----- Original Message -----
From: "Millimet, Daniel" <[email protected]>
To: <[email protected]>
Sent: Thursday, July 17, 2003 9:01 AM
Subject: st: RE: xtreg fixed effect with time trend; constant
> It's probably blowing up if you code the year as, say, 1999. Then the
> constant becomes the mean value of y fixing all X's at zero and time at
> zero. This is "right," just not relevant. If you plug in the average
> value of the year in the trend, you should get sensical values of y.
> Alternatively, rescale the time variable to start in year 0.
>
> Dann
>
> ----------------------------------------------------------
> Daniel L. Millimet, Assistant Professor
> Department of Economics
> Box 0496
> SMU
> Dallas, TX 75275-0496
> Phone: 214.768.3269
> Fax: 214.768.1821
> http://faculty.smu.edu/millimet
> ----------------------------------------------------------
>
> > -----Original Message-----
> > From: david reinstein [mailto:[email protected]]
> > Sent: Thursday, July 17, 2003 4:37 AM
> > To: [email protected]
> > Subject: st: xtreg fixed effect with time trend; constant
> >
> > I try to do an xtreg fixed effect including a
> > variable that represents the year of the data
> > observation. I assume the coefficient on this should
> > be an an average time trend. The coefficients I get
> > are plausible, but the "constant" blows up weirdly --
> > to a level much higher (or lower) than the average of
> > the dependent variable could possibly be.
> > Anyone know why?
As Dann pointed out, the constant is relatively large (or small) simply
because you've scaled up the time trend (the constant = mean(Y) - b*mean(X);
in your case the mean(X) is large). However, I believe both forms are right
and relevant and give you the correct average of the dependent variable.
Example:
. use http://www.stata-press.com/data/r8/grunfeld.dta
. xtsum time year
Variable | Mean Std. Dev. Min Max |
Observations
-----------------+--------------------------------------------+-------------
---
time overall | 10.5 5.780751 1 20 | N =
200
between | 0 10.5 10.5 | n =
10
within | 5.780751 1 20 | T =
20
| |
year overall | 1944.5 5.780751 1935 1954 | N =
200
between | 0 1944.5 1944.5 | n =
10
within | 5.780751 1935 1954 | T =
20
So, both year and time are trends with the former starting at 1935 going to
1954 and the later starting at 1 going to 20.
. xtreg inve time, fe
Fixed-effects (within) regression Number of obs =
200
Group variable (i): company Number of groups =
10
R-sq: within = 0.2121 Obs per group: min =
20
between = 0.0000 avg =
20.0
overall = 0.0509 max =
20
F(1,189) =
50.88
corr(u_i, Xb) = -0.0000 Prob > F =
0.0000
----------------------------------------------------------------------------
--
invest | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
time | 8.46052 1.186155 7.13 0.000 6.120716
10.80032
_cons | 57.12279 14.20913 4.02 0.000 29.09394
85.15165
-------------+--------------------------------------------------------------
--
sigma_u | 198.82421
sigma_e | 96.728022
rho | .808615 (fraction of variance due to u_i)
----------------------------------------------------------------------------
--
F test that all u_i=0: F(9, 189) = 84.50 Prob > F =
0.0000
If the time coefficient is multipled by its average and added to the
constant we get the average value of the dependent variable, investment.
. disp 10.5*_b[time] + _b[_cons]
145.95825
And we get the same values if we use the year variable rather than the time
variable.
. xtreg inve year, fe
Fixed-effects (within) regression Number of obs =
200
Group variable (i): company Number of groups =
10
R-sq: within = 0.2121 Obs per group: min =
20
between = . avg =
20.0
overall = 0.0509 max =
20
F(1,189) =
50.88
corr(u_i, Xb) = -0.0000 Prob > F =
0.0000
----------------------------------------------------------------------------
--
invest | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
year | 8.46052 1.186155 7.13 0.000 6.120716
10.80032
_cons | -16305.52 2306.489 -7.07
0.000 -20855.29 -11755.75
-------------+--------------------------------------------------------------
--
sigma_u | 198.82421
sigma_e | 96.728022
rho | .808615 (fraction of variance due to u_i)
----------------------------------------------------------------------------
--
F test that all u_i=0: F(9, 189) = 84.50 Prob > F =
0.0000
. disp 1944.5*_b[year] + _b[_cons]
145.95825
This is equal to the average of the dependent variable
. xtreg inve , fe
Fixed-effects (within) regression Number of obs =
200
Group variable (i): company Number of groups =
10
R-sq: within = 0.0000 Obs per group: min =
20
between = . avg =
20.0
overall = 0.0000 max =
20
F(0,190) =
0.00
corr(u_i, Xb) = 0.0000 Prob > F =
.
----------------------------------------------------------------------------
--
invest | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
_cons | 145.9583 7.685174 18.99 0.000 130.799
161.1175
-------------+--------------------------------------------------------------
--
sigma_u | 198.82421
sigma_e | 108.68477
rho | .76993402 (fraction of variance due to u_i)
----------------------------------------------------------------------------
--
F test that all u_i=0: F(9, 190) = 66.93 Prob > F =
0.0000
Or,
. sum invest
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
invest | 200 145.9583 216.8753 .93 1486.7
> > Anyone know how to impose a time trend (or better,
> > several time trends for several subgroups) within the
> > context of a panel FE model?
> > Thanks,
> > David
> >
To generate a time trend for each group you can use the -xi- command: xi
i.company*time
Hope this helps,
Scott
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