Estimating Elasticities for Different Quantiles using mmqreg and margins

[Ali Niazi]

Dear Stata Community,

I am trying to estimate elasticities at different quantiles of my dependent variable using the mmqreg command. My dependent variable is non-negative, has a mass at zero and is highly skewed. I want to avoid applying a log transformation and adjustment to the dependent variable, but I am unsure how to implement the elasticity calculation in this context.

Below is the code I am currently using:

local quantiles  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

foreach q of local quantiles {

    mmqreg y log_x c.z##c.z##c.z, absorb(id time) cluster(id) quantile(`q')

    local temp = `q' * 100
    _pctile log_x, p(`temp')
    local log_x_p`temp' = r(r1)

    _pctile z, p(`temp')
    local z_p`temp' = r(r1)

    margins, eydx(log_x) at(log_x = `log_x_p`temp''  z = `z_p`temp'') post
}

My questions are:

1. Is this a valid approach for estimating elasticities at different quantiles with the mmqreg command?
2. Is there a better way to handle skewed data with mass at zero for estimating elasticities without log-transforming the dependent variable?
3. Am I correctly implementing the use of margins and percentiles in this context?

Any suggestions on how to improve this process would be greatly appreciated!

Thank you for your time and help.