Seemingly Unrelated Regression with same independent variables

[Shuai Yan]

Hi,

I am trying to estimate two models. They are separately like this

reg y1 x
reg y2 x

Since there are two dependent variables and same independent variables, does this mean running them separately is equivalent to running SUREG with them combined?
sureg y1 y2 = x

Can I still use SUREG to address the correlation between y1 and y2? Any econometrics reference can support this?

Thank you very much!

[Carlo Lazzaro]

Shuai:
while the point estimates remain the same, the SEs change:

. use "C:\Program Files\Stata18\ado\base\a\auto.dta"
(1978 automobile data)

. sureg (price i.foreign trunk) (mpg i.foreign trunk)

Seemingly unrelated regression
------------------------------------------------------------------------------
Equation             Obs   Params         RMSE  "R-squared"      chi2   P>chi2
------------------------------------------------------------------------------
price                 74        2      2734.29      0.1288      10.94   0.0042
mpg                   74        2     4.534574      0.3773      44.83   0.0000
------------------------------------------------------------------------------

------------------------------------------------------------------------------
             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
price        |
     foreign |
    Foreign  |   1190.155   745.2236     1.60   0.110    -270.4564    2650.766
       trunk |   262.7717   80.17556     3.28   0.001     105.6304    419.9129
       _cons |   2196.541   1241.891     1.77   0.077    -237.5211    4630.603
-------------+----------------------------------------------------------------
mpg          |
     foreign |
    Foreign  |   2.661582   1.235886     2.15   0.031     .2392899    5.083874
       trunk |  -.6837128   .1329639    -5.14   0.000    -.9443173   -.4231082
       _cons |   29.91169   2.059565    14.52   0.000     25.87501    33.94836
------------------------------------------------------------------------------

. regress price i.foreign trunk

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =      5.25
       Model |  81816017.5         2  40908008.7   Prob > F        =    0.0075
    Residual |   553249379        71  7792244.77   R-squared       =    0.1288
-------------+----------------------------------   Adj R-squared   =    0.1043
       Total |   635065396        73  8699525.97   Root MSE        =    2791.5

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
     foreign |
    Foreign  |   1190.155   760.8049     1.56   0.122    -326.8468    2707.157
       trunk |   262.7717   81.85189     3.21   0.002     99.56364    425.9797
       _cons |   2196.541   1267.857     1.73   0.088    -331.4939    4724.576
------------------------------------------------------------------------------

. regress mpg i.foreign trunk

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     21.51
       Model |  921.845002         2  460.922501   Prob > F        =    0.0000
    Residual |  1521.61446        71  21.4311895   R-squared       =    0.3773
-------------+----------------------------------   Adj R-squared   =    0.3597
       Total |  2443.45946        73  33.4720474   Root MSE        =    4.6294

------------------------------------------------------------------------------
         mpg | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
     foreign |
    Foreign  |   2.661582   1.261726     2.11   0.038     .1457715    5.177393
       trunk |  -.6837128    .135744    -5.04   0.000    -.9543785    -.413047
       _cons |   29.91169   2.102626    14.23   0.000     25.71917     34.1042
------------------------------------------------------------------------------

.

[Shuai Yan]

Shuai:
while the point estimates remain the same, the SEs change:

. use "C:\Program Files\Stata18\ado\base\a\auto.dta"
(1978 automobile data)

. sureg (price i.foreign trunk) (mpg i.foreign trunk)

Seemingly unrelated regression
------------------------------------------------------------------------------
Equation Obs Params RMSE "R-squared" chi2 P>chi2
------------------------------------------------------------------------------
price 74 2 2734.29 0.1288 10.94 0.0042
mpg 74 2 4.534574 0.3773 44.83 0.0000
------------------------------------------------------------------------------

------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
price |
foreign |
Foreign | 1190.155 745.2236 1.60 0.110 -270.4564 2650.766
trunk | 262.7717 80.17556 3.28 0.001 105.6304 419.9129
_cons | 2196.541 1241.891 1.77 0.077 -237.5211 4630.603
-------------+----------------------------------------------------------------
mpg |
foreign |
Foreign | 2.661582 1.235886 2.15 0.031 .2392899 5.083874
trunk | -.6837128 .1329639 -5.14 0.000 -.9443173 -.4231082
_cons | 29.91169 2.059565 14.52 0.000 25.87501 33.94836
------------------------------------------------------------------------------

. regress price i.foreign trunk

Source | SS df MS Number of obs = 74
-------------+---------------------------------- F(2, 71) = 5.25
Model | 81816017.5 2 40908008.7 Prob > F = 0.0075
Residual | 553249379 71 7792244.77 R-squared = 0.1288
-------------+---------------------------------- Adj R-squared = 0.1043
Total | 635065396 73 8699525.97 Root MSE = 2791.5

------------------------------------------------------------------------------
price | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
foreign |
Foreign | 1190.155 760.8049 1.56 0.122 -326.8468 2707.157
trunk | 262.7717 81.85189 3.21 0.002 99.56364 425.9797
_cons | 2196.541 1267.857 1.73 0.088 -331.4939 4724.576
------------------------------------------------------------------------------

. regress mpg i.foreign trunk

Source | SS df MS Number of obs = 74
-------------+---------------------------------- F(2, 71) = 21.51
Model | 921.845002 2 460.922501 Prob > F = 0.0000
Residual | 1521.61446 71 21.4311895 R-squared = 0.3773
-------------+---------------------------------- Adj R-squared = 0.3597
Total | 2443.45946 73 33.4720474 Root MSE = 4.6294

------------------------------------------------------------------------------
mpg | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
foreign |
Foreign | 2.661582 1.261726 2.11 0.038 .1457715 5.177393
trunk | -.6837128 .135744 -5.04 0.000 -.9543785 -.413047
_cons | 29.91169 2.102626 14.23 0.000 25.71917 34.1042
------------------------------------------------------------------------------

.

Thanks. Yes, the SE is different, but I wonder what that implies? Can SUREG still be used to address the intercorrelations among DV?

[Carlo Lazzaro]

Shuai:
yes, you can.
For more details, please read -sureg- entry, Stata .pdf manual and related references. Thanks

[Joseph Coveney]

Can SUREG still be used to address the intercorrelations among DV?

I've been under the impression that SUREG is intended to address multivariate regression where the sets of explanatory (independent) variables are not identical between outcome (dependent) variables.

In your case, the predictors are the same between response variables.

So why not just use conventional MANOVA (multivariate regression) in your case? You can see their relationship by running the following code.

version 18.0

clear *

// seedem
set seed 86162503

quietly drawnorm out1 out2, double corr(1 0.5 \ 0.5 1) n(50)

generate double pre = runiform()

*
* Begin here
*
sureg (out1 c.pre) (out2 c.pre), isure small dfk noheader nolog

// MANOVA
quietly manova out1 out2 = c.pre
mvreg , noheader

// Alternative MANOVA
generate byte pid = _n
quietly reshape long out, i(pid) j(tim)
mixed out 1bn.tim 1.tim#c.pre 2.tim 2.tim#c.pre, noconstant || pid: , ///
    noconstant residuals(unstructured, t(tim)) ///
    reml dfmethod(kroger) nolrtest nolog

exit

And to answer your question: Yes.

[Joseph Coveney]

Oh, I didn't see his post before I responded, but Carlo already answered your question. Still, you can run the code to see the relationship.