Negative scale value using fixed effects quantile regression xtqreg

[Howard Bodenhorn]

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.

[Joao Santos Silva]

Dear Howard Bodenhorn,

It is true that no fixed effects quantile regression estimator is consistent with fixed T, but you have a reasonable value of T (assuming that the panel is more or less balanced) so you should be able to get reasonable estimates with xtqreg.

Having a few fitted values of the scale that are negative can be just noise, but having many suggests that your model is misspecified. I would consider changing the way the regressors enter the model, namely include squares and cross products. I would also reconsider using the asinh transformation.

Best wishes,

Joao

[Howard Bodenhorn]

Thank you. I get similar results with the natural log transform (ln(wealth + 0.1). The issue may be that the panel is unbalanced. I observe the average individual for 15 years, but it ranges between 5 and 35, depending on the individual's age. The odd results occur when I divide the sample into men and women and effectively reduce the estimation sample by half.

[Joao Santos Silva]

Dear Howard Bodenhorn,

I am afraid I'll not be able to help much more. In the next update of the command, I'll include some information about the percentage of observations for which the scale is negative as that may help users judge the severity of the problem. Anyway, something you can try is to estimate the model using only the individuals with for whom T>=10 t see if that helps.

Best wishes,

Joao