Seemingly unrelated regressions: when using and results interpretation

[Giorgio Piccitto]

Dear all, I recently run into some seemingly unrelated regressions and did some attempts to compare them with the 'truly unrelated' regressions. From these attempts, I came up with a couple of doubts which I would like to share with you regarding how to correctly proceed:

- I read that there is no point in running the SUR, because they would be equivalent to OLS, in two cases: a) When each equation contains exactly the same set of regressors: b) when there are no cross-equation correlations between the error terms. With respect to this latter point, is there some formal test or demonstration to check the absence or presence of this cross-equation correlations (so that I can justify, eventually, the use of SUR)?

- The results that I obtain with SUR are very similar to what I obtain with OLS, except for the coefficient of the a variable that is present in three of my four model but absent in the fourth. Why may this happen? The coefficients for this variable are really unrealistic with SUR, while with OLS are ok: is there something that I should consider in interpreting the coefficient of a variable which is not present in all the models estimated with SUR?

Thanks in advance for your feedback.

Best, G.

[Giorgio Piccitto]

Anyone with some tips about it?

Very appreciated, thanks, G.

[salma bibi]

Estimating model by sureg command and adding corr at end of equation will give you the correlation matrix of residual and bruesch pagan test statistics for estimated VCE of residuals and tests for independence of residual vectors. if p value rejects the null hypothesis of independence of residuals series using SUR is justified then.
further from the correlation matrix of residual you can have an idea that whether residual are correlated or not and by B.P value confirmation
first justify the use of SUR then compare the results.
wish you good luck

[salma bibi]

https://www.stata.com/manuals13/rsureg.pdf
u can get further guide about stata

[Giorgio Piccitto]

Dear Salma,

thanks a lot for your explanation. DO you gave any clue on why the only variable that is not present in all of my four models (but only in three out of four) reports a coefficient very dissimilar with respect to the coefficient of the same variable when running an OLS?

[salma bibi]

Dear
i don't knw what variables u are using for which country it is dissimilar then how can i comment on its dissimilarity and how can i knw which one is in consensus with previous literature if disimilar then we also need to sort the reason for its such behavior
hope u get piont
best wishes

[Giorgio Piccitto]

Dear Salma,

I provide you an example with my data, it would be nice to know your opinion about the interpretation of the results:

This is the sureg models I am running

sureg (depA aage i.edu i.urban i.conscious) (depB aage i.edu i.urban) ///
          (depC aage i.edu i.urban i.conscious) (depD aage i.edu i.urban i.conscious), corr

with the following results:

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
depA         |
        aage |   .0031883   .0068542     0.47   0.642    -.0102457    .0166223
             |
         edu |
          2  |  -.3202717   .1727541    -1.85   0.064    -.6588634      .01832
          3  |  -.1960064   .1696686    -1.16   0.248    -.5285507     .136538
             |
     1.urban |    .141324   .1047091     1.35   0.177    -.0639021    .3465502
 1.conscious |    7.35761   .3116861    23.61   0.000     6.746716    7.968504
       _cons |          0  (omitted)
-------------+----------------------------------------------------------------
depB         |
        aage |   -.020765   .0055777    -3.72   0.000    -.0316971   -.0098329
             |
         edu |
          2  |  -.2198229   .1405808    -1.56   0.118    -.4953562    .0557104
          3  |  -.2118299     .13807    -1.53   0.125    -.4824421    .0587823
             |
     1.urban |    .334017   .0852084     3.92   0.000     .1670116    .5010223
       _cons |   9.505728   .2536385    37.48   0.000     9.008605    10.00285
-------------+----------------------------------------------------------------
depC         |
        aage |   .0160727    .005696     2.82   0.005     .0049087    .0272367
             |
         edu |
          2  |   .1754428   .1435629     1.22   0.222    -.1059353    .4568209
          3  |   .0160077   .1409988     0.11   0.910     -.260345    .2923603
             |
     1.urban |   .1070792   .0870159     1.23   0.218    -.0634688    .2776272
 1.conscious |    1.30849   .2590189     5.05   0.000     .8008228    1.816158
       _cons |          0  (omitted)
-------------+----------------------------------------------------------------
depD         |
        aage |  -.0116211   .0024129    -4.82   0.000    -.0163503   -.0068918
             |
         edu |
          2  |   .0468824   .0608161     0.77   0.441     -.072315    .1660798
          3  |   .2083778   .0597299     3.49   0.000     .0913093    .3254463
             |
     1.urban |    .039845   .0368617     1.08   0.280    -.0324026    .1120926
 1.conscious |    4.53784   .1097256    41.36   0.000     4.322781    4.752898
       _cons |          0  (omitted)
------------------------------------------------------------------------------

Correlation matrix of residuals:

         depA     depB     depC     depD
depA   1.0000
depB   0.1286   1.0000
depC  -0.2159  -0.2984   1.0000
depD   0.1978   0.2520  -0.2548   1.0000

Breusch-Pagan test of independence: chi2(6) =   427.199, Pr = 0.0000

So, according to what you said, it is correct to estimate these equations with the sureg command right?

The results when running a simple OLS (only for depA, just as example) are anyway a bit different (see above):

. reg depA aage i.edu   i.urban i.conscious

      Source |       SS       df       MS              Number of obs =    1863
-------------+------------------------------           F(  5,  1857) =    1.96
       Model |   38.160141     5   7.6320282           Prob > F      =  0.0818
    Residual |  7235.66595  1857  3.89642754           R-squared     =  0.0052
-------------+------------------------------           Adj R-squared =  0.0026
       Total |  7273.82609  1862  3.90645869           Root MSE      =  1.9739

------------------------------------------------------------------------------
        depA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        aage |   .0016666   .0058414     0.29   0.775    -.0097898     .013123
             |
         edu |
          2  |  -.1813652   .1502034    -1.21   0.227    -.4759505    .1132201
          3  |  -.0314734   .1485207    -0.21   0.832    -.3227584    .2598116
             |
     1.urban |   .1949513   .0918416     2.12   0.034     .0148278    .3750749
 1.conscious |   .1563377   .1177107     1.33   0.184    -.0745214    .3871969
       _cons |   7.039201   .2608232    26.99   0.000     6.527664    7.550739
------------------------------------------------------------------------------

My question (sorry ifi silly for you) is: why are they varying sometimes so strongly? What is especially puzzling to me is the coefficient of conscious, which is extremely different in OLS and in sureg.

Hope you may have some tips about it.

Sincerely, G.

[salma bibi]

According to test(B.P) result sur technique is more suitable . so the technique which is most suited to the data provides most efficient estimates i am quite surprised by your question why are you comparing the coefficient from two different techniques .just compare your coeffiecient to the previous studies and what theoratics say about these, are these in consensus with earlier literature if not why not .

[salma bibi]

sureg ( dv IV1 IV2) ( dv IV1 IV2), corr dfk small
by the above syntax u will get t values instead of Z values