DP8959 Some Properties of Autocoherent Models
An autocoherent model is a model which is validated by the data if people use it to form their expectations. A structural model may be incorrect but autocoherent, thus supporting a self-confirming equilibrium. This paper explores some mathematical properties of autocoherent models. The first part clarifies the relationship between autocoherence and identification.It es- tablishes sufficient conditions under which an expert constraints is compelled to reveal the true value of some parameter. These conditions are related to the traditional notion of identification, but it must be amended to reflect the performativity of the perceived model and the fact that identification is different depending on the econometrician's assumptions about the perceived model's validity. The second part clearly spells out the conditions for an autocoherent model equilibrium to arise in the linear/Gaussian case, and provides an equivalent characterization based on an 11interpretation11. That is, an autocoherent model equilibrium can be constructed on the basis of a linear transformation which maps the actual realization of the shocks to their 11interpreted counterpart11, defined as the value of the shocks consistent with the observed outcomes on the basis of the (incorrect) perceived model. If such a transformation exists then the perceived model can support a self-confirming equilibrium.