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

[Ting JIANG <econjiang@gmail.com>]

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.
>> ×/
>>
>> *
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>
> *
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