Equation in CMP model

[Roberto Torrado]

Hello! I have been contemplating an issue for days, and after reading numerous materials, I hope to find a solution here. The matter at hand is the estimation of an instrumental variables model based on two simultaneous equations. The dependent variable in my equation of interest is quantitative, the endogenous variable is ordinal, and my instrumental variable is quantitative as well.

I have considered using the conditional mixed-process (CMP) command. After reading the help file for this command, I have come to the conclusion that the command would be as follows:

(Y = X1 X2 X3) (X1 = X2 X3 Z), ind ($cmp_cont $cmp_oprobit)

Where:

• Y is my dependent variable,
• X1 is the endogenous independent variable,
• X2 and X3 are exogenous control variables, and
• Z is the instrumental variable.

Now, the question is whether all exogenous control variables (in my example, X2 and X3) must be present in both equations. In other words, do both equations need to have the same hypothetically exogenous control variables, or can I include certain control variables in one equation and others in the other equation?
Thank you in advance
RT

[David Roodman]

Econometrically, no you don't have to include X2 and X3 in both equations. Normally they are included in both, however, because in social systems everything affects everything, roughly speaking, and so it often seems like an unnecessarily strong assumption that certain coefficients are 0. Even justifying one exclusion restriction--that Z does not belong in the Y equation--is hard to do.

[Roberto Torrado]

Dear David Roodman,

Thank you very much for your response and for your efforts with this command. I hope I am not taking up too much of your time by asking which coefficient should be studied to determine if there is indeed endogeneity in the model. Something akin to the "endogenous state" in ivregress.