Inspecting the noisy mechanism: the stochastic growth model with partial information

We derive a framework (and provide a software toolkit) which allows the dynamic general equilibrium modeller to specify what variables are in households' information sets, and the degree to which these variables are measured with error. We apply this framework to a canonical real business cycle model and show that which variables are observable has a significant effect, both qualitatively and quantitatively, on the dynamics of the model. Specifically, we find (i) The standard decentralised equilibrium, with households only observing returns and not aggregate quantities, is not stable to arbitrarily small measurement error (ii) A stable solution does exist, but it is dramatically different from the full-information case (iii) Having aggregate output data, even if relatively noisy, brings the economy much closer to the full-information solution