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Panel data analysis: Fixed Country and Time Effect

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Hi all,

I am currently running panel analysis to learn the effect of governmental incentives on battery electric vehicle (BEV) market share. The data are collected for the timeline from 2013q1 to 2018q2 (T=22) in 5 countries (N=5). Beside Grant Incentive (measured in Thousand euro) and Tax Incentive (total of tax incentives available), I also take Gasoline price and GDP percapita as the independable variable explaining the depenable variable BEV market share.

I plan to run FE model to analyse how the change in incentive policies might have impact on sale of the vehicle. Everything was fine with the first run of FE within-groups regression, but the problem arised as I tried to incorporate the time fixed effect with time dummies into the model. The coefficients for every single time dummy variable are significant and all of my main explanatory variables were found to be insignificant in the second model. I am not sure what the reasons behind this outcomes, but it is quite bizarre when there is an fixed effect for every single period of time. I would love to hear advice or comment from you guy on this, I really don't know what to do next and how i am going to interpret this in my paper.

Below are results extracted from Stata for more insight into my issue.

Code:
xtreg lnBEVshare Grant TaxIncentives lnGasoline lnGDPcapita, fe

Fixed-effects (within) regression               Number of obs     =        110
Group variable: country                         Number of groups  =          5

R-sq:                                           Obs per group:
     within  = 0.6224                                         min =         22
     between = 0.5842                                         avg =       22.0
     overall = 0.4819                                         max =         22

                                                F(4,101)          =      41.62
corr(u_i, Xb)  = -0.7650                        Prob > F          =     0.0000

-------------------------------------------------------------------------------
   lnBEVshare |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
        Grant |   .1043704   .0391062     2.67   0.009     .0267942    .1819467
TaxIncentives |   .1110161   .0892676     1.24   0.217    -.0660669     .288099
   lnGasoline |    -3.2776   .7100777    -4.62   0.000    -4.686203   -1.868996
  lnGDPcapita |   9.647115     1.5195     6.35   0.000     6.632837    12.66139
        _cons |  -95.97945   14.45418    -6.64   0.000    -124.6526   -67.30625
--------------+----------------------------------------------------------------
      sigma_u |  .70211881
      sigma_e |  .44357915
          rho |  .71472674   (fraction of variance due to u_i)
-------------------------------------------------------------------------------
F test that all u_i=0: F(4, 101) = 10.48                     Prob > F = 0.0000
Code:
xtreg lnBEVshare Grant TaxIncentives lnGasoline lnGDPcapita i.quarterly_date, fe
i.quarterly_d~e   _Iquarterly_212-233 (naturally coded; _Iquarterly_212 omitted)

Fixed-effects (within) regression               Number of obs     =        110
Group variable: country                         Number of groups  =          5

R-sq:                                           Obs per group:
     within  = 0.8110                                         min =         22
     between = 0.9691                                         avg =       22.0
     overall = 0.7331                                         max =         22

                                                F(25,80)          =      13.73
corr(u_i, Xb)  = 0.2024                         Prob > F          =     0.0000

---------------------------------------------------------------------------------
     lnBEVshare |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
          Grant |   .0645445   .0341455     1.89   0.062    -.0034071    .1324961
  TaxIncentives |   .0898662   .0783161     1.15   0.255    -.0659877    .2457202
     lnGasoline |   .3255609   1.451366     0.22   0.823    -2.562749     3.21387
    lnGDPcapita |   1.970089   2.209071     0.89   0.375    -2.426103     6.36628
_Iquarterly_213 |   .6787434   .2236741     3.03   0.003     .2336177    1.123869
_Iquarterly_214 |   .8481949   .2238284     3.79   0.000     .4027621    1.293628
_Iquarterly_215 |    1.35318   .2304915     5.87   0.000     .8944873    1.811873
_Iquarterly_216 |   1.000312   .2284411     4.38   0.000     .5456997    1.454924
_Iquarterly_217 |   1.277252   .2252816     5.67   0.000     .8289274    1.725577
_Iquarterly_218 |   1.417065   .2262529     6.26   0.000     .9668073    1.867323
_Iquarterly_219 |   1.699331   .2525966     6.73   0.000     1.196647    2.202014
_Iquarterly_220 |   1.531474   .2989914     5.12   0.000     .9364619    2.126486
_Iquarterly_221 |   1.498819   .2481277     6.04   0.000     1.005029    1.992609
_Iquarterly_222 |   1.553567   .2608006     5.96   0.000     1.034557    2.072577
_Iquarterly_223 |   1.814961   .3266448     5.56   0.000     1.164918    2.465005
_Iquarterly_224 |   1.900667   .3823498     4.97   0.000     1.139767    2.661568
_Iquarterly_225 |   1.649063   .3356678     4.91   0.000     .9810626    2.317063
_Iquarterly_226 |   1.798862   .3566489     5.04   0.000     1.089108    2.508616
_Iquarterly_227 |   1.883902   .3349619     5.62   0.000     1.217307    2.550498
_Iquarterly_228 |   2.021837   .3110803     6.50   0.000     1.402768    2.640907
_Iquarterly_229 |   1.943993   .3315663     5.86   0.000     1.284155    2.603831
_Iquarterly_230 |   2.114018   .3556878     5.94   0.000     1.406176    2.821859
_Iquarterly_231 |   2.211986   .3442955     6.42   0.000     1.526816    2.897156
_Iquarterly_232 |   2.247237   .3337425     6.73   0.000     1.583069    2.911406
_Iquarterly_233 |   2.100275   .3625178     5.79   0.000     1.378841    2.821708
          _cons |  -25.94151    20.9779    -1.24   0.220    -67.68886    15.80584
----------------+----------------------------------------------------------------
        sigma_u |  .33657871
        sigma_e |  .35264502
            rho |  .47670193   (fraction of variance due to u_i)
---------------------------------------------------------------------------------
F test that all u_i=0: F(4, 80) = 4.54                       Prob > F = 0.0023

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