This person is a professor of something. That is not to say that I don't know what he is a professor of -- public affairs and economics in fact -- but that he passed the GRE at some point (likely with pretty good scores), graduated from grad school, probably got a post-doc or associate professorship, and became tenured. And now he starts a blog post with two regressions with R^2 = 0.21 and R^2 = 0.09 with n < 10 and then concludes that it justifies something besides inconclusiveness. That is our standard beef here, but not my biggest beef today. I have a meta-beef.
The other professor (Sumner) being criticized by this post only made the claim that deviations from Okun's law were small, hence unemployment was basically explained by NGDP. Therefore showing that deviations from Okun's law are within the error of the model as Chinn does proves nothing. That is the original point. You do not show someone's point is flawed by demonstrating their point.
I will be (uncharacteristically) charitable now to get to the heart of the meta-beef. It could be that Chinn is trying claim the model does not work better with revised data. I'll call this the uncharitable form of Sumner's claim. However, the original curve inside the error of the model; it is impossible to work better. Chinn is setting Sumner up to fail by using the uncharitable form, but writes with the pretense that the uncharitable form could be correct -- that the uncharitable from is decidable given the data, and therefore you can set out to demonstrate it in an unbiased, scientific manner.
Of course, writing with the pretense that uncharitable form is decidable you'd actually have to allow that it is possible the model works worse with the revised data. That means you would have to consider the charitable form of Sumner's claim: given the revised data the model still works just as well. Since GDP revisions tend to get smaller over time, Sumner can say now that the revisions are in, we still have the same picture. That while the GDP vs employment data could have gotten revised to deviate from the model, it did not; that is Sumner's "final nail in the coffin". No one will likely ever produce data that will show that Sumner was wrong.
I know, I know: uncharitable representation is an age-old device in science. But given an uncharitable representation of Simplicio's Aristotelian position, Galileo's arguments in favor of Salviati's Copernican position did not imply a charitable representation of the Aristotelian position because both sides did not believe in the same underlying model. The underlying model was the debate. Here, Chinn and Sumner are both using the same model. The conclusions are the debate.