In Nitzens & Bichlers Capital as Power, they quote from Weinbergs Dreams of a Final Theory:
I pointed out [to Einstein] that we cannot, in fact, observe such a path [of an electron in an atom]; what we actually record are frequencies of the light radiated by the atom, intensities and transition probabilities, but no actual path. And since it is but rational to introduce into a theory only such quantities as can be directly observed, the concept of electron paths ought not, in fact, to figure in the theory.
To my astonishment, Einstein was not at all satisfied with this argument. He thought that every theory in fact contains unobservable quantities. The principle of employing only observable quantities simply cannot be consistently carried out. And when I objected that in this I had merely been applying the type of philosophy that he, too, had made the basis of his special theory of relativity, he answered simply: ‘Perhaps I did use such philosophy earlier, and also wrote it, but it is nonsense all the same’.
Contra Einstein is there a theory that has only observable quantities?
It may be that Einstein is thinking of only fundamental theories - in which case the answer must be a no. Of course numbers are unobservable, so we can't allow any mathematical theories. Nitzen & Bichler also rule out classical & marxist economics.