Multiple Rational Expectations Equilibria Research Articles

Comment on “Response of Asset Prices to Monetary Policy under Abenomics”

Comment on “Response of Asset Prices to Monetary Policy under Abenomics”

Dynamic Government Performance: Honeymoons and Crises of Confidence

We use a formal theoretical framework to explore the interplay between a government's longevity and its performance. Ministers perform well when their careers are valuable; this is so when the government's duration is expected to be long; the government's survival depends on its popularity; and, finally, that popularity depends on its ministers’ performance. The feedback loop between performance and longevity means that multiple rational-expectations equilibria can arise: Ministers work hard for a popular government, but divert efforts elsewhere if they believe the government is doomed; these alternatives are both self-fulfilling prophecies. However, the presence of (perhaps small) random events that buffet the performance and popularity of a government is sufficient to pin down a unique equilibrium. We explore the dynamics that arise: A crisis of confidence involving the rapid collapse of a government's performance is sparked when a sequence of negative shocks push the popularity of the government below a unique critical threshold.

Comment

Comment

Using a Long-Term Interest Rate as the Monetary Policy Instrument

Using a short-term interest rate as the monetary policy instrument can be problematic near its zero bound constraint. An alternative strategy is to use a long-term interest rate as the policy instrument. We find when Taylor-type policy rules are used to set the long rate in a standard New Keynesian model, indeterminacy - that is, multiple rational expectations equilibria - may often result. However, a policy rule with a long rate policy instrument that responds in a forward-looking fashion to inflation expectations can avoid the problem of indeterminacy.

INTRODUCTION TO THE SPECIAL ISSUE: NEW APPROACHES TO LEARNING IN MACROECONOMIC MODELS

The research questions addressed by the literature on learning in macroeconomics can be classified into four categories: First, there are issues related to the convergence and stability under learning in models with unique rational expectations equilibria. Authors here are concerned mainly with the learnability of a rational expectations equilibrium, as a measure of that equilibrium's plausibility as an observed outcome in an actual economy. Second, there are issues related to convergence and stability under learning in models with multiple rational expectations equilibria. In this case, learnability serves as an equilibrium selection device, helping economists decide which equilibria are the more likely to be actually observed among the many that exist under rational expectations. A third set of issues involves the examination of transitional dynamics that accompanies the equilibrium selection process. Following some type of unexpected strcutural change or change in policy regime, for instance, economies necessarily must follow temporary transitional paths to a rational expectations equilibrium associated with the new reality. Learning is sometimes used to help model such transitional dynamics. Finally, there are issues related to the examination of learning dynamics that are intrinsically different, even asymptotically, from the dynamics of the rational expectations versions of the models. In these cases, the learning dynamics do not converge to the rational expectations fixed points, and (unexploitable) expectational errors persist indefinitely. Some authors have tried to make use of this possibility in order to build explanations of otherwise puzzling macroeconomic phenomena based on constantly changing expectations.

Resolving Indeterminacy in Dynamic Settings: The Role of Shocks*

This paper shows that the phenomenon of multiple equilibria can be fragile to the introduction of aggregate shocks. We examine a standard dynamic model of sectoral choice with external increasing returns. Without shocks, the outcome is indeterminate: there are multiple rational expectations equilibria. We then introduce shocks in the form of a parameter that follows a Brownian motion and affects relative productivity in the two sectors. We assume that the parameter can reach values at which working in either sector becomes a dominant choice. A unique equilibrium emerges; for any path of the random parameter, there is a unique path that the economy must follow. There is no role for multiple, self-fulfilling prophecies or sunspots.

Rational Liquidity Crises in the Sovereign Debt Market: In Search of a Theory

This paper studies under what circumstances creditworthy sovereign borrowers may be denied liquidity by rational creditors. It is shown that, when the creditor side of the market consists of many small investors, multiple rational expectations equilibria may exist. In one equilibrium, creditors' pessimistic expectations about the borrower's creditworthiness become self-fulfilling, and the borrower experiences a liquidity crisis. Multiple equilibria can be avoided by marketing the loan appropriately or by developing a reputation for following good policies. Liquidity problems can also arise because international bond markets are temporarily disrupted owing to events unrelated to the borrower's circumstances. Policy responses are discussed.

Rational Liquidity Crises in the Sovereign Debt Market: In Search of a Theory

This paper studies under what circumstances creditworthy sovereign borrowers may be denied liquidity by rational creditors. It is shown that, when the creditor side of the market consists of many small investors there may be multiple rational expectations equilibria. In one equilibrium, creditors’ pessimistic expectations about the borrower’s creditworthiness become self-fulfilling, and the borrower experiences a liquidity crisis. Multiple equilibria can be avoided by marketing the loan appropriately or by developing a reputation for following good policies. Liquidity problems can also arise because of the temporary disruption of international bond markets due to events unrelated to the borrower’s circumstances. Policies responses are discussed.

Rational Liquidity Crises in the Sovereign Debt Market: In Search of a Theory

This paper studies under what circumstances creditworthy sovereign borrowers may be denied liquidity by rational creditors. It is shown that, when the creditor side of the market consists of many small investors there may be multiple rational expectations equilibria. In one equilibrium, creditors’ pessimistic expectations about the borrower’s creditworthiness become self-fulfilling, and the borrower experiences a liquidity crisis. Multiple equilibria can be avoided by marketing the loan appropriately or by developing a reputation for following good policies. Liquidity problems can also arise because of the temporary disruption of international bond markets due to events unrelated to the borrower’s circumstances. Policies responses are discussed.

Learning, convergence, and stability with multiple rational expectations equilibria

For a linear model with multiple rational expectations equilibria (REE) we discuss the set of possible REE. Solutions include (i) locally unique minimal state variable solutions, taking an AR(1) form and (ii) continua of solutions which may depend on sunspots. We analyze the convergence of econometric learning to the different REE. There exist cases with more than one stable AR(1) solution. It is also possible for a continuum of solutions to be stable, but this property is not robust to overparametrization. An application is developed, and it is suggested that the exhibited phenomena may arise in applied macroeconomic models.

Multiple Expectational Equilibria under Monopolistic Competition

This paper shows that a monopolistically competitive economy with real investment can have multiple rational expectations equilibria: one is associated with entrepreneurs' optimistic expectations about future demand; another with entrepreneurs' pessimism. It also shows that an optimistic expectational equilibrium Pareto dominates a pessimistic equilibrium. An investment subsidy can be beneficial both by reducing the original underinvestment distortion and by changing firms' expectations from pessimistic to optimistic. The most important assumption is increasing returns to scale, and monopolistic competition makes increasing returns consistent with each producer's optimization.

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.