> But if the economists are fighting about what will happen to a particular macroeconomic variable, they are making a prediction even if it is a log_2(3) bit prediction [1]. There must be some math that is backing that. I want to see it explicitly put into a computational model that runs on live data

This is what (some) people in finance do: make models to predict things, because if something about the future can be predicted to a sufficient degree of accuracy, it's generally possible to make money from it. In economics, the incentives are slightly different; in academia, the incentives are to publish interesting/novel/topical papers, like with other social sciences, not necessarily to make repeatable predictions. In social science nobody gets punished for making an interesting model that hasn't been rigorously proven to make repeatable predictions, while in finance on average better models make more money and get rewarded more. But sharing an effective model means other people can use the predictions too, meaning you capture less value from the predictions yourself, so people with an effective model have an incentive not to share it