# 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

## 1 Answer

It's probably the controls.

If you omit the controls, the marginal effects from the bivariate probit regression should be quite similar to the 2SLS estimates. See page 203 of Mostly Harmless Econometrics for an example.