Thank you for your help in advance.
I’m the user of Stata MP/16.0.
I have a panel data set consisting of 16 regions from year 2001 to 2017. There are four equations to estimate using Seemingly Unrelated Regression model.
In each equation, there is a single identical regressor which is GRP (Gross Regional Product).
In the system of four equations, there are four different dependent variables.
Y1, Y2, and Y3 are different measures of regional income, Y4 is regional consumption.
Therefore, the system of four equations are as follows.
1st equation: Y1=c1+b1*GRP+e1
2nd equation: Y2=c2+b2*GRP+e2
3rd equation: Y3=c3+b3*GRP+e3
4th equation: Y4=c4+b4*GRP+e4
Theoretically, b1+b2+b3+b4=1 but I do not impose the theoretical restriction in estimation.
Without any restriction on b’s, I estimated the above system using 'sureg' command and got an error message as follows.
Code:
. sureg (y1 grp) (y2 grp) (y3 grp) (y4 grp)
Covariance matrix of errors is singular
symmetric __00000C[4,4]
__000006 __000007 __000008 __000009
__000006 1.1193292
__000007 .96680075 1.2204782
__000008 .9282527 .96859259 .99608893
__000009 0 0 0 0
r(506);
end of do-file
r(506);Code:
. sureg (y1 grp) (y2 grp) (y3 grp)
Seemingly unrelated regression
--------------------------------------------------------------------------
Equation Obs Parms RMSE "R-sq" chi2 P
--------------------------------------------------------------------------
y1 272 1 2.043316 0.0953 28.65 0.0000
y2 272 1 1.952064 0.1004 30.36 0.0000
y3 272 1 2.547562 0.0532 15.29 0.0001
--------------------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
y1 |
grp | .3481933 .0650525 5.35 0.000 .2206929 .4756938
_cons | .0815574 .1239898 0.66 0.511 -.1614581 .3245729
-------------+----------------------------------------------------------------
y2 |
grp | .3424472 .0621473 5.51 0.000 .2206407 .4642537
_cons | -.1918022 .1184526 -1.62 0.105 -.423965 .0403606
-------------+----------------------------------------------------------------
y3 |
grp | .3171816 .081106 3.91 0.000 .1582168 .4761464
_cons | .0436708 .1545878 0.28 0.778 -.2593157 .3466573
------------------------------------------------------------------------------
.
end of do-fileCode:
. sureg (y1 grp) (y2 grp) (y4 grp)
Seemingly unrelated regression
--------------------------------------------------------------------------
Equation Obs Parms RMSE "R-sq" chi2 P
--------------------------------------------------------------------------
y1 272 1 2.043316 0.0953 28.65 0.0000
y2 272 1 1.952064 0.1004 30.36 0.0000
y4 272 1 1.011226 0.0002 0.06 0.8080
--------------------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
y1 |
grp | .3481933 .0650525 5.35 0.000 .2206929 .4756938
_cons | .0815574 .1239898 0.66 0.511 -.1614581 .3245729
-------------+----------------------------------------------------------------
y2 |
grp | .3424472 .0621473 5.51 0.000 .2206407 .4642537
_cons | -.1918022 .1184526 -1.62 0.105 -.423965 .0403606
-------------+----------------------------------------------------------------
y4 |
grp | -.0078221 .0321941 -0.24 0.808 -.0709215 .0552772
_cons | .066574 .0613619 1.08 0.278 -.0536931 .1868412
------------------------------------------------------------------------------
.
end of do-fileCode:
. sureg (y2 grp) (y3 grp) (y4 grp)
Seemingly unrelated regression
--------------------------------------------------------------------------
Equation Obs Parms RMSE "R-sq" chi2 P
--------------------------------------------------------------------------
y2 272 1 1.952064 0.1004 30.36 0.0000
y3 272 1 2.547562 0.0532 15.29 0.0001
y4 272 1 1.011226 0.0002 0.06 0.8080
--------------------------------------------------------------------------
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
y2 |
grp | .3424472 .0621473 5.51 0.000 .2206407 .4642537
_cons | -.1918022 .1184526 -1.62 0.105 -.423965 .0403606
-------------+----------------------------------------------------------------
y3 |
grp | .3171816 .081106 3.91 0.000 .1582168 .4761464
_cons | .0436708 .1545878 0.28 0.778 -.2593157 .3466573
-------------+----------------------------------------------------------------
y4 |
grp | -.0078221 .0321941 -0.24 0.808 -.0709215 .0552772
_cons | .066574 .0613619 1.08 0.278 -.0536931 .1868412
------------------------------------------------------------------------------
.
end of do-file(1) It seems that the above system of four equations has the problem of singularity of the residual covariance.
(2) However, the coefficient estimates and their standard errors do not change across different systems of 3 equations.
Based on these findings, I'm going to proceed as follows.
(1) I need to report all four coefficient estimates. To do that, I get estimates of b1, b2, and b3 from the system of the 1st, 2nd, and 3rd equation. And I get estimates of b4 from the system of the 1st, 2nd, and 4th equation.
(2) Since I need the equality test among b1, b2, and b3 (but not b4), I just estimate the system of the 1st, 2nd, and 3rd equation and use the estimations result for this purpose.
However, I'm not confident in my approach. So, I'm looking for any comment that I have to consider.
Is it ok to use the above approach? If not, what kind of concerns do you have about this approach?
Thank you for your help.
Sangyeon
0 Response to Dealing with singular covariance matrix in Seemingly Unrelated Regression (sureg)
Post a Comment