Instability of sunspot equilibria in real business cycle models under adaptive learning

We provide conditions under which a general, reduced-form class of real business cycle (RBC) models has rational expectations equilibria that are both indeterminate and stable under adaptive learning. Indeterminacy of equilibrium allows for the possibility that non-fundamental “sunspot” variable realizations can be used to drive the model, and several researchers have offered calibrated structural models where sunspot shocks play such a role. However, we show that the structural restrictions researchers have adopted lead to reduced-form systems that are always unstable under adaptive learning dynamics, thus calling into question the plausibility of these sunspot-driven RBC models.     

Using Survey Data of Inflation Expectations in the Estimation of Learning and Rational Expectations Models

Does survey data contain useful information for estimating macroeconomic models? We address this question by using survey data of inflation expectations to estimate the New Keynesian model by Smets and Wouters ( 2007 ) and compare its performance under rational expectations and adaptive learning. The survey information serves as an additional moment restriction and helps us to determine the learning agents' forecasting model for inflation. Adaptive learning fares similarly to rational expectations in fitting macro data, but clearly outperforms rational expectations in fitting macro and survey data simultaneously. In other words, survey data contain additional information that is not present in the macro data alone.     

Anticipated fiscal policy and adaptive learning

The impact of anticipated policy changes when agents form expectations using adaptive learning rather than rational expectations is considered. Agents are assumed to combine limited structural knowledge with a standard adaptive learning rule. These issues are analyzed using two well-known set-ups, an endowment economy and the Ramsey model. In our scenario there are important deviations from both rational expectations and purely adaptive learning. The approach could be applied to other frameworks.     

Learning and the Effectiveness of Central Bank Forward Guidance

This paper examines the link between expectations formation and the effectiveness of central bank forward guidance. A standard New Keynesian model is extended to include forward guidance shocks in the monetary policy rule. Agents form expectations about future macro‐economic variables via either the standard rational expectations hypothesis or an adaptive learning model. The results show that the assumption of rational expectations overstates the effects of forward guidance relative to adaptive learning during an economic crisis. Thus, if monetary policy is based on a model with rational expectations, the results of forward guidance could be potentially  misleading.     

The Evolution of Security Designs

We consider a competitive and perfect financial market in which agents have heterogeneous cash flow valuations. Instead of assuming that agents are endowed with rational expectations, we model their behavior as the product of adaptive learning. Our results demonstrate that adaptive learning affects security design profoundly, with securities mispriced even in the long run and optimal designs trading off underpricing against intrinsic value maximization. The evolutionary dominant security design calls for issuing securities that engender large losses with a small but positive probability, but that otherwise produce stable payoffs, almost the exact opposite of the pure state claims that are optimal in the rational expectations framework.     

Monetary Policy with Heterogeneous and Misspecified Expectations

In the recent literature on monetary policy and learning, it has been suggested that private sector's expectations should play a role in the policy rule implemented by the central bank, as they could improve the ability of the policymaker to stabilize the economy. Private sector's expectations, in these studies, are often taken to be homogeneous and rational, at least in the limit of a learning process. In this paper, instead, we consider the case in which private agents are heterogeneous in their expectations formation mechanisms and hold heterogeneous expectations in equilibrium. We investigate the impact of this heterogeneity in expectations on central bank's policy implementation and on the ensuing economic outcomes, and the general result that emerges is that the central bank should disregard inaccurate private sector expectations and solely base its policy on the accurate ones.     

Does Ricardian Equivalence Hold When Expectations Are Not Rational?

This paper considers the Ricardian Equivalence proposition when expectations are not rational and are instead formed using adaptive learning rules. We show that Ricardian Equivalence continues to hold provided suitable additional conditions on learning dynamics are satisfied. However, new cases of failure can also emerge under learning. In particular, for Ricardian Equivalence to obtain, agents’ expectations must not depend on government’s financial variables under deficit financing.     

Learning and the Yield Curve

Two central implications of Expectations Hypothesis under rational expectations are inconsistent with yield curve data: (i) future expected long yields fall, instead of rising, when yield spread rises; (ii) long yields are excessively volatile relative to short yields. I propose an optimization framework in which boundedly rational agents use adaptive learning to form expectations. The belief structure rationalizes pattern of yields observed in the data so that the first puzzle does not arise with subjective expectations: intertemporal income and substitution effects are amplified relative to rational expectations. The second puzzle is partly accounted for by extra volatility due to parameter uncertainty.     

Are inflation expectations rational?

Several recent papers report evidence of an apparent statistical bias in inflation expectations and interpret these findings as overturning the rational expectations hypothesis. In this paper, we investigate the validity of such an interpretation. We present a computational dynamic general equilibrium model capable of generating aggregate behavior similar to the data along several dimensions. By construction, model agents form “rational” expectations. We run a standard regression on equilibrium realizations of inflation and inflation expectations over sample periods corresponding to those tests performed on actual data and find evidence of an apparent bias in inflation expectations. Our experiments suggest that this incorrect inference is largely the product of a small sample problem, exacerbated by short-run learning dynamics in response to infrequent shifts in monetary policy regimes.     

Monetary Policy, Determinacy, and Learnability in a Two-Block World Economy

We study how determinacy and learnability of worldwide rational expectations equilibrium may be affected by monetary policy in a simple, two-country, New Keynesian framework under both fixed and flexible exchange rates. 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.     

A description of farmland investor expectations

We consider how best to characterize agricultural real estate market participants' expectation formation mechanism. The expectation formation mechanism links current agricultural policies to asset prices and tells us how current policies change expectations for future transfers. We examine behavior of real estate prices and returns using the present value model. We derive estimable equations incorporating two rival expectation formation mechanisms: rational and adaptive expectations. Assuming rational expectations, the present value model yields parameter estimates that imply the model should be rejected. Instead of rejecting the present value model while maintaining the rational expectations hypothesis, we let the data reveal which expectations hypothesis best fits the data. When we assume the rival hypothesis, the model yields parameter estimates that conform to adaptive expectations.     

Market forces meet behavioral biases: cost misallocation and irrational pricing

Psychological and experimental evidence, as well as a wealth of anecdotal examples, suggests that firms may confound fixed, sunk, and variable costs, leading to distorted pricing decisions. This article investigates the extent to which market forces and learning eventually eliminate these distortions. We envision firms that experiment with cost methodologies that are consistent with real‐world accounting practices, including ones that confuse the relevance of variable, fixed, and sunk costs to pricing decisions. Firms follow “naive” adaptive learning to adjust prices and reinforcement learning to modify their costing methodologies. Costing and pricing practices that increase profits are reinforced. In some market structures, but not in others, this process of reinforcement causes pricing practices of all firms to systematically depart from standard equilibrium predictions.     

A volatility model based on adaptive expectations: An improvement on the rational expectations model

Investment expectations affect stock price volatility, making asset pricing more difficult. Correctly capturing investment expectations can help alleviate this problem. In this paper, we analyze the rational expectations properties of existing volatility models. Second, we explore a volatility model based on adaptive expectations by using mathematical methods and the applicable conditions and continuity feature of the adaptive expectations volatility model. Third, under the assumption of adaptive expectations, we construct adaptive expectations GARCH (ADGARCH) and LSTM-ADGARCH models. Using daily trading data from the Shanghai stock index and SPX500 for the period 2015–2021, we find that the volatility model based on adaptive expectations has more explanatory power than one based on rational expectations.     

Information Aggregation via Contracting

When a group of investors with dispersed private information jointly invest in a risky project, how should they divide the project's profit? We show that a simple contract dividing profits in proportion to investors' risk tolerances may facilitate information aggregation by altering investors' risk-taking incentives when they decide on how investment strategies respond to private information. Our results provide a contracting-based approach for information aggregation, which is an alternative to learning from endogenous market variables (e.g., prices) via contingent schedules as seen in well-known rational expectations equilibrium models.     

The Value of Interest Rate Stabilization Policies When Agents Are Learning

We examine the expectational stability (E-stability) of rational expectations equilibrium in the "New Keynesian" model where monetary policy is optimally derived and interest rate stabilization is added to the central bank's traditional objectives of inflation and output stabilization. We consider both the case where the central bank lacks a commitment technology and the case of full commitment. We show that for both cases, optimal policy rules yield rational expectations equilibria that are E-stable for a wide range of empirically plausible parameter values. These findings stand in contrast to Evans and Honkapohja's findings for optimal monetary policy rules in environments where interest rate stabilization is not a central bank objective.     

Learnability and monetary policy: A global perspective

The recent literature on monetary policy design has emphasized the importance of equilibrium determinacy and learnability in the choice of policy rules. This paper contains an analysis of the learnability of the equilibrium in a class of simple, micro-founded models in which the policy authority uses a Taylor-type monetary policy rule. Unlike previous analyses, the model economy is not linearized about a steady state—instead, a global perspective is adopted. Globally, the nonlinear model economy can possess rational expectations equilibria other than the steady state consistent with the inflation target of the monetary authorities. These include a second, low inflation ‘liquidity trap’ steady state, periodic equilibria, and sunspot equilibria. The main results in the paper characterize the conditions under which these alternative equilibria maybe stable under adaptive learning, even when the policy rule obeys the Taylor principle. The stability of multiple equilibria is associated with policy rules which are forecast-based. An important finding is that backward-looking Taylor-type policy rules can guarantee that the unique learnable equilibrium is the steady state associated with the inflation target of the monetary authority.     

Adaptive expectations, underparameterization and the Lucas critique

A striking implication of the replacement of adaptive expectations by rational expectations was the “Lucas critique,” which showed that expectation parameters, and endogenous variable dynamics, depend on policy parameters. We consider this issue from the vantage point of bounded rationality, where for transparency we model bounded rationality by means of simple adaptive expectations. We show that for a range of processes, monetary policy remains subject to the Lucas critique. However, there are also regimes in which the expectation parameter is locally invariant and the Lucas critique does not apply.     

Monetary–Fiscal Policy Interactions under Implementable Monetary Policy Rules

This paper examines the implications of forward- and backward-looking monetary policy rules in an environment with monetary–fiscal interactions. We find that the unique stationary rational expectations equilibrium (REE) is always non-Ricardian under simple implementable monetary policy rules.     

Can perpetual learning explain the forward-premium puzzle?

Under rational expectations and risk neutrality the linear projection of exchange-rate change on the forward premium has a unit coefficient. However, empirical estimates of this coefficient are significantly less than one and often negative. We show that replacing rational expectations by discounted least-squares (or “perpetual”) learning generates a negative bias that becomes strongest when the fundamentals are strongly persistent, i.e. close to a random walk. Perpetual learning can explain the forward-premium puzzle while simultaneously replicating other features of the data, including positive serial correlation of the forward premium and disappearance of the anomaly in other forms of the test.     

Inflation Targeting,Recursive Inattentiveness,and Heterogeneous Beliefs

We consider a monetary authority that provides an explicit inflation target in order to align expectations with the policy objective. However, biased perceptions of the target may arise due to imperfect information flows. We allow agents to revise expectations over time and we model their recursive choice among prediction strategies as an optimization problem under rational inattention. We then investigate whether a simple policy rule can steer the economy toward the targeted equilibrium. Our findings suggest that determinacy under rational expectations may not be sufficient to reach the target. Instead, monetary policy should be fine‐tuned to correct agents' biased beliefs.