I haven’t seen anything along these lines, but it would certainly be interesting if there were theoretical reasons to think that prediction variance should increase exponentially.
Ultimately though I do think this is an empirical question—something I’m hoping to work on in the future. One new relevant piece of empirical work is Tetlock’s long-run forecasting results that came out last year: https://onlinelibrary.wiley.com/doi/abs/10.1002/ffo2.157
I haven’t seen anything along these lines, but it would certainly be interesting if there were theoretical reasons to think that prediction variance should increase exponentially.
Ultimately though I do think this is an empirical question—something I’m hoping to work on in the future. One new relevant piece of empirical work is Tetlock’s long-run forecasting results that came out last year: https://onlinelibrary.wiley.com/doi/abs/10.1002/ffo2.157