Hi Stata people,

I would like to replicate a model I am using in eregress (Stata 15 and up) and ivreg2 (Baum et al user-written command SSC).
I am using Stata 16.
This is all just for robustness checks of the eregress model, so I wanted to run the ivreg2 for the post-estimation diagnostics (which are fantastic, by the way). However, I would be happy with a solution in which the results of eregress = ivregress.

The complication is that my binary endogenous variable (var name = "moderator") is also used in an interaction with a categorical variable with 5 levels.
In the simulated data below, there are 3 possible categories and I don't have enough instruments. In the real data, things are worse because the I have 5 possible values for the categorical variable and I would need around 10 instruments.

As a workaround, I created a brute force interaction so that I wouldn't need 8 extra instruments (yes, I know that is not how one should handle interactions, but I ask that you please keep playing along here).
THE PROBLEM is that I can't get the two commands to give the same results with the interaction.

Starting with a plain model. these give equivalent results (coefficients are nearly identical):
Code:
ivreg2 outcome_rate   i.category ( moderator  =  c.instrument   ) controldummy growthrate , robust
Code:
eregress outcome_rate i.category i.moderator controldummy growthrate , endog (moderator=  c.instrument i.category controldummy growthrate, nomain) vce(robust)
Then, I create the fake-interaction term:
Code:
gen interaction= category*moderator
And introduce it into the models:
Code:
ivreg2 outcome_rate   i.category ( moderator interaction  =  c.instrument   c.instrument#interaction ) controldummy growthrate , robust
(note that 'category' is the direct effect, while 'interaction' is actually category*moderator)

But in eregress I either have to include the whole interaction or leave it out, but what I want to do is put just the endogenous part of the interaction into the endog() part of the model.
Neither of these next models are equivalent to the ivreg2:
Code:
eregress outcome_rate i.category moderator interaction controldummy growthrate , endog (moderator=  c.instrument i.category interaction controldummy growthrate, nomain) vce(robust)
Code:
eregress outcome_rate i.category moderator interaction controldummy growthrate, endog (moderator=  c.instrument i.category                   controldummy growthrate, nomain) vce(robust)
Code:
eregress outcome_rate i.category moderator interaction controldummy growthrate , endog (moderator =  c.instrument i.category interaction controldummy growthrate, nomain)  endog (interaction =  c.instrument i.category  controldummy growthrate, nomain)vce(robust)
Help! I'm hoping the Stata-listers might see something I have not---either to make ivreg2=eregress OR get around the lack of instruments when you have an endogenous variable that must be interacted with a 5-level category.

Thanks so much!
-Renee


Code:
* Example generated by -dataex-. For more info, type help dataex
clear
input float outcome_rate byte(category moderator controldummy) float(growthrate instrument)
  .0512572 1 0 0  -1.158599  1.200202
 1.4415318 2 1 1 -1.6130273  .8802252
  .4398367 2 0 0 -1.5614135 1.1793866
 2.0684404 1 0 1 -1.1937082  .9026076
.020747656 2 0 0  -.8504853  .8710138
 .04264894 2 0 0 -1.1334147  .8710138
 2.1645558 1 0 0  -.7279454  .8710138
-1.0435052 1 1 0  -.9729756   1.18916
 1.2788826 2 0 0  .25533304 1.2002015
  .4057586 2 0 0  -1.416769  .9069632
 1.1645558 1 0 0  -.7279454  .8710138
 1.0435052 1 1 0  -.9729756   1.18916
  .2788826 1 1 1  .25533304 1.2002015
 -.4057586 2 1 1  -1.416769  .9069632
  .0512572 3 1 0  -1.158599  1.200202
 1.4415318 3 1 1 -1.6130273  .8802252
  .4398367 3 0 1 -1.5614135 1.1793866
 2.0684404 3 1 1 -1.1937082  .9026076
.020747656 3 1 0  -.8504853  .8710138
 .04264894 3 0 0 -1.1334147  .8710138
end