using cmp for biprobit with instruments

[Elin Vimefall]

Hi
I’m annalysing the childs probability to work and be in school using a bivariate probit model. One of my explanatory variables (exp) is endogenous and to correct for this I want to use two instruments (inst). To do this I’m using the cmp program (Roodman 2011):
cmp (exp = x1 x2 x3 inst) (work = exp x1 x2 x3) (school = exp x1 x2 x3) if age>5 & age<15, cluster(district) ind($cmp_cont $cmp_probit $cmp_probit)

However; exp is only endogenous for the work decision. Is there anyway to use the instrumented variable in this equation but the original variable (exp) in the school equation?

Roodman D. (2011). Fitting fully observed recursive mixed-process models with cmp. The Stata Journal 2011, 11(2), pp 159-206.

Best regards //Elin Vimefall

[David Roodman]

Hi Elin,
Your command looks properly written. You could just run it as is, which would be conservative, in allowing for the possibility that exp is actually endogenous in both equations. You could then test this possibility by checking whether the correlation parameter atanhrho_13 is statistically different from zero. Alternatively, you could impose this assumption by doing:

constraint 1 [atanhrho_13]_cons
cmp (exp = x1 x2 x3 inst) (work = exp x1 x2 x3) (school = exp x1 x2 x3) if age>5 & age<15, cluster(district) ind($cmp_cont $cmp_probit $cmp_probit) constr(1)

--David

[Elin Vimefall]

Thank you David!

[Elin Vimefall]

A somewhat starange question, what do I call the model? I guess it is wrong to say that it is a bivariate probit with instruments?

Best regards //Elin Vimefall