Hi,

I am using panel data for US companies for the period 2000-2019. My research involves studying the impact of Geographical Diversification (Ln_GSD) on firm performance (Ln_EBIT_ROA). As you can see, I have log-transformed the original variables i,e.
1. The IV Geographic Segmentation (GSD) is log-transformed as Ln_GSD
2. The DV EBIT_ROA is log-transformed as Ln_EBIT_ROA

I have pasted by regression equation and margins command below. I am wondering how I can interpret these margins given that both IV and DV are log-transformed. Any guidance would be greatly apprecaited. Thank you.

Code:
. xtreg Ln_EBIT_ROA Ln_Revenue Ln_LTD_to_Sales Ln_Intangible_Assets  CoAge wGDPpc wCPI wDCF wExpg
> r wGDPgr wCons Ln_PS_RD c.l1.Ln_GSD##c.l1.Ln_GSD if  CoAge>=0 & NATION=="UNITED STATES" & NATIO
> NCODE==840 & FSTS>=10 & GENERALINDUSTRYCLASSIFICATION ==1 & Year_<2020 & Year_<YearInactive & D
> iscr_GS_Rev!=1, fe cluster(n_CUSIP)

Fixed-effects (within) regression               Number of obs     =      1,094
Group variable: n_CUSIP                         Number of groups  =        217

R-sq:                                           Obs per group:
     within  = 0.1070                                         min =          1
     between = 0.0010                                         avg =        5.0
     overall = 0.0001                                         max =         19

                                                F(11,216)         =          .
corr(u_i, Xb)  = -0.9029                        Prob > F          =          .

                                      (Std. Err. adjusted for 217 clusters in n_CUSIP)
--------------------------------------------------------------------------------------
                     |               Robust
         Ln_EBIT_ROA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
          Ln_Revenue |   .5763141   .1411842     4.08   0.000      .298039    .8545892
     Ln_LTD_to_Sales |  -.0995823   .0380325    -2.62   0.009    -.1745447   -.0246199
Ln_Intangible_Assets |  -.1271354   .0583075    -2.18   0.030      -.24206   -.0122108
               CoAge |  -.0258257   .0132921    -1.94   0.053    -.0520246    .0003732
              wGDPpc |   .0000464   .0000236     1.97   0.050    -8.48e-09    .0000928
                wCPI |   4.31e-06   .0232319     0.00   1.000     -.045786    .0457947
                wDCF |   1.23e-13   1.25e-13     0.99   0.323    -1.22e-13    3.69e-13
              wExpgr |   .0004585   .0102761     0.04   0.964    -.0197959    .0207128
              wGDPgr |   .0224036   .0310686     0.72   0.472    -.0388328      .08364
               wCons |  -1.44e-14   4.34e-14    -0.33   0.740    -1.00e-13    7.11e-14
            Ln_PS_RD |  -.0364973    .048478    -0.75   0.452    -.1320477    .0590531
                     |
              Ln_GSD |
                 L1. |  -.6849239   .2057833    -3.33   0.001    -1.090524   -.2793234
                     |
 cL.Ln_GSD#cL.Ln_GSD |  -.0891373   .0413972    -2.15   0.032    -.1707315    -.007543
                     |
               _cons |  -12.39407   2.418484    -5.12   0.000    -17.16092    -7.62722
---------------------+----------------------------------------------------------------
             sigma_u |  1.4895855
             sigma_e |  .59440144
                 rho |  .86264051   (fraction of variance due to u_i)
--------------------------------------------------------------------------------------

. margins, at(l1.Ln_GSD=(-4.839976 (1).2830217))

Predictive margins                              Number of obs     =      1,094
Model VCE    : Robust

Expression   : Linear prediction, predict()

1._at        : L.Ln_GSD        =   -4.839976

2._at        : L.Ln_GSD        =   -3.839976

3._at        : L.Ln_GSD        =   -2.839976

4._at        : L.Ln_GSD        =   -1.839976

5._at        : L.Ln_GSD        =    -.839976

6._at        : L.Ln_GSD        =     .160024

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |  -1.546592   .5436151    -2.85   0.004    -2.612058   -.4811256
          2  |  -1.457808   .3933611    -3.71   0.000    -2.228782   -.6868347
          3  |  -1.547299   .2963378    -5.22   0.000    -2.128111   -.9664879
          4  |  -1.815065     .20548    -8.83   0.000    -2.217798   -1.412332
          5  |  -2.261105   .0808414   -27.97   0.000    -2.419551   -2.102659
          6  |   -2.88542   .1023237   -28.20   0.000    -3.085971   -2.684869
------------------------------------------------------------------------------