I have individual-level panel wealth-at-age data with 4600 observations on 350 individuals. Because wealth tends to be skewed, I am as interested in the conditional median as the mean. When I estimate a quantile fixed effects model using xtqreg, it returns the message

WARNING: some fitted values of the scale function are negative

and I get the odd result that the predicted median is greater than the predicted mean, even though there are many more zero values ( I use the inverse hyperbolic sine of wealth as the transform) than high values. And when I plot the predicted wealth-at-age values over the scatterplot, the median values are all close to the maximum values where the predicted means at age seem plausible. I assume the odd result is consistent with Canay's (2011) contention that the fixed effect quantile estimator is not consistent with small T.