help with interpreting regression results

[Samir Doghmi]

Hello,

I was running a panel data regression with a country dummy using the command vce(cluster id), but I am having difficulties to interpret the result. I am working with a log log model specification. My dependent variable is ghg emissions by Nace activites plus households and I'm trying to analyze the effect of the independent variables described in the table below.

Variable      Storage   Display    Value
    name         type    format    label      Variable label
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
lnghg           float   %9.0g                 GHG emissions by nace activities plus households
lnnet_hh        float   %9.0g                median income by household
lEn_intensity   float   %9.0g               Energy intensity
lfossil_q       float   %9.0g                  Fossil fuel share of energy consumed
lfeng_1         float   %9.0g                 Final energy consumption
lmanufac_q      float   %9.0g             Gross value added and income by industry (% GDP)
lRenewable_q    float   %9.0g           Renewable energy % of energy consumed

the value left by dummy variable is Austria

 xtreg lnghg lnnet_hh lEn_intensity lfossil_q lfeng_1 lmanufac_q lRenewable_q i.C_id,  cluster (C_id)

Random-effects GLS regression                   Number of obs     =        260
Group variable: C_id                            Number of groups  =         20

R-squared:                                      Obs per group:
     Within  = 0.6485                                         min =         13
     Between = 1.0000                                         avg =       13.0
     Overall = 0.9987                                         max =         13

                                                Wald chi2(6)      =          .
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =          .

                                   (Std. err. adjusted for 20 clusters in C_id)
-------------------------------------------------------------------------------
              |               Robust
        lnghg | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
--------------+----------------------------------------------------------------
     lnnet_hh |  -.0434122   .0907861    -0.48   0.633    -.2213496    .1345251
lEn_intensity |   .2247449   .1157024     1.94   0.052    -.0020276    .4515173
    lfossil_q |   .5459738   .2092293     2.61   0.009      .135892    .9560556
      lfeng_1 |   .5366492   .1208554     4.44   0.000      .299777    .7735215
   lmanufac_q |   .4090986   .0956841     4.28   0.000     .2215611     .596636
 lRenewable_q |  -.0080579    .017001    -0.47   0.636    -.0413793    .0252634
              |
         C_id |
          BE  |   .2171572   .0549179     3.95   0.000     .1095201    .3247943
          CY  |  -.2581096     .31486    -0.82   0.412    -.8752238    .3590046
          DE  |   1.275556   .2310565     5.52   0.000     .8226935    1.728418
          EE  |  -.0820767   .2581901    -0.32   0.751    -.5881201    .4239667
          EL  |   .8391737   .1078409     7.78   0.000     .6278094    1.050538
          ES  |   .9759221   .1603722     6.09   0.000     .6615984    1.290246
       Eu-19  |   .5249851   .0556973     9.43   0.000     .4158203    .6341499
          FI  |   .0911443   .1525042     0.60   0.550    -.2077584     .390047
          FR  |    1.05002   .2182552     4.81   0.000     .6222472    1.477792
          IE  |   .1755433   .1580069     1.11   0.267    -.1341444    .4852311
          IT  |   1.045944   .1853721     5.64   0.000     .6826214    1.409267
          LT  |  -.3491076   .2208535    -1.58   0.114    -.7819725    .0837573
          LU  |  -.6640862   .2795643    -2.38   0.018    -1.212022   -.1161502
          LV  |  -.5345163   .2193074    -2.44   0.015    -.9643508   -.1046817
          MT  |  -1.070671   .4448609    -2.41   0.016    -1.942582   -.1987594
          NL  |   .6694279   .0983581     6.81   0.000     .4766496    .8622062
          PT  |   .2995776   .1017318     2.94   0.003      .100187    .4989682
          SK  |   -.291792   .1393528    -2.09   0.036    -.5649185   -.0186656
          SL  |  -.5991373   .2155189    -2.78   0.005    -1.021547    -.176728
              |
        _cons |  -1.443874   1.289626    -1.12   0.263    -3.971495    1.083747
--------------+----------------------------------------------------------------
      sigma_u |          0
      sigma_e |  .05673462
          rho |          0   (fraction of variance due to u_i)
-------------------------------------------------------------------------------

I am uncertain how to interpret each country's effect on cumulative greenhouse gas emissions. should I sum the slope of the regressors with the country slope to offer a clearer result?

[Carlo Lazzaro]

Samir:
welcome to this forum.
Three comments about your regression:
1) your between_Rsq=1 is clearly weird;
2) more substantively, with -sigma_u-=0, there's no evidence of panel-wise effect in your regression results (and pooled OLS seems the way to go);
3) what does the -xttest0- give you back?

[Samir Doghmi]

I honestly don't know why the between Rsq is equal to one. the reason for the problem could be that I consider too many dummies?
xttest0 gives this result

                         |       Var     SD = sqrt(Var)
                ---------+-----------------------------
                   lnghg |   2.257805       1.502599
                       e |   .0032188       .0567346
                       u |          0              0

        Test: Var(u) = 0
                             chibar2(01) =     0.00
                          Prob > chibar2 =   1.0000

[Samir Doghmi]

In your opinion, is it acceptable to group eurozone countries by GDP or gdp per capita into 3 brackets; so that there would be only three dummy variables. in this case, the regression would be xtreg y, x1 x2...xn dum1 dum2 dum3, vce (cluster C_id)?

i am open to any feedback

[Samir Doghmi]

Dear Carlo,


Reconsidering the results of the regressions, I thought of grouping the dummies variables by country into 3 bands so as to reduce the number. of variables I thought I would collect them by individual economy's contribution to overall GDP.
As a result I have so 3 dummies:
-dum1: x >4% (Italy, Germany, France....)
-dum2: 1%< x <4% (Ireland, Finland, Austria..)
- dum3: 1%< x (Lithuania, Latvia, Malta)

 xtreg lnghg lnnet_hh lEn_intensity lfossil_q lfeng_1 lmanufac_q lRenewable_q dum1 dum2 dum3 ,  cluster (C_id)
note: dum3 omitted because of collinearity.

Random-effects GLS regression                   Number of obs     =        260
Group variable: C_id                            Number of groups  =         20

R-squared:                                      Obs per group:
     Within  = 0.6430                                         min =         13
     Between = 0.9600                                         avg =       13.0
     Overall = 0.9588                                         max =         13

                                                Wald chi2(8)      =    1081.30
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

                                   (Std. err. adjusted for 20 clusters in C_id)
-------------------------------------------------------------------------------
              |               Robust
        lnghg | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
--------------+----------------------------------------------------------------
     lnnet_hh |  -.0856191   .0805486    -1.06   0.288    -.2434915    .0722533
lEn_intensity |   .1740252   .1018842     1.71   0.088     -.025664    .3737145
    lfossil_q |   .4964896   .1504567     3.30   0.001     .2015999    .7913792
      lfeng_1 |   .6838388    .080072     8.54   0.000     .5269006    .8407769
   lmanufac_q |   .3906818   .0942561     4.14   0.000     .2059433    .5754204
 lRenewable_q |  -.0149346   .0190737    -0.78   0.434    -.0523184    .0224493
         dum1 |   .8102563   .3454326     2.35   0.019     .1332209    1.487292
         dum2 |   .3499007   .2420476     1.45   0.148    -.1245039    .8243054
         dum3 |          0  (omitted)
        _cons |  -1.109019   1.073213    -1.03   0.301    -3.212479    .9944401
--------------+----------------------------------------------------------------
      sigma_u |  .31022183
      sigma_e |  .05673462
          rho |   .9676359   (fraction of variance due to u_i)
-------------------------------------------------------------------------------

is the result more acceptable?

[Carlo Lazzaro]

Samir:
the between Rsg is still too high, but the panel-wise effect seems evident now (I would recommend you to perform the -xttest0-, though).
In addition, you may want to check the correctness of the functional form of the regressand via a procedure that is reported in -linktest- entry, Stata .pdf manual, but that you should repeat by hand, since -linktest- does not work after -xtreg-.

[Samir Doghmi]

Dear Carlo,


Thank you for your input.

kind regards.