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Session 4: Computational Methods for Dynamic Economies and Games

August 1-3, 2016

Organized by:

  • Kenneth Judd, Hoover Institution, Stanford University
  • Felix Kubler, University of Zurich
  • Thomas Sargent, New York University
  • Karl Schmedders, University of Zurich
  • Christopher Sleet, Carnegie Mellon University
  • Sevin Yeltekin, Carnegie Mellon University

Pre-registration is mandatory for all non-presenter attendees. Session begins Monday, 8/1, around 9am, and ends Wednesday, 8/3, 3:15pm, and will be held at Landau Economics Bldg, Lucas Conference Room A, 579 Serra Mall.

Dynamic economies with heterogeneous agents are naturally high dimensional objects. Their quantitative analysis requires efficient and accurate optimization and approximation procedures. This session will include papers that develop numerical methods for dynamic heterogeneous agent competitive models with many agents and strategic models with finite agents. The primary focus will be on numerical solutions to contracting problems in discrete and continuous time, mean field games, dynamic recursive games and dynamic general equilibrium models. We seek applications to problems in industrial organization (e.g. firm dynamics and size distribution), finance (e.g. information percolation), and macroeconomics (e.g. income and wealth distribution, knowledge diffusion and growth, optimal social insurance).

In this Session

Aug 1 | 9:30 am to 10:45 am

On the Solution and Application of Rational Expectations Models with Function-Valued States

Presented by: David Childers, Yale University

Many variables of interest to economists take the form of time-varying distributions or functions. This high-dimensional ‘functional’ data can be interpreted in the context of economic models with function-valued endogenous variables, but deriving the implications of these models requires solving a nonlinear system for a potentially infinite-dimensional function of infinite-dimensional objects. To overcome this difficulty, I provide methods for characterizing and numerically approximating the equilibria of dynamic, stochastic, general equilibrium models with function-valued state variables by linearization in function space and representation using basis functions.

Aug 1 | 11:00 am to 12:15 pm

Controlling a Distribution of Heterogeneous Agents

Presented by: Galo Nuño, Banco de España
Co-Author(s): Benjamin Moll, Princeton University

This paper analyzes the problem of a benevolent planner who wants to control a population of heterogeneous agents subject to idiosyncratic shocks. This is equivalent to a deterministic control problem in which the state variable is the cross-sectional distribution. We show how, in continuous time, this problem can be broken down into a dynamic programming equation plus the law of motion of the distribution and we introduce a new numerical algorithm to solve it. As an application, we analyze the constrained-efficient allocation of an Aiyagari economy with a fat-tailed wealth distribution.

Aug 1 | 1:00 pm to 2:15 pm

A Toolbox for Solving and Estimating Heterogeneous Agent Macro Models

Presented by: Thomas Winberry, University of Chicago
I develop a new method to solve and estimate heterogeneous agent macro models. The main challenge is that the state vector contains the distribution of microeconomic agents, which is typically infinite-dimensional. I approximate the distribution with a flexible parametric family, reducing the dimensionality to a finite set of parameters, and solve for the dynamics of these parameters by perturbation. I implement the method in Dynare and find that it is accurate and extremely efficient. As an illustration, I use the method to estimate a heterogeneous firm model with neutral and investment-specific productivity shocks using Bayesian techniques. The behavior of firms at the micro level matters quantitatively for inference about the aggregate shock processes, suggesting an important role for micro data in estimating macro models.
Aug 1 | 2:30 pm to 3:45 pm

Approximate Aggregation in the Neoclassical Growth Model with Idiosyncratic Shocks

Presented by: Todd Walker, Indiana University
Co-Author(s): Nets Katz, California Institute of Technology; Karsten Chipeniuk, Indiana University
Aug 2 | 9:00 am to 10:15 am

The Macro-dynamics of Sorting between Workers and Firms

Presented by: Jeremy Lise, University College London
Co-Author(s): Jean-Marc Robin, Sciences Po, Paris

We develop an equilibrium model of on-the-job search with ex-ante heterogeneous workers and firms, aggregate uncertainty and vacancy creation. The model produces rich dynamics in which the distributions of unemployed workers, vacancies and worker-firm matches evolve stochastically over time. We prove that the surplus function, which fully characterizes the match value and the mobility decision of workers, does not depend on these distributions. This result means the model is tractable and can be estimated.

Aug 2 | 10:30 am to 11:45 am

Ranking Firms Using Revealed Preference

Presented by: Isaac Sorkin, Stanford University

Firms account for a substantial share of earnings inequality. Although the standard explanation is that search frictions support an equilibrium with rents, this paper finds that compensating differentials are at least as important. To reach this finding, this paper develops a structural search model and estimates it on U.S. administrative data with 1.5 million firms and 100 million workers. The model analyzes the revealed preference information contained in how workers move between firms.

Aug 2 | 12:30 pm to 1:45 pm

What Accounts for the Racial Gap in Time Allocation and Intergenerational Transmission of Human Capital?

Presented by: George-Levi Gayle, Washington University in St. Louis
Co-Author(s): Limor Golan, Washington University in St. Louis; Mehmet A. Soytas, Ozyegin University
Aug 2 | 2:00 pm to 3:15 pm

The Effects of Moral Hazard on Wage Inequality in a Frictional Labor Market

Presented by: Susanne Forstner, RWTH Aachen University
Co-Author(s): Árpád Ábrahám, European University Institute; Fernando Alvarez-Parra, CAF
Aug 2 | 3:30 pm to 4:45 pm

Asset Pricing with Heterogeneous Agents and Long-Run Risk

Presented by: Ole Wilms, University of Zurich
Co-Author(s): Karl Schmedders & Walt Pohl, University of Zurich
Aug 3 | 9:00 am to 10:15 am

Paternalism vs Redistribution: Designing Retirement Savings Policies with Behavioral Agents

Presented by: Christian Moser, Princeton University
Co-Author(s): Pedro Olea de Souza e Silva, Princeton University

This paper develops a theory of optimal savings and redistributive policies when individuals under-save for retirement because of a behavioral bias. The two central features of our model are labor income inequality, arising from unobservable earnings ability differences, and heterogeneity in savings rates, due to unobservable degrees of present bias.

Aug 3 | 10:30 am to 11:45 am

Discrete Games in Endogenous Networks: Theory and Policy

Presented by: Anton Badev, Federal Reserve Board
Aug 3 | 12:30 pm to 1:45 pm

Dynamic Principal Agent Problems

Presented by: Philipp Renner, Stanford University
Co-Author(s): Karl Schmedders, University of Zurich

This paper contributes to the theoretical and numerical analysis of discrete time dynamic principal agent problems with continuous choice sets. We first provide a new and simplified proof for the recursive reformulation of the sequential dynamic principal agent relationship. Next we prove the existence of a unique solution for the principal's value function, which solves the dynamic programming problem in the recursive formulation, by showing that the Bellman operator is a contraction mapping. Therefore, the theorem also provides a convergence result for the value function iteration.

Aug 3 | 2:00 pm to 3:15 pm

An Application of Large-Scale Dynamic Programming to Economics: Optimal Dynamic Taxation

Presented by: Ken Judd, Hoover Institution, Stanford University
Co-Author(s): Yongyang Cai, Stanford University; Philipp Renner, Stanford University; Simon Scheidegger, University of Zurich; Sevin Yeltekin, Carnegie Mellon University