I consider a real business cycle model in which agents have private information about the i.i.d. realizations of their value of leisure. For the case of logarithmic preferences I provide an analytical characterization of the solution to the associated mechanism design problem. Moreover, I show a striking irrelevance result: That the stationary behavior of all aggregate variables are exactly the same in the private information economy as in the full information case. Numerical simulations indicate that the irrelevance result approximately holds for more general CRRA preferences.