Dependent and independent variables are in proportions-proportion analysis of Panel data

[Sonia Alam]

Dear experts:

I have four dependent variables in proportion i.e. share of area under four crops by county over time (15years). and the independent variables are in proportion as well, which are climatic variables ( temperature and rainfall- standardized against the optimum values) I am using the Fractional multinomial logit model to see the impact of climate variables on share of area under each crop over time.
I ran the command :

 fmlogit prop_wArea Prop_mArea Prop_rArea Prop_cArea,eta(MinSt_wVeg MaxSt_wVeg RFSt_wVeg)

My first concern: Does this make sense to include the proportions on Both sides of equation?

If yes, how can I interpret the results?

Here are the results:

Iteration 0:   log pseudolikelihood = -696.39314  
Iteration 1:   log pseudolikelihood = -671.01186  
Iteration 2:   log pseudolikelihood = -664.43543  
Iteration 3:   log pseudolikelihood = -663.98069  
Iteration 4:   log pseudolikelihood =  -663.9614  
Iteration 5:   log pseudolikelihood = -663.96139  

ML fit of fractional multinomial logit          Number of obs     =        681
                                                Wald chi2(9)      =     394.61
Log pseudolikelihood = -663.96139               Prob > chi2       =     0.0000

--------------------------------------------------------------------------------
               |               Robust
               |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
eta_Prop_mArea |
    MinSt_wVeg |  -.5663348   .1264426    -4.48   0.000    -.8141577   -.3185118
    MaxSt_wVeg |  -1.924901   .1990114    -9.67   0.000    -2.314956   -1.534846
     RFSt_wVeg |   .1774501   .1763718     1.01   0.314    -.1682324    .5231326
         _cons |   1.878999   .2145753     8.76   0.000     1.458439    2.299559
---------------+----------------------------------------------------------------
eta_Prop_rArea |
    MinSt_wVeg |  -2.334554   .4095512    -5.70   0.000    -3.137259   -1.531848
    MaxSt_wVeg |   .3838752   .3938929     0.97   0.330    -.3881406    1.155891
     RFSt_wVeg |   .6781816   .1190355     5.70   0.000     .4448763    .9114869
         _cons |  -1.662554   .3163261    -5.26   0.000    -2.282542   -1.042566
---------------+----------------------------------------------------------------
eta_Prop_cArea |
    MinSt_wVeg |   .2229872   .0920443     2.42   0.015     .0425836    .4033907
    MaxSt_wVeg |  -1.240566   .3151324    -3.94   0.000    -1.858214   -.6229178
     RFSt_wVeg |  -2.427474   .4302069    -5.64   0.000    -3.270664   -1.584284
         _cons |    -.55246   .3477961    -1.59   0.112    -1.234128    .1292079
--------------------------------------------------------------------------------

Many Thanks in advance.

Kind Regards