Solving Heterogeneous Agent Models With The Master Equation

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Solving Heterogeneous Agent Models With The Master Equation

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Author : Adrien Bilal
language : en
Publisher:
Release Date : 2023

Solving Heterogeneous Agent Models With The Master Equation written by Adrien Bilal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.

This paper proposes an analytic representation of perturbations in heterogeneous agent economies with aggregate shocks. Treating the underlying distribution as an explicit state variable, a single value function defined on an infinite-dimensional state space provides a fully recursive representation of the economy: the 'Master Equation' introduced in the mathematics mean field games literature. I show that analytic local perturbations of the Master Equation around steady-state deliver dramatic simplifications. The First-order Approximation to the Master Equation (FAME) reduces to a standard Bellman equation for the directional derivatives of the value function with respect to the distribution and aggregate shocks. The FAME has six main advantages: (i) finite dimension; (ii) closed-form mapping to steady-state objects; (iii) applicability when many distributional moments or prices enter individuals' decision such as dynamic trade, urban or job ladder settings; (iv) block-recursivity bypassing further fixed points; (v) mapping to analytic sequence-space derivatives; (vi) fast implementation using standard numerical methods. I develop the Second-order Approximation to the Master Equation (SAME) and show that it shares these properties, making the approach amenable to settings such as asset pricing. I apply the method to two economies: an incomplete market model with unemployment and a wage ladder, and a discrete choice spatial model with migration.

Modelling With The Master Equation

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Author : Günter Haag
language : en
Publisher: Springer
Release Date : 2017-07-31

Modelling With The Master Equation written by Günter Haag and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-31 with Social Science categories.

This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples. Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences. The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach. Drawing upon the author’s extensive teaching and research experience and consulting work, the book offers a valuable guide for researchers, graduate students and professionals alike.

Solving Heterogeneous Agent Models In Discrete Time With Many Idiosyncratic States By Perturbation Methods

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Author : Christian Bayer
language : en
Publisher:
Release Date : 2018

Solving Heterogeneous Agent Models In Discrete Time With Many Idiosyncratic States By Perturbation Methods written by Christian Bayer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Econometric models categories.

This paper describes a method for solving heterogeneous agent models with aggregate risk and many idiosyncratic states formulated in discrete time. It extends the method proposed by Reiter (2009) and complements recent work by Ahn et al. (2017) on how to solve such models in continuous time. We suggest first solving for the stationary equilibrium of the model without aggregate risk. We then write the functionals that describe the recursive equilibrium as sparse expansions around their stationary equilibrium counterparts. Finally we use the perturbation method of Schmitt-Grohé and Uribe (2004) to approximate the aggregate dynamics of the model.

Solving Heterogeneous Agent Models By Projection And Perturbation

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Author : Michael Reiter, 1962-
language : en
Publisher:
Release Date : 2006

Solving Heterogeneous Agent Models By Projection And Perturbation written by Michael Reiter, 1962- and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.

Improving Heterogeneous Agent Models By Avoiding Explicit Discretizations Of Stiff Equations

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Author : Michael Heinrich Baumann
language : en
Publisher:
Release Date : 2020

Improving Heterogeneous Agent Models By Avoiding Explicit Discretizations Of Stiff Equations written by Michael Heinrich Baumann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.

Solving Heterogeneous Agent Models With Parametrized Cross Sectoral Distributions

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Author : Yann Algan
language : en
Publisher:
Release Date : 2007

Solving Heterogeneous Agent Models With Parametrized Cross Sectoral Distributions written by Yann Algan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.

Solving Heterogeneous Agent Models With Parameterized Cros Sectional Distributions

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Author : Yann Algan
language : en
Publisher:
Release Date : 2007

Solving Heterogeneous Agent Models With Parameterized Cros Sectional Distributions written by Yann Algan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.

A Perturbational Approach For Approximating Heterogeneous Agent Models

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Author : Anmol Bhandari
language : en
Publisher:
Release Date : 2023

A Perturbational Approach For Approximating Heterogeneous Agent Models written by Anmol Bhandari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.

We develop a perturbational technique to approximate equilibria of a wide class of discrete-time dynamic stochastic general equilibrium heterogeneous-agent models with complex state spaces, including multi-dimensional distributions of endogenous variables. We show that approximating policy functions and stochastic process that governs the distributional state to any order is equivalent to solving small systems of linear equations that characterize values of certain directional derivatives. We analytically derive the coefficients of these linear systems and show that they satisfy simple recursive relations, making their numerical implementation quick and efficient. Compared to existing state-of-the-art techniques, our method is faster in constructing first-order approximations and extends to higher orders, capturing the effects of risk that are ignored by many current methods. We illustrate how to apply our method to a broad set of questions such as impacts of first- and second-moment shocks, welfare effect of macroeconomic risk and stabilization policies, endogenous household portfolio formation, and transition dynamics in heterogeneous agent general equilibrium settings.

Econophysics Of Agent Based Models

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Author : Frédéric Abergel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-07

Econophysics Of Agent Based Models written by Frédéric Abergel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-07 with Science categories.

The primary goal of this book is to present the research findings and conclusions of physicists, economists, mathematicians and financial engineers working in the field of "Econophysics" who have undertaken agent-based modelling, comparison with empirical studies and related investigations. Most standard economic models assume the existence of the representative agent, who is “perfectly rational” and applies the utility maximization principle when taking action. One reason for this is the desire to keep models mathematically tractable: no tools are available to economists for solving non-linear models of heterogeneous adaptive agents without explicit optimization. In contrast, multi-agent models, which originated from statistical physics considerations, allow us to go beyond the prototype theories of traditional economics involving the representative agent. This book is based on the Econophys-Kolkata VII Workshop, at which many such modelling efforts were presented. In the book, leading researchers in their fields report on their latest work, consider recent developments and review the contemporary literature.

Improving Tatonnement Methods For Solving Heterogeneous Agent Models

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Author : Alexander Ludwig
language : en
Publisher:
Release Date : 2004

Improving Tatonnement Methods For Solving Heterogeneous Agent Models written by Alexander Ludwig and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.