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  • Panel data analysis: Fixed Country and Time Effect

    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
    Last edited by Linh Dieu Le; 12 Aug 2018, 10:19.

  • #2
    It means that factors other than grant and tax incentives, per capita GDP, and gasoline price that are changing systematically over time, and are also correlated with those three predictors, are more strongly associated with market share than those predictors themselves. In your model without quarterly fixed effects, the incentives, gdp, and gasoline price variables are serving as proxies for unobserved factors that are changing over time. When you incorporate the time variables, the time variables now adjust for those unobserved factors and the original proxies lose some of their explanatory power.

    By the way, although it has no bearing on the question you posed, it appears that you created your time indicator variables using the now nearly obsolete -xi- command. Going forward, you will find it advantageous to instead use factor-variable notation, which is simpler to start with, and also enables you to then use the -margins- command. Do read -help fvvarlist-. While there are still a few situations where factor-variable notation is not supported and one might have to resort to the old -xi-, they are quite uncommon. So learn factor-variable notation, and more or less put -xi- out of our mind.

    Comment


    • #3
      Thank you so much for your reply.
      Refering to the first point, I am not sure what you mean by
      the incentives, gdp, and gasoline price variables are serving as proxies for unobserved factors that are changing over time
      What I do understand is there are unobserved / omitted factors that my model failed to include vary over time and my approach to the problem is to add a time trend variable into FE model. I have heard about time trend variable which control for the exogenous increase in dependable variable (which i do observe from my share market data and might be able to explain the trend with relating theories), however I have never done this before, so it would be nice to know your opinion on this.

      By the way, although it has no bearing on the question you posed, it appears that you created your time indicator variables using the now nearly obsolete -xi- command
      Yes, you saw my weakness right off the bat. I am all new to stata. I was and still struggle to creat quarterly time indicator. I took the idea actually from one of your previous post which might be long time ago. I surely update my knowledge on this, thanks for your valuable input.

      Comment


      • #4
        Linh Dieu Le Welcome to Statalist!

        I'm sympathetic to you as a new user of Stata - it's a lot to absorb. I have a piece of advice I share with new users when I think it might help them.

        When I began using Stata in a serious way, I started, as have others here, by reading my way through the Getting Started with Stata manual relevant to my setup. Chapter 18 then gives suggested further reading, much of which is in the Stata User's Guide, and I worked my way through much of that reading as well. There are a lot of examples to copy and paste into Stata's do-file editor to run yourself, and better yet, to experiment with changing the options to see how the results change.

        All of these manuals are included as PDFs in the Stata installation (since version 11) and are accessible from within Stata - for example, through the PDF Documentation section of Stata's Help menu. The objective in doing the reading was not so much to master Stata as to be sure I'd become familiar with a wide variety of important basic techniques, so that when the time came that I needed them, I might recall their existence, if not the full syntax, and know how to find out more about them in the help files and PDF manuals.

        Stata supplies exceptionally good documentation that amply repays the time spent studying it - there's just a lot of it. The path I followed surfaces the things you need to know to get started in a hurry and to work effectively.

        Comment

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