On Tue, 25 Jun 2002, Mark Schaffer wrote:
>
> Not quite sure what you mean, so apologies if I'm off target. The
> coefficient estimates with -regress- won't be the same as with
> -xtreg, fe- (unless the former is estimating the same model by
> explicitly including the fixed effects as dummy vars). Both sets of
> coefficients will be different again from those produced by
> -xtreg, re-.
>
> --Mark
You may be right about this. However, I did get the same coeff from
-regress-, xtreg, fe and xtreg, re using a simulated dataset with
exchangeable corr and no dummy vars. ALso, I got different coeffs by
running an exponential corr model as expected.. Here are the details. I
may have missed something here..Thanks for your input,
Anirban
. mat C= (1, 0.6, 0.6, 0.6 \ 0.6, 1, 0.6, 0.6 \ 0.6, 0.6, 1, 0.6 \ 0.6,
0.6, 0.6, 1)
.
. drawnorm y1 y2 y3 y4, n(1000) means(1 3 4 7) corr(C)
(obs 1000)
. gen id=_n
. reshape long y , i(id) j(time)
(note: j = 1 2 3 4)
Data wide -> long
-----------------------------------------------------------------------------
Number of obs. 1000 -> 4000
Number of variables 5 -> 3
j variable (4 values) -> time
xij variables:
y1 y2 ... y4 -> y
-----------------------------------------------------------------------------
.
. reg y time, cluster(id)
Regression with robust standard errors Number of obs =4000
F( 1,999) =42518.72
Prob > F =0.0000
R-squared =0.7897
Number of clusters (id) = 1000 Root MSE =1.0946
------------------------------------------------------------------------------
| Robust
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
time | 1.896646 .0091981 206.20 0.000 1.878596 1.914696
_cons | -.9866896 .0358667 -27.51 0.000 -1.057072 -.916307
------------------------------------------------------------------------------
.
. tsset id time
panel variable: id, 1 to 1000
time variable: time, 1 to 4
. iis id
. tis time
. xtreg y time, fe
Fixed-effects (within) regression Number of obs =4000
Group variable (i) : id Number of groups =1000
R-sq: within = 0.9027 Obs per group: min =4
between = 0.0000 avg =4.0
overall = 0.7897 max =4
F(1,2999) =27835.94
corr(u_i, Xb) = -0.0000 Prob > F =0.0000
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95%
Conf. Interval]
-------------+----------------------------------------------------------------
time | 1.896646 .011368 166.84 0.000 1.874356 1.918936
_cons | -.9866896 .0311325 -31.69 0.000 -1.047733 -.9256464
-------------+----------------------------------------------------------------
sigma_u | .84490704
sigma_e | .80383774
rho | .52489398 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(999, 2999) = 4.42 Prob > F =0.0000
. xtreg y time, re
Random-effects GLS regression Number of obs =4000
Group variable (i) : id Number of groups =1000
R-sq: within = 0.9027 Obs per group: min =4
between = 0.0000 avg =4.0
overall = 0.7897 max =4
Random effects u_i ~ Gaussian Wald chi2(1) =27835.94
corr(u_i, X) = 0 (assumed) Prob > chi2 =0.0000
------------------------------------------------------------------------------
y | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
time | 1.896646 .011368 166.84 0.000 1.874365 1.918927
_cons | -.9866896 .0390072 -25.30 0.000 -1.063142 -.9102369
-------------+----------------------------------------------------------------
sigma_u | .74318848
sigma_e | .80383774
rho | .46085639 (fraction of variance due to u_i)
------------------------------------------------------------------------------
. prais y time
Number of gaps in sample: 999 (gap count includes panel changes)
(note: computations for rho restarted at each gap)
Iteration 0: rho = 0.0000
Iteration 1: rho = 0.4034
Iteration 2: rho = 0.4136
Iteration 3: rho = 0.4140
Iteration 4: rho = 0.4140
Iteration 5: rho = 0.4140
Prais-Winsten AR(1) regression -- iterated estimates
Source | SS df MS Number of obs =4000
-------------+------------------------------ F( 1, 3998) =8914.61
Model | 8913.21448 1 8913.21448 Prob > F =0.0000
Residual | 3997.37575 3998 .999843859 R-squared =0.6904
-------------+------------------------------ Adj R-squared =0.6903
Total | 12910.5902 3999 3.22845467 Root MSE =.99992
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95%Conf. Interval]
-------------+----------------------------------------------------------------
time | 1.953367 .0157109 124.33 0.000 1.922565 1.984169
_cons | -1.061051 .0456138 -23.26 0.000 -1.15048 -.9716229
-------------+----------------------------------------------------------------
rho | .4140074
------------------------------------------------------------------------------
Durbin-Watson statistic (original) 0.925711
Durbin-Watson statistic (transformed) 1.672284
>
> >
> >
> > Anirban
> >
> > ______________________________________
> > ANIRBAN BASU
> > Doctoral Student
> > Harris School of Public Policy Studies
> > University of Chicago
> > (312) 563 0907 (H)
> > ________________________________________________________________
> >
> >
> > On Tue, 25 Jun 2002, Mark Schaffer wrote:
> >
> > > Hi everybody.
> > >
> > > Just a couple of clarifying details on -cluster- vs. -xtreg-
> > and
> > > Anirban's response to John.
> > >
> > > The -cluster- option for -regress- doesn't really impose a
> > particular
> > > within-cluster correlation structure on the data. If I
> > understand it
> > > correctly, what -cluster- does instead is loosen the usual
> > assumption
> > > of independence of observations to independence of clusters.
> > The
> > > correlation between observations within clusters can be
> > arbitrary.
> > > The way this works is basically by treating all the
> > observations in a
> > > cluster as a kind of "super-observation" and then applying
> > the robust
> > > ("sandwich") formula to these super-observations in order to
> >
> > > calculate the standard errors of the coefficients produced
> > by -
> > > regress-. See the manual entry for -regress-, p. 87.
> > >
> > > The estimated coefficients (the betas) produced by -regress-
> > are the
> > > same whether or not the -cluster- option is used; the only
> > thing that
> > > is different is the standard errors.
> > >
> > > With fixed effects, you _do_ impose a particular correlation
> >
> > > structure, namely all the observations within a cluster
> > share U(k) in
> > > Anirban's notation. If you use -xtreg- with -fe- to
> > estimate, Stata
> > > does not, however, use a first-difference estimator - it
> > uses a fixed
> > > effects estimator. In other words, it doesn't
> > first-difference to
> > > get rid of the fixed effects, it uses the mean-deviation
> > > transformation to get rid of them.
> > >
> > > Hope this helps.
> > >
> > > --Mark
> > >
> > > Quoting anirban basu <[email protected]>:
> > >
> > > > Hi John,
> > > >
> > > >
> > > > With reg command and cluster option, one basically imposes
> > an
> > > > exchangeable
> > > > correlation structure on the data. i.e assume corr (y(i),
> > > > y(j)) = rho,
> > > > where i ne j and i,j are any two observation from the
> > same
> > > > cluster. Rho
> > > > is constant for every pair of observation within a
> > cluster.
> > > > So, one can
> > > > visuaize it in terms of a random effects model where :
> > > >
> > > > Y(k) = Xb + U(k) + e, where k represents clusters and U(k)
> > is
> > > > a
> > > > cluster-specific random effect that is common to all
> > > > observation in that
> > > > cluster. However, -reg- does not give estimates of this
> > random
> > > > effect. It
> > > > just estimates -betas- assuming this structure.
> > > >
> > > > However, this estimation is correct only if U(k) are
> > > > uncorrelated with
> > > > Xs. i.e. the unobserved characteristics of a cluster over
> > time
> > > > is
> > > > uncorrelated with the X over time. If not then fixed
> > effects
> > > > is useful.
> > > >
> > > >
> > > > With fixed effects, one evades the correlation problem by
> > > > taking
> > > > differences. i.e for any cluster k:
> > > >
> > > > Y(ik) - Y(1k) = [X(ik) - X(1k)]b + [e(ik) - e(1k)]
> > > >
> > > > Note that by taking the difference, the unobserved U(k) is
> > > > eliminated.
> > > > However, fixed effects assume the U(k) is fixed over time
> > for
> > > > any cluster
> > > > k. i.e. the unobserved characteristics of a cluster is not
> > > > changing over
> > > > time. Also, since we are taking a difference, fixed
> > effects
> > > > model cannot
> > > > estimate the betas for baseline covariates since they
> > cancel
> > > > out in the
> > > > difference.
> > > >
> > > > Hope this helps,
> > > >
> > > > Anirban
> > > >
> > > >
> > > >
> > > > ______________________________________
> > > > ANIRBAN BASU
> > > > Doctoral Student
> > > > Harris School of Public Policy Studies
> > > > University of Chicago
> > > > (312) 563 0907 (H)
> > > >
> > ________________________________________________________________
> > > >
> > > >
> > > > On Tue, 25 Jun 2002, John Neumann wrote:
> > > >
> > > > > Hello all,
> > > > >
> > > > > Since I frequently see panel data questions flying
> > around
> > > > the
> > > > > list, I'm thinking that some of you can provide me with
> > a
> > > > > very succinct answer to the following question, and in
> > so
> > > > > doing clarify conceptually for me the data-related
> > issue:
> > > > >
> > > > > I have data on investment products, by year. Not all
> > > > > products have data in each year. The dependent
> > > > > variable is scaled in such a way as to make time series
> > > > > variation in its levels of no concern. Here's the
> > question:
> > > > >
> > > > > What is the difference between using the reg command,
> > > > > with the robust and cluster option, vs. the xtreg
> > command
> > > > > fixed effects model? The cluster variable using reg
> > would
> > > > > naturally be the i( ) parameter for xtreg ...
> > > > >
> > > > > Thanks!
> > > > >
> > > > > John Neumann
> > > > > Boston University
>
> Prof. Mark Schaffer
> Director, CERT
> Department of Economics, School of Management
> Heriot-Watt University, Edinburgh EH14 4AS
> tel +44-131-451-3494 / fax +44-131-451-3008
> email: [email protected]
> web: http://www.som.hw.ac.uk/ecomes
> ________________________________________________________________
>
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