# Bivariate probit versus 2SLS, contradictory results (sign)

I am currently facing puzzle and I hope some of you will be able to provide me some insights. I have this model: y: binary variable, x1: binary variable (endogenous), z: binary instrument, x2: controls, i.year: dummies for each year, i.region: dummies for each region with in total about 4,000 observations

I first run my 2SLS and I obtained that the effect of x1(instrumented by z) on y is positive.

But my problem is when I turn to a bivariate probit, using the following stata code:

biprobit (y=x1 x2 i.year i.region) (x1= z x2 i.year i.region), cluster(region)
margins, dydx(x) predict(pmarg1) force


Now I obtain a negative effect, even though from what I've seen I shoud at least get the same sign in the biprobit and the 2SLS.

Does anyone has any idea for what reason I have this problem, or have some suggestion as to what I should do?

• What are your controls $x_2$? Do any of them have the potential to be huge? (what does histogram of $x_2$ look like?) I'm not familiar with bivariate probit but my intuition based upon probit vs. OLS is that the non-linearities of probit can come into play. OLS estimates can depend on extreme $x$ values in a way that probit may not. – Matthew Gunn Apr 13 '17 at 22:11
• I have 6 dummy variables, the age and age squared. So the age squared is potentially quite large (from 324 to 6,561). However, even when removing this variables I still get similar negative sign in the biprobit regression (and positive in the 2SLS). – Sarah Apr 13 '17 at 22:20