Solving a system of nonlinear equations with summations

[Sarah Aaronson]

This is my first time posting in the forum, so my apologies if this question isn't clear enough or doesn't meet all the standards. I did read the advice on posting.

I want to solve the following equation (see attached image) in Stata for each w_j from j=1 to 188. I have data on L_{Fj}, d_{ij}, and L_{Ri} as well as the constant value for \varepsilon. My data is at the i, j level.

dest_nb_workers_pre is L_{Fj}
origin_nb_workers_pre is L_{Ri}
time_pre is d_{ij}

Any suggestions on what commands I should use or just what strategies in general? I aim to have a new variable (say, wages) with the w_j for each destination_id. Thanks for any help!

* Example generated by -dataex-. For more info, type help dataex
clear
input int(origin_id destination_id) long(dest_nb_workers_pre origin_nb_workers_pre) float time_pre
 11 1 11568 16923 12.509804
155 1 11568 10075  25.47222
 27 1 11568 29488 19.314816
119 1 11568  9281 26.979166
108 1 11568 35021  18.75926
161 1 11568  9769  25.40476
107 1 11568 33708 18.383333
  2 1 11568 25126  21.73684
136 1 11568 31699  19.12745
 87 1 11568 18090 30.285715
 79 1 11568 12699 32.433334
 39 1 11568 33048 15.880953
101 1 11568 20942 13.071428
143 1 11568 11053 25.142857
 36 1 11568 30324 11.254386
186 1 11568  8450  24.03333
134 1 11568  8053 21.666666
  3 1 11568 13570 20.203703
 68 1 11568 10037 33.696968
124 1 11568 12811  41.85417
125 1 11568 37678     21.75
 60 1 11568 22955  29.40476
 32 1 11568 15031      7.15
168 1 11568 13771   21.4375
 29 1 11568 48756 13.308642
 24 1 11568 20245 21.526316
129 1 11568 18135 19.210976
138 1 11568 38623 15.458427
113 1 11568 21499  20.17857
 95 1 11568 26565 21.145834
 16 1 11568 27891 14.953704
 91 1 11568 20309 26.083334
 83 1 11568 10129  31.59524
117 1 11568  6483      32.9
 22 1 11568 22016  15.50926
 23 1 11568 15647  19.61111
 70 1 11568 13890   27.6875
130 1 11568 24611  23.58974
170 1 11568 11920 29.020834
 76 1 11568 19319  30.79487
102 1 11568 31378 12.261905
 55 1 11568 11421 33.729168
 96 1 11568 28450 18.833334
140 1 11568 19779 30.641666
120 1 11568  7435 30.574074
 57 1 11568 18720  31.02778
 15 1 11568 22508 12.287828
 43 1 11568 18596 21.927084
183 1 11568  7033 22.366667
158 1 11568 28382     28.38
133 1 11568 13059  21.61111
152 1 11568 11078 26.291666
181 1 11568  7346 24.583334
 12 1 11568 34221 12.904762
 88 1 11568 33010  24.78125
 35 1 11568 28795  10.73077
180 1 11568  7636 28.166666
157 1 11568 23929     26.64
150 1 11568  7652  28.25904
 72 1 11568 19315 29.960945
 44 1 11568 11533  20.72222
182 1 11568  7307      33.5
 42 1 11568 36102  22.61111
 82 1 11568 11991 29.703703
 33 1 11568 18661      9.25
 46 1 11568 18178 11.766666
 38 1 11568 23380 16.461538
 89 1 11568 21118 27.166666
105 1 11568 17771    9.8125
144 1 11568  5836        26
 78 1 11568 19862    36.075
146 1 11568  8054 29.805555
148 1 11568  7251  29.72222
166 1 11568 10311  18.78833
 71 1 11568 14571 30.020834
126 1 11568 12807 18.958334
154 1 11568 17941  26.51282
 18 1 11568 23908  5.236111
 75 1 11568  9317 32.633335
  8 1 11568 11364 15.242424
128 1 11568 30389 18.759226
  7 1 11568 10443 19.020834
 25 1 11568  6855 13.962963
178 1 11568 12847 24.469696
 97 1 11568 18639 17.656862
  1 1 11568 11568         0
156 1 11568 23595  24.46667
141 1 11568 13920  26.39394
153 1 11568  9940  17.13889
167 1 11568 39253 19.731884
 14 1 11568 19615  5.569445
175 1 11568  8301 37.416668
122 1 11568 10140 32.541668
 99 1 11568 23426 14.309524
 41 1 11568 21956 18.255556
114 1 11568  9324 14.166667
110 1 11568 22293  22.19697
 34 1 11568  8062  9.595238
  5 1 11568  7015    19.875
151 1 11568  6818  25.90476
end