Hello everyone,
for my Master’s thesis, I am trying to assess the impact of Non-Tariff measures on participation in global value chain (GVC) for a sample of 59 countries, over the years 2005-2015. To do so, I am planning to employ the widely used PPML model proposed in “The Log of Gravity" by Joao Santos Silva and Silvana Tenreyro (2006). Also, I would include time fixed-effects and my control variables would be lagged by one year to avoid simultaneity bias.
The question is how to deal with missing values (in both the dependent and control variables) in this context. I know the best techniques to accomplish that are usually Multiple Imputation and Maximum Likelihood Estimation. However, since they rely on strong assumptions (especially MI), I am not sure they would be suitable for the model I want to employ.
In case it may be useful, I attach a sample of my data:

Code:
* Example generated by -dataex-. For more info, type help dataex
clear
input str19 cou double year float(backward_industry forward_industry regulatory_distance) double ind_internet_users float governance_index double(education_index indt_tariff_all) float output_perworker
"ARG" 2005 13.27 14.41 .13480131 17.72058337  -1.298498 .751 11.74  48727.75
"ARG" 2006 13.76 14.76 .14648408  20.9272021 -1.2845232 .795 11.92  50906.49
"ARG" 2007 14.56 13.57 .13978474 25.94663294 -1.2868896 .796 12.17   54451.8
"ARG" 2008 14.93 13.03 .13534042 28.11262348 -1.4002676 .801 10.43  56200.43
"ARG" 2009 10.87  12.4 .13127346          34  -1.462097  .81 12.21   52314.1
"ARG" 2010 13.37 13.91 .12898874          45 -1.3469304 .818 12.52  56899.51
"ARG" 2011 14.39 14.42 .12866293          51 -1.3055593 .824 12.03   58957.2
"ARG" 2012 12.25 14.37 .13168013        55.8 -1.4430058 .822 11.92  57764.56
"ARG" 2013 12.76 12.61 .12956065        59.9 -1.4728905 .822 11.01  58618.79
"ARG" 2014 11.31 12.66 .12827909        64.7 -1.5809788 .826  11.5   57048.5
"ARG" 2015  8.84  12.6 .12865551 68.04306411 -1.4688578 .832 11.53  57786.83
"AUS" 2005 11.56 24.46 .16130497          63   1.130881 .873   3.3  87497.04
"AUS" 2006 12.96 27.37 .15125994          66  1.1455371 .876  4.09  87455.41
"AUS" 2007 12.41 27.97 .14440013       69.45  1.1747793 .879  4.26  87915.71
"AUS" 2008 12.53 30.12 .14052497       71.67  1.1908607 .914  3.88  88668.58
"AUS" 2009 11.71 23.97 .13581423       74.25  1.1608332 .916  3.96  89869.48
"AUS" 2010 10.78 28.18 .13359624          76  1.1731899 .919  3.61     89581
"AUS" 2011 11.79 29.99 .13134517 79.48769771  1.1753942 .922  2.47  90070.73
"AUS" 2012 11.76  27.7 .12964514          79  1.1649826 .928  2.58     92605
"AUS" 2013 11.25 27.28 .12634803 83.45349717   1.149351 .906  2.63  94264.84
"AUS" 2014 12.54  26.3 .12659031          84   1.237604 .908  2.69  95982.16
"AUS" 2015 12.86  23.3 .13436815 84.56051491  1.1575513 .918  2.72   96255.5
"AUT" 2005 33.45 15.55         .          58  1.1933757 .749  3.54 107436.75
"AUT" 2006 34.65 16.09         .        63.6   1.256133 .759  3.33 109263.92
"AUT" 2007 34.81 16.43         .       69.37  1.3186415 .806  3.23  110463.5
"AUT" 2008 35.63 16.46         .       72.87  1.2495222 .809  2.99  109966.3
"AUT" 2009 31.22 14.97  .1709518       73.45   1.104642 .819  3.23 105829.32
"AUT" 2010 36.48 16.33 .17025463       75.17  1.1341419 .837  3.08 106515.04
"AUT" 2011 38.59 16.69         .  78.7399931  1.0636568 .838     3 108410.82
"AUT" 2012 38.42 17.07  .1927023 80.02999392  1.1140922 .841  2.84 108173.76
"AUT" 2013    38 17.01 .20606017     80.6188  1.1291875 .833  2.95  107663.9
"AUT" 2014  37.2 17.01  .2025728 80.99582496  1.1652439 .854  3.07  108348.5
"AUT" 2015 34.49  16.7 .19996904 83.94014193  1.0770923 .861  3.09  108804.6
"BEL" 2005 39.14 14.01         .       55.82   .7303864 .856  3.54 114243.72
"BEL" 2006 40.98 14.44         .       59.72   .7130213 .869  3.33 116406.07
"BEL" 2007 41.82 14.51         .       64.44   .7566316 .871  3.23 117432.25
"BEL" 2008 44.56 14.29         .          66   .7131057 .865  2.99 116316.22
"BEL" 2009 40.18 12.42  .1709518          70   .7802215  .87  3.23 114651.14
"BEL" 2010 44.18 13.99 .17025463          75   .7913547 .871  3.08  116248.9
"BEL" 2011 47.88 14.64         .   81.609996   .8254853 .873     3 117962.47
"BEL" 2012 48.48 14.26  .1927023 80.71999055   .8231871 .874  2.84 118462.27
"BEL" 2013 47.69 14.12 .20606017     82.1702   .8500193  .88  2.95 118647.02
"BEL" 2014 46.84 13.88  .2025728          85   .8134795 .883  3.07 119828.45
"BEL" 2015 44.35 13.17 .19996904 85.05294175   .8030965  .89  3.09  121767.4
"BGR" 2005 44.66  9.42         .       19.97  -.7154181 .715  3.54  36530.25
"BGR" 2006 49.67 11.39         .       27.09  -.7713166 .727  3.33  37324.45
"BGR" 2007 50.75 11.19         .       33.64  -.7347545 .743  3.23   38062.3
"BGR" 2008  53.5 10.75         .       39.67  -.7868066 .747  2.99  39129.32
"BGR" 2009  42.4 10.13  .1709518          45   -.706669 .752  3.23  39115.96
"BGR" 2010 44.32 11.22 .17025463       46.23  -.7361029 .761  3.08  41866.05
end
where backward_industry (backward participation in GVC) and forward_industry (forward participation in GVC) are my dependent variables. Regulatory_distance is an index that goes from 0 to 1, and in which for values closer to 1 we have a higher average distance of import regulations between a country and all its trade partner.

Thank you very much to whoever is willing to give his/her contribution to the community on this topic.
Best regards

Alessio Lombini