Quantile regression for panel data

[Barbora Sedova]

Dear all,

what is the best approach to conduct a quantile regression for a first difference and for a fixed effects models using panel data in Stata?
Can you recommend me some article and some commands?

Many thanks.

[Carlo Lazzaro]

Barbora:
-search qregpd-.

[Joao Santos Silva]

Dear Barbara,

I am working on a command to estimate QR with fixed effects. If you email me directly, I can send you the beta version of the command. Carlo rightly suggested qregpd, but notice that it does not estimate a model with fixed effects in the usual sense.

Best wishes,

Joao

[Adam Bordeman]

HI all,

Does qregpd allow for two different types of fixed effects (e.g., individual and time). Is that what id() and fix() do? Or is the fixed effect limited to the single variable in fix()?

Thanks

[Joao Santos Silva]

Just to follow up on #3 above, the command to estimate quantile regression with fixed effects is now available in SSC (thanks to Kit Baum), search for xtqreg.

Best wishes,

Joao

[Lukas Ferner]

I'm currently conduting a quantile regression analysis on panel data as well and would have some follow-up questions regarding the commands qregpd and xtqreg. For both qregpd (method: Nelder-Meads) and xtqreg, the calculaed estimators for all variables at most of the quantiles are highly insignificant with p-values above 0.7 (I'm pretty sure they should be significant!). By using the MCMC method in qregpd, the results vary considerable with respect to sign, value and significance depending on the respective set seed even at 100,000 draws. Does anyone have a suggestions how to improve on of these methods to get "better" results? Or other approches to handle quantile regression on panel data? The panel consists of ~ 15000 observations on 3000 individuals.

Many thanks in advance!
Lukas

[Joao Santos Silva]

Dear Lukas,

From what you say, you have on average 5 observations per individual; xtqreg requires the "time" dimension to be large, so it is not appropriate for your case. Notice also that qregpd and xtqreg estimate very different models.

Best wishes,

Joao

[River Huang]

Dear Joao, I found that you have said (many times) that qregpd estimates a fixed effect quantile model not in the `usual' sense. Could you please explicitly explain its differences with your helpful/interesting xtqreg command? Thanks.

[Joao Santos Silva]

Dear River,

In a standard fixed effects model, the fixed effects enter the model as dummies and this is equivalent to having a different intercept for each unit in the panel. The model estimated by qregpd is different in that the fixed effects are not included in the model (therefore, all units have the same intercept); they are used in the estimation but not included in the model. This is a bit like IV estimation in which the instruments are used in the estimation but are not part of the model.

Best wishes,

Joao

[Carlo Lazzaro]

Joao:
is that a sort of conditional fixed effect?
Thanks.

[River Huang]

Dear Joao, Thank you for your explanation. It helps.

[Lukas Ferner]

Dear Joao,
many thanks for this helpful reply! I wasn't aware that xtqreg is not appropriate for a small time dimension!

May I ask a question on your explanation of the qregpd model?

Does the fact that the fixed effects are not included in the model but only used in the estimation change anything about the interpretation of the calculated coefficients? In Powell (2015) it is stated that they can be interpreted in the same manner as cross-sectional quantile regression results. Is there a limitation on this statement?
And moreover, do you have an idea why the qregpd command is calculating only insignificant estimators for Nelder-Meads? Is this also due to the small number of observations per individual?

Best wishes and Thanks,
Lukas

[Joao Santos Silva]

Dear All,

Carlo Lazzaro: I do not really use that terminology (how do you distinguish conditional from unconditional FE?), but what qregpd does is very different from what is done in the logit, Poisson, or linear models. The FE are used in the moment conditions, but they are not part of the model in any way; they are a sort of instruments.

Lukas Ferner: The interpretation is as in cross-sectional data because in a cross-section we do not have fixed effects in the model. However, the model is model is based on very strong assumptions and in that sense it is very different from cross sectional quantiles. About the insignificant estimates, I have no idea what is causing that. To be honest, I never used that estimator

Best wishes,

Joao

[Carlo Lazzaro]

Joao:
many thanks for your kind clarification.

[Lukas Ferner]

Dear Joao,

thanks for this explanation! I think there is a problem with strong assumtions in every model dealing with quantile regression on panel data, right?

Do you have any suggestion on how to proceed with my panel? I just need a reliable set of quantile estimators (if possible with a straightforward interpretion) that somehow takes the panel structure into account. That's why I chose "qregpd" in the first place.

Thanks,

Lukas