Solved – Endogeneity in Stata

I was using Stata to measure the effects of outsourcing on employment using a panel data and after I ran the regression, I found this in my results:

corr(u_i, Xb)  = -0.5617 

I used fixed effect and time specific dummies to overcome the endogeneity problem. Now I wanted to know whether the result above tells me that I still have endogeneity in my Model?

This number is the empirical correlation between the fixed effect estimate u_i and and expected employment from knowing the time-varying characteristics like outsourcing. This tells you at least three things:

  1. The fact that this is large and negative tells you that if you leave the FE out from your model, you are likely to have omitted variable bias in a particular direction because of endogeneity.
  2. It also tells you that you probably should not fit a random effects model. You can also formalize this by conducting a Hausman test, which will be more rigorous.
  3. It indicates that places that are expected to have high employment also seem to have large negative FEs, which could be given an interesting economic interpretation.

Using the FE effects estimator will take of the time-invariant endogeneity because the FE will be differenced out by the demeaning transformation. If it is removed, it cannot be correlated with the (transformed) error term, creating endogeneity. You might still have time-varying heterogeneity that will mess your estimates up, but this correlation does not really help you figure this out.

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