Benjamin Moll
Heterogeneous Agent Models
in Continuous Time
This is a collection of codes that solve a number of heterogeneous agent models in continuous time using finite difference methods.
Huggett Model
Explanation of Algorithm
HJB equation, explicit method (Section 1.1)
HJB equation, implicit method (Section 1.2)
KFE Equation (Section 2, using matrix from HJB implicit method)
Plotting the asset supply function (Section 3.1)
Finding the equilibrium interest rate (Section 3.2)
All of (4a)-(4c) need inputs huggett_initial.m, huggett_terminal.m
(4b) Newton method
(4c) Newton method using @myAD
HJB equation with diffusion, implicit method (section 5.1)
KFE Equation (Section 5.2, using HJB matrix)
Credit Crunch (courtesy of Gustavo Mellior)
Consumption-Saving Problem with Endogenous Labor Supply
Aiyagari Model
Explanation of Algorithm
Stationary Equilibrium with Poisson Process
Steady State Asset Supply Function with Poisson Process
Python version (Jupyter notebook)
aiyagari_continuous_time.ipynb
should be compared with QuantEcon’s discrete-time version of the Aiyagari model
“MIT Shock” with Poisson Income Process
Stationary Eq. with Diffusion (Section 6.1, courtesy of Galo Nuno)
aiyagari_diffusion_equilibrium.m
Julia version of code: aiyagari_diffusion_equilibrium.jl
(download Juno for nice GUI)
C++ version of code: aiyagari_diffusion_equilibrium.cpp
(instructions for Mac users, makefile)
Transition Dynamics with Diffusion (Section 6.2)
aiyagari_diffusion_transition.m
Julia code for MIT Shock with Diffusion (courtesy of Matthieu Gomez): aiyagari_diffusion_MITshock.jl
Make movie of evolution of wealth distribution (Section 6.4)
Aiyagari Model with Fat-tailed Wealth Distribution (Section 8)
fat_tail_partialeq.m, uses non-uniform grid as explained in Section 7
Sequence-Space Methods for Models with Aggregate Shocks
René Glawion’s continuous-time sequence-space methods
Adrien Bilal and Shlok Goyal’s continuous-time sequence-space methods
For reference: original discrete-time implementation by Adrien Auclert, Bence Bardóczy, Matt Rognlie, and Ludwig Straub
Lifecycle Model
Partial Equilibrium
Two Endogenous State Variables: Wealth and Human Capital
Partial Equilibrium
Model with Two Assets and Kinked Adjustment Costs
Soroush Sabet and Patrick Schneider’s algorithm for models with two or more endogenous state variables
Description of Model and Algorithm
This algorithm dominates and supersedes the codes posted below which is also what we used in Kaplan, Moll, Violante (AER, 2018)
For reference: outdated algorithm dominated by Sabet-Schneider
Investment under Uncertainty by Heterogeneous Firms
Partial Equilibrium
Handling Non-Convexities I
Neoclassical Growth Model with Convex-Concave Production Function (Skiba, 1978)
Finding the “Skiba point”
Handling Non-Convexities II
Entrepreneurship and Financial Frictions
Stationary Equilibrium
MIT Shock
Handling Non-Convexities III
Indivisible Housing and Mortgages
Partial Equilibrium
Stopping Time Problem I
Exercising an Option
Solve as Linear Complementarity Problem (LCP)
Python version of LCP solver (courtesy of Saeed Shaker)
LCP_Python.ipynb (Python version of LCP.m)
Stopping Time Problem II
Firm Entry and Exit (Hopenhayn, 1992)
Solve as Linear Complementarity Problem (LCP)
hopenhayn.m plus LCP.m (LCP solver)
Julia version of code: hopenhayn.jl (courtesy of Chase Abram)
Stopping Time Problem III
An Indivisible Durable
Solve as Linear Complementarity Problem (LCP)
car.m plus LCP.m (LCP solver)
Stopping Time Problem IV
Liquid and Illiquid Assets and Fixed Adjustment Costs
Solve as Linear Complementarity Problem (LCP)
liquid_illiquid_LCP.m plus LCP.m (LCP solver) and lininterp1.m (interpolation routine)
Stopping Time Problem V
Consumption and Saving with Default
(courtesy of Gustavo Mellior and Katsuyuki Shibayama)
Solve as LCP
default.m plus LCP.m (LCP solver) and cTsolver.m (subroutine)
Consumption, Saving and Wealth Distribution with Hansen-Sargent Robustness Concerns
Description of Model and Algorithm with Edouard Djeutem
Code
Labor-Market Matching with Precautionary Savings
Description of Model and Algorithm courtesy of Bence Bardoczy
Codes
Additional Codes
No uncertainty, explicit method (Section 1.1)
No uncertainty, implicit method (Section 1.2)
Neoclassical Growth Model, explicit method (Section 2.1)
Neoclassical Growth Model, implicit method (Section 2.2)
RBC Model with diffusion for TFP, implicit method
João Duarte's Python Codes
João Duarte’s GitHub Repository with python versions of many of the codes on this website
Matthieu Gomez's GitHub Repository
Matthieu Gomez’s GitHub Repository with great Julia codes, incl. the Bansal-Yaron (2004) Long-Run Risk Model
Constantin Schesch's Spectral Methods (Collocation Methods)
Schesch (JEDC, 2024) “Pseudospectral methods for continuous-time heterogeneous-agent models”
Constantin Schesch’s GitHub Repository with codes for solving heterogeneous agent models using pseudo-spectral methods (collocation methods).