Good link - thanks! Now I know about 2SLS regression. :-)
I think a big problem with the AEI analysis is the questionable choice of instrumental variable; from the paper: "The standard method of controlling for this endogeneity bias is to use a variable that is well correlated with the endoge- nous variable (the immigrant share) but not related to shocks to the outcome variable (the native employment rate) as an instrumental variable for the endogenous variable. [...] This paper uses the number of immigrants in the population as an instrument for the number of immigrants in the workforce".
Who says number of immigrants in the population is not related to shocks to the native employment rate? Immigrants come here in no small part for economic opportunity, and changes to the native employment rate can very well affect immigrants' perception of economic opportunity - particularly the better educated (and thus better aware of such factors) immigrants with whom the paper is primarily concerned.
The truth be told, I didn't know about 2SLS regressions either before I started trying to replicate these studies. In fact, I find it disturbing that nobody appears to be peer-reviewing, much less replicating, these studies. As you can see at this link, even papers on the White House web site are quoting these numbers. Yet, in all the research that I've done on the Zavodny paper, I have found no evidence that anyone has reviewed it, much less replicated it. All of those quoting it just seem to be following the principle that "dey couldn't print it if it wernt troo!"
I think a big problem with the AEI analysis is the questionable choice of instrumental variable;
Agreed. I can't help but think that some of these instrumental variables are chosen through trial and error. That is, the researchers tries a variable and, if it helps make their case, they include it. Zavodny did look at 2000-2007 and 2000-2010 in her study. The former better makes her case and, by no surprise, she came up with a rationale for why that is a better span to study. That is why I think that researchers need to provide the environment or program by which they created their results. It's not enough to just verify that their calculations are mathematically correct. One needs to look at the other equally good (or arguably better) choices that could have been made in the research. I included all of my R programs at this link to replicate my analysis. The 262 number can be replicated with numbers posted on the internet and the 183 requires Zavodny's data file which she or I can provide upon request. I'm hoping that many more mathematically-inclined people will see how powerful the language R is and use it to replicate these studies. Just think of it as a useful adventure game!