Previous work with survey data on inflationary expectations casts doubt on the Rational Expectations Hypothesis. In this paper, we develop a model of expectation formation where agents form their forecasts of inflation by selecting a predictor function from a set of costly alternatives whereby they may rationally choose a method other than the most accurate. We use this model to test whether survey data exhibit rationally heterogeneous expectations. Maximum likelihood is applied to a new discrete choice setting where the observed variable is continuous and the latent variable is discrete. The results show there is dynamic switching that depends on the relative mean squared errors of the predictors.

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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

We compare the performance of alternative recursive forecasting models. A simple constant gain algorithm, used widely in the learning literature, both forecasts well out of sample and also provides the best fit to the Survey of Professional Forecasters.JEL classification codes: E37, D84, D83.

This paper compares three reduced-form models of heterogeneity in survey inflation expectations. On the one hand, we specify two models of forecasting inflation based on limited information flows of the type developed in Mankiw and Reis [2002. Sticky information versus sticky prices: a proposal to replace the new Keynesian Phillips curve. Quarterly Journal of Economics 117(4), 1295-1328]. We present maximum likelihood results that suggests a sticky information model with a time-varying distribution structure is consistent with the Michigan survey of inflation expectations. We also compare these 'sticky information' models to the endogenous model uncertainty approach in Branch [2004. The theory of rationally heterogeneous expectations: evidence from survey data on inflation expectations. Economic Journal 114, 497]. Non-parametric evidence suggests that models which allow the degree of heterogeneity to change over time provide a better fit of the data. r