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So, one thing I have never been able to understand as an empirical economist is the dominance of OLS in regression analysis. Because you are minimizing the sum of squared residuals, you are putting vastly more weight on outlier observations.
As a practitioner of empirical economics, however, I often find that there is something strange going on with outliers. For example, in my first paper I wrote, I discovered initial results were driven by a var which had a small # of obs with neg. values when should have been pos.
Often, there are reasons to think that the outliers have special circumstances going on, and thus there is reason, if anything, to discount them from an intuitive perspective.
Yet, I was always puzzled why, not only have quantile regressions not caught on, but I've never heard of anyone running a reg by minimizing the sum of the square root of residuals. The question is, why is this the case?
The answer, as best as I can tell from speaking with actual econometricians, is partly hysteresis. Academics got used to using OLS in an age when a quantile regressions were tough to solve & took ages to run. Now, with computer speeds faster, one could often do, except, habits.
Additionally, b/c there is still only nascent demand for quantile regs, a lot of the statistical packages for running quantile regs for specific types of regressions don't exist. (I.e., does there exist a package to run a quantile PPML w/ HDFE? I haven't seen...)
But, b/c empirical academia still relies on OLS, it can be gamed easier than a quantile reg, where a single outlier will rarely make much of a difference in any case. Some of the most well-published p̶-̶h̶a̶c̶k̶e̶r̶s̶ researchers frequently play games w/ "windsorizing" the sample
Indeed, even the most prestigious journals don't believe reporting whether a reg has been "windsorized" (setting outliers at max/min. points), or "half-windsorized" (limited in one direction but not the other), or to drop the outliers is something that even needs to be footnoted.
In addition, I think I've complained enough here about the bizarre anti-data plotting preferences of leading journals, to the extent that many require upwards of 4-5 pages of text for readers to skip over per graph.
In any case, I'll admit although I took the Metrics sequence in grad school, I don't consider myself an econometrician, so someone in that field, or a statistician, may have a very different take.
