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> If you want to estimate causal effects you need a randomly assigned treatment. When studying the effects of wealth a lottery gives you exactly that.

It gives you exactly the opposite of that. How many financially prudent individuals do you know who buy lottery tickets? It is not a representative sample.

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Not a good criticism of this paper in particular.

Read the details of the “save to win” program in the Data section. Save to win was not a conventional lottery program. (Two more conventional lottery programs are also included for which your criticism is more accurate.)

Unless I misunderstand, all three lottery programs studied are voluntary. Kombi subscription lottery, Triss scratch and win, and Prize Linked Savings Account (PLSA) are all voluntary, and therefore not representative of the general population.

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