st: Useful first stage statistics in IV with multiple endogenous regressors

[Nick Sanders <sandersn@stanford.edu>]

Happy Thanksgiving fellow stataphiles,

I'm running an IV with two endogenous regressors (x1 and x2) and two instruments (z1 and z2) using xtivreg2. I'd like to report some relevant statistics showing the validity of the instruments from the first stage regression, but I find myself in a bit overwhelmed by the sheer number of tests and results available. I'd appreciate people's thoughts on what they would consider to be the most convincing "strength of instrument" tests to report (let's assume for now that my instruments are justifiably excludable).

In a single endogenous variable situation, my instinct would be to report the first-stage F stat and start with the "larger than 10" rule, but my reading of Angrist and Pischke is that the Cragg-Donald F-test isn't as informative in a two-endogenous variable world. This makes me consider the reported "F test of excluded instruments" and the "Angrist-Pischke multivariate F test of excluded instruments", provided after each of the x1 and x2 first stage regressions, as alternatives. But which is most relevant in demonstrating instrument strength? Does the "greater than 10" rule apply here as well? Or is there a better statistic to report for demonstrating instrument strength in a world of multiple endogenous regressors? What about for showing the strength of one of the two instruments (say, z1) in particular, beyond reporting the t-stat and the partial r-squared from the first stage regression?

Thanks very much,
Nick
 
--
Nicholas J. Sanders, Ph.D.
Postdoctoral Fellow
Stanford Institute for Economic Policy Research
366 Galvez St, Room 228
Stanford, CA 94305


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