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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. These methods permit arbitrary infinite-dimensional variation in the state variables, do not impose exclusion restrictions on the relationship between variables or limit their impact to a finite-dimensional sufficient statistic, and, most importantly, come with demonstrable guarantees of consistency and polynomial time computational complexity. I demonstrate the applicability of the theory by providing an analytical characterization and computing the solution to a dynamic model of trade, migration, and economic geography.

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. We find that the constrained-efficient allocation features more wealth inequality than the competitive equilibrium.

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
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. We illustrate the quantitative implications of the model by fitting to US aggregate labor market data from 1951-2012. The model has rich implications for the cyclical dynamics of the distribution of skills of the unemployed, the distribution of types of vacancies posted, and sorting between heterogeneous workers and firms.

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. Compensating differentials are revealed when workers systematically move to lower-paying firms, while rents are revealed when workers systematically move to higher-paying firms. With the number of parameters proportional to the number of firms (1.5 million), standard estimation approaches are infeasible. The paper develops an estimation approach that is feasible for data on this scale. The approach uses tools from numerical linear algebra to measure central tendency of worker flows, which is closely related to the ranking of firms revealed by workers' choices.

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. The interaction between government’s redistributive preferences and its paternalistic motive to correct savings leads to a novel insight: the optimal policy offers low income individuals a one-size-fits-all savings instrument, resembling social security, whereas it offers high income individuals a set of policies tailored to their heterogeneous preferences, similar to 401(k) and IRA accounts in the United States. The rationale for this policy is that the government uses flexibility at high earnings as a reward for generating income that can be taxed and used for redistribution. In a quantitative exercise, we use our normative model to evaluate the current U.S. social security and tax-transfer system. We find the current system to be inefficient, independent of redistributive preferences. Relative to the utilitarian benchmark, current social security benefits are consistent with more progressive social preferences, while the tax-transfer system suggests lower progressivity. We explore the implications of our theory for other behavioral contexts as well as for non-behavioral Pigouvian tax policies.

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. To compute a solution for the problem we have to solve a collection of static principal agent problems at each iteration. Under the assumption that the agent's expected utility is a rational function of his action, we can transform the bilevel optimization problem into a standard nonlinear program (NLP). We can then solve these nonlinear problems with a standard NLP solver. The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal agent model. We illustrate our solution method by solving variations of two prominent social planning models from the economics literature.

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