• Selected
• Entire List

Abstract:
The rational expectations hypothesis swept through macroeconomics during the 1970's and permanently altered the landscape. It remains the prevailing paradigm in macroeconomics, and rational expectations is routinely used as the standard solution concept in both theoretical and applied macroeconomic modelling. The rational expectations hypothesis was initially formulated by John F. Muth Jr. in the early 1960s. Together with Robert Lucas Jr., Thomas (Tom) Sargent pioneered the rational expectations revolution in macroeconomics in the 1970s. We interviewed Tom Sargent for Macroeconomic Dynamics.

Abstract:
Using New Keynesian models, we compare Friedman's k-percent money supply rule to optimal interest rate setting, with respect to determinacy, stability under learning and optimality. We first review the recent literature. Open-loop interest rate rules are subject to indeterminacy and instability problems, but a properly chosen expectations-based rule yields determinacy and stability under learning, and implements optimal policy. We then show that Friedman's rule also can generate equilibria that are determinate and stable under learning. However, in computing the mean quadratic welfare loss, we find that for calibrated models Friedman's rule performs poorly compared to the optimal interest rate rule.

Monetary policy, determinacy, stability under learning

Abstract:
A fundamentals based monetary policy rule, which would be the optimal monetary policy without commitment when private agents have perfectly rational expectations, is unstable if in fact these agents follow standard adaptive learning rules. This problem can be overcome if private expectations are observed and suitable incorporated into the policy maker's optimal rule. These strong results extend to the case in which there is simultaneous learning by the policy maker and the private agents. Our findings show the importance of conditioning policy appropriately, not just on fundamentals, but also directly on observed household and firm expectations.

Abstract:
A fundamentals based monetary policy rule, which would be the optimal monetary policy without commitment when private agents have perfectly rational expectations, is unstable if in fact these agents follow standard adaptive learning rules. This problem can be overcome if private expectations are observed and suitably incorporated into the policy maker's optimal rule. These strong results extend to the case in which there is simultaneous learning by the policy maker and the private agents. Our findings show the importance of conditioning policy appropriately, not just on fundamentals, but also directly on observed household and firm expectations.

monetary policy, learning, expectational stability, optimal discretionary policy

Abstract:
A fundamentals-based monetary policy rule, which would be the optimal monetary policy without commitment when private agents have perfectly rational expectations, is unstable if in fact these agents follow standard adaptive learning rules. This problem can be overcome if private expectations are observed and suitably incorporated into the policy maker's optimal rule. These strong results extend to the case in which there is simultaneous learning by the policy maker and the private agents. Our findings show the importance of conditioning policy appropriately, not just on fundamentals, but also directly on observed household and firm expectations.

Adaptive learning, instability, stability, private expectations

Abstract:
A fundamentals based monetary policy rule, which would be the optimal monetary policy without commitment when private agents have perfectly rational expectations, is unstable if in fact these agents follow standard adaptive learning rules. This problem can be overcome if private expectations are observed and suitably incorporated into the policy maker's optimal rule. These strong results extend to the case in which there is simultaneous learning by the policy maker and the private agents. Our findings show the importance of conditioning policy appropriately, not just on fundamentals, but also directly on observed household and firm expectations.

expectations, stability, monetary policy, least squares learning

Abstract:
Expectations about the future are central for determination of current macroeconomic outcomes and the formulation of monetary policy. Recent literature has explored ways for supplementing the benchmark of rational expectations with explicit models of expectations formation that rely on econometric learning. Some apparently natural policy rules turn out to imply expectational instability of private agents' learning. We use the standard New Keynesian model to illustrate this problem and survey the key results for interest-rate rules that deliver both uniqueness and stability of equilibrium under econometric learning. We then consider some practical concerns such as measurement errors in private expectations, observability of variables and learning of structural parameters required for policy. We also discuss some recent applications, including policy design under perpetual learning, estimated models with learning, recurrent hyperinflation, and macroeconomic policy to combat liquidity traps and deflation.

imperfect knowledge, learning, interest-rate setting, fluctuations, stability, determinacy

Abstract:
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.

Lucas critique, expectations, underparameterization, bounded rationality, learning.

Abstract:
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.

Abstract:
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 optimal reaction functions and instrument rules in terms of whether they lead to an RE equilibrium that is both locally determinate and stable under adaptive learning by private agents. A reaction function that appropriately depends explicitly on private expectations performs well on both counts.

Commitment, interest rate setting, adaptive learning, stability determinacy

Abstract:
Full commitment in monetary policy leads to equilibria that are superior to those from optimal discretionary policies. Different types of reactions functions to implement and instrument rules to approximate full commitment have been proposed in the literature. We assess optimal reaction functions and instrument rules, in terms of whether they lead to an RE equilibrium that is both locally determinate and stable under adaptive learning by private agents. The reaction function that appropriately depends explicitly on private expectations performs best on both counts.

Commitment, Interest Rate Setting, Adaptive Learning, Stability, Determinacy

Abstract:
We review the recent work on interest rate setting, which emphasizes the desirability of designing policy to ensure stability under learning. Appropriately designed expectations-based rules can yield optimal rational expectations equilibria that are both determinate and stable under learning. Some simple instrument rules and approximate targeting rules also have these desirable properties. We discuss various complications in implementing optimal policy, including the observability of key variables and the required knowledge of structural parameters. An additional issue that we take up concerns the implications of expectation shocks not arising from transitional learning effects.

Commitment, interest rate setting, adaptive learning, stability, determinacy, expectations shocks

Abstract:
We review the recent work on interest rate setting, which emphasizes the desirability of designing policy to ensure stability under private agent learning. Appropriately designed expectations based rules can yield optimal rational expectations equilibria that are both determinate and stable under learning. Some simple instrument rules and approximate targeting rules also have these desirable properties. We take up various complications in implementing optimal policy, including the observability of key variables and the required knowledge of structural parameters. An additional issue that we take up concerns the implications of expectation shocks not arising from transitional learning effects.

Commitment, interest rate setting, adaptive learning, stability, determinacy, expectations shocks

Abstract:
We present a new application of Samuelson's Correspondence Principle to the analysis of comparative dynamics in stochastic rational expectations models. Our version, which we call the E-correspondence principle, applies to rational expectations equilibria that are stable under least squares and closely related learning rules. With this technique it is sometimes possible to study, without explicitly solving for the equilibrium, how qualitative properties of the equilibrium are affected by changes in the model parameters. Applications to overlapping generations and New Keynesian models illustrate the potential of the technique.

Abstract:
We introduce the E-correspondence principle for stochastic dynamic expectations models as a tool for comparative dynamics analysis. The principle is applicable to equilibria that are stable under least squares and closely related learning rules. With this technique it is possible to study, without explicit solving for the equilibrium, how properties of the equilibrium are affected by changes in the structural parameters of the model. Even when qualitative comparative dynamics results are not obtainable, a quantitative version of the principle can be applied.

comparative dynamics, rational expectations, stability of equilibrium, adaptive

Abstract:
We develop a monetary model with flexible supply of labor, cash in advance constraints and government spending financed by seignorage. This model has two regimes. One regime is conventional with two steady states. The other regime has a unique steady state which can be determinate or indeterminate. In the latter case there exist sunspot equilibria which are stable under adaptive learning, taking the form of noisy finite state Markov processes at resonant frequencies. For a range of parameter values, a sufficient reduction in government purchases will eliminate these equilibria.

Indeterminacy, Learnability, Expectational Stability, Endogenous Fluctuations, Seignorage

Abstract:
We study how the use of judgement or "add-factors" in macroeconomic forecasting may disturb the set of equilibrium outcomes when agents learn using recursive methods. We isolate conditions under which new phenomena, which we call exuberance equilibria, can exist in standard macroeconomic environments. Examples include a simple asset pricing model and the New Keynesian monetary policy framework. Inclusion of judgement in forecasts can lead to self-fulfilling fluctuations, but without the requirement that the underlying rational expectations equilibrium is locally indeterminate. We suggest ways in which policymakers might avoid unintended outcomes by adjusting policy to minimize the risk of exuberance equilibria.

Learning, expectations, excess volatility, bounded rationality, monetary policy

Abstract:
We consider the stability under adaptive learning of the complete set of solutions to the basic linear forward looking model in which the current value of the state variable depends linearly on the (subjectively) expected value of the state next period and the coefficient of the expected state is bigger than one in absolute value. In addition to the fundamentals solution, the literature describes both finite-state Markov sunspot solutions, satisfying a resonant frequency condition, and autoregressive solutions depending on an arbitrary martingale difference sequence. We clarify the relationships between these solutions and show that the stability properties of equilibria may depend crucially on the representation used by agents in the learning process. Only the finite-state Markov sunspot solutions can be stable under learning.

Indeterminacy, Representations of Solutions, Learnability, Expectational Stability, Endogenous Fluctuations

Abstract:
In this paper we consider inflation and government debt dynamics when monetary policy employs a global interest rate rule and private agents' forecasts using adaptive learning. Because of the zero lower bound on interest rates, active interest rate rules are known to imply the existence of a second, low inflation steady state, below the target inflation rate. Under adaptive learning dynamics we find the additional possibility of a liquidity trap, in which the economy slips below this low inflation steady state and is driven to an even lower inflation floor which, in turn, is supported by a switch to an aggressive money supply rule. Fiscal policy alone cannot push the economy out of the liquidity trap. However, raising the threshold at which the money supply rule is employed can dislodge the economy from the liquidity trap and ensure a return to the target equilibrium.

stability of equilibria, fiscal and monetary policy, interest rate and

Abstract:
We examine the nonlinear one-step forward-looking model, in which the current state is a function of the (subjective) expected value of a nonlinear function of the state next period. Stationary Markov Sunspot Equilibria (SSEs) are known to exist near an indeterminate steady state, i.e. when the derivative of the function at the steady state is bigger than one in absolute value. We show that there exist Markov SSEs that are E- stable, and therefore locally stable under adaptive learning, if the value of this derivative is less than minus one.

Indeterminacy, Learnability, Expectational Stability, Endogenous Fluctuations

Abstract:
We investigate both the rational explosive inflation paths studied by McCallum (2001) and the classification of fiscal and monetary policies proposed by Leeper (1991) for stability under learning of rational expectations equilibria (REE). Our first result is that the fiscalist REE in the model of McCallum (2001) is not locally stable under learning. By contrast, in the setting of Leeper (1991), different possibilities can obtain. We find, in particular, that there are parameter domains for which the fiscal theory solution - in which fiscal variables affect the price level - can be a stable outcome under learning. For other parameter domains, the monetarist solution is the stable equilibrium.

Inflation, expectations, fiscal and monetary policy, explosive price paths

Abstract:
We investigate both the rational explosive inflation paths studied by McCallum (2001) and the classification of fiscal and monetary policies proposed by Leeper (1991) for stability under learning of rational expectations equilibria (REE). Our first result is that the fiscalist REE in the model of McCallum (2001) is not locally stable under learning. By contrast, in the setting of Leeper (1991), different possibilities can obtain. We find, in particular, that there are parameter domains for which the fiscal theory solution - in which fiscal variables affect the price level - can be a stable outcome under learning. For other parameter domains, the monetarist solution is the stable equilibrium.

Inflation, expectations, fiscal and monetary policy, explosive price paths

Abstract:
We study the properties of generalized stochastic gradient (GSG) learning in forward-looking models. We examine how the conditions for stability of standard stochastic gradient (SG) learning both differ from and are related to E-stability, which governs stability under least squares learning. SG algorithms are sensitive to units of measurement and we show that there is a transformation of variables for which E-stability governs SG stability. GSG algorithms with constant gain have a deeper justification in terms of parameter drift, robustness and risk sensitivity.

adaptive learning, E-stability, recursive least squares, robust estimation

Abstract:
Earlier studies of the seigniorage inflation model have found that the high-inflation steady state is not stable under adaptive learning. We reconsider this issue and analyze the full set of solutions for the linearized model. Our main focus is on stationary hyperinflationary paths near the high-inflation steady state. The hyperinflationary paths are stable under learning if agents can utilize contemporaneous data. However, in an economy populated by a mixture of agents, some of whom only have access to lagged data, stable inflationary paths emerge only if the proportion of agents with access to contemporaneous data is sufficiently high.

Indeterminacy, Inflation, Stability of Equilibria, Seigniorage

Abstract:
The development of tractable forward looking models of monetary policy has lead to an explosion of research on the implications of adopting Taylor-type interest rate rules. Indeterminacies have been found to arise for some specifications of the interest rate rule, raising the possibility of inefficient fluctuations due to the dependence of expectations on extraneous "sunspots." Separately, recent work by a number of authors has shown that sunspot equilibria previously thought to be unstable under private agent learning can in some cases be stable when the observed sunspot has a suitable time series structure. In this paper we generalize the "common factor" technique, used in this analysis, to examine standard monetary models that combine forward looking expectations and predetermined variables. We consider a variety of specifications that incorporate both lagged and expected inflation in the Phillips Curve, and both expected inflation and inertial elements in the policy rule. We find that some policy rules can indeed lead to learnable sunspot solutions and we investigate the conditions under which this phenomenon arises.

Monetary Policy, sunspots, expectations, learning, stability

Abstract:
We consider "robust stability" of a rational expectations equilibrium, which we define as stability under discounted (constant gain) least-squares learning, for a range of gain parameters. We find that for operational forms of policy rules, i.e. rules that do not depend on contemporaneous values of endogenous aggregate variables, many interest-rate rules do not exhibit robust stability. We consider a variety of interest-rate rules, including instrument rules, optimal reaction functions under discretion or commitment, and rules that approximate optimal policy under commitment. For some reaction functions we allow for an interest-rate stabilization motive in the policy objective. The expectations-based rules proposed in Evans and Honkapohja (2003, 2006) deliver robust learning stability. In contrast, many proposed alternatives become unstable under learning even at small values of the gain parameter.

Adaptive learning, Commitment, determinacy, interest-rate setting, stability

Abstract:
We consider the robust stability of a rational expectations equilibrium, which we define as stability under discounted (constant gain) least-squares learning, for a range of gain parameters. We find that for operational forms of policy rules, ie rules that do not depend on contemporaneous values of endogenous aggregate variables, many interest-rate rules do not exhibit robust stability. We consider a variety of interest-rate rules, including instrument rules, optimal reaction functions under discretion or commitment, and rules that approximate optimal policy under commitment. For some reaction functions we allow for an interest-rate stabilization motive in the policy objective. The expectations-based rules proposed in Evans and Honkapohja (2003, 2006) deliver robust learning stability. In contrast, many proposed alternatives become unstable under learning even at small values of the gain parameter.

Commitment, interest-rate setting, adaptive learning, stability, determinacy.

Abstract:
This paper addresses the output-price volatility puzzle by studying the interaction of optimal monetary policy and agents' beliefs. We assume that agents choose their information acquisition rate by minimizing a loss function that depends on expected forecast errors and information costs. Endogenous inattention is a Nash equilibrium in the information processing rate. Although a decline of policy activism directly increases output volatility, it indirectly anchors expectations, which decreases output volatility. If the indirect effect dominates then the usual trade-off between output and price volatility breaks down. This provides a potential explanation for the great moderation that began in the 1980s.

expectations, optimal monetary policy, bounded rationality, economic stability, adaptive learning

Abstract:
We consider a linear stochastic univariate rational expectations model, with a predetermined variable, and provide alternative representations of SSEs (stationary sunspot equilibria). For a strict subset of the parameter space there exist SSEs that are locally stable under least squares learning provided agents use a common factor representation for their estimated law of motion. These results indicate that for some parameter regions SSEs are more likely to arise under private agent learning than previously recognized.

Endogenous fluctuations, learning, expectational stability, sunspot equilibria

Abstract:
This paper develops an adaptive learning formulation of an extension to the Ball, Mankiw, and Reis (2005) sticky information model that incorporates endogenous inattention. We show that, following an exogenous increase in the policymaker's preferences for price vs. output stability, the learning process can converge to a new equilibrium in which both output and price volatility are lower.

expectations, optimal monetary policy, bounded rationality, economic stability, adaptive learning

Abstract:
We consider a linear stochastic univariate rational expectations model, with a predetermined variable, and consider solutions driven by an extraneous finite state Markov process as well as by the fundamental noise. We obtain conditions for existence of noisy k-state sunspot equilibria (noisy k-SSEs) and, for the case k=2, of noisy k-state dependent sunspot equilibria (noisy k-*SDSs). k-*SDSs are driven by a finite state sunspot but have an infinite range of values even in the nonstochastic model. Stability under econometric learning is analyzed using representations that nest both types of solution. For the case k=2, we find that noisy 2-SSEs and noisy 2-*SDSs are learnable for parameters in proper subsets of the regions of their existence.

Indeterminacy, sunspots, stability, learning, expectations

Abstract:
We consider the impact of anticipated policy changes when agents form expectations using adaptive learning rather than rational expectations. To model this we assume that agents combine limited structural knowledge with a standard adaptive learning rule. We analyze these issues using two well-known set-ups, an endowment economy and the Ramsey model. In our set-up there are important deviations from both rational expectations and purely adaptive learning. Our approach could be applied to many macroeconomic frameworks.

taxation, expectations, Ramsey model

Abstract:
We extend common factor analysis to a multi-dimensional setting by considering a bivariate reduced form model consistent with many Real Business Cycle type models. We show how to obtain new representations of sunspots and find that there are parameter regions in which these sunspots are stable under learning. However, once the parameters are restricted to coincide with those generated by certain standard models of indeterminacy, we find, under one information assumption, that no stable sunspots exist, and under another information assumption, that they exist only for a very small part of the indeterminacy region. This leads to the following puzzle: Why does indeterminacy almost always imply instability in RBC-type models?

business cycles, sunspots, expectations, learning, stability

Abstract:
We study how the use of judgment or "add-factors" in forecasting may disturb the set of equilibrium outcomes when agents learn using recursive methods. We isolate conditions under which new phenomena, which we call exuberance equilibria, can exist in a standard self-referential environment. Local indeterminacy is not a requirement for existence. We construct a simple asset pricing example and find that exuberance equilibria, when they exist, can be extremely volatile relative to fundamental equilibria.

Learning, expectations, excess volatility, bounded rationality

Abstract:
We construct a rational expectations model in which aggregate growth alternates between a low growth and a high growth state. When all agents expect growth to be slow, the returns on investment are low, and little investment takes place. This slows growth and confirms the prediction that the returns on investment will be low. But if agents expect fast growth, investment is high, returns are high, and growth is rapid. This expectational indeterminacy is induced by complementarity between different types of capital goods. In a growth cycle there are stochastic shifts between high and low growth states and agents take full account of these transitions. The rules that agents need to form rational expectations in this equilibrium are simple. The equilibrium with growth cycles is stable under the dynamics implied by a correspondingly simple learning rule

Abstract:
We investigate local strong rationality (LSR) in a one step forward looking univariate model with memory one. Eductive arguments are used to determine when common knowledge (CK) that the solution is near some perfect foresight path is sufficient to trigger complete coordination on that path (I.e. the path is LSR). Coordination of expectations is shown to depend on three factors: the nature of the CK initial beliefs, the degree of structural heterogeneity and the information structure. Our sufficient conditions for LSR precisely reflect these features and provide basic consistent justifications for the choice of the saddle path solution.

Abstract:
We investigate local strong rationality (LSR) in a one step forward looking univariate model with memory one. Eductive arguments are used to determine when common knowledge (CK) that the solution is near some perfect foresight path is sufficient to trigger complete coordination on that path (I.e. the path is LSR). Coordination of expectations is shown to depend on three factors: the nature of the CK initial beliefs, the degree of structural heterogeneity and the information structure. Our sufficient conditions for LSR precisely reflect these features and provide basic consistent justifications for the choice of the saddle path solution.

Abstract:
We develop a monetary model with flexible supply of labor, cash in advance constraints and government spending financed by seignorage. This model has two regimes. One regime is conventional with two steady states. The other regime has a unique steady state which can be determinate or indeterminate. In the latter case there exist sunspot equilibria which are stable under adaptive learning, taking the form of noisy finite state Markov processes at resonant frequencies. For a range of parameter values, a sufficient reduction in government purchases will eliminate these equilibria.

Indeterminacy, learnability, expectational stability, endogenous fluctuations, seignorage

Abstract:
We study how the use of judgment or "add-factors" in macroeconomic forecasting may disturb the set of equilibrium outcomes when agents learn using recursive methods. We examine the possibility of a new phenomenon, which we call exuberance equilibria, in the New Keynesian monetary policy framework. Inclusion of judgment in forecasts can lead to self-fulfilling fluctuations in a subset of the determinacy region. We study how policymakers can minimize the risk of exuberance equilibria.

Learning, expectations, excess volatility, bounded rationality, monetary policy

Abstract:
We analyze a monetary model with flexible labor supply, cash-inadvance constraints and seigniorage-financed government deficits. If the intertemporal elasticity of substitution of labor is greater than one, there are two steady states, one determinate and the other indeterminate. If the elasticity is less than one, there is a unique steady state, which can be indeterminate. Only in the latter case do there exist sunspot equilibria that are stable under adaptive learning. A sufficient reduction in government purchases can in many cases eliminate the sunspot equilibria while raising consumption/labor taxes even enough to balance the budget may fail to achieve determinacy.

Indeterminacy, learnability, expectational stability, endogenous fluctuations, seigniorage

Abstract:
We consider inflation and government debt dynamics when monetary policy employs a global interest rate rule and private agents forecast using adaptive learning. Because of the zero lower bound on interest rates, active interest rate rules are known to imply the existence of a second, low inflation steady state, below the target inflation rate. Under adaptive learning dynamics we find the additional possibility of a liquidity trap, in which the economy slips below this low inflation steady state and is driven to an even lower inflation floor that is supported by a switch to an aggressive money supply rule. Fiscal policy alone cannot push the economy out of the liquidity trap. Raising the threshold at which the money supply rule is employed can, however, dislodge the economy from the liquidity trap and ensure a return to the target equilibrium.

Learning, deflation, economic policy

Abstract:
We study the properties of generalized stochastic gradient (GSG) learning in forward-looking models. We examine how the conditions for stability of standard stochastic gradient (SG) learning both differ from and are related to E-stability, which governs stability under least squares learning. SG algorithms are sensitive to units of measurement and we show that there is a transformation of variables for which E-stability governs SG stability. GSG algorithms with constant gain have a deeper justification in terms of parameter drift, robustness and risk sensitivity.

Abstract:
Expectations about the future are central for determination of current macroeconomic outcomes and the formulation of monetary policy. Recent literature has explored ways for supplementing the benchmark of rational expectations with explicit models of expectations formation that rely on econometric learning. Some apparently natural policy rules turn out to imply expectational instability of private agents' learning. We use the standard New Keynesian model to illustrate this problem and survey the key results about interest-rate rules that deliver both uniqueness and stability of equilibrium under econometric learning. We then consider some practical concerns such as measurement errors in private expectations, observability of variables and learning of structural parameters required for policy. We also discuss some recent applications including policy design under perpetual learning, estimated models with learning, recurrent hyperinflations, and macroeconomic policy to combat liquidity traps and deflation.

Determinacy, fluctuations, imperfect knowledge, interest-rate setting, learning, stability

Abstract:
We consider the impact of anticipated policy changes when agents form expectations using adaptive learning rather than rational expectations. To model this we assume that agents combine limited structural knowledge with a standard adaptive learning rule. We analyze these issues using two well-known set-ups, an endowment economy and the Ramsey model. In our set-up there are important deviations from both rational expectations and purely adaptive learning. Our approach could be applied to many macroeconomic frameworks.

Expectations, Ramsey model, taxation

Abstract:
We examine global economic dynamics under infinite-horizon learning in a New Keynesian model in which the interest-rate rule is subject to the zero lower bound. As in Evans, Guse and Honkapohja (2008), we find that under normal monetary and fiscal policy the intended steady state is locally but not globally stable. Unstable deflationary paths can arise after large pessimistic shocks to expectations. For large expectation shocks pushing interest rates to the zero lower bound, temporary increases in government spending can be used to insulate the economy from deflation traps.

Adaptive Learning, Fiscal Policy, Monetary Policy, Zero Interest Rate Lower Bound

Abstract:
This article considers the interaction of optimal monetary policy and agents' beliefs. We assume that agents choose their information acquisition rate by minimising a loss function that depends on expected forecast errors and information costs. Endogenous inattention is a Nash equilibrium in the information processing rate. Although a decline of policy activism directly increases output volatility, it indirectly anchors expectations, which decreases output volatility. If the indirect effect dominates then the usual trade-off between output and price volatility breaks down.

Abstract:
We examine global economic dynamics under learning in a New Keynesian model in which the interest-rate rule is subject to the zero lower bound. Under normal monetary and fiscal policy, the intended steady state is locally but not globally stable. Large pessimistic shocks to expectations can lead to deflationary spirals with falling prices and falling output. To avoid this outcome we recommend augmenting normal policies with aggressive monetary and fiscal policy that guarantee a lower bound on inflation. In contrast, policies geared toward ensuring an output lower bound are insufficient for avoiding deflationary spirals.

Adaptive learning, fiscal policy, indeterminacy, monetary policy, zero interest rate lower bound

Abstract:
Earlier studies of the seigniorage inflation model have found that the high-inflation steady state is not stable under learning. We reconsider this issue and analyze the full set of solutions for the linearized model. Our main focus is on stationary hyperinflationary paths near the high-inflation steady state. These paths are shown to be stable under least squares learning if agents can utilize contemporaneous data. In an economy with a mixture of agents, some of whom only have access to lagged data, stable hyperinflationary paths emerge only if the proportion of agents with access to contemporaneous data is sufficiently high.

Indeterminacy, inflation, stability of equilibria, seigniorage

Abstract:
We consider the stability under adaptive learning of the complete set of solutions to the model x(t)= b*Ex{t+1} when |b| > 1. In addition to the fundamentals solution, the literature describes both finite-state Markov sunspot solutions and autoregressive solutions depending on an arbitrary martingale difference sequence. We clarify the relationships between these solutions and show that the stability properties of equilibria may depend crucially on the representation used by agents in the learning process. Autoregressive forms of solutions are not learnable, but finite-state Markov sunspot solutions are stable under learning if b < -1.

indeterminacy, representations of solutions, learnability, expectational stability, endogenous fluctuations

Abstract:
We examine the nonlinear model x(t)=E(t)F(x(t+1)). Markov SSEs (stationary sunspot equilibria) exist near an indeterminate steady state, x=F(x), provided |F'(x)| >1. Despite the importance of indeterminacy in macroeconomics, earlier results have not provided conditions for the existence of adaptively stable SSEs near an indeterminate steady state. We show that there exist Markov SSEs near x that are E-stable, and therefore locally stable under adaptive learning, if F'(x)<-1.

Indeterminacy, Learnability, Expectational Stability, Endogenous Fluctuations

Abstract:
Drawing upon recent contributions in the statistical literature, we present new results on the convergence of recursive, stochastic algorithms which can be applied to economic models with learning and which generalize previous results. The formal results provide probability bounds for convergence which can be used to describe the local stability under learning of rational expectations equilibria in stochastic models. Economic examples include local stability in a multivariate linear model with multiple equilibria and global convergence in a model with a unique equilibrium.

Abstract:
Drawing upon recent contributions in the statistical literature, we present a new result on the convergence of recursive, stochastic algorithms which can be applied to economic models with learning. The formal result provides probability bounds for convergence which can be used to describe the local stability under learning of rational expectations equilibria. Our treatment also generalizes previous results by permitting the state variable to follow a nonlinear Markov process. Two economic applications are discussed.