Invertible and non-invertible information sets in linear rational expectations models

Abstract

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Sequential Action and Beliefs Under Partially Observable DSGE Environments

“…And thereby, the solution algorithm proposed here does not require that the entire perceived and actual laws of motion, both predictable parts and residuals, are identical at a fixed point. With respect to the filtering properties, the present paper precisely replicates those obtained by Svensson andWoodford (2003, 2004) and Baxter, Graham, and Wright (2011), since the baseline reasoning in their works and the present paper is the same in a Bayesian direction and the environments considered are all linear and Gaussian. So it is not surprising to see a modification of the Kalman filter from both their works and here, because it is already known that the Kalman filter is optimal under linear environments with the Gaussian distribution.…”

“…9 Even when ry < r θ but provided that ry = rz, the state may be 'asymptotically invertible' from the observables (in the sense used by Baxter, Graham, and Wright, 2011) under some regularity conditions.…”

Consumer misperceptions, uncertain fundamentals, and the business cycle

“…Introducing imperfect information necessitates an adjustment of solution methods as proposed in Baxter et al (2011). In this case private agents cannot directly observe the components of labor productivity, i.e.x t and z t .…”

“…The matrices A, B, C and D where already introduced in the filtering problem (Appendix A). Given the contemporaneous estimates about the unobserved state ξ t−1|t−1 and the linearity of the model, certainty equivalence applies (see Baxter et al, 2011) and hence…”

Intersectoral linkages, diverse information, and aggregate dynamics

“…Our results also contrast with the analogous new-Keynesian literature, which argues that strategic interactions among information constrained agents have important consequences for aggregate dynamics. A relatively small literature using more neoclassical "island" economies, such as Baxter et al (2011) and Acharya (2013), also finds important consequences of similar information frictions.…”