Quantile regressions-panel data, Pre-reqs

[Aamina Khurraa]

Hi Joao Santos Silva

I am worried about two things in quantile regressions for panel data.

1. My data is not normally distributed and has outliers as well. I have done my qreg analysis for a panel of 360 firms, but haven't considered data transformations to treat outliers or to impose normality. I have read that quantile regressions are robust to non-normality. Would you suggest any data transformations to treat outliers or non-normality.

2. I have estimated the estimates of qreg and have derived t stat, se and p values along with other coeffs and constant terms. Could you please comment on how the qregs are checked for their significance. I have 360 regressions. How the significance would be interpreted in all of them for a set of variables. or do we need to interpret them at all?

Kindest Regards
Aamina

[Clyde Schechter]

1. My data is not normally distributed and has outliers as well. I have done my qreg analysis for a panel of 360 firms, but haven't considered data transformations to treat outliers or to impose normality. I have read that quantile regressions are robust to non-normality. Would you suggest any data transformations to treat outliers or non-normality.

There is absolutely no requirement of normality for -qreg-. So don't even waste another second thinking about that. It's completely irrelevant.

As for outliers, the only thing you really need to do is to check them to make sure that they are correct data. If they are errors, then, of course, you should fix the errors. Otherwise, there is nothing particular to do with them. Now, if you have a very skew distribution (so there are lots of "outliers", then some monotone transformation that compresses the data (a power less than 1, logarithm, for examples) might enable you to to get more precise (i.e. smaller standard errors) estimates of your regression coefficients. Moreover, because quantiles are ordinal statistics, back-transforming your results to the original outcome variable is simple.

2. I have estimated the estimates of qreg and have derived t stat, se and p values along with other coeffs and constant terms. Could you please comment on how the qregs are checked for their significance. I have 360 regressions. How the significance would be interpreted in all of them for a set of variables. or do we need to interpret them at all?

Interpreting the estimates from -qreg- is no different from interpreting the estimates of any other regression model. You just have to bear in mind that your model is not predicting mean outcomes but is instead predicting some particular quantile of the distribution of the outcome conditional on the predictors. But the interpretations of t-statistics and p-values is no different from anything else.

That said, let me remind you that the American Statistical Association has recommended that the concept of statistical significance be abandoned. See https://www.tandfonline.com/doi/full...5.2019.1583913 for the "executive summary" and https://www.tandfonline.com/toc/utas20/73/sup1 for all 43 supporting articles. Or https://www.nature.com/articles/d41586-019-00857-9 for the tl;dr. Accordingly, it is better not to think about the "statistical significance" of your results but rather to focus on whether the estimates suggest meaningfully large (in the real-world practical sense) effects of your predictors, and whether the effects are estimated with sufficient precision for your purposes. The precision of your estimates is perhaps most easily assessed by looking at the confidence intervals you get. If the upper and lower limits of the confidence intervals are close enough to each other that you would draw no different qualitative conclusions about the world, nor take any different actions on the basis of your results, if the actual effect fell anywhere within the interval, then your have adequate precision for your purposes. If that is not the case, then your results are not sufficiently precise to draw firm conclusions or make firm recommendations for decisions. As such, more or better research of the question might be warranted.