Causal Inference and Exogenous Variables

[Mohamad Cea]

Hello,

This is not a stata question per se, but an economics one and hope you would be able to offer some guidance.

I've been trying to understand the importance of the exogenous variable when it comes to causal inference. Let's say I want to understand the impact of aid on changing attitudes of the local population regarding donor countries (does aid improve the perception of donor countries among local communities?). In this case aid is not a exogenous variable, can I use a causal inference to understand how receiving aid affects perceptions of donor countries? Assuming I have two communities, one that received aid and another that did not. What exactly has to be exogenous? Do I need to find an instrumental variable for this (and that has to be exogenous?). Any good reading material that could help me understand the basics?

Thanks!

[Rhys Williams]

Hi Mohamad,

You want to estimate something like Perception = a + b(Aid) + u, where a is a constant and u is an error. You say Aid is not exogenous. Why is this? Is it reverse causality (Aid is determined by the perception of the community?) or omitted variable bias (there are variables which affect both perception and aid which you can't measure/control for)?

If Aid is not exogenous then you run the risk of finding a biased estimate of b.

To overcome this, you could try and control for variables which might be leading to omitted variable bias. If this isn't possible, then as you say, you might use an instrument and the instrumental variable technique. For the IV technique, you need an instrument which is correlated with Aid but not with Perception/u (i.e. it is exogenous). In practice, it is pretty difficult to find a suitable instrument.

With the two community set-up you describe, if you have panel data you might be able to use fixed effects, if you assume your omitted variables are driven by time-invariant factors then you can estimate an unbiased b.

I don't have a particular reference but I don't doubt that a google search for these terms would be fruitful.

Best,
Rhys