The idea in those articles is to translate standard statistical approaches for historical cases.
I still think that is the right basic approach. However, to be honest the implementation isn't that great, and I'd do thing rather differently if I were doing something similar now.
No problem - happy to discuss what specifically you could do - but it depends a lot on what kinds of other information you have (e.g. about population occupational distributions) and what assumptions you want to make. Maybe here is not the ideal forum for that!
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About 20-years ago I wrote a couple of articles attempting to translate those ideas to historical cases:
https://direct.mit.edu/jinh/article-abstract/36/2/209/48104/Propensity-Score-Methods-and-the-Lenin-School
I still think that is the right basic approach. However, to be honest the implementation isn't that great, and I'd do thing rather differently if I were doing something similar now.