First stage IV results change when I change dependent variable

[Konstantinos Ioannidis]

As the title says, I am running an IV estimation. When I use different dependent variables (but same first stage estimation), the results of first stage change when using ivprobit. Is there something I am missing? This is not expected to happen since the first-stage estimation is identical. When running ivregress with non-binary variables, it works as expected, but when going to ivprobit, somehow first stage results change.

Minimum working example below:

use http://www.stata-press.com/data/r13/hsng, clear
gen rent2 = (rent + runiform(150,400))/2

ivregress 2sls rent pcturban (hsngval = faminc i.region), first
ivregress 2sls rent2 pcturban (hsngval = faminc i.region), first

gen rent_bin = rent > 200
gen rent2_bin = rent2 > 200

ivprobit rent_bin pcturban (hsngval = faminc i.region), first
ivprobit rent2_bin pcturban (hsngval = faminc i.region), first

The first stage results from the two ivregress commands are (as expected) identical. The first stage results from the two ivprobit regressions are not identical. Why is this happening?

[Carlo Lazzaro]

Konstantinos:
-ivprobit- uses MLE, whereas -ivregress- does not.

[Konstantinos Ioannidis]

Carlo:
I understand that, but my question is not why ivprobit and ivregress produce different results, I expected that. My comparison is not between the two commands, but within the two commands. I do not understand why

 
 ivregress 2sls rent pcturban (hsngval = faminc i.region), first ivregress 2sls rent2 pcturban (hsngval = faminc i.region), first

produce identical first stage results despite having a difference dependent variable, whereas

 
 ivprobit rent_bin pcturban (hsngval = faminc i.region), first ivprobit rent2_bin pcturban (hsngval = faminc i.region), first

produce difference first stage results when changing dependent variable.

[George Ford]

adding twostep option to ivprobit produces same results since the two equations are estimated separately. the mle estimates jointly, so the DV plays a role in the first stage.

https://friosavila.github.io/playingwithstata/main_ivprobit.html

[Konstantinos Ioannidis]

Thank you for the link George, that seems to be the issue. I understand it now and highly appreciate it!