# Multiple endogenous variables – now what?!

Diligent reader Daniela Falzon, who works at  the World Bank (in France . . . or Washington, DC) writes us with the following interesting problem concerning multiple endogenous variables in 2SLS:

I am estimating Y = b0+ b1*X1 +b2* X2 + b3*X1*X2 + X3

Y is a dummy variable
X1 is a dummy variable and endogenous,
X2 is continuous and endogenous
X3 is a set of additional control variables.
I am running ivreg2 and so I just dump in the three endogenous variables and  the instruments and of course I get very weird coefficients/results. And even if they were not weird, I would not be sure on how to interpret them.
Do you have a better idea of how I should do it or should I just focus on the interaction term and instrument it?
Or Could you please indicate me where in  your book “Mostly Harmless Econometrics”  I should get the answer?

thanks for your question Daniela.  Models with multiple endogenous variables are indeed hard to identify and the results can be hard to interpret.

So we don’t usually like to see them – for one thing it’s not clear why you’re tackling two causal questions at the same time; one is hard enough.
You may have noticed that the only model with more than one endogenous regressor in MHE is the peer effects regression (equation 4.6.6, based on Acemoglu and Angrist, 2000).  Here we have both individual and state-level schooling endogenous in a wage equation.

But we are really only interested in the peer effect in this case – the effect of state average schooling. Individual schooling is there because we realize that any instrument for average schooling must also be correlated with individual schooling.  We therefore try to fix this violation of the exclusion restriction by treating individual schooling as endogenous as well. This is the best reason for having a second endog variable that I can think of.  And the model may work – in the case of schooling we have enough instruments.  But not very often, I would think.

More generally, it doesn’t make sense to think of one endogenous variable as a “control” when looking at the effects of another, at least not a good one (in the sense in which we use the terms good and bad control in chapter 3).  So any time someone shows me a problem with more than one endogenous variable, my first question is always: why?

1. Daniela
Posted January 5, 2011 at 7:56 pm | Permalink

What would one do to capture gender inequality? What if X1 is a gender dummy which is not endogenous but would like to be interacted with the endogenous variable X2. Or is it just better to split the sample into two: the female sample and the male sample and see what the causal effect for each sample is? The presence of the gender dummy would not increase the validity of instrument and is irrelevant but is added in to check the presence of gender inequality. Which one would be right to do? Your response much appreciated!

• josh
Posted January 11, 2011 at 11:58 pm | Permalink

either works, Daniela

if you interact endogenous with gender, then interact the instrument with gender as well. Or just split em up, boys vs girls! JA

2. lulu millcreek
Posted January 12, 2011 at 12:20 am | Permalink

What about “Instrumental variables methods in experimental criminological research: what why and how?” by Angrist (which describes multiple endogenous regressors).
Now I am confused…

• josh
Posted January 13, 2011 at 12:11 am | Permalink

Good eye Lulu! This is a case of the exception proving the rule perhaps. In Angrist (2006), two treatments are randomly assigned with less than full compliance. Two instruments for compliance are available in the form of the original assignment. Pretty clean set-up! As I wrote earlier, “models with multiple endogenous variables are indeed hard to identify and the results can be hard to interpret”. But not this one: its a randomized trial, and IV is the appropriate adjustment for non-compliance. JA

1. By ivreg2 update on February 20, 2010 at 10:34 pm