ivprobit twostep command - intuition?

Ashwin Sivakumar

Join Date: Jul 2022

Posts: 10
#1

ivprobit twostep command - intuition?

26 Sep 2022, 07:45

Hi all,
Is the

HTML Code:

ivprobit, twostep

command appropriate if I want to:

(1) estimate an endogenous regressor x using an instrument variable z - using OLS
(2) use x_hat to then estimate for dummy dependant variable y, using probit (because it is a binary dummy variable)

Many thanks
Tags: None

Andrew Musau

Join Date: Oct 2014
Posts: 10077

26 Sep 2022, 15:18

Newey's procedure involves running a linear regression model where the endogenous variable is the outcome and the instruments and other independent variables are regressors, predicting the residuals and including these as a regressor in a second stage probit model. This is the estimator implemented by specifying the -twostep- option. His article (linked below) outlines the intuition.

Reference
Newey, W. (1987). "Efficient estimation of limited dependent variable models with endogenous explanatory variables." Journal of Econometrics, 36: 231-250.

Code:

webuse laborsup, clear

*IVPROBIT -TWOSTEP-
ivprobit fem_work fem_educ kids (other_inc = male_educ), twostep

*NEWEY'S PROCEDURE: FIRST STAGE REGRESSION
regress other_inc fem_educ kids male_educ

*PREDICT RESIDUALS
predict res, r

*SECOND STAGE PROBIT (SEs NOT CORRECTED FOR 2 STAGE ESTIMATION)
probit fem_work other_inc fem_educ kids res

Res.

Code:

. *IVPROBIT -TWOSTEP-

.
. ivprobit fem_work fem_educ kids (other_inc = male_educ), twostep
Checking reduced-form model...

Two-step probit with endogenous regressors        Number of obs   =        500
                                                  Wald chi2(3)    =      93.97
                                                  Prob > chi2     =     0.0000

------------------------------------------------------------------------------
             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   other_inc |   -.058473   .0093364    -6.26   0.000    -.0767719    -.040174
    fem_educ |    .227437   .0281628     8.08   0.000     .1722389     .282635
        kids |  -.1961748   .0496323    -3.95   0.000    -.2934522   -.0988973
       _cons |   .3956061   .4982649     0.79   0.427    -.5809752    1.372187
------------------------------------------------------------------------------
Instrumented:  other_inc
Instruments:   fem_educ kids male_educ
------------------------------------------------------------------------------
Wald test of exogeneity: chi2(1) = 6.50                   Prob > chi2 = 0.0108

.
.
. *NEWEY'S PROCEDURE: SECOND STAGE PROBIT (SEs NOT CORRECTED FOR 2 STAGE ESTIMATION)

.
. probit fem_work other_inc fem_educ kids res

Iteration 0:   log likelihood = -344.63508  
Iteration 1:   log likelihood = -252.10819  
Iteration 2:   log likelihood = -252.04529  
Iteration 3:   log likelihood = -252.04529  

Probit regression                                       Number of obs =    500
                                                        LR chi2(4)    = 185.18
                                                        Prob > chi2   = 0.0000
Log likelihood = -252.04529                             Pseudo R2     = 0.2687

------------------------------------------------------------------------------
    fem_work | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
   other_inc |   -.058473   .0090228    -6.48   0.000    -.0761573   -.0407887
    fem_educ |    .227437   .0273171     8.33   0.000     .1738964    .2809775
        kids |  -.1961748   .0478084    -4.10   0.000    -.2898776    -.102472
         res |   .0240492   .0094295     2.55   0.011     .0055677    .0425306
       _cons |   .3956061   .4784993     0.83   0.408    -.5422352    1.333448
------------------------------------------------------------------------------

.

Last edited by Andrew Musau; 26 Sep 2022, 15:30.

Comment

Ashwin Sivakumar

Join Date: Jul 2022

Posts: 10
#3

26 Sep 2022, 15:39

Thank you for the well explained response Andrew.

So, if I am correct in understanding, you need to run all four lines of code specified, with the final output as you have shown being probit regression ?

Would I then need to run -margins- to get the marginal effect at the mean?
Comment

Andrew Musau

Join Date: Oct 2014
Posts: 10077

26 Sep 2022, 16:01

No need to run the estimation in several steps, this is already programmed into ivprobit. I would recommend using the maximum likelihood estimator. The requirement is that the outcome is binary, but the endogenous variable must be continuous. Then, you indeed can use margins, same as you would do when estimating a probit model.

Code:

webuse laborsup, clear
ivprobit fem_work fem_educ kids (other_inc = male_educ)
margins, dydx(fem_educ) predict(pr)

So this, e.g., gives you the average marginal effect of female education on probability that a woman works.

Code:

. ivprobit fem_work fem_educ kids (other_inc = male_educ)

Fitting exogenous probit model

Iteration 0:   log likelihood = -344.63508  
Iteration 1:   log likelihood = -252.10819  
Iteration 2:   log likelihood = -252.04529  
Iteration 3:   log likelihood = -252.04529  

Fitting full model

Iteration 0:   log likelihood = -2368.2142  
Iteration 1:   log likelihood = -2368.2062  
Iteration 2:   log likelihood = -2368.2062  

Probit model with endogenous regressors                 Number of obs =    500
                                                        Wald chi2(3)  = 163.88
Log likelihood = -2368.2062                             Prob > chi2   = 0.0000

----------------------------------------------------------------------------------------------
                             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-----------------------------+----------------------------------------------------------------
                   other_inc |  -.0542756   .0060854    -8.92   0.000    -.0662028   -.0423485
                    fem_educ |    .211111   .0268648     7.86   0.000     .1584569    .2637651
                        kids |  -.1820929   .0478267    -3.81   0.000    -.2758315   -.0883542
                       _cons |   .3672086   .4480724     0.82   0.412    -.5109971    1.245414
-----------------------------+----------------------------------------------------------------
 corr(e.other_inc,e.fem_work)|   .3720375   .1300518                      .0946562    .5958136
              sd(e.other_inc)|   16.66621   .5270318                      15.66461    17.73186
----------------------------------------------------------------------------------------------
Instrumented:  other_inc
Instruments:   fem_educ kids male_educ
----------------------------------------------------------------------------------------------
Wald test of exogeneity (corr = 0): chi2(1) = 6.70        Prob > chi2 = 0.0096

.
. margins, dydx(fem_educ) predict(pr)

Average marginal effects                                   Number of obs = 500
Model VCE: OIM

Expression: Average structural function probabilities, predict(pr)
dy/dx wrt:  fem_educ

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    fem_educ |   .0646175   .0073529     8.79   0.000      .050206     .079029
------------------------------------------------------------------------------

.

Last edited by Andrew Musau; 26 Sep 2022, 16:22.

Comment

Ashwin Sivakumar

Join Date: Jul 2022

Posts: 10
#5

26 Sep 2022, 16:18

No need to run the estimation in several steps, this is already programmed into ivprobit.

Got it. I understand now you were just breaking it down if you did each step manually.

My regression fits

The requirements are that the outcome is binary, but the endogenous variable and instruments must be continuous.

Many thanks for you help!
Comment

Kazi Aiman Udoy

Join Date: Dec 2022
Posts: 33

25 Feb 2023, 19:35

Andrew Musau I urgently need your help. Hoping to get positive response from you.

I am doing probit model where i am using an instrument. My dependent variable in vocational training which is a dummy (0 and 1) and have list of regressors. One of my regressors is remittance (remitt) which I suspect as endogenous. That's why I am using an instrument which is nonfarm (whether hh owns any nonfarm entrepreneurship) which is also a dummy (0 and 1). I have run the following regression:

Code:

ivprobit vocationaltraining hhsize gender literacy uneduc_adults mfs_use loan scatosavings scatoassets mobile1 barisal chittagong khulna rajshahi rangpur sylhet members_in_agri agrishock distfacility3 (remitt = nonfarm), twostep

The output looks like this:

Code:



Two-step probit with endogenous regressors        Number of obs   =     18,366
                                                  Wald chi2(19)   =     333.32
                                                  Prob > chi2     =     0.0000

---------------------------------------------------------------------------------
                |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
         remitt |  -1.510386   .3144558    -4.80   0.000    -2.126708   -.8940643
         hhsize |  -.0329519   .0101655    -3.24   0.001    -.0528759   -.0130279
         gender |  -.8139006   .1565242    -5.20   0.000    -1.120683   -.5071187
       literacy |   .0023912   .0166741     0.14   0.886    -.0302895    .0350718
  uneduc_adults |  -.0912452   .0228638    -3.99   0.000    -.1360574   -.0464329
        mfs_use |   .1571294   .0352415     4.46   0.000     .0880574    .2262014
           loan |  -.0105326   .0366643    -0.29   0.774    -.0823934    .0613282
   scatosavings |  -.0001195   .0000965    -1.24   0.216    -.0003086    .0000697
    scatoassets |   .0000167   5.51e-06     3.04   0.002     5.95e-06    .0000275
        mobile1 |   .1492968   .0155468     9.60   0.000     .1188257     .179768
        barisal |     .03892   .0667708     0.58   0.560    -.0919483    .1697883
     chittagong |  -.0186855   .0620932    -0.30   0.763    -.1403859    .1030149
         khulna |   -.121161   .0584884    -2.07   0.038    -.2357961   -.0065259
       rajshahi |  -.0558219   .0584396    -0.96   0.339    -.1703615    .0587176
        rangpur |  -.1035035   .0597487    -1.73   0.083    -.2206088    .0136018
         sylhet |   .0893287   .0466704     1.91   0.056    -.0021436     .180801
members_in_agri |  -.1848795   .0312157    -5.92   0.000     -.246061   -.1236979
      agrishock |   .0635239   .0460319     1.38   0.168    -.0266969    .1537448
  distfacility3 |   .0002565   .0033592     0.08   0.939    -.0063274    .0068404
          _cons |  -.3183147   .2404636    -1.32   0.186    -.7896148    .1529854
---------------------------------------------------------------------------------
Instrumented:  remitt
Instruments:   hhsize gender literacy uneduc_adults mfs_use loan scatosavings
               scatoassets mobile1 barisal chittagong khulna rajshahi rangpur
               sylhet members_in_agri agrishock distfacility3 nonfarm
---------------------------------------------------------------------------------
Wald test of exogeneity: chi2(1) = 23.97                  Prob > chi2 = 0.0000

. 
end of do-file

. 


.

Now my questions are:

1. Have I run the regression correctly?
2. Can I use two step?
3. To get the marginal effect do I need to run "margins, dydx(*) post"?
4. How to know whether my model has endogeneity or not?
5. and last how to know whether my instrument is strong or weak?

Thank You.

Comment

Andrew Musau

Join Date: Oct 2014

Posts: 10077
#7

27 Feb 2023, 06:37

As far as I see, yes to 1-3. For 4, at the foot of the table, you have a test of endogeneity of the instrumented regressor. If the test statistic is significant, you reject the null of exogeneity. For 5, check this by estimating the linear IV model as the reduced form is linear.
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