I am looking for a way to compare coefficients obtained from quantile regression. The two surveyed models are nested, estimated on the same sample and for the same quantile. $$ Y = \beta_1X+\epsilon_2\\ Y = \beta_2X+\gamma Z + \epsilon_1 $$ Given the estimates and the respective standard errors I want to know if $\beta_1$ and $ \beta_2$ differ significantly.
All I could find up to now are tests for coefficient differences between regressions for different quantiles or for different groups (samples).



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