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Heterogeneous Agents Resources and toolKit (HARK)

HARK is a toolkit for the structural modeling of economic choices of optimizing and non-optimizing heterogeneous agents. For more information on using HARK, see the Econ-ARK Website.

The Econ-ARK project uses an open governance model and is fiscally sponsored by NumFOCUS. Consider making a tax-deductible donation to help the project pay for developer time, professional services, travel, workshops, and a variety of other needs.

This project is bound by a Code of Conduct.


We have a Gitter Econ-ARK community.

Table of Contents


Install from Anaconda Cloud by running:

conda install -c conda-forge econ-ark

Install from PyPi by running:

pip install econ-ark


We start with almost the simplest possible consumption model: A consumer with CRRA utility

has perfect foresight about everything except the (stochastic) date of death.

The agent's problem can be written in Bellman form as:

To model the above problem, start by importing the PerfForesightConsumerType model from the appropriate HARK module then create an agent instance using the appropriate paramaters:

import HARK

from HARK.ConsumptionSaving.ConsIndShockModel import PerfForesightConsumerType

PF_params = {
    'CRRA' : 2.5,           # Relative risk aversion
    'DiscFac' : 0.96,       # Discount factor
    'Rfree' : 1.03,         # Risk free interest factor
    'LivPrb' : [0.98],      # Survival probability
    'PermGroFac' : [1.01],  # Income growth factor
    'T_cycle' : 1,
    'cycles' : 0,
    'AgentCount' : 10000

# Create an instance of a Perfect Foresight agent with the above paramaters
PFexample = PerfForesightConsumerType(**PF_params)

Once the model is created, ask the the agent to solve the problem with .solve():

# Tell the agent to solve the problem

Solving the problem populates the agent's .solution list attribute with solutions to each period of the problem. In the case of an infinite horizon model, there is just one element in the list, at index-zero.

You can retrieve the solution's consumption function from the .cFunc attribute:

# Retrieve the consumption function of the solution

Or you can retrieve the solved value for human wealth normalized by permanent income from the solution's .hNrm attribute:

# Retrieve the solved value for human wealth normalized by permanent income

For a detailed explanation of the above example please see the demo notebook A Gentle Introduction to HARK.

For more examples please visit the econ-ark/DemARK repository.


If using Econ-ARK in your work or research please cite our Digital Object Identifier or copy the BibTex below.


[1] Carroll, Christopher D, Palmer, Nathan, White, Matthew N., Kazil, Jacqueline, Low, David C, & Kaufman, Alexander. (2017, October 3). econ-ark/HARK


  author    = { {C}hristopher {D}. {C}arroll and {A}lexander {M}. {K}aufman and {J}acqueline {L}. {K}azil and {N}athan {M}. {P}almer and {M}atthew {N}. {W}hite },
  title     = { {T}he {E}con-{A}{R}{K} and {H}{A}{R}{K}: {O}pen {S}ource {T}ools for {C}omputational {E}conomics },
  booktitle = { {P}roceedings of the 17th {P}ython in {S}cience {C}onference },
  pages     = { 25 - 30 },
  year      = { 2018 },
  editor    = { {F}atih {A}kici and {D}avid {L}ippa and {D}illon {N}iederhut and {M} {P}acer },
  doi       = { 10.25080/Majora-4af1f417-004 }

For more on acknowledging Econ-ARK visit our website.


Looking for help? Please open a GitHub issue or reach out to the TSC.

Release Types

  • Current: Under active development. Code for the Current release is in the branch for its major version number (for example, v0.10.x).
  • Development: Under active development. Code for the Current release is in the development.

Current releases follow Semantic Versioning. For more information please see the Release documentation.

API Documentation

Documentation for the latest release is at HARK ReadTheDocs. Version-specific documentation is available from the same source.


For Students: A Gentle Introduction to HARK

Most of what economists have done so far with 'big data' has been like what Kepler did with astronomical data: Organizing the data, and finding patterns and regularities and interconnections.

An alternative approach called 'structural modeling' aims to do, for economic data, what Newton did for astronomical data: Provide a deep and rigorous mathematical (or computational) framework that distills the essence of the underlying behavior that produces the 'big data.'

The notebook A Gentle Introduction to HARK details how you can easily utilize our toolkit for structural modeling. Starting with a simple Perfect Foresight Model we solve an agent problem, then experiment with adding income shocks and changing constructed attributes.

For Economists: Structural Modeling with HARK

Dissatisfaction with the ability of Representative Agent models to answer important questions raised by the Great Recession has led to a strong movement in the macroeconomics literature toward 'Heterogeneous Agent' models, in which microeconomic agents (consumers; firms) solve a structural problem calibrated to match microeconomic data; aggregate outcomes are derived by explicitly simulating the equilibrium behavior of populations solving such models.

The same kinds of modeling techniques are also gaining popularity among microeconomists, in areas ranging from labor economics to industrial organization. In both macroeconomics and structural micro, the chief barrier to the wide adoption of these techniques has been that programming a structural model has, until now, required a great deal of specialized knowledge and custom software development.

HARK provides a robust, well-designed, open-source toolkit for building such models much more efficiently than has been possible in the past.

Our DCEGM Upper Envelope notebook illustrates using HARK to replicate the Iskhakov, Jørgensen, Rust, and Schjerning paper for solving the discrete-continuous retirement saving problem.

The notebook Making Structural Estimates From Empirical Results is another demonstration of using HARK to conduct a quick structural estimation based on Table 9 of MPC Heterogeneity and Household Balance Sheets by Fagereng, Holm, and Natvik.

For Computational Economics Developers

HARK provides a modular and extensible open-source toolkit for solving heterogeneous-agent partial-and general-equilibrium structural models. The code for such models has always been handcrafted, idiosyncratic, poorly documented, and sometimes not generously shared from leading researchers to outsiders. The result being that it can take years for a new researcher to become proficient. By building an integrated system from the bottom up using object-oriented programming techniques and other tools, we aim to provide a platform that will become a focal point for people using such models.

HARK is written in Python, making significant use of libraries such as numpy and scipy which offer a wide array of mathematical and statistical functions and tools. Our modules are generally categorized into Tools (mathematical functions and techniques), Models (particular economic models and solvers) and Applications (use of tools to simulate an economic phenomenon).

For more information on how you can create your own Models or use Tools and Model to create Applications please see the HARK Manual.

Contributing to HARK

We want contributing to Econ-ARK to be fun, enjoyable, and educational for anyone, and everyone.

Contributions go far beyond pull requests and commits. Although we love giving you the opportunity to put your stamp on HARK, we are also thrilled to receive a variety of other contributions including:

  • Documentation updates, enhancements, designs, or bugfixes
  • Spelling or grammar fixes
  • corrections or redesigns
  • Adding unit, or functional tests
  • Triaging GitHub issues -- e.g. pointing out the relevant files, checking for reproducibility
  • Searching for #econ-ark on twitter and helping someone else who needs help
  • Answering questions from StackOverflow tagged with econ-ark
  • Teaching others how to contribute to HARK
  • Blogging, speaking about, or creating tutorials about HARK
  • Helping others in our mailing list

If you are worried or don’t know how to start, you can always reach out to the TSC or simply submit an issue and a member can help give you guidance!

After your first contribution please let us know and we will add you to the Contributors list below!

To install for development see the Quickstart Guide.

For more information on contributing to HARK please see

Collaborators follow the COLLABORATOR_GUIDE in maintaining the Econ-ARK project.


This is a beta version of HARK. The code has not been extensively tested as it should be. We hope it is useful, but there are absolutely no guarantees (expressed or implied) that it works or will do what you want. Use at your own risk. And please, let us know if you find bugs by posting an issue to the GitHub page!