News Shocks or Correlated Sunspots? An Observational Equivalence Result in Linear Rational Expectations Model

This paper studies identification of linear rational expectations models under news shocks. Exploiting the general martingale difference solution approach, we show that news shocks models are observationally equivalent to a class of indeterminate equilibrium frameworks which are subject only, though arbitrarily, to i.i.d. fundamental shocks. The equivalent models are characterized by a lagged expectations structure, which arises typically when choice variables are predetermined or rather based on past information with respect to current observables. This particular feature creates room for serially correlated sunspot variables to arise in equilibrium reduced forms, whose dynamics can be equivalently induced by news shocks processes. This finding, which is inherent to the rational expectations theoretical construct, calls for carefully designing empirical investigations of news shocks in estimated DSGE models.