Interpretation of coefficient when independent is in proportion, and dependent variable is in log form

[farah roslan]

Dear all,

I am having difficulty in interpreting one of the main independent variables in FE regression. The main independent var,

rois

is ROI for small solar PV sector which its calculated value is ranging from -0.25 to 3.37. The dependent var. is

lpv_small

which equals to log of added installed capacity for small solar PV sector.

xtreg lpv_small rois tax grant import1 sharee carbon2 lgdp i.year, fe

Fixed-effects (within) regression               Number of obs     =        340
Group variable: country1                        Number of groups  =         19

R-sq:                                           Obs per group:
     within  = 0.8173                                         min =         16
     between = 0.0646                                         avg =       17.9
     overall = 0.3151                                         max =         18

                                                F(24,297)         =      55.34
corr(u_i, Xb)  = -0.7630                        Prob > F          =     0.0000

------------------------------------------------------------------------------
   lpv_small |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        rois |    .234995   .0896794     2.62   0.009     .0585074    .4114827
         tax |     .00061   .2644453     0.00   0.998    -.5198139     .521034
       grant |  -.6905872   .2653985    -2.60   0.010    -1.212887   -.1682873
     import1 |  -.0298407   .0094992    -3.14   0.002    -.0485349   -.0111465
      sharee |   .0848137   .0173136     4.90   0.000     .0507409    .1188865
     carbon2 |   .0386653   .0569898     0.68   0.498    -.0734898    .1508204
        lgdp |     .86633   .4472544     1.94   0.054    -.0138593    1.746519
             |
        year |
       1999  |   1.182406    .439037     2.69   0.007     .3183888    2.046424
       2000  |    2.33013   .4459633     5.22   0.000     1.452481    3.207778
       2001  |   2.315135   .4515315     5.13   0.000     1.426529    3.203742
       2002  |   2.625077   .4589965     5.72   0.000     1.721779    3.528375
       2003  |   2.795346   .4866044     5.74   0.000     1.837716    3.752975
       2004  |   3.283991    .497777     6.60   0.000     2.304374    4.263607
       2005  |   3.461291   .5227286     6.62   0.000      2.43257    4.490012
       2006  |   3.895308   .5451787     7.15   0.000     2.822406    4.968211
       2007  |   3.927511   .5640918     6.96   0.000     2.817388    5.037635
       2008  |    4.71122   .5692008     8.28   0.000     3.591042    5.831398
       2009  |    5.15504   .5860513     8.80   0.000     4.001701    6.308379
       2010  |   6.380798   .6127162    10.41   0.000     5.174983    7.586613
       2011  |   6.872372   .6328262    10.86   0.000     5.626981    8.117764
       2012  |   7.108892   .6631365    10.72   0.000      5.80385    8.413934
       2013  |   6.867976   .6947964     9.88   0.000     5.500628    8.235324
       2014  |   7.168307   .7161169    10.01   0.000     5.759001    8.577614
       2015  |    7.48759   .7455636    10.04   0.000     6.020333    8.954846
             |
       _cons |  -24.06997   10.05616    -2.39   0.017    -43.86032   -4.279621
-------------+----------------------------------------------------------------
     sigma_u |  3.7798881
     sigma_e |  1.3507518
         rho |  .88676013   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(18, 297) = 15.47                    Prob > F = 0.0000

If I want to explain the effect of

rois

on

lpv_small

, am I correct if I explain 10 percentage point increase in ROI will result in 2.6% (exp(0.234) increase in solar PV from small scale?

Your feedbacks are really appreciated.

Thank you.
Farah

[Joro Kolev]

d(log(Y))/dX = (1/Y)(dY/dX), so I would say that 1 unit increase in rois leads to 23.4995% increase in lpv_small. So it seems that yes, 10 percentage points in crease in ROI leads to 2.35 percent increase in solar PV, which is about the same as what you have concluded. (I take exponents like you have done only for dummy variables.)

[farah roslan]

Thank you Joro for your comment. I shall proceed it in my thesis writing