Theories of learning and economic policy

The benchmark rational expectations (RE) assumption both assumes an unrealistic degree of rationality for economic agents and fails to address how agents would come to coordinate on an equilibrium. This essay reviews how theories of learning, and more specifically adaptive learning, address these issues and can lead to policy conclusions distinct from those obtained under RE. Applications discussed include monetary policy in New Keynesian models, the neo-Fisherian policy view, inflation targets, hyperinflation models, and macroeconomic policy to avoid stagnation at the zero lower bound.PostprintPeer reviewe

The RPEs of RBCs and other DSGEs

In a broad class of non-linear representative agent models, represented by a system of difference equations, we replace rational expectations with linear forecast models conditioning on a predetermined set of regressors. Within this framework, a restricted perceptions equilibrium (RPE) corresponds to a forecast rule that is optimal within that class of models. Local uniqueness of a stationary rational expectations equilibrium (REE) near the non-stochastic steady state is shown to guarantee the existence, uniqueness and E-stability of an RPE local to that steady state. A benchmark RBC model with government spending shocks illustrates the theoretical results.Peer reviewe

Interest rate pegs in New Keynesian models

Financial support from National Science Foundation Grant No. SES-1559209 is gratefully acknowledged.The conventional policy perspective is that lowering the interest rate increases output and inflation in the short run, while maintaining inflation at a higher level requires a higher interest rate in the long run. In contrast, it has been argued that a Neo‐Fisherian policy of setting an interest‐rate peg at a fixed higher level will increase the inflation rate. We show that adaptive learning argues against the Neo‐Fisherian approach. Pegging the interest rate at a higher level will induce instability and most likely lead to falling inflation and output over time. Eventually, this would precipitate a change of policy.PostprintPeer reviewe

Eductive stability in real business cycle models

We re-examine issues of coordination in the standard RBC model. Can the unique rational expectations equilibrium be “educed” by rational agents who contemplate the possibility of small deviations from equilibrium? Surprisingly, we find that coordination along this line cannot be expected. Rational agents anticipating small but possibly persistent deviations have to face the existence of retroactions that necessarily invalidate any initial tentative “common knowledge” of the future. This "impossibility" theorem for eductive learning is not fully overcome when adaptive learning is incorporated into the framework.standard RBC model ; coordination

Stable near-rational sunspot equilibria

Financial support from National Science Foundation Grant No. SES-1559209 is gratefully acknowledged.We introduce a new class of solutions to nonlinear forward-looking models called near-rational sunspot equilibria (NRSE). NRSE are natural nonlinear extensions of the usual sunspot equilibria associated with the linearized version of the economy, and are near-rational in that agents use the optimal linear forecasting model when forming expectations. Generic results for existence and stability under learning are established. NRSE in indeterminate nonlinear models are found to be stable under learning provided that the corresponding linearized model's minimal state variable solution is E-stable. NRSE are readily computable, and our results make it possible to use the standard linear tools to search for stable NRSE. We illustrate our results using a canonical nonlinear New Keynesian model.PostprintPeer reviewe

Eductive stability in real business cycle models

This work has been supported by National Science Foundation Grant no. SES-1025011 and by the French National Research Agency, through the program Investissements d’Avenir, ANR-10—LABX_93-01.Within the standard RBC model we examine issues of expectational coordination on the unique rational expectations equilibrium. We show the sensitivity of agents’ plans and decisions to their short-run and longrun expectations is too great to trigger eductive coordination in a world of rational agents who are endowed with knowledge of the economic structure and contemplate the possibility of small deviations from equilibrium: eductive stability never obtains. We conclude adaptive learning must play a role in real-time dynamics. Our eductive instability theorem has a counterpart under adaptive learning: even with asymptotic stability the transition dynamics can involve large departures from rational expectations.PostprintPeer reviewe

E-Stability vis-a-vis Determinacy Results for a Broad Class of Linear Rational Expectations Models

It is argued that learnability/E-stability is a necessary condition for a RE solution to be plausible. A class of linear models considered by Evans and Honkapohja (2001) is shown to include all models of the form used by King and Watson (1998) and Klein (2000), which permits any number of lags, leads, and lags of leads. For this broad class it is shown that, if current-period information is available in the learning process, determinacy is a sufficient condition for E-stability. It is not a necessary condition, however; there exist cases with more than one stable solution in which the solution based on the decreasing-modulus ordering of the system’s eigenvalues is E-stable. If in such a case the other stable solution(s) are not E-stable, then the condition of indeterminacy may not be important for practical issues.

Equilibrium selection, observability and backward-stable solutions

Financial support from National Science Foundation Grant No. SES-1559209 is gratefully acknowledged.The robustness of stability under learning to observability of exogenous shocks is examined. Regardless of observability assumptions, the minimal state variable solution is robustly stable under learning provided the expectational feedback is not both positive and large, while the nonfundamental solution is never robustly stable. Overlapping generations and New Keynesian models are considered and concerns raised in [Cochrane, J., 2011. Determinacy and identification with Taylor rules. Journal of Political Economy 119, 565-615, Cochrane, J., 2017. The new-Keynesian liquidity trap. Journal of Monetary Economics, forthcoming.] are addressed.PostprintPeer reviewe

Are sunspots learnable? An experimental investigation in a simple macroeconomic model

We conduct experiments with human subjects in a model with a positive production externality in which productivity is a nondecreasing function of the average level of employment of other firms. The model has three steady states and a sunspot equilibrium that fluctuates between the high and low steady states. Steady states are payoff ranked: low values give lower profits than higher values. We investigate whether subjects can learn a sunspot equilibrium. We observe coordination on the extrinsic announcements in our experimental economies. Cases of apparent convergence to the low and high steady states are also observed.PostprintPeer reviewe

Robustifying learnability

In recent years, the learnability of rational expectations equilibria (REE) and determinacy of economic structures have rightfully joined the usual performance criteria among the sought-after goals of policy design. Some contributions to the literature, including Bullard and Mitra (2001) and Evans and Honkapohja (2002), have made significant headway in establishing certain features of monetary policy rules that facilitate learning. However a treatment of policy design for learnability in worlds where agents have potentially misspecified their learning models has yet to surface. This paper provides such a treatment. We begin with the notion that because the profession has yet to settle on a consensus model of the economy, it is unreasonable to expect private agents to have collective rational expectations. We assume that agents have only an approximate understanding of the workings of the economy and that their learning the reduced forms of the economy is subject to potentially destabilizing perturbations. The issue is then whether a central bank can design policy to account for perturbations and still assure the learnability of the model. Our test case is the standard New Keynesian business cycle model. For different parameterizations of a given policy rule, we use structured singular value analysis (from robust control theory) to find the largest ranges of misspecifications that can be tolerated in a learning model without compromising convergence to an REE.Robust control ; Monetary policy