Quantile regressions - coefficients near zero at median

[Helen Hughson]

Hi all,

I'm running quantile regressions for the first time and getting some funny-looking results - I'm just hoping I haven't missed anything obvious like an option I should be specifying or something like that.

My commands are of the form:

sqreg ch_consumption dummy#c.(continuous variables) i.(dummy#(factor variables)), reps(100) q(.01 .05 .1 .15 .2 .25 .3 .35 .4 .45 .5 .55 .6 .65 .7 .75 .8 .85 .9 .95 .99)

I'm using household-level data: my dependent variable is the annual change in consumption, my continuous variables include things income and house value (also in changes), the dummy splits households into 'types', and the factor variables are things like employment status.

The puzzle is that when I graph the estimated coefficients, I always get a U-shaped distribution with coefficients close to (but not exactly) zero at the median of the dependent variable. I've never seen anything like that in the papers I've read on quantile regressions - if anything, the coefficients usually seem to look like they either increase or decrease over the distribution (see for example http://www.econ.uiuc.edu/~roger/research/intro/rq.pdf, pg 8). I've had a bit of a look around to see whether it's the sort of thing others have asked about in the past but have had no joy. I guess it might well be right, it's just a bit odd.

I'm using Stata 13.0 SE in Windows.

Any thoughts would be much appreciated. Thanks!

[Nick Cox]

A graph of the distribution of the outcome or response is surely your point of reference here. What could be more appropriate than a quantile plot as possible through -quantile- (or more flexibly -qplot- (Stata Journal))?

[Joao Santos Silva]

Dear Helen,

If you believe the permanent income theory with (more or less) rational expectations you would expect a result like this. Essentially, your regressors are explaining the heterogeneity in the sample (heteroskedasticity), but cannot predict changes in consumption.

All the best,

Joao

[Helen Hughson]

Thanks both for your quick replies.

My dependent variable is far from normal:


Perhaps more of a concern is the fairly flat distribution in one of the main explanatory variables, the change in income:


But even if I trim outliers from this variable (as below) I still get the same U-shaped outcome in the coefficients.


It's not easy to find an intuitive explanation for why this might be the case - Joao I take your point about the permanent income hypothesis, but in other iterations (for example, even an OLS version of the same regression) we have found some significant relationships between changes in consumption and other variables.

[Nick Cox]

All seems to hang together...,

[Joao Santos Silva]

So, you find that the permanent income hypotheses does not hold for the (conditional) mean but holds for the median; that is interesting. Personally, I would be interested to see what happens at the conditional mode. Please email me if you want to discuss that.

All the best,

Joao