Insignificant results with Panel Quantile Regression

[Anuradha Saikia]

Hello all.
My dataset has N= 178 and T =14
Is it appropriate to run a panel quantile regression?
also I ran the following code

xtqreg ROA DT  LEV HHI GDPpercapita Size Age,i(Companynum) quantile(.75)

which has given me insignificant p values in 25th percentile as well as the median.
I do not know how to proceed with this issue.

[Joao Santos Silva]

Dear Anuradha Saikia,

Your T is on the short side, but it may just be enough. Before giving you further advice, perhaps you can tell show us your results when you estimate the model using xtreg with fixed effects and robust standard errors; it may just be that your variables have little variation over time.

Best wishes,

Joao

[Anuradha Saikia]

Hello Joao Santos Silva . these are my results first for fixed effects and then the quantiles.

Also is i(Companynum) specification correct as Companynum stands for cross-sectional units in my panel set.
Also I came across Fixed effects in unconditional quantile regression, Borgen 2016 paper where xtrifreg command is used . will my results be different then?

xtreg ROA DTTA LEV HHI Size Age GDPpercapita, fe

Fixed-effects (within) regression               Number of obs     =      2,771
Group variable: Companynum                      Number of groups  =        174

R-sq:                                           Obs per group:
within  = 0.1635                                         min =          6
between = 0.0232                                         avg =       15.9
overall = 0.0668                                         max =         16

F(6,2591)         =      84.38
corr(u_i, Xb)  = -0.4393                        Prob > F          =     0.0000


ROA       Coef.   Std. Err.      t    P>t     [95% Conf. Interval]

DTTA    .0299043   .0090632     3.30   0.001     .0121324    .0476761
LEV   -.0002281   .0000564    -4.05   0.000    -.0003387   -.0001176
HHI   -.0002872   .0007077    -0.41   0.685    -.0016748    .0011004
Size   -.2056343   .0139549   -14.74   0.000    -.2329981   -.1782705
Age   -.0079105   .0195387    -0.40   0.686    -.0462235    .0304025
GDPpercapita   -.0001388   .0002126    -0.65   0.514    -.0005557    .0002781
_cons    5.094392   .2285356    22.29   0.000     4.646261    5.542523

sigma_u   1.0162116
sigma_e   1.0422795
rho   .48733846   (fraction of variance due to u_i)

F test that all u_i=0: F(173, 2591) = 11.03                  Prob > F = 0.0000

xtqreg ROA DTTA LEV HHI GDPpercapita Size Age,i(Companynum) quantile(.75)



                              MM-QR regression results
Number of obs = 2771
.75 Quantile regression
------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        DTTA |   .0396198   .0365549     1.08   0.278    -.0320264    .1112661
         LEV |  -.0001427   .0000986    -1.45   0.148     -.000336    .0000505
         HHI |  -.0004614   .0017461    -0.26   0.792    -.0038836    .0029608
GDPpercapita |  -.0005523   .0005265    -1.05   0.294    -.0015842    .0004796
        Size |   -.281465   .0462987    -6.08   0.000    -.3722087   -.1907212
         Age |   .0420307   .0492641     0.85   0.394    -.0545251    .1385866
------------------------------------------------------------------------------


. xtqreg ROA DTTA LEV HHI GDPpercapita Size Age,i(Companynum) quantile(.25)



                              MM-QR regression results
Number of obs = 2771
.25 Quantile regression
------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        DTTA |   .0225541    .023868     0.94   0.345    -.0242264    .0693346
         LEV |  -.0002927   .0000645    -4.54   0.000    -.0004192   -.0001663
         HHI |  -.0001554     .00114    -0.14   0.892    -.0023897     .002079
GDPpercapita |   .0001741   .0003441     0.51   0.613    -.0005005    .0008486
        Size |  -.1482656   .0304646    -4.87   0.000     -.207975   -.0885561
         Age |  -.0456928   .0322386    -1.42   0.156    -.1088793    .0174936
------------------------------------------------------------------------------

[Anuradha Saikia]

The results are also insignificant with the code mmqreg.

[Anuradha Saikia]

But this is showing some good results . if you can comment on xtrifreg results .

xtrifreg ROA DTTA LEV Age Size GDPpercapita , fe i(Companynum) q(90) bootstrap    reps(200)
Bootstrap xtrifreg (200)
1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50
..................................................   100
..................................................   150
..................................................   200

        
Model UQR
        

Fixed-effects (within) regression               Number of obs      =      2771
Group variable: Companynum                      Number of groups   =       174

R-sq:  within  = 0.1196                         Obs per group: min =         6
between = 0.0421                                        avg =      15.9
overall = 0.0599                                        max =        16

F(5,2592)          =     70.41
corr(u_i, Xb)  = -0.4861                        Prob > F           =    0.0000


Observed   Bootstrap                         Normal-based
rif_90       Coef.   Std. Err.      t    P>t     [95% Conf. Interval]

DTTA    .0925268   .0373864     2.47   0.013     .0192167     .165837
LEV    .0001079   .0007908     0.14   0.891    -.0014427    .0016585
Age    .0353178    .038197     0.92   0.355     -.039582    .1102176
Size   -.3334913   .0532377    -6.26   0.000    -.4378839   -.2290986
GDPpercapita   -.0005379   .0004108    -1.31   0.190    -.0013434    .0002676
_cons    7.603776   .6330178    12.01   0.000     6.362505    8.845048

sigma_u   1.4472781
sigma_e     1.76775
rho   .40130132   (fraction of variance due to u_i)

F test that all u_i=0: F(173, 2592) = 6.54                   Prob > F = 0.0000

[Jared Greathouse]

You should be using the statistical technique which is ideal for your situation. I know nothing about quantile regression, but if it works here, it works.

Statistical significance shouldn't be a concern here, if the method you've used is sound, then that's the important part. Not how many stars a standard error has.

[Joao Santos Silva]

Dear Anuradha Saikia,

I start by echoing Jared's comments above: you need to define what you want to estimate and then proceed accordingly. Moreover, you must understand the methods you use.

The commands mmqreg and xtqreg implement the same estimator, therefore it is not surprising that they give similar results; in contrast, xtrifreg implements a very different estimator and estimates very different parameters. You need to decide which parameters you want to estimate before choosing the estimation method, and the choice should not depend on the results you get (rather the results depend on the choice).

Anyway, if you want to estimate quantile regression with fixed effects, I suggest you continue to use xtqreg and use the jackknife correction and bootstrap the standard errors, as illustrated here. For more details, please see the original paper.

Best of luck with your work,

Joao

[Anuradha Saikia]

Okay thank you Joao Santos Silva Jared Greathouse

[merve kaya]

Dear Anuradha Saikia,

Your T is on the short side, but it may just be enough. Before giving you further advice, perhaps you can tell show us your results when you estimate the model using xtreg with fixed effects and robust standard errors; it may just be that your variables have little variation over time.

Best wishes,

Joao

Dear Silva,

What should be the minimum T dimension to estimate panel quantile regression?

[Joao Santos Silva]

Dear merve kaya,

That depends on N, but anything shorter than 10 should be avoided.

Best wishes,

Joao

[merve kaya]

Dear Joao Santos Silva,

Thank you for your reply.

When we estimate quantile regression through Eviews 12, would it be enough to look at the results of the Wald test, which gives the quantile slope equality test, to test the validty of the model?

[Joao Santos Silva]

I am afraid I am not familiar with that software, but the test does not seem to be related to the "validity" of the model.

[merve kaya]

Dear Joao Santos Silva,

With your permission, I would like to ask one more question. What tests should we do to test the validity of the quantile regression (qreg, bqreg,sqreg, iqreg) model estimated in Stata?

[Joao Santos Silva]

It depends on what you want to do, but you probably do not need more than a RESET test (or you may need no test at all). In any case, make sure you use the correct standard errors.