Refining linear rational expectations models and equilibria

This paper develops the case for forward convergence as a model refinement scheme for linear rational expectations models and an associated no-bubble condition as a solution selection criterion. We relate these two concepts to determinacy and characterize the complete set of economically relevant rational expectations solutions to the linear rational expectations models under determinacy and indeterminacy. Our results show (1) why a determinate solution is economically cogent in most, but not all, cases, and (2) that those models that are not forward-convergent have no economically relevant solutions.     

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.     

Soft landing in a Markov-switching economy

We analyse the monetary policy implications of boom–bust cycles in asset prices using a Markov-switching rational expectations model. In our simulations, when a bubble bursts, the Taylor rule fails to achieve a soft landing, contrary to the optimal policy.     

Model reference adaptive expectations in Markov-switching economies

This paper offers a theory of model reference adaptive beliefs as a selection device in Markov-switching economies under equilibrium indeterminacy. Consistent with the classical rational choice paradigm, our theory requires that endogenous expectations be replaced with a general-measurable function of the observable states of the model, to be determined optimally. This forecasting function is derived as the regime-independent feedback control minimizing the mean-square deviation of the equilibrium path from the corresponding perfect-foresight state motion (the reference model). We show that model reference adaptive expectations always generate a rational expectations equilibrium, irrespective of the presence of nonlinearities and/or imperfect information. Under equilibrium indeterminacy, this forecasting mechanism enforces the unique mean-square stable solution producing nearly perfect-foresight dynamics.     

WHEN DOES DETERMINACY IMPLY EXPECTATIONAL STABILITY?

Since the introduction of rational expectations, there have been issues with multiple equilibria and equilibrium selection. We study the connections between determinacy of rational expectations equilibrium and learnability of that equilibrium in a general class of purely forward‐looking models. Our framework is sufficiently flexible to encompass lags in agents' information and either finite horizon or infinite horizon approaches to learning. We are able to isolate conditions under which determinacy does and does not imply learnability and also conditions under which long‐horizon forecasts make a clear difference for learnability. Finally, we apply our result to a relatively general New Keynesian model.     

Saddlepath learning

Saddlepath learning occurs when agents learn adaptively using a perceived law of motion that has the same form as the saddlepath relationship in rational expectations equilibrium. Under saddlepath learning, we obtain a completely general relationship between determinacy and e-stability, and generalise minimum state variable results previously derived only under full information. When the system is determinate, we show that a learning process based on the saddlepath is always e-stable. When the system is indeterminate, we find there is a unique MSV solution that is iteratively e-stable. However, in this case there is a sunspot solution that is learnable as well. We conclude by demonstrating that our results hold for any information set.     

Business cycle amplification with heterogeneous expectations

This paper studies the implications for business cycle dynamics of heterogeneous expectations in a stochastic growth model. The assumption of homogeneous, rational expectations is replaced with a heterogeneous expectations model where a fraction of agents hold rational expectations and the remaining fraction adopt parsimonious forecasting models that are, in equilibrium, optimal within a restricted class. Our approach nests the literature on rational expectations in business cycle models with a recent approach based on adaptive learning. We demonstrate that (i.) heterogeneous expectations can lead to substantial improvement in the internal propagation of equilibrium business cycle models and (ii.) the internal propagation depends on the degree of heterogeneity. A calibrated model with heterogeneity provides a closer fit to business cycle data than its representative agent, rational expectations counterpart.     

Closed-form likelihood function of Markov-switching models

For a class of Markov-switching models, the likelihood function and inferred state distributions for a given sample are shown to have closed-form representations under a set of sufficient conditions. Based on these results, it is demonstrated that the closed-form partial derivatives (when exist) of the likelihood function can be readily found. These results may be used to improve the efficiency of numerical optimization techniques used for estimating the Markov-switching models.     

News shocks or parametric indeterminacy? An observational equivalence result in linear rational expectations models

This paper studies identification in linear rational expectations models with news shocks. We show that news-driven models and indeterminate equilibrium economies with i.i.d. fundamentals are observationally equivalent. This finding calls for carefully designing empirical investigations of news shocks in estimated DSGE models.     

DOES NEAR‐RATIONALITY MATTER IN FIRST‐ORDER APPROXIMATE SOLUTIONS? A PERTURBATION APPROACH

This paper studies first‐order approximate solutions to near‐rational dynamic equilibrium models. Under near‐rationality, agents' subjective beliefs are distorted away from rational expectations via a change of measure process which fulfills some regularity conditions. In most applications, the beliefs distortion process is also directly observed by (a subset of) the decision‐makers – e.g., ambiguity‐averse households or policy‐makers with a concern for robustness – and therefore included into their optimization problems. We investigate conditions for existence and local uniqueness of solutions under endogenous distortions, as well as the relation with their rational expectations counterparts. We show that linearly perturbed solutions may well be affected by the presence of distorted beliefs, depending on the underlying model economy. In particular, while directly affecting first‐order decision rules, near‐rationality may also induce failure of the certainty equivalence principle. Moreover, the martingale representation of distorted beliefs might prove non‐unique, pointing to a subtle form of equilibrium indeterminacy.     

Rational expectations for large CGE models: A practical algorithm and a policy application

We describe a simple iterative method for solving large dynamic CGE models under rational expectations. Details are given for Australia's MONASH model but the approach applies to a wide range of CGE models. The method is automated in the RunMONASH Windows software, putting CGE modelling under rational expectations within the reach of non-specialist modellers. We provide an illustrative application in which MONASH results under rational expectations are compared with results under static expectations. The application and supporting software can be downloaded. Results from the application are interpreted in terms of elementary economic mechanisms.     

Interest-rate policy and rational expectations

The choice of monetary instrument under rational expectations is discussed in a general equilibrium model for the financial sector. It is shown that a supply rule leads to indeterminate asset prices, whereas the prices are determinate under an appropriately formulated interest-rate policy.     

Price level determinacy and the choice of policy targets under rational expectations

We show that in a conventional macro model with rational expectations, the government can use monetary policy to peg real interest rates, and still attain a determinate price level provided it also pegs some nominal policy variable, e.g., nominal expenditures.     

Terminal conditions as a means of ensuring unique solutions for rational expectations models with forward expectations

Terminal conditions are imposed on rational expectations models as a means of finding a unique solution among a continuum of potential solutions. It is argued that using terminal conditions is superior to invoking stability. The method can be applied to non-linear as well as linear systems.     

Heterogeneous learning

There is by now a large literature characterising conditions under which learning schemes converge to rational expectations equilibria (REEs). It has been claimed that these results depend on the assumption of homogeneous agents and homogeneous learning. This paper analyses the stability of REEs under heterogeneous adaptive learning, for the class of self-referential linear stochastic models. Agents may differ in their initial perceptions about the evolution of the economy, the degrees of inertia in revising their expectations, or the learning rules they use. General conditions are provided for local stability of an REE. In general, it is not possible to show that stability under homogeneous learning implies stability under heterogeneous learning. To illustrate how to apply the results, several examples are provided.     

Encompassing and rational expectations: How sequential corroboration can imply refutation

Even though pieces of empirical evidence individually may corroborate an economic theory, their joint existence may refute that same theory. Testing of rational expectations models provides a concrete illustration of this principle. Surprisingly, empirical refutation of a rational expectations model may occur without having to estimate that model, and the refutation may be for a large class of expectations-based models and not just for a particular model specification. Narrow money demand in the United Kingdom illustrates such refutation. The general proposition concerning corroboration and refutation strongly favors the building of empirical models that are consistent with all available evidence. First version received: July 1994/final version received: July 1997     

Rational expectations and M2 demand

This essay expands on existing studies of M2 money demand. It differs in that it applies a rational expectations approach to an adaptive expectation model. Unlike the adaptive expectations models, the author includes an explanatory variable for expectations of future inflation. The expectation variables used are: the actual inflation rate (t + 1) and the Livingston Survey from the Philadelphia Fed. By using the different measures of expectations the author is able to compare several adaptive expectations models that appear in the literature and the rational expectations models for fit and forecast ability. The empirical results are such that the importance of including the rational expectations variable is evident even though the overall fit of the equation is comparable to one of the existing adaptive expectations models.     

Mixed-frequency VAR models with Markov-switching dynamics

This paper extends the Markov-switching vector autoregressive models to accommodate both the typical lack of synchronicity that characterizes the real-time daily flow of macroeconomic information and economic indicators sampled at different frequencies. The results of the empirical application suggest that the model is able to capture the features of the NBER business cycle chronology very accurately.     

A Markov analysis of social learning and adaptation

A number of recent contributions to the literature have modelled social learning and adaptation in an economic context. Understanding the processes driving these models is important in order to explain and predict the behaviour of the economy. In this paper, we analyze the economic applications for a class of adaptive learning models with bounded rational agents. The dynamics of these economies can be thought of as arising from discrete-time Markov chains. In particular, conditions for uniqueness of equilibria, convergence and stability in the economic systems follow from the accessibility and communication structures of these Markov chains. We establish a correspondence between absorbing states of the Markov chains and economic equilibria, whether stable or unstable, and develop theorems giving conditions for absorption and recurrence. Furthermore, we develop practical applications of these theorems using a cobweb model. We use a genetic algorithm, operating under election, as an example of a well known adaptive learning process.