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I’m interested in the estimating the effect on an explanatory variable along the distribution (quantiles) of a dependent variable. I am aware that quantile regression will allow me to do so. However, the issue is that I have panel data and quantile regression is not suggested for panel data unless the number of years is large and tends to infinite (which is not my case).

Would you mind giving me suggestions how to look at the effect of an explanatory variable along the distribution of a dependent variable for panel data?

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I suggest to read the paper Parent and Santos Silva (2013), Quantile regression with clustered data. If I am correct, they explain that with their method you can analyze panel data with the quantile regression, by clustering the standard errors as they illustrate. If you use Stata to carry out your analyses, you might be interested in the fact that these same two authors and Machado have also written a Stata command that will compute the standard errors for you and test whether clustered standard errors are needed (since you use panel data I think they are needed). As far as I know, this is the first best at the moment for your specific problem.

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