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Author: Anmol Bhandari Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
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.
Author: Anmol Bhandari Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
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.
Author: Christian Bayer Publisher: ISBN: Category : Econometric models Languages : en Pages : 0
Book Description
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.
Author: Michael Reiter Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This paper develops a method to compute second-order perturbations of discretetime heterogeneous agent models. It addresses the three main tasks to make secondorder approximations tractable: state reduction, generating sufficient smoothness, and fast computation of the quadratic terms in the perturbation solution. The method is applied to a model with divisible labor, one with indivisible labor, and to an OLG model with stochastic aging. Compared to a linearized solution, second-order perturbations achieve substantially higher accuracy if models are subject to large or medium-sized aggregate shocks. They also capture precautionary behavior with respect to aggregate shocks. A general method of state reduction is developed, called "conditional-expectations approach". In the example models, it performs better in terms of accuracy and reliability than alternative approaches.
Author: Sergio Ocampo Díaz Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Computing population moments for heterogeneous agent models is a necessary step for their estimation and evaluation. Computation based on Monte Carlo methods is usually time- and resource-consuming because it involves simulating a large sample of agents and potentially tracking them over time. We argue in favor of an alternative method for computing both cross-sectional and longitudinal moments that exploits the endogenous Markov transition function that defines the stationary distribution of agents in the model. The method relies on following the distribution of populations of interest by iterating forward the Markov transition function rather than focusing on a simulated sample of agents. Approximations of this function are readily available from standard solution methods of dynamic programming problems. The method provides precise estimates of moments like top-wealth shares, auto-correlations, transition rates, or age-profiles, at lower time- and resource-costs compared to Monte Carlo based methods.
Author: Anmol Bhandari
Author: Anmol Bhandari
Author: Michael Reiter, 1962-
Author: Christian Bayer
Author: Michael Reiter
Author: Carsien Harm Hommes
Author: Michael Heinrich Baumann
Author: Carsien Harm Hommes
Author: Laura Liu
Author: Sergio Ocampo Díaz
Author: Yann Algan