So I'm looking at salary differentials between two occupations, and I'm really interested in medians. Initially I just had the descriptive statistics up, and reported the difference but I really want to control for a few things. So I'm getting the differential with a quantile regression.
Now, that's all well and good for the difference itself - but if I'm interested in a percentage difference, is it legitimate to regress the natural log of the salary on the occupational dummy I'm interested in a quantile regression? Essentially, does the natural log behave the same way in a quantile regression that it does in OLS regression?
I ask because the coefficients for the level salaries are identical to the median differentials from the descriptive statistics (which I expected), but the coefficients for the regressions of the log salaries are not the same as the percent difference.
Thursday, September 1, 2011
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This is not immediately helpful (which I think you are looking for). This google book: http://books.google.com/books?id=nKVBXePWtSoC&printsec=frontcover#v=onepage&q&f=false
ReplyDeletepage 100-105 seems to answer your question almost directly but the crucial page 102 is missing. Fortunately you now have access to a big university library.
I looked a littke closer. Page 78 has your answer.
ReplyDeleteThough now that is missing from my google books preview. I guess I dont get how google books works.
ReplyDeleteAnyway, long story short Hao Lingxin and Daniel Q. Naiman "Quantile Regression" answers your question almost directly (they use inequality as their main example).
Please clean up this mess I've made in your comments.
Also if you need to know this now. While I cant get at their reasoning, they say in a couple of places that using log-scale is a bad idea.
ReplyDeleteAwesome - thanks. I can obviously do the same calculation by hand so that's no trouble, but it's good to know the estimate from the model is not the one to use.
ReplyDeleteDaniel,
ReplyDeleteI have a question for you. I am planning to write an article on the status of the supposed "Keynes vs. Hayek debate" (as in, it's not really "the" debate at all, and in fact Hayekians/Austrians are doing very little in popularizing themselves in academia), and I think an interesting related research project would deal with how the "mainstream" debate influences the academic debate. As in, if the Hayek/Keynes debate on the blogosphere and mainstream online media (especially WSJ, for example) has any impact on academics. I wonder what type of empirical data collection I could do to offer me some evidence in whatever direction.
What do you suggest?
I'm not sure.
ReplyDeleteI don't know what kind of investment you want to make, but this seems like the sort of thing where an online survey or even interviews might be beneficial. I know economists don't think much of qualitative data collection, but this seems appropriate to it. The thing is, ideas take time to stew in peoples' brains, and then they take time to get on paper and get published. You could always look at changes in references to Hayek or Mises in published work and see if there's been an uptick outside of Austrian journals, but I'm not sure what that would come up with.
Working papers are another option - and you'd probably have easier access. That will be somewhat easier because it's earlier in the publication process.
You also might just want to do more of a case study approach. There have been major instances like Cabalerro's JEP article. I'm sure there are a few others like that that are worth just analyzing in turn.