XTQREG: module to compute quantile regression with fixed effects now available in SSC

[Joao Santos Silva]

Dear All:

Thanks to Kit Baum, xtqreg is now available in SSC. This module estimates quantile regressions with fixed effects using the method of Machado and Santos Silva (forthcoming in the Journal of Econometrics). Unlike qregpd, the new xtqreg module estimates a standard linear model with additive fixed effects, which is the model most practitioners have in mind when considering regression with fixed effects.

Please do let me know if you find any problems with the new module.

Best wishes,

Joao

[Chan Lim]

Is there a way to include both time and panel variables (e.g. industry / year) in the place of fixed effect in the command? It seems qregpd has separate options for panelvar and timevar; I hope to know how to do the similar thing with xtqreg.

[Joao Santos Silva]

Dear Chan Lim

Strictly speaking, in the paper we did not prove any results for that case. Having said that, my guess is that including also time dummies will be OK; we will work on that case as soon as we have time to do it. Finally, note that qregpd allows you to control for the two types of fixed effects, but does not really include them.

Best wishes,

Joao

[Mohammad Azeem Khan]

Hello Mr. Joao, I am a new learner of quantile regression techniques.
I am also trying to apply xtqreg in my study which has data on 36 cross-sectional units for 18 years. Are these much time series observations sufficient to run this model?
The second thing is I have done some preliminary analysis in which results are showing that my coefficients of interest are continuously increasing with the quantiles. Same nature of coefficient is found in the "sysuse auto" data provided by the Stata help menu. Why is this so? Means why this coefficient is increasing monotonously with the quantiles? While it is not the case with qregpd command. Lastly, as you said that xtqreg gives us the quantile regression with the fixed effect but how do we get that fixed effect in our results? I mean how to generate those different intercepts for each cross-sectional id?

Thanks Sincerely.

[Joao Santos Silva]

Dear Mohammad Azeem Khan,

Yes, N=36 and T=18 should be just OK. qregpd and xtqreg estimate very, very different models, so it is not surprising that they lead to very different results; you need to decide which model you want to estimate and then choose the corresponding estimator. If you want to get estimates of the fixed effects, then you need xtqreg. Currently, xtqreg does not automatically compute the fixed effects, but you can do it using the results in the paper.

Best wishes,

Joao

[Mohammad Azeem Khan]

Thanks a lot, Joao, And Sorry for the inconvenience but I think you could not comprehend my second questions. Actually, I have run the xtqreg model at different quantiles and I found that the coefficients of interest are monotonously increasing in magnitudes with the quantiles. Now my question is why is it so? And it is not related to the nature of my variables only. I have seen other studies where results are showing a similar increasing trend. I am worried about it because while interpreting the results we conclude that the responsiveness of our dependent variable to a change in the independent variable is increasing from lower to higher quantiles of its conditional distribution. But this is very impractical as far as I know. The more common case is the irregularities in the responses of the dependent variable at different quantiles which means that the response may be high or low anywhere regardless of the quantiles.
Thanks in advance.

[Joao Santos Silva]

Dear Mohammad Azeem Khan,

The method we use imposes the (valid) restriction that quantiles do not cross, the pattern you observe is a consequence of that. In most standard models, such as the linear-heteroskedasticity model, you expect the coefficients of the conditional quantiles to vary monotonically with the quantile.

Best wishes,

Joao

[Chan Lim]

Joao, thank you for your kind answer; your codes and answers are extremely helpful. I am also very interested in knowing why xtqreg does not allow clustered standard errors, since using both fixed effect and clustered standard error is usual practice in OLS setting.

[Joao Santos Silva]

Dear Chan Lim,

The answer is that we did not have the time to do that; I suggest you bootstrap by cluster.

Best wishes,

Joao

[Chan Lim]

Joao, thank you for your kind answer. I was wondering whether it is not allowed to consider clustered SE with fixed effect in theory.

[Mohammad Azeem Khan]

Thanks a lot, Mr. Joao. Now I can proceed with this model.

[Mohammad Azeem Khan]

@Joao Santos Silva

Sorry, again I came back with some new questions. First, with regard to the answer to the last question, you said "The method we use imposes the (valid) restriction that quantiles do not cross", I could not understand it properly. Second thing is that how do you interpret such coefficients of your model?
I have gone through your paper where you assumed that all the covariates are iid. So how would I check that the covariates in my model are iid? The second thing is that if some of my covariates are endogenous then how will I proceed to apply xtqreg?
Sorry for the inconvenience and a great and sincere thanks in advance.

[Joao Santos Silva]

Dear Mohammad Azeem Khan,

1 - By definition quantiles cannot cross. That is, the first quartile cannot be above the median and so on. Standard quantile regression does not impose that restriction and we often find that estimated quantiles actually cross, which is a sign of misspecification. Our estimator does not allow quantiles to cross.

2 - The interpretation is exactly like in standard quantile regression.

3 - Do not worry about that; it is a "technicality"; it is not need for the core results but helps with the proofs.

Best wishes,

Joao

[Mohammad Azeem Khan]

Dear Joao Santos Silva

That means using xtqreg will always give us a coefficient which increases with the quantiles but still, it will have the same interpretation as that of standard quantile model's coefficient estimates.
This also means that the dependent variable of our model has an asymmetric response to the change of our explanatory variable but that asymmetric response increases in magnitude monotonously from lower to higher quantiles. Hope I could understand it properly.

Many Heartiest Thanks.

[Joao Santos Silva]

Dear Mohammad Azeem Khan,

The estimates xtqreg increase or decrease with the quantile and indeed the interpretation is as in standard quantile regression models.

I am not sure I understand the second part of your question, but the possible asymmetry of the distribution is taken into account in the estimation.

Best wishes,

Joao