Heterogeneous learning

Giannitsarou, Chryssi

doi:10.1016/s1094-2025(03)00011-5

Cited by 42 publications

(54 citation statements)

References 24 publications

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“…it has eigenvalues with strictly negative real parts). 5 A widely used learning algorithm is the recursive least squares, which is expressed as…”

Section: The Modelmentioning

confidence: 99%

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E-Stability Does Not Imply Learnability

Giannitsarou

2005

Macroecon. Dynam.

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Abstract. The concept of E-stability is widely used as a learnability criterion in studies of macroeconomic dynamics with adaptive learning. In this paper, it is demonstrated, via a counterexample, that E-stability does not in general imply learnability of rational expectations equilibria. The result indicates that E-stability may not a robust device for equilibrium selection.JEL Classification: D83, C62 Keywords: Adaptive learning, E-stability, learnability of REE Introduction and BackgroundIn recent years, there has been an explosion in research that studies macroeconomic dynamics with adaptive learning. 1 A key question in this literature is whether it is possible for agents that update their expectations using econometric algorithms (i.e. learn adaptively) to learn the rational expectations equilibrium (REE) as the sample size of their data set increases. This is also known as learnability of an REE. Since conditions for learnability are typically hard to pin down in a direct way, researchers have been looking for (and have often successfully developed) indirect ways for identifying them. One such popular approach is the E-stability criterion.In this paper, I revisit the concept of E-stability and demonstrate, via a counterexample, that E-stability does not always imply learnability of an REE. The example used is a generic reduced form model with expectations dated at time t and a lag of the endogenous variable. In particular, it is shown that, for certain parameter regions for which E-stability holds for a minimal state variable (MSV) solution, there is a learning algorithm (namely stochastic gradient) that does not converge to the solution, i.e. the REE is not learnable. Furthermore, I discuss some examples of economic models that can be expressed in this reduced form.The fact that E-stability may not always be an appropriate learnability criterion is not entirely new to the literature. This possibility has been pointed out by Barucci and Landi (1997) and further explored by Heinemann (2000). Nevertheless, in the former article, there is no example confirming the assertion. The latter article provides an example for which numerical simulations indicate that stability or instability under stochastic gradient learning is independent of the Estability conditions; in particular, it is shown that the stochastic gradient algorithm converges to an E-unstable solution, i.e. that E-stability is not a necessary condition for learnability. In the present paper, it is further shown that there may exist E-stable equilibria that are not learnable by a stochastic gradient algorithm, or in other words, that E-stability is not a sufficient condition for learnability.

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“…it has eigenvalues with strictly negative real parts). 5 A widely used learning algorithm is the recursive least squares, which is expressed as…”

Section: The Modelmentioning

confidence: 99%

“…The analysis of E-stability or instability of such solutions is beyond the scope of this paper. 5 The concept of E-stability is extensively discussed in Evans and Honkapohja (2001).…”

Section: The Modelmentioning

confidence: 99%

E-Stability Does Not Imply Learnability

Giannitsarou

2005

Macroecon. Dynam.

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“…Berardi (2007) finds the conditions under which the HEE is learnable while the REE is not under a correctly specified learning rule. Berardi (2009b) argues that heterogeneity plays an important role in the central bank's policy 2 See Giannitsarou (2003) and Honkapohja and Mitra (2006) to find the stream of research on heterogeneous learning. Heterogeneous learning has also been discussed from two other viewpoints.…”

Section: Introductionmentioning

confidence: 99%

“…Heterogeneous learning has also been discussed from two other viewpoints. First, Honkapohja (1996, 2001), Giannitsarou (2003), and Honkapohja and Mitra (2006) investigate stability conditions in a situation in which agents have different initial beliefs about the parameters in their homogeneous econometric models. They find that the heterogeneity in adaptive learning gradually disappears, and the equilibrium is as learnable as to converge to a REE.…”

Section: Introductionmentioning

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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“…Some other authors, namely, Arthur et al (1997), Martin and Sunley (2007) and Fontana (2008), systematize the main features a model fitted to discuss real world events should contain: besides contemplating agent heterogeneity, it must take into consideration that dynamic processes are not immutable in time, because agents are evolving organisms that adapt and learn; furthermore, it should capture the evidence 1 See, e.g., Barucci (1999), Chiarella and He (2002), Giannitsarou (2003), Negroni (2003), Branch and McGough (2004), Gomes (2005) and Gallegati et al (2011), on evolutionary and adaptive learning, herding behavior, bubbles and related phenomena, in connection with the presence of belief heterogeneity in the economic system. 2 The idea that the economic system should be viewed and analyzed as a complex entity is vigorously emphasized by authors such as Colander et al (2004), Markose (2005) that interaction determines aggregate outcomes because the economy is an interconnected and selforganized world.…”

Section: Introductionmentioning

confidence: 99%

Attentiveness cycles: synchronized behavior and aggregate fluctuations

Gomes

2012

Rev. Bras. Econ.

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A sticky-information macroeconomic model is developed in order to analyze the behavior of the time trajectories of the inflation rate and of the output gap, when disturbed by eventual monetary policy shocks. In opposition to what is typical in the literature on this subject, different paces on information updating explicitly lead to a setting with interaction among heterogeneous agents. Specifically, we consider firms with different information updating frequencies whose behavior implies the emergence of attentiveness cycles of possibly large lengths; within these cycles we deduct a differently shaped Phillips curve for each time period. Systematic changes on the form of the aggregate supply relation will be the engine that triggers a sluggish response to shocks and the eventual persistence of business fluctuations. Um modelo macroeconómico envolvendo rigidez de informação é desenvolvido de forma a analisar o comportamento das trajetórias temporais

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Heterogeneous learning

Cited by 42 publications

References 24 publications

E-Stability Does Not Imply Learnability

E-Stability Does Not Imply Learnability

Learnability of Heterogeneous Misspecification Equilibrium

Attentiveness cycles: synchronized behavior and aggregate fluctuations

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