The Effects of Permanent and Transitory Shocks under Imperfect Information

We study an economic environment affected by shocks that may be either permanent or transitory in nature. Contrary to the standard perfect information setup, we assume that households cannot distinguish between the two types of shocks. We describe how to solve the model under this imperfect information assumption in the context of the one-sector neoclassical model. We show that the solution involves a recasting of the driving process in terms of estimates of the exogenous states and forecast errors made by households rather than the states themselves. Given observations on the driving process, the signal extraction problem used to obtain these estimates and forecast errors may be solved independently of the calculation determining the stability of the model's dynamics. Moreover, standard linear rational expectations toolkits still apply. Given that information available to households is imperfect, the paper highlights the possibility of real economic responses to errors made in reading the economic environment rather than to actual changes in fundamentals.