CODEWITHSUNDEEP
statisticsregressionstataestimation
Aflatoun
Aflatoun

Reputation: 37

Non-linear constraint in a system of linear equations

I am trying to estimate a system of simultaneous labor supply within couples (called eq1 for women and eq2 for men) with the sureg command in Stata 14 for Windows.

When I try to add a linear constraint the regression works. However, I need to impose a non-linear constraint on four coefficients but as soon as I add this, I get the following error message:

the constraint caused an error

Below you can find a reproducible example:

sysuse auto.dta

constraint 1 [Eq1]mpg*[Eq2]headroom = [Eq1]headroom*[Eq2]length

sureg (Eq1: price = mpg trunk weight rep78 headroom) ///
      (Eq2 : price = headroom length), /// 
      corr constraint(1)

(note: constraint number 1 caused error r(131))
(note: constraint number 1 caused error r(131))

Seemingly unrelated regression
--------------------------------------------------------------------------
Equation             Obs   Parms        RMSE    "R-sq"       chi2        P
--------------------------------------------------------------------------
Eq1                   69       5    2392.918    0.3150      29.32   0.0000
Eq2                   69       2    2581.831    0.2026      18.01   0.0001
--------------------------------------------------------------------------

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Eq1          |
         mpg |  -26.58347   29.65312    -0.90   0.370    -84.70252    31.53558
       trunk |   31.52432   38.05785     0.83   0.407    -43.06769    106.1163
      weight |   1.363126   .3241408     4.21   0.000     .7278219     1.99843
       rep78 |    171.411   113.7883     1.51   0.132    -51.60992     394.432
    headroom |  -377.2506   360.8804    -1.05   0.296    -1084.563     330.062
       _cons |   2687.868   1603.852     1.68   0.094    -455.6242    5831.361
-------------+----------------------------------------------------------------
Eq2          |
    headroom |  -325.9389   402.3103    -0.81   0.418    -1114.453    462.5749
      length |   50.51478   12.27884     4.11   0.000      26.4487    74.58087
       _cons |  -2387.561   2125.435    -1.12   0.261    -6553.338    1778.215
------------------------------------------------------------------------------

Correlation matrix of residuals:

        Eq1     Eq2
Eq1  1.0000
Eq2  0.9292  1.0000

Breusch-Pagan test of independence: chi2(1) =    59.574, Pr = 0.0000

When using my real data, I get the same error. This makes it impossible to implement a non-linear constraint in the sureg estimation, which I really need to impose in my model.

Upvotes: 0

Views: 348

Answers (1)

user8682794
user8682794

Reputation:

You can re-cast your non-linear constraint as two linear ones and include both in sureg:

sysuse auto.dta, clear

constraint 1 [Eq1]mpg = [Eq1]headroom
constraint 2 [Eq2]headroom = [Eq2]length

sureg (Eq1: price = mpg trunk weight rep78 headroom) (Eq2: price = headroom length), ///
      corr constraint(1 2)

You can then test if the constraint is satisfied as follows:

assert _b[Eq1:mpg] * _b[Eq2:headroom] == _b[Eq1:headroom] * _b[Eq2:length]

Upvotes: 1

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