----- Original Message -----
From: "ash_alankar" <[email protected]>
To: <[email protected]>
Sent: Thursday, June 19, 2003 4:57 PM
Subject: Re: st: RE: Fixed Effects Panel Regression with correlation between
panels
> Hi Dolores,
>
> Thanks for the info. But when I mean correlation between panels I
> mean that the errors for unit i are correlated with the errors for
> unit j. I am assuming that the errors are independent across time
> i.e. no autocorrelation.
>
> Do you know how to do this in a fixed effects framework? I was
> thinking of using xtgls with a dummy of ones for each different unit
> to capture the fixed effects, but was hoping that there might be a
> better way.
>
> Thanks.
> Ash.
A possible alternative to fixed effects GLS would be to reshape the data and
use -sureg-. If you constrain the coefficients to be equal across
equations, it will give you the same results fixed effects GLS, however,
sureg would allow the slope coefficients to vary by equation as well as
contemporaneous correlation between the error terms across equations.
Hope this helps,
Scott
Example:
The do file:
preserve
use http://www.stata-press.com/data/r8/grunfeld.dta
drop kstock
keep if comp <4
xtreg invest mvalue , fe
xi i.com
xtgls invest mva _*, panel(corr)
drop _*
reshape wide invest mvalue , i(year) j(company)
forv i = 1/3 {
local rhs " `rhs' (invest`i' mvalue`i' )"
}
di "`rhs'"
constraint 1 [invest1]mvalue1 = [invest2]mvalue2
constrain 2 [invest2]mvalue2 = [invest3]mvalue3
sureg `rhs' ,const(1 2) corr
restore
The results:
. preserve
. use http://www.stata-press.com/data/r8/grunfeld.dta
. drop kstock
. keep if comp <4
(140 observations deleted)
.
. xtreg invest mvalue , fe
Fixed-effects (within) regression Number of obs =
60
Group variable (i): company Number of groups =
3
R-sq: within = 0.3725 Obs per group: min =
20
between = 0.6451 avg =
20.0
overall = 0.5131 max =
20
F(1,56) =
33.25
corr(u_i, Xb) = -0.3598 Prob > F =
0.0000
----------------------------------------------------------------------------
--
invest | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
mvalue | .1982563 .0343844 5.77 0.000 .1293759
.2671366
_cons | -171.4112 96.63739 -1.77 0.082 -364.9991
22.17679
-------------+--------------------------------------------------------------
--
sigma_u | 166.11924
sigma_e | 155.73559
rho | .53222836 (fraction of variance due to u_i)
----------------------------------------------------------------------------
--
F test that all u_i=0: F(2, 56) = 19.81 Prob > F =
0.0000
.
. xi i.com
i.company _Icompany_1-3 (naturally coded; _Icompany_1 omitted)
. xtgls invest mva _*, panel(corr)
Cross-sectional time-series FGLS regression
Coefficients: generalized least squares
Panels: heteroskedastic with cross-sectional correlation
Correlation: no autocorrelation
Estimated covariances = 6 Number of obs =
60
Estimated autocorrelations = 0 Number of groups =
3
Estimated coefficients = 4 Time periods =
20
Wald chi2(3) =
244.45
Log likelihood = -362.3947 Prob > chi2 =
0.0000
----------------------------------------------------------------------------
--
invest | Coef. Std. Err. z P>|z| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
mvalue | .1166626 .0323914 3.60 0.000 .0531767
.1801485
_Icompany_2 | 78.01431 86.04438 0.91 0.365 -90.62957
246.6582
_Icompany_3 | -226.6125 89.96582 -2.52
.012 -402.9423 -50.2827
_cons | 102.4225 149.0675 0.69 0.492 -189.7444
394.5895
----------------------------------------------------------------------------
--
.
. drop _*
.
. reshape wide invest mvalue , i(year) j(company)
(note: j = 1 2 3)
Data long -> wide
----------------------------------------------------------------------------
-
Number of obs. 60 -> 20
Number of variables 5 -> 8
j variable (3 values) company -> (dropped)
xij variables:
invest -> invest1 invest2 invest3
mvalue -> mvalue1 mvalue2 mvalue3
----------------------------------------------------------------------------
-
. forv i = 1/3 {
2. local rhs " `rhs' (invest`i' mvalue`i' )"
3. }
. di "`rhs'"
(invest1 mvalue1 ) (invest2 mvalue2 ) (invest3 mvalue3 )
.
. constraint 1 [invest1]mvalue1 = [invest2]mvalue2
. constrain 2 [invest2]mvalue2 = [invest3]mvalue3
. sureg `rhs' ,const(1 2) corr
Seemingly unrelated regression
Constraints:
( 1) [invest1]mvalue1 - [invest2]mvalue2 = 0
( 2) [invest2]mvalue2 - [invest3]mvalue3 = 0
----------------------------------------------------------------------
Equation Obs Parms RMSE "R-sq" chi2 P
----------------------------------------------------------------------
invest1 20 1 244.2778 0.3446 12.97 0.0003
invest2 20 1 109.6837 0.1947 12.97 0.0003
invest3 20 1 55.1047 -0.3541 12.97 0.0003
----------------------------------------------------------------------
----------------------------------------------------------------------------
--
| Coef. Std. Err. z P>|z| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
invest1 |
mvalue1 | .1166626 .0323914 3.60 0.000 .0531767
.1801485
_cons | 102.4225 149.0675 0.69 0.492 -189.7444
394.5895
-------------+--------------------------------------------------------------
--
invest2 |
mvalue2 | .1166626 .0323914 3.60 0.000 .0531767
.1801485
_cons | 180.4368 68.18261 2.65 0.008 46.80137
314.0723
-------------+--------------------------------------------------------------
--
invest3 |
mvalue3 | .1166626 .0323914 3.60 0.000 .0531767
.1801485
_cons | -124.19 65.30971 -1.90 0.057 -252.1946
3.814733
----------------------------------------------------------------------------
--
Correlation matrix of residuals:
invest1 invest2 invest3
invest1 1.0000
invest2 0.6410 1.0000
invest3 0.4171 0.5185 1.0000
Breusch-Pagan test of independence: chi2(3) = 17.076, Pr = 0.0007
.
. restore
*
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