Monday, July 06, 2009

Beyond the Central Tendency: Quantile Regression

I’m sure everyone has heard of this before but I’ve been reading up recently on quantile regression. This article by Chris Gowlland, Zhijie Xiao and Qi Zeng offers a nice overview of how the method has developed over the years.

Abridged Abstract from The Journal of Portfolio Mgmt. Spring 2009, Vol. 35, No. 3:

Quantitative investors frequently analyze factor performance using regression based on the familiar ordinary least squares approach. This is highly effective for understanding the central tendency within a dataset, but will often be less useful for assessing the behavior of datapoints close to the upper or lower extremes within a population. But from the perspective of active investors or risk managers, the datapoints at the extremes may be precisely the ones of greatest interest. For such applications, a more appropriate methodology is quantile regression...

3 comments:

Kevin Denny said...

I spent a few days at a masterclass on this method given by Roger Koenker who co-invented it. It was fascinating and make me want to do more. Its a generalization of Least Absolute Deviations which Edgeworth worked on & possibly Laplace before him. The number of applications has grown since it appeared in Stata but a lot of these are not very good in my experience. The question is how do you interpret differences in coefficients across quantiles? Many papers are either vague or just plain wrong on this (or else I don't understand it: take your pick). The key issue is that one is estimating conditional quantile functions but many draw inferences about unconditional quantiles. So the 90th percentile function is not telling you about the "high Y" but "high Y , given X". I might be high in the income distribution but low in the conditional distribution, given say my education, sex etc. "Mostly Harmless Econometrics" I think has a good discussion.

Martin Ryan said...

Kevin,

Thanks for reminding me about the discussion in Mostly Harmless.

Also, Olivier Bargain and Prudence Kwenda have used the method to look at the informal sector wage gap (using panel data):

http://www.ucd.ie/t4cms/wp09.05.pdf

M

Kevin Denny said...

I don't know the paper by Olivier & Prudence but I have seen a few use it to look at wage gaps :the first I saw was by Dolado et al on "glass ceilings".
However you need to be careful combining quantile regression (QR) with Oaxaca Blinder methods (OB). The OB decomposition is exact because a regression explains deviations from the means. It doesn't work that way with QR because the difference in the median is not the median of the differences (for example) so the two usual OB components will not add up to exactly to the difference in the quantiles of the two groups (or the difference in the means or anything else). Although people seem to cheerfully ignore this.
That aside, I am not sure how you interpret a difference between the returns to education at the n'th conditional quantile for men & women compared to the same difference at a different quantile. Its not exactly obvious is it?