To the developers of QREGPD and others,

I am estimating the impact of institutional integrity on carbon emissions using quantile regression for an unbalanced dataset that runs from 1984 to 2016 for about 123 countries. I'm interested in quantile regression to view the relationship at different points in the conditional distribution of y.

Because T spans over 30 years, therefore i have differenced my variables. Thus 'd' in front of every variable.
Definition of variables"
dlrgdp = Log of real per capita GDP, dlrgdp2 = squared dlrgdp, dfrleg = institutional integrity, dfrleg2 = squared dfrleg, dlpopden = log of population density, dlenguse = log of energy use, dfr_lrgdp = interaction term between institutional integrity and GDP

Code:
qregpd dlpccarb dlrgdp dlrgdp2 dfrleg dfrleg2 dlpopden dlenguse  dfr_lrgdp dfr2_lrgdp2 , quantile(.25) id(cty) fix(year) optimize(mcmc) noisy draws(1000) burn(100) arate(.5)
qregpd dlpccarb dlrgdp dlrgdp2 dfrleg dfrleg2 dlpopden dlenguse  dfr_lrgdp dfr2_lrgdp2 , quantile(.75) id(cty) fix(year) optimize(mcmc) noisy draws(1000) burn(100) arate(.5)

Code:
Quantile Regression for Panel Data (QRPD)
     Number of obs:              3231
     Number of groups:            120
     Min obs per group:             3
     Max obs per group:            30
------------------------------------------------------------------------------
    dlpccarb |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      dlrgdp |   .5437956   .0590741     9.21   0.000     .4280124    .6595787
     dlrgdp2 |  -.0184208   .0035656    -5.17   0.000    -.0254094   -.0114323
      dfrleg |  -2.656076   .1897324   -14.00   0.000    -3.027944   -2.284207
     dfrleg2 |   1.623832   .0635615    25.55   0.000     1.499253     1.74841
    dlpopden |  -.3040617   .0167634   -18.14   0.000    -.3369172   -.2712061
    dlenguse |   .8296468   .0032042   258.93   0.000     .8233667    .8359269
   dfr_lrgdp |   .2209018   .0216103    10.22   0.000     .1785463    .2632573
 dfr2_lrgdp2 |  -.0129949   .0008071   -16.10   0.000    -.0145767    -.011413
------------------------------------------------------------------------------
No excluded instruments - standard QRPD estimation.


MCMC diagonstics:
     Mean acceptance rate:      0.473
     Total draws:                1000
     Burn-in draws:               100
     Draws retained:              900
     Value of objective function:   
             Mean:             -74.3432
             Min:              -84.6212
             Max:              -70.4597
MCMC notes:
     *Point estimates correspond to mean of draws.
     *Standard errors are derived from variance of draws.
Edited MCMC optimzation. These results are for q=.25.

These results are too good to be true. Now I have 3 questions related to these results.
1). How can I check the validity of these results? Is there any post estimation command that verifies that these results are correct?
2). Would it be correct to use -qplot- in panel data ? if no, then what command would be the most appropriate to generate a graph similar to that generated by -qplot-?
3). Is there a command similar to grqreg to generate graphs over quantiles in a panel data setting?