Simultaneous equation model without instrumental variables

[Janka Vanschoenwinkel]

Crossposted here : Apologies for crossposting! I noticed that this forum has more posts on instrumental variables so I give it also a shot here!

Very short question: are there tools (by preference in R or Stata) to solve a simultaneous equation model, without needing instrumental variables?

In my case, I would like to model irrigation and croptype. A farmer needs more or less irrigation depending on the croptype. However, the croptype that he chooses also depends on the possibility to irrigate.

Therefore:
Irrigation = climate + Croptype + ....... Croptype = geography + climate + Irrigation + ......
In my understanding, I need instruments for irrigation and croptype to solve this system. Is this correct, or can I also solve this without instruments?

[Phil Bromiley]

As a matter of econometrics (not Stata per se), if you have a simultaneous equation model and all of the exogenous variables appear in all of the equations, then the model is probably not estimable. Read up on identification in simultaneous equation models.

[Janka Vanschoenwinkel]

Hey Phil!

Yes, I know. Thanks for mentioning. There are some variables that are different, but the majority is the same. I am aware that this can cause problems but with some creativity in variable choice, this should be solvable.

Anyhow: the solution to my problem is probably the reg3 models. However, they are not valid for dependent categorical variables so I am still looking for a solution for this. I posted a new more specific question therefore.

[Maarten Buis]

There are some variables that are different, but the majority is the same.

The variables that are different are your instruments.

[Janka Vanschoenwinkel]

Hey Maarten,

I have read a number of your works (thanks). However, the variables that are different are not "good" instruments (quite low correlation with the dependent variable). They are rather "control" variables. It's because of that that I added that I would need a little creativity in variable selection.