks.

On Wed, Mar 12, 2014 at 7:47 PM, Austin Nichols <austinnichols@gmail.com> wrote:
> Ting JIANG <econjiang@gmail.com>:
> 
> See manual entries on e.g. -xtreg- for methods and formulas.
> 
> On Wed, Mar 12, 2014 at 2:30 AM, Ting JIANG <econjiang@gmail.com> wrote:
>> Dear all,
>> 
>> I'm using Stata 12, and I'm trying to understand xtreg with simulated
>> panel data. When I try the following three lines,
>> 
>> reg y x i.id, cluster(id)
>> 
>> areg y x, a(id) cluster(id)
>> 
>> xtreg y x, fe robust
>> 
>> Theoretically they should give identical results. I noticed that they
>> give the same coefficient estimates as expected, but the clustered
>> standard errors are different.
>> 
>> The results from OLS (the first and second lines) are in accordance
>> with the fact that Stata has a multiplier (finite sample adjustment)
>> for clustered variance G/(G-1) *(n-1)/(n-k), where G is the number of
>> clusters.
>> 
>> But the clustered standard error reported after xtreg (the third line)
>> does not match those I got after reg and areg. They are different from
>> the numbers without finite sample adjustment too.
>> 
>> On the other hand, if conditional homoskedasticity is assumed, reg,
>> areg, xtreg give exactly the same results.
>> 
>> So my questions are:
>> 
>> (1) How exactly does Stata calculate standard errors in the ``xtreg +
>> cluster'' case?
>> 
>> (2) Can I expect reg and xtreg to give the same answer when properly specified?
>> 
>> (3) By the way, I also noticed that the t-statistic produced after
>> xtreg with cluster option does not follow Stock & Watson's (ECMA,
>> 2008) suggestion -- multiply the traditional t-statistic by
>> sqrt(G/(G-1)). Am I correct?
>> 
>> Thanks.
>> 
>> I'm providing details of my simulation exercise below.
>> 
>> clear all
>> set seed 20140312
>> set obs 10
>> gen id=_n
>> gen u=rnormal()
>> expand 4
>> sort id
>> gen t=mod(_n-1,4)+1
>> gen x=rnormal()
>> gen y=x+u+rnormal()
>> tab id, gen(d)
>> 
>> xtset id t
>> reg y x i.id
>> areg y x, a(id)
>> xtreg y x, fe
>> 
>> /*
>> In all three cases, coefficient estimates on x is 1.138147, with
>> standard error .2372135
>> */
>> 
>> reg y x i.id, cluster(id)
>> areg y x, a(id) cluster(id)
>> xtreg y x, fe robust
>> 
>> /*
>> In the first two cases, standard error of the coefficient estimate on
>> x is .2779968, whereas in the third case, it is .2428549. Coefficient
>> estimates remain unchanged.
>> */
>> 
>> reg y x d*
>> predict e, residual
>> mat opaccum A=x d2-d10, group(id) op(e)
>> mat accum B=x d2-d10
>> mat V=invsym(B)*A*invsym(B)
>> di sqrt(V[1,1]*10/(10-1)*(40-1)/(40-11))
>> di sqrt(V[1,1])
>> 
>> /*
>> The numbers displayed are .27799676 and .22741949. The first number
>> coincides with the results after reg and areg when specifying cluster
>> option. The standard error after xtreg matches neither of the numbers.
>> ×/
>> 
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>> *   http://www.ats.ucla.edu/stat/stata/
> 
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/faqs/resources/statalist-faq/
> *   http://www.ats.ucla.edu/stat/stata/

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/


*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/