Probit models with multiple binary endogenous regressors

[malik hasan]

I'm estimating the following 2SLS model to calculate a local average treatment effect, with X1 and X2 instrumented by Z1 and Z2:

 ivregress 2sls Y (X1 X2 = Z1 Z2)

However, Y, X1, X2, Z1 and Z2 are all binary variables, so I'd like to use a probit model for the estimates.

I've been reading into ivprobit, but it seems as though that assumes continuous endogenous regressors. Furthermore, the biprobit command seems to be limited to cases with one binary endogenous regressor. Is there a suitable command that I can use in this situation, which has multiple binary endogenous regressors?

[Joerg Luedicke (StataCorp)]

Have a look at Stata's eprobit command, see help eprobit and https://www.stata.com/manuals/ermeprobit.pdf. For more information about Stata's extended regression model suite of commands, see https://www.stata.com/bookstore/exte...erence-manual/ .

Here is an eprobit example with two binary endogenous regressors:

. webuse class10
(Class of 2010 profile)

. sum hsgpa, mean
. gen x1 = hsgpa > r(mean)
. sum income, mean
. gen x2 = income > r(mean)
. eprobit graduate i.roommate, endogenous(x1 x2 = i.hscomp, probit)

Iteration 0:   log likelihood = -4633.2504  (not concave)
Iteration 1:   log likelihood = -4616.3877  
Iteration 2:   log likelihood = -4609.5964  
Iteration 3:   log likelihood = -4607.2282  
Iteration 4:   log likelihood = -4605.9447  
Iteration 5:   log likelihood = -4605.4684  
Iteration 6:   log likelihood = -4605.3105  
Iteration 7:   log likelihood = -4605.2872  
Iteration 8:   log likelihood = -4605.2846  
Iteration 9:   log likelihood = -4605.2846  

Extended probit regression                              Number of obs =  2,500
                                                        Wald chi2(3)  =  60.43
Log likelihood = -4605.2846                             Prob > chi2   = 0.0000

------------------------------------------------------------------------------
             | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
graduate     |
    roommate |
        yes  |   .1466341   .0641256     2.29   0.022     .0209502     .272318
        1.x1 |   .2372862   .3236906     0.73   0.464    -.3971357    .8717082
        1.x2 |  -.8155107    .303309    -2.69   0.007    -1.409985    -.221036
       _cons |   .3568377   .1962746     1.82   0.069    -.0278535     .741529
-------------+----------------------------------------------------------------
x1           |
      hscomp |
   moderate  |  -.3765497   .0562527    -6.69   0.000    -.4868029   -.2662965
       high  |  -.6801581   .0927774    -7.33   0.000    -.8619986   -.4983177
             |
       _cons |   .2761785   .0464743     5.94   0.000     .1850906    .3672664
-------------+----------------------------------------------------------------
x2           |
      hscomp |
   moderate  |   -.012206   .0522629    -0.23   0.815    -.1146395    .0902275
       high  |   .1521359   .0908533     1.67   0.094    -.0259333    .3302051
             |
       _cons |  -.1494087   .0447219    -3.34   0.001    -.2370619   -.0617555
-------------+----------------------------------------------------------------
   corr(e.x1,|
  e.graduate)|   .5752745   .1355615     4.24   0.000     .2526604    .7827722
   corr(e.x2,|
  e.graduate)|   .8958147   .1700337     5.27   0.000    -.2323188    .9962443
   corr(e.x2,|
        e.x1)|   .5097743   .0256705    19.86   0.000     .4577379    .5583301
------------------------------------------------------------------------------

[malik hasan]

Thank you so much, I'll have a look!

[Dennis Wajda]

Joerg- the Stata manual does not address if extended regression models require overidentifcation and an exclusion restriction like traditional instrumental variables analysis. At the risk of sounding ignorant, do ERMs require this?

[miroslav suchanec]

Hi everybody. Is there way in STATA how to estimate endogenous treatment effect (non-random treatment assignment) with survival data? If I am correct "stteffects" does not account for endogenity, whereas "eregress" is not suitable for survival data..? Hope this reaches you well. Miroslav