real analysis in econometrics

[poleringer]

regarding the 1st year phd sequence, it seems real analysis is most directly applicable to the micro sequence, with things like point-set topology, set theory, and overall proof writing stressed. what (if any) are the important parts of RA needed for the first year metrics sequence? thanks all

[apropos]

Depending on who is teaching it, you might have to see and even write delta-epsilon style proofs in the statistics/econometrics courses. You don't need to worry about much else.

I remember that our one of our graduate econometrics TAs tried to be geeky or something, so every once in a while he would present same material we saw in class in a more rigorous matter (taken straight out of his copy of Amemiya for sure). So he would throw around concepts like compact sets and uniform continuity, but I don't really think any professor expected us to know anything beyond knowing how to apply the results in research. Oh yeah, some theorems on important properties of MLE estimators make assumptions like "the parameter space is compact", but again, you will not actually see a proof of such results in a first year course, so relax. Basically, the first year metrics (as well as some more advanced courses) are not that rigorous at all. To teach theoretical statistics and econometrics rigorously, one needs to assume familiarity with measure theory, which you can't really expect from most people in Econ PhD program.