I estimated a (panel data) quantile regression model using qregpd in Stata 13. It is not clear what is the interpretation of the estimate. Let's say that I choose the 50th quantile, and I find that the estimate of the main parameter of interest is -0.5.
What is the interpretation of the estimate -0.5? Let's say that -0.5 is the estimated parameter for the effect of random variable x on random variable y. Let's say that x increases by 1, so that y will decrease by (-0.5 * 1) = -0.5. Is this effect true only for the guy at the median, or for all individuals?