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isn't the entire market down today though? how can it be proven that his tweet impacted the price versus a broad market loss?

you can do this with a synthetic control. i did this at https://www.alexpghayes.com/blog/elon-musk-send-tweet/

Very nice little article. While my kind might not be the target audience would you mind adding a short ELI'mNotAnEconomist explanation?