Dear Statalist,

I am using a bilateral exchange rate variable in the gravity model. However, when I use the exchange rate variables in the log form, it changes the overall results mainly with opposite sign. However, using without log make the thing in the right way. Please let me know what are reasons and how to deal with it. The descriptive statistics and regression are appended below.
Thanks.

sum exc lexc

PHP Code:
   Variable |       Obs        Mean    StdDev.       Min        Max
-------------+--------------------------------------------------------
         
exc |     78176    591.1251    3470.122   .0004463   115588.5
        lexc 
|     78176    1.843932     3.34576  -7.714482   11.65779 
Regression without natural log for bilateral exchange rate

xtreg lremit $xlist1 i.year, vce(cluster pairid) fe

PHP Code:
Fixed-effects (withinregression               Number of obs      =      1089
Group variable
pairid                          Number of groups   =       267

R
-sq:  within  0.1237                         Obs per groupmin =         1
       between 
0.4856                                        avg =       4.1
       overall 
0.5531                                        max =         7

                                                F
(11,266)          =      5.67
corr
(u_iXb)  = 0.0832                         Prob F           =    0.0000

                               
(StdErradjusted for 267 clusters in pairid)
------------------------------------------------------------------------------
             |               
Robust
      lremit 
|      Coef.   StdErr.      t    P>|t|     [95ConfInterval]
-------------+----------------------------------------------------------------
       
lgdpc |   .3832628   .1523686     2.52   0.012     .0832609    .6832647
   lgdpc_hos 
|   .2996346   .3462619     0.87   0.388    -.3821282    .9813974
      lcost2 
|  -.1845849   .0986203    -1.87   0.062    -.3787607    .0095908
     lmig_st 
|   .3717788   .1603001     2.32   0.021     .0561603    .6873973
         exc 
|  -.0001012   .0000531    -1.91   0.058    -.0002058    3.40e-06
             
|
        
year |
       
2012  |   .0051369   .0194579     0.26   0.792    -.0331742     .043448
       2013  
|    -.02299   .0473106    -0.49   0.627    -.1161409    .0701608
       2014  
|  -.0251942   .0545859    -0.46   0.645    -.1326696    .0822811
       2015  
|   .1554102   .0574091     2.71   0.007     .0423762    .2684442
       2016  
|   .0830776   .0632646     1.31   0.190    -.0414855    .2076407
       2017  
|   .1111879   .0632979     1.76   0.080    -.0134407    .2358166
             
|
       
_cons |  -7.122939   5.249512    -1.36   0.176    -17.45882    3.212942
-------------+----------------------------------------------------------------
     
sigma_u |  1.2772635
     sigma_e 
|  .34175982
         rho 
|  .93318862   (fraction of variance due to u_i)
----------------------------------------------------------------------------- 
Regression with natural log

xtreg lremit $xlist1 i.year, vce(cluster pairid) fe

PHP Code:
Fixed-effects (withinregression               Number of obs      =      1089
Group variable
pairid                          Number of groups   =       267

R
-sq:  within  0.2208                         Obs per groupmin =         1
       between 
0.1570                                        avg =       4.1
       overall 
0.1428                                        max =         7

                                                F
(11,266)          =      6.06
corr
(u_iXb)  = -0.9014                        Prob F           =    0.0000

                               
(StdErradjusted for 267 clusters in pairid)
------------------------------------------------------------------------------
             |               
Robust
      lremit 
|      Coef.   StdErr.      t    P>|t|     [95ConfInterval]
-------------+----------------------------------------------------------------
       
lgdpc |   1.104068   .2582936     4.27   0.000     .5955077    1.612628
   lgdpc_hos 
|  -.7614625   .3678625    -2.07   0.039    -1.485755   -.0371698
      lcost2 
|  -.1180805   .0793946    -1.49   0.138    -.2744023    .0382413
     lmig_st 
|   .5051947   .1796623     2.81   0.005     .1514536    .8589359
        lexc 
|   1.283118   .3861076     3.32   0.001     .5229025    2.043334
             
|
        
year |
       
2012  |   -.077954   .0267472    -2.91   0.004    -.1306171   -.0252908
       2013  
|  -.1662693   .0760294    -2.19   0.030    -.3159652   -.0165734
       2014  
|  -.2275463   .0978052    -2.33   0.021    -.4201172   -.0349753
       2015  
|  -.0994765   .0704605    -1.41   0.159    -.2382079    .0392548
       2016  
|  -.2454423   .0879119    -2.79   0.006    -.4185339   -.0723506
       2017  
|  -.2453342   .1058131    -2.32   0.021     -.453672   -.0369964
             
|
       
_cons |  -5.906389   4.652194    -1.27   0.205     -15.0662     3.25342
-------------+----------------------------------------------------------------
     
sigma_u |   3.962099
     sigma_e 
|  .32225379
         rho 
|  .99342824   (fraction of variance due to u_i)
------------------------------------------------------------------------------