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2003, SSRN Electronic Journal
In this paper we analyse disinflation policy in two environments. In the first, the central bank has perfect knowledge, in the sense that it understands and observes the process by which private sector inflation expectations are generated; in the second, the central bank has to learn the private sector inflation forecasting rule. With imperfect knowledge, results depend on the learning scheme that is employed. Here, the learning scheme we investigate is that of least-squares learning (recursive OLS) using the Kalman filter. A novel feature of a learningbased policy -as against the central bank's disinflation policy under perfect knowledge -is that the degree of monetary accommodation (the extent to which the central bank accommodates private sector inflation expectations) is no longer constant across the disinflation, but becomes state-dependent. This means that the central bank's behaviour changes during the disinflation as it collects more information.
Handbook of Monetary Economics, 2010
This chapter investigates the implications of adaptive learning in the private sector's formation of inflation expectations for the conduct of monetary policy. We analyze the determinants of optimal monetary policy in the standard New Keynesian model, when the central bank minimizes an explicit loss function and has full information about the structure of the economy, including the precise mechanism generating private sector's expectations. The focus on optimal policy allows us to investigate how and to what extent a change in the assumption of how agents form their inflation expectations affects the principles of optimal monetary policy. It also provides a benchmark to evaluate simple policy rules. We find that departures from rational expectations increase the potential for instability in the economy, thereby strengthening the importance of managing (anchoring) inflation expectations. We also find that the simple commitment rule under rational expectations is robust when expectations are formed in line with adaptive learning.
European Economic Review, 2014
Earlier research on optimal monetary policy under learning uses optimality conditions derived under rational expectations. In this paper instead, we derive optimal monetary policy when the central bank knows the algorithm followed by agents to form their expectations and makes active use of the learning behavior. There is a well known intratemporal tradeoff between inflation and output gap stabilization. We show there is also an intertemporal tradeoff generated by the central banks possibility to influence future expectations. The optimal interest rate rule reacts more aggressively to out-of-equilibrium inflation expectations than what would be optimal under rational expectations, as the central bank exploits its possibility to "drive" future expectations closer to equilibrium. Moreover, if beliefs are updated according to recursive least squares, the optimal policy is time-varying. * We are grateful to Seppo Honkapohja, Albert Marcet and Ramon Marimon for very helpful comments and suggestions. All the remaining errors are our own.
Computing in Economics and Finance, 2006
We consider optimal policy when private sector expectations are formed through adaptive learning. Earlier research has found that adaptive learning is consistent with empirical evidence on private sector expectations. In this paper, we consider the (admittedly) extreme case of sophisticated central banking, whereby the central bank has full knowledge about the structure of the economy. Our results confirm that the management of inflation expectations is crucial for the conduct of monetary policy. n particular, when the private sector perceives that inflation persistence is high, optimal policy responds strongly to lagged inflation and inflation shocks thereby stabilizing inflation and anchoring inflation expectations. For our parametrization it does so at no cost for output gap stability
2002
Various measures indicate that inflation expectations evolve sluggishly relative to actual inflation. In addition, they often fail conventional tests of unbiasedness. These observations are sometimes interpreted as evidence against rational expectations. The authors embed, within a standard monetary dynamic stochastic general-equilibrium model, an information friction and a learning mechanism regarding the interest-rate-targeting rule that monetary policy authorities follow. The learning mechanism enables optimizing economic agents to distinguish between transitory shocks to the policy rule and occasional shifts in the inflation target of monetary policy authorities. The model's simulated data are consistent with the empirical evidence. When the information friction is activated, simulated inflation expectations fail conventional unbiasedness tests much more frequently than in the complete-information case when this friction is shut down. These results suggest that an important size distortion may occur when conventional tests of unbiasedness are applied to relatively small samples dominated by a few significant shifts in monetary policy and sluggish learning about those shifts.
SSRN Electronic Journal, 2000
In this paper we incorporate the term structure of interest rates in a standard inflation forecast targeting framework. Learning about the transmission process of monetary policy is introduced by having heterogeneous agents -i.e. the central bank and private agents -who have different information sets about the future sequence of short-term interest rates. We analyse inflation forecast targeting in two environments. One in which the central bank has perfect knowledge, in the sense that it understands and observes the process by which private sector interest rate expectations are generated, and one in which the central bank has imperfect knowledge and has to learn the private sector forecasting rule for short-term interest rates. In the case of imperfect knowledge, the central bank has to learn about private sector interest rate expectations, as the latter affect the impact of monetary policy through the expectations theory of the term structure of interest rates. Here following , the learning scheme we investigate is that of least-squares learning (recursive OLS) using the Kalman filter. We find that optimal monetary policy under learning is a policy that separates estimation and control. Therefore, this model suggests that the practical relevance of the breakdown of the separation principle and the need for experimentation in policy may be limited.
The Economic Journal, 2013
We analyze the e¤ects of social learning in a widely-studied monetary policy context. Social learning might be viewed as more descriptive of actual learning behavior in complex market economies. Ideas about how best to forecast the economy's state vector are initially heterogeneous. Agents can copy better forecasting techniques and discard those techniques which are less successful. We seek to understand whether the economy will converge to a rational expectations equilibrium under this more realistic learning dynamic. A key result from the literature in the version of the model we study is that the Taylor Principle governs both the uniqueness and the expectational stability of the rational expectations equilibrium when all agents learn homogeneously using recursive algorithms. We …nd that the Taylor Principle is not necessary for convergence in a social learning context. We also contribute to the use of genetic algorithm learning in stochastic environments.
SSRN Electronic Journal, 2000
The paper studies the implications for the effectiveness of discretionary monetary policymaking of departing from the assumption of rational expectations. Society, whose welfare function is quadratic, can appoint a central banker whose preferences are either quadratic or lexicographic, to achieve the best mix of inflation and output stability. The focus on lexicographic preferences is justified on the grounds that they imply a strict ordering of policy objectives, which is typical of the mandate of several central banks. Both the private sector and the monetary policymaker have incomplete knowledge of the working of the economy and rely upon adaptive learning to form expectations and decide policy moves. The model economy is assumed to be subject to recurrent unobserved shifts, and the monetary authority, who has private information on the shocks hitting the economy, cannot credibly commit. The main finding of the paper is that when agents rely on an adaptive learning technology, a bias against activist policies arises. The paper also shows that when society has quadratic utility, a strategy based on a strict ordering of objectives is close to optimal for a wide range of values of the inflation aversion parameter.
The normal assumption of full information is dropped and the choice of monetary policy rules is instead examined when private agents must learn the rule. A small, forward-looking model is estimated and stochastic simulations conducted with agents using discounted least squares to learn of a change of preferences or a switch to a more complex rule. We "nd that the costs of learning a new rule may be substantial, depending on preferences and the rule that is initially in place. Policymakers with strong preferences for in#ation control incur substantial costs when they change the rule in use, but are nearly always willing to bear the costs. Policymakers with weak preferences for in#ation control may actually bene"t from agents' prior belief that a strong rule is in place. : S 0 1 6 5 -1 8 8 9 ( 9 9 ) 0 0 0 7 5 -5 examine rules that are optimal in each of three models for their performance in the other models as a check on robustness of candidate rules.
Macroeconomic Dynamics
In a canonical monetary policy model in which the central bank learns about underlying fundamentals by estimating the parameters of a Phillips curve, we show that the bank’s loss function is asymmetric such that parameter overestimates may be more or less costly than underestimates, creating a precautionary motive in estimation. This motive suggests the use of a more efficient variance-adjusted least-squares estimator for learning about fundamentals. Informed by this “precautionary learning” the central bank sets low inflation targets, and the economy can settle near a Ramsey equilibrium.
Macroeconomic Dynamics, 2020
Drawing on a considerable empirical literature that reveals persistent and endogenously time-varying heterogeneity in inflation expectations, this paper embeds two inflation forecasting strategiesone based on costly ex ante full rationality or perfect foresight, and the second based on costless ex ante bounded rationality or extrapolative trend-followingin a dynamic macroeconomic model. Drawing also on the significant empirical evidence that inflation forecast errors may have to exceed some threshold before agents abandon their previously selected inflation forecasting strategy, we describe agents as switching between inflation forecasting strategies according to evolutionarily satisficing learning dynamics. We find that convergence to a long-run equilibrium consistent with growth, unemployment and inflation at their natural levels may be achieved even when heterogeneity in inflation expectations (with predominance of the extrapolative trend-following foresight strategy) is an attractor of an evolutionarily satisficing learning dynamic perturbed by mutant agents. Therefore, in keeping with robust empirical evidence, heterogeneity in strategies to form inflation expectations (with prevalence of boundedly rational expectations) can be a stable long-run equilibrium.
SSRN Electronic Journal, 2000
We study the impact of the publication of central bank's macroeconomic projections on the dynamic properties of an economy where: (i) private agents have incomplete information and form their expectations using recursive learning algorithms, (ii) the short-term nominal interest rate is set as a linear function of the deviations of inflation and real output from their target level and (iii) the central bank, ignoring the exact mechanism used by private agents to form expectations, assumes that it can be reasonably approximated by perfect rationality and releases macroeconomic projections consistent with this assumption. Results in terms of stability of the equilibrium and speed of convergence of the learning process crucially depend on the set of macroeconomic projections released by the central bank. In particular, while the publication of inflation and output gap projections enlarges the set of interest rate rules associated with stable equilibria under learning and helps agents to learn faster, the announcement of the interest rate path exerts the opposite effect. In the latter case, in order to stabilize expectations and to speed up the learning process the response of the policy instrument to inflation should be stronger than under no announcement.
The macroeconomic costs of disinflation are considered for the United States in a rational expectations macroeconometric model with sticky prices and imperfect information regarding monetary policy objectives. The analysis centers on simulation experiments using the Board's new quarterly macroeconometric model, FRB/US, within which are nested both expectations formation that is 'rational' (i.e., model consistent) and 'restricted-information rational' (i.e., where the information set is restricted to that captured by a small-scale VAR model). We characterize monetary policy as being governed by rules. Disinflations are represented by changes in the target inflation rate of a interest-rate reaction function. Two kinds of rules are considered: a version of the Taylor rule and the other being a more aggressive and richer specification estimated using data for the last 15 years. We assume agents are not fully cognizant of changes in the Fed's inflation target and must instead adjust their perceptions of the target according to a linear updating rule. Simulation results for sacrifice ratios are compared with results from other models and with econometric results and calculations reported in the literature.
2017
The paper studies how a prolonged period of subdued price developments may induce a de-anchoring of inflation expectations from the central bank's objective. This is shown within a framework where agents form expectations using adaptive learning, choosing among a set of alternative forecasting models. The analysis is accompanied by empirical evidence on the properties of inflation expectations in the euro area. Our results also suggest that monetary policy may lose effectiveness if delayed too much, as expectations are allowed to drift away from target for too long. JEL Classification: E31, E37, E58, D83
Journal of Money, Credit, and Banking, 2003
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.
SSRN Electronic Journal, 2008
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 interestrate 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.
2008
This paper introduces adaptive learning and endogenous indexation in the New-Keynesian Phillips curve and studies disinflation under inflation targeting policies. The analysis is motivated by the disinflation performance of many inflation-targeting countries, in particular the gradual Chilean disinflation with temporary annual targets. At the start of the disinflation episode price-setting firms’ expect inflation to be highly persistent and opt for backwardlooking indexation. As the central bank acts to bring inflation under control, price-setting firms revise their estimates of the degree of persistence. Such adaptive learning lowers the cost of disinflation. This reduction can be exploited by a gradual approach to disinflation. Firms that choose the rate for indexation also re-assess the likelihood that announced inflation targets determine steady-state inflation and adjust indexation of contracts accordingly. A strategy of announcing and pursuing short-term targets for inflation ...
Journal of Economic Dynamics and Control, 2007
Under the assumption of bounded rationality, economic agents learn from their past mistaken predictions by combining new and old information to form new beliefs. The purpose of this paper is to investigate how the policy-maker, by affecting private agents' learning process, determines the speed at which the economy converges to the rational expectation equilibrium. I find that by reacting strongly to private agents' expected inflation, a central bank increases the speed of convergence and shortens the length of the transition to the rational expectation equilibrium. I use speed of convergence as an additional criterion for evaluating alternative monetary policies. I find that a fast convergence is not always desirable.
SSRN Electronic Journal, 2003
We investigate the effectiveness of an aggressive anti-inßation monetary policy on the ability of agents to achieve rational expectations equilibrium (REE) forecasts of inßation. An aggressive anti-inßation policy includes a willingness to respond more forcefully to deviations from an inßation target. Using an adaptive learning framework, we develop a model that uses a real contracting rigidity in conjunction with an interest rate rule and an IS curve. The model equilibrium indicates that only an aggressive anti-inßation policy enables agents to learn the REE inßation forecast. The model also shows that inßation persistence (volatility) has a negative relation with policy aggressiveness. Empirical tests conÞrm this negative relation but these tests also indicate there is a lag between aggressive policy shifts and effective changes in inßation persistence (volatility).
Journal of Economic Dynamics and Control, 2005
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.
Macroeconomic Dynamics, 2001
Inflation and the monetary financing of deficits are analyzed in a model in which the deficit is constrained to be less than a given fraction of a measure of aggregate market activity. Depending on parameter values, the model can have multiple steady states. Under adaptive learning with heterogeneous learning rules, there is convergence to a subset of these steady states. In some cases, a high-inflation constrained steady state will emerge. However, with a sufficiently tight fiscal constraint, the low-inflation steady state is globally stable. We provide experimental evidence in support of our theoretical results.
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