I think it's very unlikely that we will see in psychology or economics any kind of progress like what we saw in physics. In physics anything new that we learn doesn't change the experiments at all, that is we can't ignore physical laws just because we are aware of them.
But in psychology or economics as soon as you learn something new, that new knowledge is going to be a new variable to account for, for example as soon as you are made aware of the Bystander effect[1] it is trivial to avoid it, but you can't really predict what will come out of it. You can as well find ways to game any economic prediction by being aware of it, I guess you can find stable models that sort of work until something like the 2008 financial crisis happens and they don't anymore.
So either the investigators stay out of the economy/society or they will mess with their own results by making them public.
[1] https://en.wikipedia.org/wiki/Bystander_effect