Convergence of least squares learning mechanisms in self-referential linear stochastic models

Marcet, Albert; Sargent, Thomas J.

doi:10.1016/0022-0531(89)90032-x

Cited by 708 publications

(460 citation statements)

References 13 publications

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“…While Rational Expectations provides a natural benchmark, there is a rapidly expanding literature, e.g. Marcet and Sargent (1989), Brock and Hommes (1997), Sargent (1999), Evans and Honkapohja (2001), and Marcet and Nicolini (2003), which replaces rational expectations with statistical learning rules. This alternative approach, it is argued, is a reasonable description of agents' actual forecasting acumen because it assumes behavior consistent with econometric practice.…”

Section: Introductionmentioning

confidence: 99%

Model uncertainty and endogenous volatility

Branch

Evans

2007

Review of Economic Dynamics

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This paper identifies two channels through which the economy can generate endogenous inflation and output volatility, an empirical regularity, by introducing model uncertainty into a Lucas-type monetary model. The equilibrium path of inflation depends on agents' expectations and a vector of exogenous random variables. Following Branch and Evans agents are assumed to underparameterize their forecasting models [Branch, W., Evans, G.W., 2006a. Intrinsic heterogeneity in expectation formation. Journal of Economic Theory 127, 264-295]. A Misspecification Equilibrium arises when beliefs are optimal, given the misspecification, and predictor proportions are based on relative forecast performance. We show that there may exist multiple Misspecification Equilibria, a subset of which is stable under least squares learning and dynamic predictor selection. The dual channels of least squares parameter updating and dynamic predictor selection combine to generate regime switching and endogenous volatility.

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Section: Introductionmentioning

confidence: 99%

Model uncertainty and endogenous volatility

Branch

Evans

2007

Review of Economic Dynamics

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“…A credible benchmark against which to compare these robust rules, are what we shall refer to as optimized rules. These are rules that minimize (35) subject to (29), (30), (31) and one of either (32), (34) or (33). Such rules can be optimized using a standard hill-climbing algorithm using methods well described in the appendix to Tetlow and von zur…”

Section: Resultsmentioning

confidence: 99%

“…expectations applications since proponents had an answer to the question "how could people come to have rational expectations?" The theory has been advanced by the work of Marcet and Sargent [33] and Evans and Honkapohja [various]. Our rendition follows Evans and Honkapohja [17], chapters 8-10.…”

Section: Expectational Equilibrium Under Adaptive Learningmentioning

confidence: 99%

“…4 The learnability literature takes a step back from rational expectations and asks whether the choices of uninformed private agents could be expected to converge on a rational expectations equilibrium (REE) as the outcome of a process of learning. Important early papers in this literature include Bray [5], Bray and Savin [6] and Marcet and Sargent [33]. Evans and Honkapohja summarize some of their many contributions to this literature in their book [17].…”

Section: Introductionmentioning

confidence: 99%

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Robustifying learnability

Tetlow

Muehlen

2009

Journal of Economic Dynamics and Control

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“…where c + i,t is a m × n matrix (0, ..., 0, c i,t , 0, ..., 0), which corresponds to c t ≡ (c 1,t , c 2,t , ..., c n,t The convergence of the SRA is studied as the stochastic approximation approach by Marcet and Sargent (1989). This is also introduced by Evans and Honkapohja (2001, chapter 6).…”

Section: A Derivation Of Definitionmentioning

confidence: 99%

Learnability of Heterogeneous Misspecification Equilibrium

Nakagawa

2012

SSRN Journal

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This paper investigates the learnability of the equilibrium under adaptive learning with heterogeneous and misspecified models. Agents have imperfect and mutually different information sets of economic variables, so they form heterogeneous expectations under learning rules that are differently underparameterized. Under heterogeneous learning, the economy converges to a type of restricted perceptions equilibrium, which here is called a Heterogeneous Misspecification Equilibrium (HME). The paper finds that the HME is more learnable than the equilibrium under homogeneous and correctly specified learning rules that corresponds to a rational expectations equilibrium (REE); in other words, the stability conditions of the HME are less stringent than those of the REE. In a basic NK model with a Taylor-type monetary policy rule, for example, the central bank is allowed to choose a wider range of values of policy parameters to ensure the learnability of the HME than that permitted to ensure the learnability of the REE, that is, the Taylor principle. In addition, if the correlation between demand and supply shocks is low, the stability conditions of the HME become further less stringent so that the central bank might not have to address the learnability of the equilibrium.

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Convergence of least squares learning mechanisms in self-referential linear stochastic models

Cited by 708 publications

References 13 publications

Model uncertainty and endogenous volatility

Model uncertainty and endogenous volatility

Robustifying learnability

Learnability of Heterogeneous Misspecification Equilibrium

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