Should-read: George W. Evans and Bruce McGough: Equilibrium selection, observability and backward-stable solutions

Should-Read: One of the several disastrous consequences of Robert Lucas was the severe downweighting of the “disequilibrium foundations of equilibrium” agenda of Frank Fisher and company. But George Evans and company have revived it: George W. Evans and Bruce McGough: Equilibrium Selection, Observability and Backward-stable Solutions: “We examine robustness of stability under learning to observability of exogenous shocks…

The minimal state variable solution is robustly stable under learning provided the expectational feedback is not both positive and large, while the nonfundamental solution is never robustly stable…. We examine the concerns raised in Cochrane (2009, 2011, 2017) about the New Keynesian model. These concerns arise in large part by his adoption of RE as a modeling primitive. We view RE as more naturally arising as an emergent outcome of an adaptive learning process, and we find that by modeling agents as adaptive learners Cochrane’s concerns vanish….

Under adaptive learning agents are assumed to form expectations using forecasting models, which they update over time in response to observed data. There is a well-developed theory that allows the researcher to assess whether agents, using least-squares updating of the coefficients of their forecasting model, will come to behave in a manner that is asymptotically consistent with RE, i.e. whether the rational expectations equilibrium (REE) is stable under learning: see Marcet and Sargent (1989) and Evans and Honkapohja (2001)….

The “minimal state variable” (MSV) solution, also referred to as the backward- stable solution… is always stationary… a “non-fundamental” (NF) solution, which may or may not be stationary. We then turn to stability under learning. In a model with observable shocks, McCallum (2009a) showed that determinacy implies that only the MSV solution is stable under learning. However, Cochrane (2009, 2011) argued that McCallum’s stability results hinged on observability of these shocks…. The MSV solution is robustly stable under learning, provided only that the positive feedback from expectations is not too large. In contrast the NF solution is never robustly stable under learning…