Q - A problem with qregpd: a Quantile Regression in an Unbalanced Panel Data set

[Mattthew Kellan]

Hi everyone,

I am trying to perform a Quantile Regression with an unbalanced panel data set, to find out whether the effect of IDV on Gini differs in the .25th and the .75th quantile.
Therefore, I downloaded the following package:

qregpd

I entered the following command:

qregpd Gini_DispSWIID IDV GLPIntensity InflationGDPdeflatorannual Ruralpopulation LevelofdemocracyPolityV Populationgrowthannual TradeofGDP Schoolenrollmentsecondary GDPgrowthannual Wageandsalariedworkerstotal Currenthealthexpenditureof Arablelandoftotal, id(Country_ID) fix(Year) quantile(.75)

However, I obtain the following output:

. qregpd Gini_DispSWIID IDV GLPIntensity InflationGDPdeflatorannual Ruralpopulation Levelofdemocr
> acyPolityV Populationgrowthannual TradeofGDP Schoolenrollmentsecondary GDPgrowthannual Wageands
> alariedworkerstotal Currenthealthexpenditureof Arablelandoftotal, id(Country_ID) fix(Year) quan
> tile(.75)
Nelder-Mead optimization
initial:       f(p) = -87.285174
rescale:       f(p) = -87.285174
Iteration 0:   f(p) = -87.285174  
Iteration 1:   f(p) = -5.0307519  
Iteration 2:   f(p) = -.78734938  
Iteration 3:   f(p) = -.78734938  
Iteration 4:   f(p) = -.78734938  
Iteration 5:   f(p) = -.78734938  
Iteration 6:   f(p) = -.78734938  
Iteration 7:   f(p) = -.78734938  
Iteration 8:   f(p) = -.78734938  
Iteration 9:   f(p) = -.78734938  
Iteration 10:  f(p) = -.78734938  
Iteration 11:  f(p) = -.78734938  
Iteration 12:  f(p) = -.78734938  
Iteration 13:  f(p) = -.78734938  
Iteration 14:  f(p) = -.78734938  
Iteration 15:  f(p) = -.78734938  
Iteration 16:  f(p) = -.78734938  
Iteration 17:  f(p) =  -.6038165  
Iteration 18:  f(p) =  -.6038165  
Iteration 19:  f(p) =  -.6038165  
Iteration 20:  f(p) =  -.6038165  
Iteration 21:  f(p) =  -.6038165  
Iteration 22:  f(p) =  -.6038165  
Iteration 23:  f(p) =  -.6038165  
Iteration 24:  f(p) =  -.6038165  
Iteration 25:  f(p) =  -.6038165  
Iteration 26:  f(p) =  -.6038165  
Iteration 27:  f(p) =  -.6038165  
Iteration 28:  f(p) =  -.6038165  
Iteration 29:  f(p) =  -.6038165  
Iteration 30:  f(p) =  -.6038165  
Iteration 31:  f(p) =  -.6038165  
Iteration 32:  f(p) =  -.6038165  
Iteration 33:  f(p) =  -.6038165  
Iteration 34:  f(p) =  -.6038165  
Iteration 35:  f(p) =  -.6038165  
Iteration 36:  f(p) =  -.6038165  
Iteration 37:  f(p) =  -.6038165  
Iteration 38:  f(p) =  -.6038165  
Iteration 39:  f(p) =  -.6038165  
Iteration 40:  f(p) =  -.6038165  
Iteration 41:  f(p) =  -.6038165  
Iteration 42:  f(p) =  -.6038165  
Iteration 43:  f(p) =  -.6038165  
Iteration 44:  f(p) =  -.6038165  
Iteration 45:  f(p) =  -.6038165  
Iteration 46:  f(p) =  -.6038165  
Iteration 47:  f(p) =  -.6038165  
Iteration 48:  f(p) =  -.6038165  


Quantile Regression for Panel Data (QRPD)
     Number of obs:               301
     Number of groups:             19
     Min obs per group:            11
     Max obs per group:            19
---------------------------------------------------------------------------------------------
             Gini_DispSWIID | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
----------------------------+----------------------------------------------------------------
                        IDV |  -.0515317          .        .       .            .           .
               GLPIntensity |  -118.5223          .        .       .            .           .
 InflationGDPdeflatorannual |  -.2093337          .        .       .            .           .
   Ruralpopulationasaoftota |  -23.02208          .        .       .            .           .
    LevelofdemocracyPolityV |   .8931058          .        .       .            .           .
     Populationgrowthannual |   1.354606          .        .       .            .           .
                 TradeofGDP |   .0269068    .235968     0.11   0.909     -.435582    .4893956
  Schoolenrollmentsecondary |   -.021503   .0731588    -0.29   0.769    -.1648916    .1218855
            GDPgrowthannual |   .1055383          .        .       .            .           .
Wageandsalariedworkerstotal |  -.3813951          .        .       .            .           .
 Currenthealthexpenditureof |   .8699441          .        .       .            .           .
          Arablelandoftotal |   4.889251          .        .       .            .           .
---------------------------------------------------------------------------------------------
No excluded instruments - standard QRPD estimation.

As you can see a lot of output is missing. Could you help me to solve this problem?

Thank you so much.

Kind regards,
Matthew

[FernandoRios]

Hi Matthew,
I dont think that is something that can be "solved".
qregpd (which uses a kind of unconditional quantile regression and that uses fixed effects for the moment conditions, but do not explicitly accounts for them) has a few limitations, as you can see.
If you think this is your best approach, you could
a) try to do a few other runs. It may be that other "solution" may come up.
b) look for and try rqreg. (residual quantile regression). While the method is different than qregpd, at its core they aim to identify the same kind effects

Otherwise, you may want to
c) using some methods like xtqreg , which introduces fixed effects explicitly (kind of adding dummies)
d) use correlated random effect model for QREG
e) use Canay (2011) (https://onlinelibrary.wiley.com/doi/...X.2011.00349.x), which also has a relatively easy to implement approach for panel qreg.
HTH

[Mattthew Kellan]

Dear Fernando,

Thank you for your quick response! I will try several of your recommendations, and I will come back to you.

Could you maybe explain to me why it is something that cannot be solved? I fail to understand why all those outputs are missing.

Thanks in advance,
Matthew

[FernandoRios]

It may be that you have
a) too many controls + fixed effects on your model
b) some of your covariates are time-invariant (or are near time-invariant). So there is not enough residual variation to find a solution
There is also the problem (to me) that the way this model is estimated remains behind a black-box. So I cant say much about other alternative solutions.

[Mattthew Kellan]

Regarding b), my independent variable of interest, IDV (a cultural dimension, namely Individualism vs Collectivism), is indeed fixed. With this knowledge, would you know a possible alternative solution?

[Mattthew Kellan]

Moreover, I already ran sqreg:

sqreg Gini_DispSWIID IDV GLPIntensity InflationGDPdeflatorannual Ruralpopulation LevelofdemocracyPolityV Populationgrowthannual TradeofGDP Schoolenrollmentsecondary GDPgrowthannual Wageandsalariedworkerstotal Currenthealthexpenditureof Arablelandoftotal, q(.25 .5 .75) reps(1000)

test [q25]IDV = [q75]IDV

This provided me with the following results:

Simultaneous quantile regression                    Number of obs =
>         309
  bootstrap(1000) SEs                               .25 Pseudo R2 =
>      0.6098
                                                    .50 Pseudo R2 =
>      0.5766
                                                    .75 Pseudo R2 =
>      0.5114

-------------------------------------------------------------------
> -----------
             |              Bootstrap
Gini_DispS~D | Coefficient  std. err.      t    P>|t|     [95% conf
> . interval]
-------------+-----------------------------------------------------
> -----------
q25          |
         IDV |   .0621627   .0402077     1.55   0.123    -.0169665 
>     .141292
GLPIntensity |  -15.09564   57.04752    -0.26   0.791    -127.3658 
>    97.17449
InflationG~l |  -.1796746   .0427945    -4.20   0.000    -.2638946 
>   -.0954546
Ruralpopul~a |  -22.46318   3.892317    -5.77   0.000     -30.1233 
>   -14.80306
Levelofdem~V |   .9068833   .1173834     7.73   0.000     .6758715 
>    1.137895
Populati~ual |   1.201762   .4077418     2.95   0.003     .3993217 
>    2.004202
  TradeofGDP |    .022163   .0161614     1.37   0.171    -.0096428 
>    .0539688
Schoolenro~y |   -.021961   .0274474    -0.80   0.424    -.0759778 
>    .0320558
GDPgrowtha~l |   .0438488   .0628339     0.70   0.486    -.0798089 
>    .1675065
Wageandsal~l |  -.2915845   .0434977    -6.70   0.000    -.3771883 
>   -.2059806
Currenthea~f |  -.1595835   .3418894    -0.47   0.641    -.8324255 
>    .5132585
Arableland~l |  -.1507407   .0292173    -5.16   0.000    -.2082405 
>   -.0932408
       _cons |    61.6235   3.318998    18.57   0.000     55.09168 
>    68.15532
-------------+-----------------------------------------------------
> -----------
q50          |
         IDV |   -.027398   .0239206    -1.15   0.253     -.074474 
>     .019678
GLPIntensity |  -109.2457   28.78524    -3.80   0.000    -165.8953 
>   -52.59604
InflationG~l |  -.2199388   .0270142    -8.14   0.000    -.2731031 
>   -.1667746
Ruralpopul~a |   -19.6259   3.039259    -6.46   0.000     -25.6072 
>   -13.64461
Levelofdem~V |   .9521651   .1020938     9.33   0.000     .7512434 
>    1.153087
Populati~ual |   1.304531   .3384198     3.85   0.000     .6385173 
>    1.970545
  TradeofGDP |   .0206275   .0104486     1.97   0.049     .0000645 
>    .0411905
Schoolenro~y |  -.0092621   .0164646    -0.56   0.574    -.0416646 
>    .0231404
GDPgrowtha~l |   .1653781   .0721563     2.29   0.023     .0233737 
>    .3073826
Wageandsal~l |  -.3453577   .0274608   -12.58   0.000    -.3994008 
>   -.2913147
Currenthea~f |   .5299716    .267185     1.98   0.048     .0041486 
>    1.055795
Arableland~l |  -.1622347   .0271923    -5.97   0.000    -.2157495 
>   -.1087199
       _cons |   63.35494   3.176216    19.95   0.000     57.10411 
>    69.60577
-------------+-----------------------------------------------------
> -----------
q75          |
         IDV |  -.0552767   .0276158    -2.00   0.046     -.109625 
>   -.0009285
GLPIntensity |  -114.7688   34.25533    -3.35   0.001    -182.1837 
>   -47.35399
InflationG~l |  -.2141787   .0541846    -3.95   0.000    -.3208145 
>   -.1075429
Ruralpopul~a |  -22.88303   3.294227    -6.95   0.000    -29.36611 
>   -16.39996
Levelofdem~V |   .8683934   .1968631     4.41   0.000     .4809647 
>    1.255822
Populati~ual |   1.342222   .4025617     3.33   0.001     .5499759 
>    2.134467
  TradeofGDP |   .0237979   .0116377     2.04   0.042     .0008947 
>    .0467011
Schoolenro~y |  -.0211156   .0141656    -1.49   0.137    -.0489937 
>    .0067626
GDPgrowtha~l |    .104547    .079948     1.31   0.192    -.0527914 
>    .2618854
Wageandsal~l |  -.3751846   .0342158   -10.97   0.000    -.4425217 
>   -.3078475
Currenthea~f |   .8020906   .1569203     5.11   0.000     .4932698 
>    1.110911
Arableland~l |  -.1092221   .0395091    -2.76   0.006    -.1869764 
>   -.0314678
       _cons |   67.55661   3.133162    21.56   0.000     61.39051 
>     73.7227
-------------------------------------------------------------------
> -----------

. 
. test [q25]IDV = [q75]IDV

 ( 1)  [q25]IDV - [q75]IDV = 0

       F(  1,   296) =    7.58
            Prob > F =    0.0063

This gives me all the output required. However, do you know if I can use sqreg with panel data?