## Chapter 9 - Simultaneous Equations Models

### Examples

```-----------------------------------------------------------------------------------------------
name:  SN
log:  myReplications\iiexample9
log type:  smcl
opened on:  11 Jun 2019, 11:27:56

. **********************************************
. * Solomon Negash - Examples
. * Wooldridge (2010). Economic Analysis of Cross-Section and Panel Data. 2nd ed.
. * STATA Program, version 15.1.

. * Chapter 9  - Simultaneous Equations Models
. * Computer Exercises (Problems)
. **********************************************

. // Example 9.1 (NA)
. // Example 9.2 (NA)
. // Example 9.3 (NA)
. // Example 9.4 (NA)
. // Example 9.5 (Labor Supply for Married, Working Women):
. bcuse mroz, clear nodesc
. reg hours lwage educ age kidslt6 kidsge6 nwifeinc

Source |       SS           df       MS      Number of obs   =       428
-------------+----------------------------------   F(6, 421)       =      5.04
Model |  17228385.4         6  2871397.56   Prob > F        =    0.0001
Residual |   240082635       421   570267.54   R-squared       =    0.0670
Total |   257311020       427   602601.92   Root MSE        =    755.16

------------------------------------------------------------------------------
hours |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwage |  -17.40781   54.21544    -0.32   0.748    -123.9745    89.15886
educ |  -14.44486   17.96793    -0.80   0.422    -49.76289    20.87317
age |  -7.729976    5.52945    -1.40   0.163    -18.59874    3.138792
kidslt6 |  -342.5048   100.0059    -3.42   0.001     -539.078   -145.9317
kidsge6 |  -115.0205   30.82925    -3.73   0.000     -175.619   -54.42208
nwifeinc |  -4.245807   3.655815    -1.16   0.246    -11.43173    2.940117
_cons |   2114.697   340.1307     6.22   0.000     1446.131    2783.263
------------------------------------------------------------------------------

. ivregress 2sls hours (lwage = exper expersq) educ age kidslt6 kidsge6 nwifeinc

Instrumental variables (2SLS) regression          Number of obs   =        428
Wald chi2(6)    =      20.80
Prob > chi2     =     0.0020
R-squared       =          .
Root MSE        =     1291.2

------------------------------------------------------------------------------
hours |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwage |   1544.818   476.7912     3.24   0.001     610.3248    2479.312
educ |   -177.449   57.66517    -3.08   0.002    -290.4706   -64.42731
age |  -10.78409   9.498705    -1.14   0.256    -29.40121    7.833032
kidslt6 |  -210.8339   175.4811    -1.20   0.230    -554.7705    133.1028
kidsge6 |  -47.55707   56.45049    -0.84   0.400     -158.198    63.08385
nwifeinc |   -9.24912   6.427897    -1.44   0.150    -21.84757    3.349328
_cons |   2432.198    589.293     4.13   0.000     1277.205    3587.191
------------------------------------------------------------------------------
Instrumented:  lwage
Instruments:   educ age kidslt6 kidsge6 nwifeinc exper expersq

. predict u, r
(325 missing values generated)

. reg u educ age kidslt6 kidsge6 nwifeinc exper expersq

Source |       SS           df       MS      Number of obs   =       428
-------------+----------------------------------   F(7, 420)       =      0.12
Model |  1430782.97         7  204397.567   Prob > F        =    0.9969
Residual |   712152488       420  1695601.16   R-squared       =    0.0020
Total |   713583271       427   1671155.2   Root MSE        =    1302.2

------------------------------------------------------------------------------
u |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ |   .3573408   29.48776     0.01   0.990    -57.60464    58.31932
age |  -3.441065   10.57543    -0.33   0.745    -24.22843     17.3463
kidslt6 |  -8.574062   173.0567    -0.05   0.961    -348.7392    331.5911
kidsge6 |   2.453998   54.47557     0.05   0.964    -104.6247    109.5327
nwifeinc |   .8964355   6.483562     0.14   0.890    -11.84784    13.64071
exper |  -15.88408   26.11816    -0.61   0.543    -67.22268    35.45452
expersq |   .6408396   .7847342     0.82   0.415    -.9016561    2.183335
_cons |   177.4856   621.6837     0.29   0.775    -1044.514    1399.485
------------------------------------------------------------------------------

. display "Rsquare = " e(r2) ", Test statistic = " e(N)* e(r2) " & p = " chi2tail(1, e(r2)*e(N))
Rsquare = .00200507, Test statistic = .85816909 & p = .35425157

. reg lwage educ age kidslt6 kidsge6 nwifeinc exper expersq

Source |       SS           df       MS      Number of obs   =       428
-------------+----------------------------------   F(7, 420)       =     11.78
Model |  36.6476854         7  5.23538363   Prob > F        =    0.0000
Residual |  186.679766       420  .444475633   R-squared       =    0.1641
Total |  223.327451       427  .523015108   Root MSE        =    .66669

------------------------------------------------------------------------------
lwage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ |   .0998844   .0150975     6.62   0.000     .0702084    .1295604
age |  -.0035204   .0054145    -0.65   0.516    -.0141633    .0071225
kidslt6 |  -.0558726   .0886034    -0.63   0.529     -.230034    .1182889
kidsge6 |  -.0176485    .027891    -0.63   0.527    -.0724718    .0371749
nwifeinc |   .0056942   .0033195     1.72   0.087    -.0008307    .0122192
exper |   .0407097   .0133723     3.04   0.002     .0144249    .0669946
expersq |  -.0007473   .0004018    -1.86   0.064    -.0015371    .0000424
_cons |  -.3579973   .3182963    -1.12   0.261    -.9836496     .267655
------------------------------------------------------------------------------

. test age kidslt6 kidsge6 nwifeinc

( 1)  age = 0
( 2)  kidslt6 = 0
( 3)  kidsge6 = 0
( 4)  nwifeinc = 0

F(  4,   420) =    0.91
Prob > F =    0.4555

. ivreg lwage (hours=age kidslt6 kidsge6 nwifeinc) educ exper*

Instrumental variables (2SLS) regression

Source |       SS           df       MS      Number of obs   =       428
-------------+----------------------------------   F(4, 423)       =     18.80
Model |  24.8336451         4  6.20841129   Prob > F        =    0.0000
Residual |  198.493806       423  .469252497   R-squared       =    0.1112
Total |  223.327451       427  .523015108   Root MSE        =    .68502

------------------------------------------------------------------------------
lwage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
hours |   .0001608   .0002154     0.75   0.456    -.0002626    .0005842
educ |   .1111175   .0153319     7.25   0.000     .0809814    .1412537
exper |    .032646    .018061     1.81   0.071    -.0028545    .0681465
expersq |  -.0006765   .0004426    -1.53   0.127    -.0015466    .0001935
_cons |  -.6927902   .3066002    -2.26   0.024     -1.29544   -.0901405
------------------------------------------------------------------------------
Instrumented:  hours
Instruments:   educ exper expersq age kidslt6 kidsge6 nwifeinc
------------------------------------------------------------------------------

. // Example 9.6 (Nonlinear Labor Supply Function):
. bcuse mroz, clear nodesc
. foreach x of var lwage educ age nwifeinc {
. g `x'sq=`x'^2
. }
(325 missing values generated)

. ivreg hours (lwage lwagesq = exper expersq educsq agesq nwifeincsq) educ age kidslt6 kidsge6 nwifeinc

Instrumental variables (2SLS) regression

Source |       SS           df       MS      Number of obs   =       428
-------------+----------------------------------   F(7, 420)       =      3.54
Model |  -308860249         7 -44122892.8   Prob > F        =    0.0010
Residual |   566171269       420  1348026.83   R-squared       =         .
Total |   257311020       427   602601.92   Root MSE        =      1161

------------------------------------------------------------------------------
hours |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwage |    1873.62   635.9912     2.95   0.003      623.498    3123.743
lwagesq |   -437.291   350.0765    -1.25   0.212    -1125.411    250.8293
educ |  -87.85113   66.39337    -1.32   0.186    -218.3558    42.65357
age |  -9.142302    8.57342    -1.07   0.287    -25.99446    7.709855
kidslt6 |  -185.0553   162.2808    -1.14   0.255     -504.039    133.9283
kidsge6 |  -58.18948    50.1046    -1.16   0.246    -156.6765    40.29754
nwifeinc |  -7.233422   5.805744    -1.25   0.213    -18.64536    4.178512
_cons |   1657.926   777.2758     2.13   0.034     130.0905    3185.761
------------------------------------------------------------------------------
Instrumented:  lwage lwagesq
Instruments:   educ age kidslt6 kidsge6 nwifeinc exper expersq educsq agesq
nwifeincsq
------------------------------------------------------------------------------

. predict u6, r
(325 missing values generated)

. reg u6 educ age kidslt6 kidsge6 nwifeinc exper expersq educsq agesq nwifeincsq

Source |       SS           df       MS      Number of obs   =       428
-------------+----------------------------------   F(10, 417)      =      0.26
Model |     3455380        10      345538   Prob > F        =    0.9897
Residual |   562715880       417  1349438.56   R-squared       =    0.0061
Total |   566171260       427  1325928.01   Root MSE        =    1161.7

------------------------------------------------------------------------------
u6 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ |   128.0985   184.0341     0.70   0.487    -233.6516    489.8487
age |   22.79413   87.72426     0.26   0.795    -149.6428     195.231
kidslt6 |   7.451197   156.7426     0.05   0.962    -300.6529    315.5553
kidsge6 |  -1.182785   50.09191    -0.02   0.981     -99.6469    97.28133
nwifeinc |   5.764532   14.08098     0.41   0.682    -21.91402    33.44309
exper |  -20.36932   24.30678    -0.84   0.403    -68.14842    27.40978
expersq |   .8696309   .7385333     1.18   0.240    -.5820812    2.321343
educsq |  -5.028233   7.113492    -0.71   0.480      -19.011    8.954539
agesq |   -.323187    1.02805    -0.31   0.753    -2.343992    1.697618
nwifeincsq |  -.0699239   .2071181    -0.34   0.736    -.4770496    .3372019
_cons |  -1172.042   2162.256    -0.54   0.588    -5422.322    3078.238
------------------------------------------------------------------------------

. display "Rsquare = " e(r2) ", Test statistic = " e(N)* e(r2) " & p = " chi2tail(3, e(r2)*e(N))
Rsquare = .00610306, Test statistic = 2.6121118 & p = .45537014

. log close
name:  SN
log:  myReplications\iiexample9
log type:  smcl
closed on:  11 Jun 2019, 11:27:58
-----------------------------------------------------------------------------------------------
```