Probit Instrumental Variable with a Binary Endogenous variable and interaction term.

[Ibai Ostolozaga Falcon]

Dear Statalist,

I have been reading a lot of time about how to deal with my problem, but I could not find a solution to my problem. I am trying to estimate the next equation for my sample of firms:

 exporter = b0 + b1*corr11 + b2*j2 + b3*corr11*j2 + controls + u

exporter is a dummy variable that takes value of 1 when the firm is an exporter, 0 otherwise. corr11 which is my main independent variable is also a dummy variable that takes value of 1 when the firm consider the corruption an obstacle for doing business, 0 otherwise. j2 is a continuous variables that measures the time that the firm spends in bureaucracy stuffs. However, an according to the literature of my field, corr11 is potentially a endogenous regressor, as a consequence I want to estimate my model by using IV approach. As instrument for corr11 I have the variable mean_indreg_corr which is a continuos variable, and for the interaction term corr11*j2 I am using as an instrument mean_indreg_corr*j2. With all this on hand I show you the code that I am using:

 gen corr11Xj2 = corr11#c.j2  ivprobit exporter (corr11 corr11Xj2 = c.mean_indreg_corr c.mean_indreg_corr#c.j2) c.j2 c.lnwk14 i.year [pw = wt], vce(cl indus_region) first

However, in other posts I have read that for using ivprobit the endogenous variable must be a continuous one, so, is the code that am I using incorrect? In afirmative case, what method do you recommend me?

Here I show you an extract of my data:

* Example generated by -dataex-. For more info, type help dataex
clear
input float(exporter corr11) double j2 float lnwk14 double year float indus_region
0 1  0 1.6739764 2019  8055
1 0  .  6.109248 2019  5040
0 0  0 2.0037298 2019  5920
0 1 15   1.94591 2019 8064
0 1  .  3.295837 2019  5376
0 0  0 2.0794415 2013 12888
0 1  2 1.9924302 2013  8064
0 0  0   2.70805 2013  8592
0 1  0 1.7917595 2013  8592
0 0  .  5.043425 2013  6360
0 1  3 4.3820267 2013  5376
1 0  .  4.060443 2008  5550
1 1  3 4.1536613 2008  5040
0 .  .  3.970292 2008  6360
1 0  .  3.433987 2008  6784
0 1  . 2.0794415 2008 20256
0 1 20   1.94591 2008  8064
0 0  .  2.782951 2008  5550
0 0  0 4.0943446 2008  5920
. 0  0  3.545779 2013  5550
0 0  0  3.135494 2019 13504
0 1  . 3.2834144 2008  5376
0 1  .  2.772589 2008  5040
0 1  .  3.970292 2008  5040
1 1  .  5.135798 2019 12660
0 0  0  2.944439 2019 12660
0 1  0 1.0986123 2013 12888
0 1 20  2.890372 2013  8592
0 1  .  3.320228 2019  5376
0 1  . 1.8458267 2008  8064
0 1 15 3.3322046 2008  5040
0 0 15  4.106767 2008 20256
1 0  0 4.3609734 2008  8055
0 0  .  4.976734 2013 20256
0 0  0  3.218876 2013 13504
0 0  5   3.84303 2008 20256
0 1  9  2.564949 2008  8064
1 1  . 3.0445225 2019 12660
0 1  0  1.609438 2008  8055
0 0  0  3.295837 2008 20256
0 0  0  5.351858 2013 20256
0 0  .   1.94591 2013  6360
0 1  0 2.1972246 2008  5376
0 1  0 2.3025851 2008 20256
0 0  . 3.0910425 2008  6360
0 1  0   3.64632 2008  8055
0 0  0 2.1972246 2008  8880
0 1  0 3.0910425 2008  8055
0 1  0  4.941642 2008  5376
0 1  .  2.484907 2008  5040
0 0  0  3.560099 2008 12660
0 0  0  1.609438 2008 20256
0 0  0 1.7917595 2008  8880
0 1  .   1.94591 2008  8064
0 0  0 1.7917595 2008  5920
0 0  .  5.147494 2008  6360
0 .  0 3.8066626 2008  8592
0 1  0  3.218876 2008  5040
0 0  . 2.0794415 2013  5040
1 1  0 1.9694406 2019 12660
1 1  . 4.1108737 2008 20256
0 0  0 3.6888795 2008 12660
0 1  .  5.309916 2008  5376
1 0  5 4.6051702 2008 12660
0 0  0 4.1271343 2008  8592
0 1  0  2.833213 2008 13504
0 0  0 2.3353748 2008 20256
0 0  0 2.0794415 2008 12888
0 1  0         . 2008 13504
1 . 15  4.787492 2008  8592
0 1  1  2.564949 2008  8064
1 0  0  6.429719 2008  8055
0 1  0   5.32301 2008  8055
0 1  0  2.833213 2008  5376
0 1  .  4.029806 2008  5040
0 0  .  2.890372 2008  5920
1 0  0  2.944439 2008  5550
0 0  0   2.70805 2008 13504
0 1  .  6.231137 2008 20256
0 1  . 4.3820267 2008  5376
0 0  0 2.3025851 2008  5550
0 0  0 2.3025851 2008 10176
0 0  0   1.94591 2008  6784
0 .  .  3.218876 2008 13504
0 0  0   1.94591 2008 20256
0 1  .  4.189655 2008 20256
0 0  . 3.8066626 2008  6784
0 0  0  2.833213 2008  8592
0 0  0  3.465736 2008 12660
1 0  0  3.218876 2008  5550
0 0  .         . 2008 12660
1 1  8  3.135494 2013 13504
1 0 15 4.5849676 2008 13504
0 1  0  2.995732 2008  8055
1 1  0  3.555348 2008  5920
1 1  0  .6931472 2008  8592
0 0  0 3.8501475 2008 12660
1 1  0 3.5263605 2019  5920
1 0  0 2.8716795 2008  5550
0 1  0 2.3025851 2008  5040
end
label values j2 J2
label def J2 0 "No time was spent", modify

Thank you!
Ibai

[George Ford]

A control function might be useful in this case.

[George Ford]

see #2 here.

https://www.statalist.org/forums/forum/general-stata-discussion/general/1535012-multinomial-logit-with-binary-endogenous-explanatory-variable

[Ibai Ostolozaga Falcon]

see #2 here.

https://www.statalist.org/forums/forum/general-stata-discussion/general/1535012-multinomial-logit-with-binary-endogenous-explanatory-variable

Hi George,

Thank you for the thread, it was very helpfull! Specially the paper of Jeff Woolridge cited in #3 which shows the posibility of using a binary EEV in a nonlinear context.