Quantile regression for dynamic panel data

[Chiraz KARAMTI]

Hi every body,
I'm using quantile regression with panel data in my paper and I saw the package qregpd – quantile regression with panel data in Stata by Powell (2015).I'm glad with this new package to deal with panel data.
However, is this package capable to take into account dynamics? My model is a quantile dynamic panel model with fixed effects, I have all the theory part done but I don('t know how to treat all these aspect in STATA.
I saw the commands in the help of the package, :
qregpd ln_wage tenure union, id(idcode) fix(year) optimize(grid) min1(0) max1(0.06) intvl1(0.005) min2(0.05) max2(0.1) intvl2(0.005 where's the lagged dependant variable???
Any ideas please?

[Chiraz KARAMTI]

Hi, no one have an answer about quantile dynamic regression??

[Carlo Lazzaro]

Chiraz:
I assume you did not receive any reply so far due to the lack of any built-in Stata or user-written command whuich can support what you're after:

(please, see https://www.researchgate.net/post/Ho...le_regression_ using_STATA).

As an aside, as reminded by Nick Cox some threads ago, http://www.statalist.org/forums/help#adviceextras #1 gives advice on bumping.

[Matthew J. Baker]

Chiraz KARAMTI --

Sorry, I had not seen your post until today! In any case, there is no reason why you can't have "dynamics" in your model and in the application of qregpd. You would just have to think about how you wanted to treat the lag of the dependent variable. You can either include it as a variable. For example:

webuse nlswork
tsset idcode year
gen l_ln_wage = l.ln_wage
qregpd ln_wage tenure union l_ln_wage, id(idcode) fix(year)

Without knowing if there is something particular about your problem, there is no reason to think you can't do this. Hope that helps...

Matthew J. Baker

[Chiraz KARAMTI]

Hi...than y ou for your response. I thought about the same solution. However the lagged dependant variable had to be instrumented as in xtabond command. I don't know how it will be instrumented with quantile command...

[Chiraz KARAMTI]

I will try to introduce my lagged variable and instrument it with the option instruments😊😊

[Matthew J. Baker]

Chiraz KARAMTI --

That makes things a bit more difficult if you really need to go the full-blown Arellano-Bond route, but I am not convinced that you do. The Arellano-Bond estimator is used in the small T, large N circumstances for very well-defined reasons: One wishes to have group-level fixed effects in the model, but because the data has a lot of groups, introducing dummies for each group is infeasible and perhaps undesirable because of the incidental parameters problem.

Thus, one sweeps out fixed effects using differencing. Great, but now the dependent variable y-l.y and the lagged dependent variable l.y - l2.y are explicitly correlated (both have l.y in them). This is what necessitates instrumenting the (now lagged and differenced) dependent variable.

All that having been said, I would argue that one should use qregpd with a lagged dependent variable as-is, so long as one is not worried about some other problem with the model, such as autocorrelated disturbances. I might even go so far as to argue that qregpd is exactly the right estimator for this situation! This is because, as David Powell describes in his paper, his transform uses expectations, not differencing, to sweep out fixed effects, and thus no endogeneity is introduced between the lagged dependent variable and the dependent variable. There is thus no theoretical problem with using a lagged dependent variable on the right-hand side. One then avoids transforming the data too, which changes the interpretation of results. So, I would go with something like:

webuse nlswork
tsset idcode year
gen l_ln_wage = l.ln_wage
qregpd ln_wage tenure union l_ln_wage, id(idcode) fix(year)

Of course, I could be all wrong about this, so maybe one of the silverbacks of the Stata list will chime in and correct me!

Best,

Matt

[Chiraz KARAMTI]

I think that your justification is convincing ! I'll read by my self Powell's paper. I also asked Dr Powell's about it yesterday and he said that I can introduce lagged variable and use the instruments command. Anyway it seems very interesting topic to me and ill try to introduce my lagged variable and see the results.
Many thanks for all these interesting explanations.
Best regards

[Sebastian Kripfganz]

I am not an expert on quantile regression but I tend to disagree with Matthew. If there was a way to sweep out the fixed effects without "introducing" endogeneity between the lagged dependent variable and the error term, then such a method would also work in the standard linear dynamic regression model and no one would ever have to use GMM procedures such as the Arellano-Bond estimator.

[Chiraz KARAMTI]

Ok I'm confused now...but I have to read more about the subject

[Joao Santos Silva]

Dear Sebastian et al,

If I recall it correctly, Powell's estimator conditions on the fixed effects but does not include them in the model, much in the same way as an IV estimator conditions on instruments that are not included in the model. This is different form the models considered by Arellano, Bond, and others, because in these models the fixed effects are included in the model.

So, it is perfectly possible that Matthew is right (I think he is) and people still use GMM estimators when dealing with panel data estimators for the conditional mean.

Joao

[Sebastian Kripfganz]

Thanks for chipping in, Joao. I just had a look at Powell's paper and it seems you are right. If we start from the outset with a different model that does not have the usual additive fixed effects (at least as a nested case), then the whole story could indeed be different (but I am not in a position to make a final judgment here). I am not sure though if I would still call this a "panel model with fixed effects".

[Joao Santos Silva]

Dear Sebastian,

You are right, Powell's paper is not about a model with the usual additive fixed effects; it proposes an estimator of a structural model (that does not include fixed effects) that conditions on fixed effects. Indeed, this is not what people have in mind when they talk about fixed effects models.

Best wishes,

Joao

[Chiraz KARAMTI]

Hi everyone,
ok, if the fixed effects in Powell's paper are not the individual fixed effects as we know in panel data, how should i take into account real fixed effeccts? Do i have to introduce dummies?

[Joao Santos Silva]

I think there is a paper by Antonio Galvao about that, in Journal of Econometrics if I am not mistaken. Please google it.

Best wishes,

Joao