scholarly journals A generalized approach to indeterminacy in linear rational expectations models

10.3982/qe949 ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 843-868 ◽  
Author(s):  
Francesco Bianchi ◽  
Giovanni Nicolò
Keyword(s):  
State Space ◽  
Rational Expectations ◽  
Solution Method ◽  
Original Model ◽  
New Keynesian ◽  
Rational Bubbles ◽  
Software Packages ◽  
Keynesian Model ◽  
Novel Approach ◽  
Standard Software

We propose a novel approach to deal with the problem of indeterminacy in linear rational expectations models. The method consists of augmenting the original state space with a set of auxiliary exogenous equations to provide the adequate number of explosive roots in presence of indeterminacy. The solution in this expanded state space, if it exists, is always determinate, and is identical to the indeterminate solution of the original model. The proposed approach accommodates determinacy and any degree of indeterminacy, and it can be implemented even when the boundaries of the determinacy region are unknown. Thus, the researcher can estimate the model using standard software packages without restricting the estimates to the determinacy region. We combine our solution method with a novel hybrid Metropolis–Hastings algorithm to estimate the New–Keynesian model with rational bubbles by Galí (2021) over the period 1982:Q4–2007:Q3. We find that the data support the presence of two degrees of indeterminacy, implying that the central bank was not reacting strongly enough to the bubble component.

LEARNING THE INFLATION TARGET

2009 ◽  
Vol 13 (2) ◽  
pp. 167-188 ◽  
Author(s):  
Ricardo Nunes
Keyword(s):  
Rational Expectations ◽  
Solution Method ◽  
Phillips Curve ◽  
New Keynesian ◽  
New Keynesian Model ◽  
Inflation Target ◽  
Rule Of Thumb ◽  
Keynesian Model

We propose a framework in which expectations have a rational and a learning component. We describe a solution method for these frameworks and provide an application to the Volcker disinflation with the New Keynesian model. Although the model with rational expectations does not seem to account for this episode, results improve when a small and empirically plausible proportion of private agents are learning. The learning component is argued to be more robust and plausible than the rule-of-thumb expectations present in the hybrid Phillips curve.

scholarly journals Walk on the Wild Side: Temporarily Unstable Paths and Multiplicative Sunspots

2019 ◽  
Vol 109 (5) ◽  
pp. 1805-1842 ◽  
Author(s):  
Guido Ascari ◽  
Paolo Bonomolo ◽  
Hedibert F. Lopes
Keyword(s):  
Stochastic Volatility ◽  
Rational Expectations ◽  
New Keynesian ◽  
New Keynesian Model ◽  
Inflation Dynamics ◽  
Generalized Model ◽  
Keynesian Model

We propose a generalization of the rational expectations framework to allow for temporarily unstable paths. Our approach introduces multiplicative sunspot shocks and it yields drifting parameters and stochastic volatility. Then, we provide an econometric strategy to estimate this generalized model on the data. The methodology allows the data to choose between different possible alternatives: determinacy, indeterminacy, and temporary instability. We apply our methodology to US inflation dynamics in the 1970s through the lens of a simple New Keynesian model. When temporarily unstable paths are allowed, the data unambiguously select them to explain the stagflation period in the 1970s. (JEL D84, E12, E31, E32, E52)

scholarly journals The effect of central bank credibility on forward guidance in an estimated New Keynesian model

2021 ◽  
pp. 1-39
Author(s):  
Stephen J. Cole ◽  
Enrique Martínez-García
Keyword(s):  
Central Bank ◽  
Rational Expectations ◽  
New Keynesian ◽  
New Keynesian Model ◽  
Survey Of Professional Forecasters ◽  
Forward Guidance ◽  
Keynesian Model ◽  
The Us ◽  
Imperfect Credibility ◽  
Central Bank Credibility

Abstract This paper examines the effectiveness of forward guidance shocks in the US. We estimate a New Keynesian model with imperfect central bank credibility and heterogeneous expectations using Bayesian methods and survey data from the Survey of Professional Forecasters (SPF). The results provide important takeaways: (1) The estimated credibility of the Fed’s forward guidance announcements is relatively high, but anticipation effects are attenuated. Accordingly, output and inflation do not respond as favorably as in the fully credible counterfactual. (2) The so-called “forward guidance puzzle” arises partly from the unrealistically large responses of macroeconomic variables to forward guidance under perfect credibility and homogeneous fully informed rational expectations, assumptions which are found to be jointly inconsistent with the observed US data. (3) Imperfect credibility provides a plausible explanation for the empirical evidence of forecasting error predictability based on forecasting disagreement found in the SPF data. Thus, we show that accounting for imperfect credibility and forecasting disagreements is important to understand the formation of expectations and the transmission mechanism of forward guidance.

scholarly journals The implementation of stabilization policy

2021 ◽  
Vol 16 (2) ◽  
pp. 677-716
Author(s):  
Olivier Loisel
Keyword(s):  
Rational Expectations ◽  
Local Equilibrium ◽  
Policy Instrument ◽  
New Keynesian ◽  
Stabilization Policy ◽  
Keynesian Model ◽  
Dynamic Stochastic ◽  
Business Cycle Model ◽  
Feasible Path

In locally linearized dynamic stochastic rational‐expectations models, I introduce the concepts of feasible paths (paths on which the policy instrument can be expressed as a function of the policymaker's observation set) and implementable paths (paths that can be obtained, in a minimally robust way, as the unique local equilibrium under a policy‐instrument rule consistent with the policymaker's observation set). I show that, for relevant observation sets, the optimal feasible path under monetary policy can be non‐implementable in the new Keynesian model, while constant‐debt feasible paths under tax policy are always implementable in the real business cycle model. The first result sounds a note of caution about one of the main lessons of the new Keynesian literature, namely the importance for central banks to track some key unobserved exogenous rates of interest, while the second result restores to some extent the role of income or labor‐income taxes in safely stabilizing public debt. For any given implementable path, I show how to design arithmetically a policy‐instrument rule consistent with the policymaker's observation set and implementing this path as the robustly unique local equilibrium.

scholarly journals Discretionary policy and multiple equilibria in a new Keynesian model

2019 ◽  
Author(s):  
Volker Hahn
Keyword(s):  
Rational Expectations ◽  
Multiple Equilibria ◽  
Alternative Explanation ◽  
New Keynesian ◽  
Macroeconomic Fluctuations ◽  
Economic Fundamentals ◽  
Keynesian Model ◽  
Endogenous Variables ◽  
New Policies ◽  
High Degree

Abstract We show that discretionary policymaking can lead to multiple rational-expectations equilibria where the central bank responds to inflation sentiments, which are driven by past endogenous variables but are unrelated to current economic fundamentals. Some of these equilibria have favourable consequences for welfare, resulting in outcomes superior even to those achieved under timeless-perspective commitment. Inflation sentiments also provide a novel explanation for the sizeable macroeconomic fluctuations in many countries in the 1970s. Compared to interest-rate rules violating the Taylor principle, our explanation has the advantage of providing a rationale for why central banks that are confronted with inefficiently large macroeconomic fluctuations may not be able to deviate to new policies with superior macroeconomic outcomes. Moreover, we show that our approach provides an alternative explanation for the high degree of inflation persistence found in the data.

A NOTE ON TREND GROWTH AND LEARNING ABOUT MONETARY POLICY RULES IN A TWO-BLOCK WORLD ECONOMY

2015 ◽  
Vol 21 (1) ◽  
pp. 243-258
Author(s):  
Eric Schaling ◽  
Mewael F. Tesfaselassie
Keyword(s):  
Monetary Policy ◽  
Rational Expectations ◽  
World Economy ◽  
New Keynesian ◽  
Policy Rules ◽  
Monetary Policy Rules ◽  
Elasticity Of Intertemporal Substitution ◽  
Keynesian Model ◽  
Long Run ◽  
Trend Growth

We analyze the implications of openness and growth for determinacy and learnability of rational expectations equilibria in a two-country New Keynesian model with alternative monetary policy rules. Under the contemporaneous data rule, the conditions for determinacy and learnability become more stringent as a result of openness but less stringent as a result of growth, so that growth weakens the effect of openness. Under the expectations-based rule, the conditions for determinacy and learnability also become more stringent as a result of openness, whereas as a result of trend growth the conditions for determinacy also become more stringent (thus reinforcing the effect of openness) but those for learnability become less stringent (thus weakening the effect of openness). As in related studies, the elasticity of intertemporal substitution is key to our result, but within a framework that is consistent with long-run labor supply and balanced growth facts.

scholarly journals A FREQUENCY-DOMAIN APPROACH TO DYNAMIC MACROECONOMIC MODELS

2019 ◽  
pp. 1-31
Author(s):  
Fei Tan
Keyword(s):  
Frequency Domain ◽  
Rational Expectations ◽  
Likelihood Function ◽  
New Keynesian ◽  
Unified Framework ◽  
Policy Regimes ◽  
Keynesian Model ◽  
Competing Models ◽  
Frequency Domain Techniques ◽  
Frequency Domain Approach

This article proposes a unified framework for solving and estimating linear rational expectations models with a variety of frequency-domain techniques, some established, some new. The solution methodology is applicable to a wide class of models and leads to straightforward construction of the spectral density for performing likelihood-based inference. We also generalize the well-known spectral decomposition of the Gaussian likelihood function to a composite version implied by several competing models. Taken together, these techniques yield fresh insights into the model’s theoretical and empirical implications beyond conventional time-domain approaches can offer. We illustrate the proposed framework using a prototypical new Keynesian model with fiscal details and two determinate monetary–fiscal policy regimes. The model is simple enough to deliver an analytical solution that makes the policy effects transparent under each regime, yet still able to shed light on the empirical interactions between US monetary and fiscal policies along different frequencies.

MONETARY POLICY OVER TIME

2006 ◽  
Vol 10 (2) ◽  
pp. 207-229 ◽  
Author(s):  
VITOR GASPAR ◽  
FRANK SMETS ◽  
DAVID VESTIN
Keyword(s):  
Adaptive Learning ◽  
Optimal Policy ◽  
Rational Expectations ◽  
New Keynesian ◽  
Expectation Formation ◽  
Macroeconomic Modeling ◽  
Keynesian Model ◽  
Active Stabilization ◽  
Stabilization Policies ◽  
The U.S

Progress in stochastic macroeconomic modeling justifies revisiting Milton Friedman's program on the relation between macroeconomic stability and active stabilization policies. In the lecture, we use a standard new Keynesian model but depart from rational expectations by assuming that agents behave in line with adaptive learning, which increase the potential for instability in the economy.Optimal policy under adaptive learning displays some similarity with optimal policy under commitment in the rational expectations setting. Specifically, we find that optimal policy responds in a persistent manner when expectations threaten to become unhinged. Finally, we illustrate the dynamics associated with the change from a simple regime that ignores the expectation formation, to the optimal policy that does. The results are not unlike the behavior of the U.S. economy around the Volcker transition (October 1979).

scholarly journals Monetary Policy and Bubbles in a New Keynesian Model with Overlapping Generations

2021 ◽  
Vol 13 (2) ◽  
pp. 121-167
Author(s):  
Jordi Galí
Keyword(s):  
Monetary Policy ◽  
Rational Expectations ◽  
Overlapping Generations ◽  
Asset Price ◽  
New Keynesian ◽  
New Keynesian Model ◽  
Asset Price Bubbles ◽  
Price Bubbles ◽  
Keynesian Model ◽  
Welfare Implications

I analyze an extension of the New Keynesian model that features overlapping generations of finitely lived agents and (stochastic) transitions to inactivity. In contrast with the standard model, the proposed framework allows for the existence of rational expectations equilibria with asset price bubbles. I study the conditions under which bubble-driven fluctuations may emerge and the type of monetary policy rules that may prevent them. I conclude by discussing some of the model’s welfare implications. (JEL E12, E32, E44, E52, E63)

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