George W. Evans

Monetary Policy, Expectations and Commitment

Commitment in monetary policy leads to equilibria that are superior to those from optimal discretionary policies. A number of interest-rate reaction functions and instrument rules have been proposed to implement or approximate commitment policy. We assess these rules in terms of whether they lead to a rational expectations equilibrium that is both locally determinate and stable under adaptive learning by private agents. A reaction function that appropriately depends explicitly on private sector expectations performs particularly well on both counts.

Adaptive Learning and Monetary Policy Design

We review the recent work on interest rate setting, which emphasizes the desirability of designing policy to ensure stability under private agent learning. Appropriately designed expectations based rules can yield optimal rational expectations equilibria that are both determinate and stable under learning. Some simple instrument rules and approximate targeting rules also have these desirable properties. We take up various complications in implementing optimal policy, including the observability of key variables and the required knowledge of structural parameters. An additional issue that we take up concerns the implications of expectation shocks not arising from transitional learning effects.

Intrinsic heterogeneity in expectation formation

We introduce the concept of Misspecification Equilibrium to dynamic macroeconomics. Agents choose between a list of misspecified econometric models and base their selection on relative forecast performance. A Misspecification Equilibrium is a stochastic process in which agents forecast optimally given their choices, with forecast model parameters and predictor proportions endogenously determined. Under appropriate conditions, the Misspecification Equilibrium will exhibit Intrinsic Heterogeneity, in which all predictors are used at all times, even in the neoclassical limit in which only the most successful predictors are used. This equilibrium is attainable under least-squares learning and dynamic predictor selection based on average profits.

Expectational Stability and the Multiple Equilibria Problem in Linear Rational Expectations Models

Linear models involving expectations of future endogenous variables generally have multiple rational expectations equilibria. This paper investigates the stability of solutions in the disequilibrium sense of whether, given a small deviation of expectations functions from some rational expectations equilibrium, the system returns to that solution under a natural revision rule. Weak and strong local stability are distinguished. Stability conditions are calculated for a simple general linear model and applied to two macroeconomic examples. In some cases there is a unique stable equilibrium. In other cases a continuum of equilibria forms a weakly but not strongly stable class.

The fragility of sunspots and bubbles

Abstract Expectational stability (E-stability) is used to examine the multiplicity of solutions in a range of rational expectations models of interest, including Muths inventory model and an overlapping generations model. In these model it is found that sunspot and other ‘rational bubble’ solutions are either E-unstable or weakly but not strongly E-stable.

Information, forecasts, and measurement of the business cycle☆

The Beveridge-Nelson (BN) technique provides a forecast-based method of decomposing a variable such as output, into trend and cycle when the variable is integrated of order one (I (1)). This paper considers the multivariate generalization of the BN decomposition when the information set includes other I (1) and/or stationary variables. We show that the relative importance of the cyclical component depends on the information set, and in particular that multivariate BN decompositions necessarily ascribe more importance to the cyclical component than does the univariate decomposition, provided the information set includes a variable which Granger-causes output. We illustrate the results for post-war data for the United States. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

Economic Dynamics with Learning: New Stability Results

Drawing upon recent contributions in the statistical literature, we present new results on the convergence of recursive, stochastic algorithms which can be applied to economic models with learning and which generalize previous results. The formal results provide probability bounds for convergence which can be used to describe the local stability under learning of rational expectations equilibria in stochastic models. Economic examples include local stability in a multivariate linear model with multiple equilibria and global convergence in a model with a unique equilibrium.

Expectations, learning and monetary policy: an overview of recent research

Expectations about the future are central for determination of current macroeconomic outcomes and the formulation of monetary policy. Recent literature has explored ways for supplementing the benchmark of rational expectations with explicit models of expectations formation that rely on econometric learning. Some apparently natural policy rules turn out to imply expectational instability of private agents’ learning. We use the standard New Keynesian model to illustrate this problem and survey the key results about interest-rate rules that deliver both uniqueness and stability of equilibrium under econometric learning. We then consider some practical concerns such as measurement errors in private expectations, observability of variables and learning of structural parameters required for policy. We also discuss some recent applications including policy design under perpetual learning, estimated models with learning, recurrent hyperinflations, and macroeconomic policy to combat liquidity traps and deflation.

Selection criteria for models with non-uniqueness

Abstract Three objections are considered to the use of McCallums rules for picking the minimal state set solution in rational expectations models with multiple equilibria. It is shown that these difficulties can be resolved using the concept of expectational stability as a selection criterion.

Local Convergence of Recursive Learning to Steady States and Cycles in Stochastic Nonlinear Models

We examine a recursive algorithm for learning steady states and cycles in stochastic nonlinear models. Necessary and sufficient conditions for local convergence are shown to be equivalent to easily computable expectational-stability conditions. These conditions are affected by the distribution of the random shocks. For the case of small noise it is shown that stochastic cycles exist near nonstochastic ones and that a projection facility in the algorithm is not required for convergence with probability 1 to stable steady states and cycles. The results are applied to an overlapping generations model with productivity shocks.