[Limdep Nlogit List] Probit model with endogenous right hand side variable

William Greene wgreene at stern.nyu.edu
Sun Jan 10 06:11:19 EST 2010


Annemie:
First, some misconceptions:
(1) The estimator is not an instrumental variable estimator.
It is full information maximum likelihood, both in Stata and in
LIMDEP. It is unfortunate that they (Stata) have publicized the
estimator with that name.
(2) (Hence) it not a two step estimator; it is a one step,
FIML estimator (both in Stata and in LIMDEP).

The command to use in LIMDEP is

PROBIT ; Lhs = binary variable, endogenous continuous variable
       ; RH1 = right hand side for probit (including endogenous var.)
       ; RH2 = right hand side for endogenous variable
       ; Marginal effects $

An application follows:

--> probit;lhs=doctor,hhninc
    ;rh1=one,age,educ,married,addon,hhninc
    ;rh2=one,age,educ,hhkids,working
    ;marg$

------------------------------------------------------------------
Probit   Regression Start Values for DOCTOR
Dependent variable               DOCTOR
Log likelihood function    -17691.35340
Estimation based on N =  27326, K =   6
Information Criteria: Normalization=1/N
              Normalized   Unnormalized
AIC              1.29528    35394.70680
Fin.Smpl.AIC     1.29528    35394.70988
Bayes IC         1.29708    35444.00037
Hannan Quinn     1.29586    35410.59379
Model estimated: Jan 09, 2010, 14:02:34
--------+---------------------------------------------------------
        |                  Standard           Prob.       Mean
  DOCTOR| Coefficient        Error       z    z>|Z|       of X
--------+---------------------------------------------------------
Constant|     .03971         .05407      .73  .4626
     AGE|     .01531***      .00072    21.31  .0000    43.5257
    EDUC|    -.02904***      .00351    -8.28  .0000    11.3206
 MARRIED|    -.00960         .01888     -.51  .6110     .75862
   ADDON|     .25919***      .05974     4.34  .0000     .01881
  HHNINC|    -.10906**       .04633    -2.35  .0186     .35208
--------+---------------------------------------------------------
Note: ***, **, * ==>  Significance at 1%, 5%, 10% level.
------------------------------------------------------------------


------------------------------------------------------------------
OLS Starting Values for HHNINC....................
Ordinary     least squares regression ............
LHS=HHNINC   Mean                 =         .35208
             Standard deviation   =         .17691
             Number of observs.   =          27326
Model size   Parameters           =              5
             Degrees of freedom   =          27321
Residuals    Sum of squares       =      764.85286
             Standard error of e  =         .16732
Fit          R-squared            =         .10562
             Adjusted R-squared   =         .10549
Model test   F[  4, 27321] (prob) =   806.6(.0000)
Diagnostic   Log likelihood       =    10083.74944
             Restricted(b=0)      =     8558.60603
             Chi-sq [  4]  (prob) =  3050.3(.0000)
Info criter. LogAmemiya Prd. Crt. =       -3.57554
             Akaike Info. Criter. =       -3.57554
             Bayes Info. Criter.  =       -3.57404
Model was estimated on Jan 09, 2010 at 02:02:34 PM
--------+---------------------------------------------------------
        |                  Standard           Prob.       Mean
  HHNINC| Coefficient        Error       z    z>|Z|       of X
--------+---------------------------------------------------------
Constant|     .02357***      .00762     3.09  .0020
     AGE|     .00149***   .9937D-04    14.99  .0000    43.5257
    EDUC|     .01844***      .00045    41.26  .0000    11.3206
  HHKIDS|     .01322***      .00221     5.98  .0000     .40273
 WORKING|     .07331***      .00226    32.48  .0000     .67705
--------+---------------------------------------------------------
Note: nnnnn.D-xx or D+xx => multiply by 10 to -xx or +xx.
Note: ***, **, * ==>  Significance at 1%, 5%, 10% level.
------------------------------------------------------------------

------------------------------------------------------------------
Probit with Endogenous RHS Variable
Dependent variable               DOCTOR
Log likelihood function     -7141.45104
Restricted log likelihood  -16599.60800
Chi squared [  11 d.f.]     18916.31391
Significance level               .00000
McFadden Pseudo R-squared      .5697819
Estimation based on N =  27326, K =  13
Information Criteria: Normalization=1/N
              Normalized   Unnormalized
AIC               .52364    14308.90208
Fin.Smpl.AIC      .52364    14308.91541
Bayes IC          .52755    14415.70480
Hannan Quinn      .52490    14343.32388
Model estimated: Jan 09, 2010, 14:02:37
--------+---------------------------------------------------------
  DOCTOR|                  Standard           Prob.       Mean
  HHNINC| Coefficient        Error       z    z>|Z|       of X
--------+---------------------------------------------------------
        |Coefficients in Probit Equation for DOCTOR
Constant|     .03971         .05790      .69  .4928
     AGE|     .01531***      .00075    20.42  .0000    43.5257
    EDUC|    -.02904***      .00594    -4.89  .0000    11.3206
 MARRIED|    -.00960         .01886     -.51  .6106     .75862
   ADDON|     .25919***      .05991     4.33  .0000     .01881
  HHNINC|    -.10906         .23959     -.46  .6490     .35208
        |Coefficients in Linear Regression for HHNINC
Constant|     .02354***      .00745     3.16  .0016
     AGE|     .00149***      .00010    14.57  .0000    43.5257
    EDUC|     .01842***      .00040    46.21  .0000    11.3206
  HHKIDS|     .01320***      .00219     6.02  .0000     .40273
 WORKING|     .07322***      .00233    31.48  .0000     .67705
        |Standard Deviation of Regression Disturbances
Sigma(w)|     .16711***      .00025   670.88  .0000
        |Correlation Between Probit and Regression Disturbance
Rho(e,w)|     .02126         .04062      .52  .6007
--------+---------------------------------------------------------
Note: ***, **, * ==>  Significance at 1%, 5%, 10% level.
------------------------------------------------------------------

+---------------------------------------------------------+
|Predictions for Binary Choice Model.  Predicted value is |
|1 when probability is greater than  .500000, 0 otherwise.|
|Note, column or row total percentages may not sum to     |
|100% because of rounding. Percentages are of full sample.|
+------+---------------------------------+----------------+
|Actual|         Predicted Value         |                |
|Value |       0                1        | Total Actual   |
+------+----------------+----------------+----------------+
|  0   |    417 (  1.5%)|   9718 ( 35.6%)|  10135 ( 37.1%)|
|  1   |    465 (  1.7%)|  16726 ( 61.2%)|  17191 ( 62.9%)|
+------+----------------+----------------+----------------+
|Total |    882 (  3.2%)|  26444 ( 96.8%)|  27326 (100.0%)|
+------+----------------+----------------+----------------+
+---------------------------------------------------------+
|Crosstab for Binary Choice Model.  Predicted probability |
|vs. actual outcome. Entry = Sum[Y(i,j)*Prob(i,m)] 0,1.   |
|Note, column or row total percentages may not sum to     |
|100% because of rounding. Percentages are of full sample.|
+------+---------------------------------+----------------+
|Actual|      Predicted Probability      |                |
|Value |    Prob(y=0)        Prob(y=1)   | Total Actual   |
+------+----------------+----------------+----------------+
| y=0  |   3907 ( 14.3%)|   6227 ( 22.8%)|  10135 ( 37.1%)|
| y=1  |   6223 ( 22.8%)|  10967 ( 40.1%)|  17191 ( 62.9%)|
+------+----------------+----------------+----------------+
|Total |  10130 ( 37.1%)|  17195 ( 62.9%)|  27326 (100.0%)|
+------+----------------+----------------+----------------+

-----------------------------------------------------------------------
Analysis of Binary Choice Model Predictions Based on Threshold =  .5000
-----------------------------------------------------------------------
Prediction Success
-----------------------------------------------------------------------
Sensitivity = actual 1s correctly predicted                     63.795%
Specificity = actual 0s correctly predicted                     38.550%
Positive predictive value = predicted 1s that were actual 1s    63.780%
Negative predictive value = predicted 0s that were actual 0s    38.569%
Correct prediction = actual 1s and 0s correctly predicted       54.432%
-----------------------------------------------------------------------
Prediction Failure
-----------------------------------------------------------------------
False pos. for true neg. = actual 0s predicted as 1s            61.441%
False neg. for true pos. = actual 1s predicted as 0s            36.199%
False pos. for predicted pos. = predicted 1s actual 0s          36.214%
False neg. for predicted neg. = predicted 0s actual 1s          61.431%
False predictions = actual 1s and 0s incorrectly predicted      45.561%
-----------------------------------------------------------------------


------------------------------------------------------------------
Partial derivatives of E[y] = F[*]   with
respect to the vector of characteristics.
They are computed at the means of the Xs.
Observations used for means are All Obs.
--------+---------------------------------------------------------
        |                  Standard           Prob.       Mean
    HSAT| Coefficient        Error       z    z>|Z|       of X
--------+---------------------------------------------------------
Constant|     .01497***      .00364     4.11  .0000
     AGE|     .00577***   .2850D-04   202.54  .0000    43.5257
    EDUC|    -.01095***      .00072   -15.19  .0000    11.3206
        |Marginal effect for dummy variable is P|1 - P|0.
 MARRIED|    -.00362***      .00034   -10.73  .0000     .75862
        |Marginal effect for dummy variable is P|1 - P|0.
   ADDON|     .09276***      .00208    44.51  .0000     .01881
  HHNINC|    -.04111         .03538    -1.16  .2452     .35208
--------+---------------------------------------------------------
Note: nnnnn.D-xx or D+xx => multiply by 10 to -xx or +xx.
Note: ***, **, * ==>  Significance at 1%, 5%, 10% level.
------------------------------------------------------------------



----- Original Message -----
From: "Annemie Maertens" <maertens_annemie at hotmail.com>
To: limdep at limdep.itls.usyd.edu.au
Sent: Saturday, January 9, 2010 1:33:19 PM GMT -05:00 Colombia
Subject: [Limdep Nlogit List] Probit model with endogenous right hand side variable


Dear all, 
 
I am trying to use limdep to do something stata  does not do well: Probit model with endogenous right hand side variable. 
 
So basically, I would like to run an IV probit (two-step) and compute the marginal effects and their errors. 
 
I do not have access to any recent manual here at Cornell - few people use the program here, and cannot figure out from the help function which command to use. 
 
Any suggestions on where to start? 
 
Annemie 
 		 	   		  
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