Unique Rational Expectations Equilibrium Research Articles

Monetary Policy, Determinacy, and Learnability in the Open Economy

We study how determinacy and learnability of global rational expectations equilibrium may be affected by monetary policy in a simple, two country, new Keynesian framework. The two blocks may be viewed as the U.S. and Europe, or as regions within the euro zone. We seek to understand how monetary policy choices may interact across borders to help or hinder the creation of a unique rational expectations equilibrium worldwide which can be learned by market participants. We study cases in which optimal policies are being pursued country by country as well as some forms of cooperation. We find that open economy considerations may alter conditions for determinacy and learnability relative to closed economy analyses, and that new concerns can arise in the analysis of classic topics such as the desirability of exchange rate targeting and monetary policy cooperation.

Monetary Policy and Fiscal Rules

This paper studies the performance of monetary policy under alternative fiscal regimes in a dynamic New Keynesian optimizing general equilibrium model with wealth effects. The interactions between fiscal policy and interest rate rules are shown to have relevant implications for the existence of a unique rational expectations equilibrium. When calibrated to Euro Area quarterly data, the model simulation results show that the preferred monetary-fiscal regime for inflation stabilization consists of a generalized Taylor rule with a low degree of inertia coupled with a public debt-GDP ratio targeting rule.

Switching Regimes in the Term Structure of Interest Rates during U.S. Post-War: A Case for the Lucas Proof Equilibrium?

Farmer (1991) suggests that in a model in which there are multiple rational expectations (RE) equilibria agents may find it useful to coordinate their expectations in a unique RE equilibrium which is immune to the Lucas Critique. In this paper, we evaluate Lucas proof (LP) equilibrium performance in the context of the term structure of interest rates model by using post-war US data. Estimation results show that LP equilibrium exhibits some important features of the data that are not reproduced by the fundamental equilibrium. For instance, the short rate behaves as a random walk in a regime characterized by low conditional volatility, whereas the term spread Granger-causes changes in the short-rate in periods characterized by high conditional volatility.

An equilibrium analysis of information aggregation and fluctuations in markets with discrete decisions

This paper shows how the interaction between decentralized information gathering and discreteness of investment decisions at the individual level can generate random fluctuations in aggregate investment that involve occasionally large allocation errors. This interaction is illustrated in a model in which private information is costly to acquire and prices reveal information. The unique rational expectations equilibrium outcome of the model is shown to always be noisy and characterized by investment levels which may be high simply because uninformed investors are buying under the impression that the high price is a signal of good investment opportunities.

Introduction: Recent Developments in Monetary Macroeconomics

IntroductionRecent Developments in Monetary Macroeconomics David Altig The contents of this volume hardly require explanation beyond its title: "Recent Developments in Monetary Macroeconomics." Our intent for the conference was to collect a set of papers reflecting the cutting edge of applied monetary macroeconomics. As befitting such an ambitious-sounding goal, the contributions are wide ranging. For purposes of this brief introduction, however, we might organize the papers as answers to three questions. (1) What is the "optimal" Taylor rule? (2) Are "New Keynesian" or "New Neoclassical Synthesis" models the final word on the monetary transmission mechanism? (3) Is there a role for money in the conduct of monetary policy? What is the "Optimal" Taylor Rule The inclusion of the Taylor rule issue is almost a prerequisite for any collection of papers purporting to survey recent developments in monetary macroeconomics. In policy discussions, the Taylor rule is ubiquitous, and it is currently the choice among alternative specifications of central bank behavior. More precisely, perhaps, the general form of the Taylor rule is the choice, as it has come to represent the general class of equations that relate the federal funds rate to some measure of an output gap and inflation rate. There is substantially less unanimity about whether output gaps and inflation rates should be past, present, or (expected) future values, whether past values of the funds rate need to be included, and what are the appropriate magnitudes of the responses to each of these measures. Marc Giannoni and Michael Woodford offer the natural approach to addressing the dispute: find the representation that is optimal within the framework being employed for policy analysis. The model in question here is essentially a derivative of the "New Neoclassical Synthesis" class of models that are currently the workhorses of most monetary policy analyses among academic and central bank staffs alike. Their approach to discovering the optimal policy within this structure has the flavor of [End Page 1039] the "Ramsey problem" familiar from optimal tax policy, although with the strong requirement that the derived policy rule be "robustly optimal": it must support the optimal equilibrium no matter what the distribution of disturbances the model policymakers face. Giannoni and Woodford offer two essential lessons. First, whether optimal policy incorporates forecasts of future price-level growth or output gaps depend critically on the dynamics of the inflation rate. If the adjustment of the price-level to shocks is inertial, then optimal policy necessarily depends on forecasts of future inflation. Second, the response of the funds rate to its own past is inertial. In fact, it is super-inertial, meaning that (all else equal), the contemporaneous funds rate responds more than one-for-one with the lagged value of the funds rate (and lagged changes in the rate). The proposition that monetary authorities ought to aggressively respond to lagged values of the funds rate also arises in the papers by Jess Benhabib, Stephanie Schmitt-Grohé, and Martín Uribe, and George Evans and Seppo Honkapohja. In the latter case, the authors consolidate and expand on their well-known work on learning dynamics. A central contribution of the work presented in this article is the notion that convergence to a unique rational expectations equilibrium under learning, as well as the stability of that equilibrium, serves as basis for the choice (or rejection) of an optimal policy formulation. An apparent lesson from Evans and Honkapohja's analysis is that the learnability criterion prescribes a policy rule that differs in some important ways from the conventional wisdom coming from analyses that invoke the Taylor rule in a pure rational expectations environment. In particular, they conclude that the optimal policy rule in the environment they consider requires the monetary authority to respond directly to private-sector expectations. The environment they consider is essentially the same as in Giannoni and Woodford, with the exception of the central bank's assumed loss function: Giannoni and Woodford assume a preference for interest rate smoothing, Evans and Honkapohja do not. In his comments, John Duffy points out that the introduction of interest-smoothing motive yields an optimal policy rule under learning that is much closer to the conventional view. In particular, it does not require...

Does the Lucas critique apply during hyperinflation?: empirical evidence from four hyperinflationary episodes

Farmer (Review of Economic Studies, 58, 321–32, 1991) suggests that in a model in which there are multiple rational expectations equilibria agents may find it useful to coordinate their expectations in a unique rational expectations equilibrium which is supported by a self-fulfilling forecast rule having the property of being immune to the Lucas Critique. In this paper, Farmer's hypothesis is tested using data from hyperinflationary episodes. It is believed that those episodes are suitable for testing this hypothesis because an agent who lives in a hyperinflationary environment usually faces frequent changes in policy regime. The agent may thus choose a selffulfilling forecast rule which is immune to the Lucas Critique as a way of hedging against unanticipated policy regime switches. The empirical results show mixed evidence on Farmer's hypothesis during the hyperinflationary episodes studied.

Stochastic gradient learning in the cobweb model

We consider the effects of replacing least squares learning by stochastic gradient learning in the multivariate `cobweb' model. Are the stability conditions altered? For this model, we show global convergence of stochastic gradient learning to the unique rational expectations equilibrium provided the E-stability condition is satisfied. This is identical to the stability condition governing convergence under least squares learning.

Least squares learning with heterogeneous expectations

With finitely many classes of agents with possibly different expectations, we show global convergence of least squares learning to the unique rational expectations equilibrium under a simple stability condition. Analogous local results are obtainable in models with multiple rational expectations solutions.

Rational expectations and the Markov property of temporary equilibrium processes

The note gives an example of a sequence economy, in which (i) every sequence of selections of the temporary equilibrium correspondences determines a Markov process and (ii) the unique rational expectations equilibrium process is not Markov.