[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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