Quantile regression interpretation

[sedki zn]

Dear all,

I hope you are doing well

Running a quantile regression and i have got the following results:

- At low quantiles of \(Y\), the slope is negative. - At medium quantiles, the slope is positive.
- At high quantiles, the slope is negative again.

Here how i should interpret these results

A- The variation in slopes indicates that the relationship between \(X\) and \(Y\) is **heterogeneous** (non-uniform) across the distribution of \(Y\).
So i conclude that the relationship is non-uniform

B- the relationship is positive at some quantiles and negative at others, the slope is changing, directly contradicting the definition of linearity. Quantile regression reveals this change in slope across different parts of the dependent variable's distribution. The presence of both positive and negative relationships across quantiles strongly suggests a non-linear relationship.
So i conclude that the relationship is nonlinear


Kind regards,
Sedki

[Joao Santos Silva]

Dear sedki zn,

I am not sure if I understand your interpretation, but it would be useful if you could provide a bit more context and some illustrative results.

Best wishes,

Joao

[sedki zn]

Dear Joao Santos Silva

Thank you for you intervention

Studying the impact of renewable energy on energy justice using quantile regression approach.

At low quantiles i find a negative impact
At medium quantiles, the Impact becomes positive and it becomes negative again at higher quantiles of energy justice.

Here my question:
How i should interpret this result ? As a non-uniform relationship ( linear impact regarding each single quantile) or as a nonlinear relationship ( as there is a positive an negative impact at the same time)?

Kind regards,
Sedki

[Joao Santos Silva]

Dear sedki zn,

Thank you for the additional information. It may only mean that the regressor has different effects on different regions of the conditional distribution, or it can be just noise. To give you a better answer I would need to now what data (is it a panel? what is the size, etc) and the command you are using.

Best wishes,

Joao

[sedki zn]

Dear Joao Santos Silva,

Thank you !
Well yes, it is a panel data of 70 countries covering the 2000-2022 period.
And i use the Ivqreg2

Kind regards,
Sedki

[Joao Santos Silva]

OK!

[sedki zn]

So is it appropriate that way ?
And about the interpretation?

I would appreciate your help

Kind regards

[Joao Santos Silva]

The results suggest that the regressor has different effects in different regions of the conditional distribution, indicating that this regressor is likely to change the shape of the distribution in complex ways.

[sedki zn]

Thank you so much

So there this nothing to do with nonlineary ? Right ?

[Joao Santos Silva]

Well, you are only estimating linear models, so I cannot see how non-linearity would come into it.

[sedki zn]

Yes i do have the same opinion
But trying to convince the audience about it, i find it hard as they are saying: you find both positive and negative impact.. so it is a nonlinear relationship!

So to sum up, while dealing with QR, we should interpret it as each quantile alone.

Thank you very much dear Joao !