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I want to talk about a simple but illuminating thing: "distribution regression".
You have a design and a continuous outcome, but get noisy junk for the average?
Make dummies, 1{y>x}, move x through support of y, estimate effects on each dummy. Traces out effects on F(y). 1/4
You have a design and a continuous outcome, but get noisy junk for the average?
Make dummies, 1{y>x}, move x through support of y, estimate effects on each dummy. Traces out effects on F(y). 1/4
Chernozhukov, Fernandez-Val, and Melly (2013) discuss it in all the metricsy detail, but I have found actually using it to be very straightforward.
Here it is for my long-run Medicaid paper. I get a noisy-ish thing for avg earnings, but really striking effects for the dist. 2/4
Here it is for my long-run Medicaid paper. I get a noisy-ish thing for avg earnings, but really striking effects for the dist. 2/4
Also, because these are effects on CDFs, and the integral of the CDF is the mean, if you multiply each dot by bin size you basically recover the OLS coef on means. Thanks, Riemann! 3/4
I think it's a good alternative to quantile regression (quantile folks can chime in here).
Especially in the Census where I have the obs, this is proved to be a very very helpful strategy that is also very very easy to do. 4/4
Especially in the Census where I have the obs, this is proved to be a very very helpful strategy that is also very very easy to do. 4/4
Putting this in the main thread b/c I mean to say it and its one of the favorites about this strategy:
Insight on mapping changes in CDFs to quantile effect in a DD type model:
The same mapping for RD:
inference inference inference
