线性方程组中的非线性约束

Question

我正在尝试使用 Stata 14 中的 sureg 命令估计夫妻内的同时劳动力供应系统（女性称为 eq1，男性称为 eq2）Windows。

当我尝试添加线性约束时，回归有效。但是，我需要对四个系数施加非线性约束，但是一旦我添加它，我就会收到以下错误消息：

the constraint caused an error

您可以在下面找到一个可重现的示例：

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

使用我的真实数据时，我得到了同样的错误。这使得无法在 sureg 估计中实现非线性约束，我确实需要在我的模型中施加非线性约束。

Answer 1

您可以 re-cast 您的 non-linear 约束作为两个线性约束并包含在 sureg 中：

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)

然后您可以按如下方式测试约束是否满足：

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

线性方程组中的非线性约束

Non-linear constraint in a system of linear equations

statistics

estimation

regression

stata