The data they use is usually publicly available, the models used by these must not be very secret. Is it not possible to hook this all up into a nice package, where I can go in and tune some knobs to my liking (there will always be knobs) to get a prediction on the inflation over the next three quarters.
Then, I can publicly claim, "Given this data, and this model, and my knob settings, here are my prediction." Then some other economist can come and dispute the data, model and the knob settings. They select a different data source, model and their own knobs.
Then three quarters later we check who made the right prediction.
Notice, I am not asking for the correct model of reality. Only a playground where people can argue using concrete data, models and knobs.