Intrinsic heterogeneity in expectation formation

Abstract

We introduce the concept of a Misspecification Equilibrium to dynamic macroeconomics. A Misspecification Equilibrium occurs in a stochastic process when agents forecast optimally given that they must choose from a list of misspecified econometric models. With appropriate restrictions on the asymptotic properties of the exogeneous process and on the feedback of expectations, the Misspecification Equilibrium will exhibit Intrinsic Heterogeneity. Intrinsic Heterogeneity is a Misspecification Equilibrium where all misspecified models receive positive weight in the distribution of predictors across agents. Interestingly, the existence of heterogeneity depends on the self-referential property of the model. Our derivation of heterogeneous expectations as the equilibrium outcome of a model is a departure from the previous literature which makes ad hoc assumptions about the degree of heterogeneity. JEL Classifications: C62; D83; D84; E30

Model uncertainty and endogenous volatility

“…This alternative approach, it is argued, is a reasonable description of agents' actual forecasting acumen because it assumes behavior consistent with econometric practice. Branch and Evans (2006a), though, note that with computational costs and degree of freedom limitations, econometricians often underparameterize their forecasting models. It has long been recognized that Vector Autoregressive (VAR) models have degrees of freedom limitations.…”

“…Motivated by the idea that cognitive and computing time constraints and degrees of freedom limitations lead agents to adopt parsimonious models, we impose that agents only incorporate a subset of these variables into their forecasting model. Following Branch and Evans (2006a), we require that these expectations are optimal linear projections given the underparameterization restriction and that agents only choose best performing statistical models. Despite the bounded rationality assumption, this remains in the spirit of Muth (1961) in the sense that for each statistical model the parameters are chosen optimally.…”

Learnability of Heterogeneous Misspecification Equilibrium

“…Branch and Evans (2006) imply that the learnability of the ME depends on the method for estimating the forecasting performance of the models. Branch and Evans (2007) show that multiple MEs may be learnable under least squares learning in a Lucas-type monetary model.…”

“…Thus, our results are directly applicable to the analysis of the learnability of a variety of linear macroeconomic models under 3 Brock and Hommes (1997) is the first study to investigate equilibria under the heterogeneity of agents choosing the best-performing models. Branch and Evans (2006) extend the model to the ME model where agents do not choose between a costly accurate forecast and a costless unsophisticated forecast, but choose between equally underparametrized costless models.…”

Top-Down versus Bottom-Up Macroeconomics

“…This kind of simple heuristic has often been used in the behavioural finance literature where agents are assumed to use fundamentalist and chartist rules (see Brock and Hommes(1997), Branch and Evans(2006), De Grauwe and Grimaldi (2006)). It is probably the simplest possible assumption one can make about how agents, which experience cognitive limitations, use rules that embody limited knowledge to guide their behavior.…”