mmqreg, xtqreg or qregpd for dynamic panel model

[Sebastian Kruk]

Hello everybody.

I wish to apply quantile regression to a panel dataset of 21 countries over a 48 year period.

* Example generated by -dataex-. For more info, type help dataex
clear
input str28 Country long pais2 float(ln_co2pc ln_co2pc_gr ln_gdppc_gr ei_ch res_share_ch)
"Argentina" 1   8.13736   -.003316879 .00005722046   .0009368509  -.5843963
"Argentina" 1  8.172827    .035467148    .01150322   .0010287017 -.19065896
"Argentina" 1  8.155382    -.01744461    .03779411  -.0017663687  1.1816183
"Argentina" 1  8.113881    -.04150105  -.016004562  -.0006288141 -1.1635613
"Argentina" 1  8.141445     .02756405  -.035694122    .004128687  -.4502255
"Argentina" 1  8.168763       .027318    .05205154   -.003269479   .4519265
"Argentina" 1  8.149868    -.01889515   -.06098747    .005923823   .7232267
"Argentina" 1  8.188429     .03856087    .08229637   -.003776513 -.03159031
"Argentina" 1  8.154454   -.033974648  -.000295639 .000064082444  1.6892276
"Argentina" 1  8.121045    -.03340912   -.06901169    .003573708   .3562208
"Argentina" 1  8.091192   -.029852867   -.02334976   .0005264431     .22335
"Argentina" 1  8.101911    .010718346    .02646637  -.0008517876  .55891395
"Argentina" 1  8.075928   -.025982857 -.0005168915   .0005473718   .3025955
"Argentina" 1  7.984149    -.09177828   -.06927109    .001306817   .2845615
"Argentina" 1  8.046303     .06215334    .04386711  -.0015678406 -.57471985
"Argentina" 1  8.082119    .035816193    .01099968   .0022074506 -.04727695
"Argentina" 1  8.102077     .01995754   -.02637863   .0035996065 -2.0891473
"Argentina" 1  8.050529      -.051548   -.08927727    .003797956  -.8556552
"Argentina" 1  7.970507    -.08002138   -.03951073 -.00005368143  2.5997005
"Argentina" 1  8.018763     .04825544    .07338333  -.0037634596  -.7621235
"Argentina" 1  8.033707    .014944077    .06285858   -.004395187   .8977495
"Argentina" 1  8.054319    .020612717    .06581497   -.005773418   .9866562
"Argentina" 1  8.079103     .02478409    .04406929  .00046010315  .05130513
"Argentina" 1  8.066797   -.012306213   -.04115677     .00382334   .1040608
"Argentina" 1  8.107716     .04091835    .04185677  -.0021086782   -.889446
"Argentina" 1  8.115711   .0079956055   .066394806  -.0032310635   .5504242
"Argentina" 1  8.129745    .014033318   .026456833  -.0015993714  .14474016
"Argentina" 1  8.159109    .029364586   -.04557419    .004682116 -1.4123623
"Argentina" 1   8.14549   -.013619423   -.01892853     .00665576  -.7077209
"Argentina" 1  8.103066    -.04242325   -.05600929  -.0001920089  1.7975198
"Argentina" 1  8.038289   -.064777374   -.12618446    .007865772   .4461319
"Argentina" 1  8.097865     .05957603    .07396126   -.001951866  -.9268353
"Argentina" 1  8.173456     .07559109     .0758953  .00006687641 -1.3884256
"Argentina" 1  8.202891     .02943516    .07445145   -.005813979  .53251714
"Argentina" 1  8.245454     .04256248   .067243576   -.003355786  .10701164
"Argentina" 1  8.326015     .08056164    .07625961  -.0004028007 -1.0392638
"Argentina" 1  8.349349     .02333355   .029844284  -.0015919358   .4650531
"Argentina" 1  8.271428    -.07792091   -.07100296   -.000819169  1.7649453
"Argentina" 1  8.342472     .07104397     .0862999   -.003054425   .3953756
"Argentina" 1  8.379102    .036629677    .04797363  -.0014053434  .19075124
"Argentina" 1  8.384642    .005539894   -.02078247     .00164406  -.5361876
"Argentina" 1  8.402295    .017653465    .01326561  .00021656603 .006848871
"Argentina" 1  8.376057    -.02623844   -.03585434   .0021337345   .9186995
"Argentina" 1  8.389862     .01380539    .01672554  -.0012462884 -1.0696038
"Argentina" 1  8.375152   -.014710426  -.031024933   .0019309297   .5231693
"Argentina" 1  8.350884   -.024267197   .017990112  -.0033791065  1.1013072
"Argentina" 1 8.3014765    -.04940796   -.03612709   .0008261427  -.1671047
"Argentina" 1   8.26208    -.03939629  -.029878616   .0004553869  -.0826373
"Bolivia"   2  6.417964     .11560774    .06134224  .00028506666 -.27220392
"Bolivia"   2  6.502983     .08501911    .04071999 8.7842345e-06 -1.1737288
"Bolivia"   2  6.568667     .06568384   .013886452    .002845157 -1.4350955
"Bolivia"   2  6.675215      .1065483     .0552597   .0034069084 -2.2711718
"Bolivia"   2  6.748501     .07328606   .030041695    .002345994  -.3423438
"Bolivia"   2  6.826501     .07800007   .027706146    .003293414  -1.382017
"Bolivia"   2  6.871734     .04523277 -.0006895065   .0026355125  -.8965138
"Bolivia"   2  6.866856   -.004878521   -.01944828     .00717634  -1.699529
"Bolivia"   2  6.855255   -.011600494  -.034768105    .018463783  12.919066
"Bolivia"   2  6.869163     .01390791  -.018164635  -.0007222965 -.18970098
"Bolivia"   2   6.82934    -.03982353   -.06105423    .006938927   1.632059
"Bolivia"   2  6.755651   -.073688984   -.06207848   -.002753846   6.000739
"Bolivia"   2  6.714844    -.04080629  -.022953033    .003282882 -1.1723045
"Bolivia"   2  6.652743    -.06210136   -.03777981    .002304025  .15865235
"Bolivia"   2  6.644448   -.008295059     -.046875  -.0014007166  2.0801692
"Bolivia"   2  6.693766     .04931831   .003443718   -.006210499  -9.055454
"Bolivia"   2  6.692139  -.0016274452   .007709503    .002043061  2.1021533
"Bolivia"   2  6.770207     .07806873   .016329765    .002484992  -3.758691
"Bolivia"   2  6.729681    -.04052639    -.0556879    .002510376  1.1791264
"Bolivia"   2  6.722625    -.00705576   .028149605  -.0020847544  1.0702497
"Bolivia"   2  6.741838      .0192132  -.007154465     .00249432  -2.622808
"Bolivia"   2  6.758414    .016575336   .018341064   .0018295944 -.25524372
"Bolivia"   2  6.823371     .06495714    .02246952    .003341369  -3.983248
"Bolivia"   2  6.903273      .0799017   .023166656     .00595139  -2.921757
"Bolivia"   2  6.804934     -.0983386   .020656586    .020102695  -6.227832
"Bolivia"   2  6.789863   -.015071392   .026638985    .005877331  -1.674051
"Bolivia"   2  6.819801     .02993822    .02772522   -.005191907  -.7293355
"Bolivia"   2  6.827318    .007516861   -.01666832    -.01882285   4.780262
"Bolivia"   2  6.770886    -.05643177   -.00352478   -.032242276  -1.355452
"Bolivia"   2  6.728434    -.04245186 -.0021419525    .002985671  -.8685746
"Bolivia"   2  6.784127     .05569315   .006061554    .013262115  -3.769071
"Bolivia"   2   6.86026      .0761323    .00859642  -.0003261119  -.9186755
"Bolivia"   2  6.938504      .0782442    .02305603   -.002343118  .16695635
"Bolivia"   2  7.003305    .064801216     .0257473    .005370155   -1.99451
"Bolivia"   2   7.07073     .06742525    .02963829  -.0021358952   .3173762
"Bolivia"   2  7.161592      .0908618   .027708054  -.0019321963  .26841784
"Bolivia"   2  7.226458     .06486559    .04302597   -.003432579  .11485765
"Bolivia"   2  7.241869    .015411377   .016647339 -.00028829277  -.3807515
"Bolivia"   2  7.317679     .07581043   .024331093    .003269054 -1.3078908
"Bolivia"   2  7.386178     .06849861   .034879684    .002412088  -.8603185
"Bolivia"   2   7.43899     .05281162   .034342766    .002733275  -1.050217
"Bolivia"   2  7.502742    .063752174    .05072784    -.00496278   .1757908
"Bolivia"   2   7.55739      .0546484    .03823757    .003894068  -1.459804
"Bolivia"   2  7.561952    .004561901    .03261566   -.004148811   .2880547
"Bolivia"   2  7.599395     .03744268    .02707863   .0012438297 -1.3111032
"Bolivia"   2  7.603081    .003685951    .02657223 -.00010018796  .15679426
"Bolivia"   2  7.603012 -.00006866455    .02697849   -.002455078  .29033864
"Bolivia"   2  7.568829   -.034183502   .007639885  -.0019835234   .8072431
"Brasil"    3  6.844649     .06707764    .08870983  -.0045852438  -1.772898
"Brasil"    3  6.985705     .14105606    .10700321  -.0043715984  -3.683734
"Brasil"    3  7.053004     .06729889    .05474091  -.0011309758 -1.7145983
"Brasil"    3  7.088357    .035353184    .02668667  -.0009966865 -1.1710585
end
label values pais2 pais2
label def pais2 1 "Argentina", modify
label def pais2 2 "Bolivia", modify
label def pais2 3 "Brasil", modify

My model:

p(i,t) = b(0) + T(t) + C(i) + b(1)*p(i,t-1) + b(2)*x(i,t) + e(i,t)

I have come across the following commands but am confused on which one to go for:

1. mmqreg
2. xtqreg
3. qregpd

Is fine my next script?

gen ln_con2pc_gr_1 = l.ln_co2pc_gr
qregpd ln_co2pc_gr ln_co2pc_gr_1 ln_gdppc_gr ei_ch res_share_ch, id(pais2) fix(year) q(25)
xtqreg ln_co2pc_gr ln_co2pc_gr_1 ln_gdppc_gr ei_ch res_share_ch year, i(pais2) quantile(.25)
mmqreg  ln_co2pc_gr ln_co2pc_gr_1 ln_gdppc_gr ei_ch res_share_ch year, abs(pais2) q(25)

Regards,
Sebastián.

[FernandoRios]

Hi Sebastian
I think they are all fine. Just extra food for thought.
1. mmqreg is based on xtqreg. So the results should be almost the same
2. qregpd does a different kind of "fixed effects". It doesn't implement fixed effects as we usually think about it. Instead, it is kind of controlling for the distribution of your dep variable across the fixed effects
3. mmqreg could also control for time fixed effects : mmqreg y x, abs(id1 id2)
4. I don't think mmqreg or xtqreg were constructed to deal with dynamic models. So i would be careful there.
HTH

[Joao Santos Silva]

Dear Sebastian Kruk,

Further to Fernando's helpful comment, I would like to add or reiterate two things:

1 - The model estimated by qregpd is indeed very different from the usual fixed effects model we tend to have in mind. Moreover, the approach is not universally liked; see here.
2 - In the paper where we introduced the MM-QR estimator, we have an illustration with a dynamic model. The coefficient on the lagged dependent variable will have the usual bias, but if that variable has low correlation with your variable of interest, the results should be reasonable.

Best wishes,

Joao

[Sebastian Kruk]

Hi Sebastian
I think they are all fine. Just extra food for thought.
1. mmqreg is based on xtqreg. So the results should be almost the same
2. qregpd does a different kind of "fixed effects". It doesn't implement fixed effects as we usually think about it. Instead, it is kind of controlling for the distribution of your dep variable across the fixed effects
3. mmqreg could also control for time fixed effects : mmqreg y x, abs(id1 id2)
4. I don't think mmqreg or xtqreg were constructed to deal with dynamic models. So i would be careful there.
HTH

Fernando,

Which model do you suggest to use in my problem?

A panel ARDL?

Greetings,
Sebastián.

[Sebastian Kruk]

Dear Sebastian Kruk,

Further to Fernando's helpful comment, I would like to add or reiterate two things:

1 - The model estimated by qregpd is indeed very different from the usual fixed effects model we tend to have in mind. Moreover, the approach is not universally liked; see here.
2 - In the paper where we introduced the MM-QR estimator, we have an illustration with a dynamic model. The coefficient on the lagged dependent variable will have the usual bias, but if that variable has low correlation with your variable of interest, the results should be reasonable.

Best wishes,

Joao

Joao,

My laggeed dependent variable is my independent variable lagged.

I found your 2019 UK Stata Conference's slides where you said that 'simulations suggest that the bias is negligible for n/T ≤ 10'.

Maybe I should use other model.

What do you think?

Regards,
Sebastian.

[Joao Santos Silva]

Dear Sebastian Kruk,

I realize that your lagged dependent variable is your independent variable lagged, but the question is about the correlation between it and your variable of interest (or is the lagged variable the variable of interest?). In any case, with T = 48 you should be OK.

Best wishes,

Joao