...everyone likes the local Wald estimators for regression discontinuities because they're non-parametric. But it's precisely because they're non-parametric that you throw the local continuity at the cutoff assumption overboard. There is no guarante of local continuity at all. That's true of a lot of parametric versions that people like to do too.
This is not small potatoes. The only reason the regression discontinuity model is identified is the local continuity assumption, right?
I've never written a purely econometrics paper before. I don't know how it's really done. But the regression discontinuity literature - although relatively old - is new to economics. And this seems worth pinning down. It's easy enough to point out how the local continuity assumption is required to identify the model. I would think it would just be helpful to simulate a high variance data generating process with modest sample size and check on each method.
Parametric attempts at regression discontinuity models are not a silver bullet if the relationship is unusual or non-linear. But they're not sensitive to a few points around the cut-off the way the non-parametric estimates are. And it's precisely behavior around the cut-off that we have to be worried about.
It's been a while since I looked at RD stuff, but I think the identification is more nuanced than the local continuity assumption.
ReplyDeleteI know a lot of people cite Imbens (and Lemieux) on RD, but I thought the Lee and Lemieux paper gave the best overview. Scanning the paper now, there's some discussion in section 3 that might be of use to you...
We had always cited Imbens and Lemieux at the Urban Institute, but I just came across Lee and Lemieux for this year. It really is an excellent paper... I'll take a look back at section 3.
DeleteI've seen Austin Nichols (who wrote the stata routine for the local Wald estimate) caution about the problem with outliers right at the cutoff, so it seemed like an issue that in practice people acknowledge, but it also seems to make the local Wald estimator itself a lot more questionable - particularly if you're working with noisy data.
Granted, I think most people will run both parametric and non-parametric models so they still will often report both. My pet peeve is when they're parametric model itself violates the local continuity (for example, if it allows asymptotic behavior at the cutoff.
Thanks Grant