Dear Statalist,

I am investigating the impact of a binary endogenous variable 'W(house own(own=1,rent=0))' on a binary outcome variable 'B(female birth(birth=1,birth=0))'.
To conduct my analysis i used a Recursive Bivariate Probit model(RBP) using the stata command 'biprobit'

B = X1 + X2 + W (birth equation)
W = X1 + X3 (house own equation)

When I run the biprobit, I get an insignificant rho, which seemingly indicates little to no correlation between unobserved factors affecting decision B and decision W.
In other words, this would tell me that I need not correct for sample selection, and that the bivariate probits are independent and can be estimated separately(see Greene 2003, p712).

But on the attached file1(Filippini et al.,2018)
i) a zero correlation parameter in a Bivariate Probit model(BP), usually interpreted as evidence of independence between the binary variables under study, may actually mask the presence of a RBP process
ii) the interpretation of the correlation parameter in the RBP is not the same as in the BP —i.e. the RBP correlation parameter does not necessarily reflect the correlation between the binary variables
So, I want to ask two questions

Q1: In Recusive Bivariate Probit result, In case W(house own)'s coefficient is significant even if rho is insignificant, Will model results be effective?

Q2: How can measure the Margianal Effects?
(To control endogeniety of W, can I use 'margins, dydx(*) predict(fix(W))' (see stata manual ERM 42p) Is it right?
And Is there any method thatmeasure Direct effect(X1,X2=>B, X1,X3=>W) and Indirect effect(X1,X3=>W=>B) separately?)

I appreciate all answers in advance!!