Hoxby responds with the squid defense, rebutting Rothstein's weaker and more technical points, while not providing a convincing answer to his main criticism. An economist at the Lowest Deep blog is taken in, writing: "Rothstein's criticisms are lengthy, technical, and enumerated in excruciating detail." So is Brad DeLong, writing "I don't have a dog in this fight. I'm not qualified to judge this fight."
Oh! It's all so complicated! How can a layperson judge! Or even an economist in another subfield! Well let me explain these deeply technical and complicated matters.
As far as I can tell, Hoxby doesn't dispute this point. She has a vague and unconvincing argument that her count of small rivers is the right one, but mostly tries to shift attention to more technical matters.Rothstein's main point is summarized pretty well in his abstract
In an influential paper, Hoxby (2000) studies the relationship between the degree of so-called "Tiebout choice" among local school districts within a metropolitan area and average test scores. She argues that choice is endogenous to school quality, and instruments with the number of larger and smaller streams. She finds a large positive effect of choice on test scores, which she interprets as evidence that school choice induces greater school productivity. This paper revisits Hoxby's analysis. I document several important errors in Hoxby's data and code. I also demonstrate that the estimated choice effect is extremely sensitive to the way that "larger streams" are coded. When Hoxby's hand count of larger streams is replaced with any of several alternative, easily replicable measures, there is no significant difference between IV and OLS, each of which indicates a choice effect near zero. There is thus little evidence that schools respond to Tiebout competition by raising productivity.See, not really all that complicated. It's all a matter of which streams count as large and which as small. The depressing thing is that Hoxby is a better writer than Rothstein, so I bet she's going to win the debate.