# st: Simultaneous equations once more

 From "Tobias Hofmann" To Subject st: Simultaneous equations once more Date Fri, 20 Aug 2004 04:48:47 +0100

```Dear all,

I hope you can help me with respect to three related problems/questions.

First: Has there been any developments concerning Stata routines for
estimating time-series cross-section/panel simultaneous equation models
since March 2004 (cf.
http://www.stata.com/statalist/archive/2004-03/msg00623.html)? I'm
particularly interested in an xt version of the -cdsimeq- command, which
implements a two-stage estimation method for simultaneous equations models
in which one of the endogenous variables is continuous and the other
endogenous variable is dichotomous.

Second: If such Stata routines existed, I would like to lag all the
endogenous and exogenous explanatory variables in both simultaneous
equations. The model would look like this:

Y1i,t = a1 + b1*Y2i,t-1 + b2*X1i,t-1 + b3*X2i,t-1 + ... + ei,t
Y2i,t = a2 + b4*Y1i,t-1 + b5*X1i,t-1 + b6*X3i,t-1 + ... + ei,t

Would it be appropriate to lag (especially) the endogenous explanatory
variables (cf.
http://www.stata.com/statalist/archive/2003-10/msg00633.html)? How could it
be done using Stata?

Third: Currently I'm using the -cdsimeq- command to analyze a simple
cross-section dataset. However, I'm having some problems with respect to the
results (cf. enclosed exemplary Stata output). How can it be that the
corrected standard errors for the first regression of "THE SECOND STAGE
REGRESSIONS WITH CORRECTED STANDARD ERRORS" are almost 10.000 times as large
as the uncorrected standard errors for the first regression of "THE SECOND
STAGE REGRESSIONS WITH INSTRUMENTS"? Why doesn't Stata report the corrected
standard errors for the second regression of "THE SECOND STAGE REGRESSIONS
WITH CORRECTED STANDARD ERRORS"?

Tobias

. cdsimeq (y_cont x1 x2 x3) (y_dich x2 x3 x4 x5)

NOW THE FIRST STAGE REGRESSIONS

Source |       SS       df       MS              Number of obs =
536
-------------+------------------------------           F(  5,   530) =
32.41
Model |  2197.74185     5  439.548369           Prob > F      =
0.0000
Residual |  7187.44021   530  13.5612079           R-squared     =
0.2342
0.2269
Total |  9385.18206   535  17.5423964           Root MSE      =
3.6826

----------------------------------------------------------------------------
--
y_cont |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
x1 |  -.0578088   .0084591    -6.83   0.000    -.0744263
-.0411913
x2 |  -.1679869   .0242766    -6.92   0.000    -.2156771
-.1202967
x3 |   .0759898   .1179953     0.64   0.520     -.155806
.3077856
x4 |   .3384814   .0382162     8.86   0.000     .2634076
.4135552
x5 |   .0240823   .0161272     1.49   0.136    -.0075988
.0557635
_cons |   18.58596   .8659791    21.46   0.000     16.88479
20.28714
----------------------------------------------------------------------------
--

Iteration 0:   log likelihood = -371.28805
Iteration 1:   log likelihood = -201.43246
Iteration 2:   log likelihood =   -162.489
Iteration 3:   log likelihood =  -151.9387
Iteration 4:   log likelihood = -151.02364
Iteration 5:   log likelihood = -151.01204
Iteration 6:   log likelihood = -151.01204

Probit estimates                                  Number of obs   =
536
LR chi2(5)      =
440.55
Prob > chi2     =
0.0000
Log likelihood = -151.01204                       Pseudo R2       =
0.5933

----------------------------------------------------------------------------
--
y_dich |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
x1 |   .0189883   .0054346     3.49   0.000     .0083367
.02964
x2 |  -.0192266   .0161163    -1.19   0.233     -.050814
.0123609
x3 |   .1900641   .0632085     3.01   0.003     .0661778
.3139505
x4 |   .3613688   .0330317    10.94   0.000     .2966278
.4261098
x5 |  -.0158672   .0128439    -1.24   0.217    -.0410408
.0093063
_cons |  -5.740676   .7333928    -7.83   0.000      -7.1781
-4.303253
----------------------------------------------------------------------------
--

note: 0 failures and 16 successes completely determined.

NOW THE SECOND STAGE REGRESSIONS WITH INSTRUMENTS

Source |       SS       df       MS              Number of obs =
536
-------------+------------------------------           F(  4,   531) =
38.66
Model |  2116.60605     4  529.151514           Prob > F      =
0.0000
Residual |    7268.576   531  13.6884671           R-squared     =
0.2255
0.2197
Total |  9385.18206   535  17.5423964           Root MSE      =
3.6998

----------------------------------------------------------------------------
--
y_cont |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
I_y_dich |   .9549185   .1059842     9.01   0.000     .7467187
1.163118
x1 |  -.0709968   .0092547    -7.67   0.000    -.0891772
-.0528164
x2 |   -.149041   .0245761    -6.06   0.000    -.1973192
-.1007627
x3 |   -.035948   .1201037    -0.30   0.765    -.2718847
.1999887
_cons |   23.95326   .8628885    27.76   0.000     22.25817
25.64836
----------------------------------------------------------------------------
--

Iteration 0:   log likelihood = -371.28805
Iteration 1:   log likelihood = -201.43246
Iteration 2:   log likelihood =   -162.489
Iteration 3:   log likelihood =  -151.9387
Iteration 4:   log likelihood = -151.02364
Iteration 5:   log likelihood = -151.01204
Iteration 6:   log likelihood = -151.01204

Probit estimates                                  Number of obs   =
536
LR chi2(5)      =
440.55
Prob > chi2     =
0.0000
Log likelihood = -151.01204                       Pseudo R2       =
0.5933

----------------------------------------------------------------------------
--
y_dich |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
I_y_cont |  -.3284679   .0940103    -3.49   0.000    -.5127248
-.144211
x2 |  -.0744049    .014563    -5.11   0.000    -.1029478
-.0458619
x3 |   .2150243   .0644788     3.33   0.001     .0886482
.3414005
x4 |    .472549   .0478296     9.88   0.000     .3788047
.5662933
x5 |   -.007957   .0125808    -0.63   0.527    -.0326149
.0167009
_cons |   .3642162   1.353521     0.27   0.788    -2.288637
3.017069
----------------------------------------------------------------------------
--

note: 0 failures and 16 successes completely determined.

NOW THE SECOND STAGE REGRESSIONS WITH CORRECTED STANDARD ERRORS

----------------------------------------------------------------------------
--
y_cont |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
I_y_dich |   .9549185   786.7151     0.00   0.999    -1544.501
1546.411
x1 |  -.0709968   68.69738    -0.00   0.999     -135.023
134.881
x2 |   -.149041   182.4267    -0.00   0.999    -358.5156
358.2175
x3 |   -.035948   891.5231    -0.00   1.000    -1751.381
1751.309
_cons |   23.95326   6405.173     0.00   0.997    -12558.63
12606.54
----------------------------------------------------------------------------
--
----------------------------------------------------------------------------
--
y_dich |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
I_y_cont |  -.3284679          .        .       .            .
.
x2 |  -.0744049          .        .       .            .
.
x3 |   .2150243          .        .       .            .
.
x4 |    .472549          .        .       .            .
.
x5 |   -.007957          .        .       .            .
.
_cons |   .3642162          .        .       .            .
.
----------------------------------------------------------------------------
--

.

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```

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