- English
- DRE 7029
- 4 Credits

## Introduction

This course will provide a hands-on introduction to the construction, calibration and estimation of models with 'serious' heterogeneity (that is, heterogeneity that matches the microeconomic facts that theory suggests should matter for macroeconomic outcomes like consumption dynamics); will explain why such heterogeneous agent ('HA') models have implications different from those of RA models; and illustrate how existing HA models can be adapted to new questions. ('Hands-On' means that students with their own laptops will run the and experiment with the code that solves these models in class.)

## Course content

https://github.com/econ-ark/TITLARK/blob/master/Courses/HA-Macro/2020-01-Oslo/syllabus/Syllabus.md

### 1 Preliminaries

- Install Anaconda: https://docs.anaconda.com/anaconda/install
- Get Git
- Get the command-line tool: https://atlassian.com/git/tutorials/install-git
- Get a GitHub Account
- Download the GitHub Desktop App
- And connect it to your online GitHub account

- Install HARK: Go to “Quick Start” in the README.md
- Follow the instructions for installing HARK for Anaconda

- Clone the DemARK and REMARK repos
- git clone https://github.com/econ-ark/DemARK
- git clone https://github.com/econ-ark/REMARK

- Using python from the command line:
- pip install nose
- python -c import HARK ; print(HARK.__file__)
- cd [root directory for HARK]
- python -m nose

### 2 Motivation

Models with serious microfoundations yield fundamentally different conclusions than RA models about core questions in macroeconomics.

- How monetary policy works
- HA channels account for most of the mechanism of monetary transmission

- Whether fiscal policy works
- ‘serious’ HA models are consistent with evidence of MPC’s of 0.5

- What made the Great Recession Great
- RA models: Mostly a supply shock
- HA models: Mostly a demand shock

Slides:

Readings:

- Ahn et al (2017), Introduction, Conclusion
- Compact and well written discussion of the state and progress of HA macro.

- Carroll and Crawley (2017), Sections 1, 2, and 4
- This discussion of that paper puts the relationship of HA to RA models in context.

### 3 Micro Models

#### 3.1 Micro Consumption Theory Refresher

The course will assume that students are familiar with standard quantitative tools for solving RA models, like DYNARE. The bulk of the “hands-on” part of the course will therefore involve learning and using tools for solving micro problems with ‘serious’ microfoundations.

##### 3.1.1 The Infinite Horizon Perfect Foresight Model

Absolute, Return, and Growth Impatience

Notes:

##### 3.1.2 Consumption With Labor Income Uncertainty

- Notes: A Tractable Model of Buffer Stock Saving
- Notebook: Interactive Demo

Readings

- Carroll (2001)

##### 3.1.3 Rate-Of-Return Uncertainty without Labor Income

Under CRRA utility, without labor income risk:

- The consumption function is linear
- An increase in risk reduces consumption and the MPC

Notes: Consumption out of Risky Assets

Consumption With Portfolio Choice

Origins: Merton (1969), Samuelson (1969)

##### 3.1.4 Habits

Notes:

### 4 Computational Tools

#### 4.1 Vision for the Econ-ARK Project

### 5 Hands-On Introduction

Here we will explain how to begin using the Econ-ARK toolkit for heterogeneous agent macro modeling. Students will be taught how to use the toolkit to solve increasingly sophisticated models, starting with partial equilibrium perfect foresight models and ending with some exercises using a full general equilibrium micro-macro model with idiosyncratic and aggregate risks.

#### 5.1 A Gentle Introduction

This section builds our first simple models using the toolkit

##### 5.1.1 Perfect Foresight

Notebook: A Gentle Introduction to HARK - Perfect Foresight

##### 5.1.2 Adding ‘Serious’ Income Uncertainty

Notebook: A Gentle Introduction to Buffer Stock Saving

#### 5.2 Liquidity Constraints, Precautionary Saving, and Impatience

- The Growth Impatience Condition
- Liquidity Constraints and Precautionary Saving
- Impatience and Target Wealth

Notebook: BufferStockTheory Problems

#### 5.3 ‘Serious’ Wealth Inequality

Notebook: Micro-and-Macro-Implications-of-Very-Impatient-HHs-Problems

References: Carroll, Slacalek, Tokuoka, and White (2017)

#### 5.4 Matching the Distribution – of the MPC

#### 5.5 Hands-On with Real HA Models

For an economy in steady state (that is, with constant factor prices like interest rates and wages), models with ‘serious’ income heterogeneity have been solvable in partial equilibrium since about 1990 (Zeldes (1989), Deaton (1991)). Calculating an equilibrium distribution of wealth that results from those policy functions and matching it to the total amount of observed wealth (and a corresponding interest rate) was first done by Hubbard, Skinner, and Zeldes (1994) using a supercomputer. Aiyagari (1994) proposed a radically simple model that did not attempt to match the distributions of wealth and income, but could be solved without a supercomputer.

In a rational expectations steady state, there are no expected changes in interest rates, wages, or the distribution. Aggregate fluctuations make calculation of an RE equilibrium massively more difficult, because:

- Meaningful aggregate fluctuations will change the distribution of wealth and income
- The amount of aggregate saving depends on how aggregate wealth and income are distributed
- The amount of saving determines future factor prices
- In principle, RE therefore requires that everyone know the entire distribution of wealth, income, and any other state variables in the population

The problem therefore suffers from a severe case of the “curse of dimensionality.” (That is, it’s really hard!). The first paper to tackle the problem was Krusell and Smith (1998). Work by Bayer and Luetticke (2018) builds on all of the prior work to construct a reasonable HANK model that can be solved in a few minutes on a laptop. The key contribution of Krusell and Smith (1998) was to discover that, in practice, highly accurate predictions of future aggregate states could be made using only the mean of the current aggregate capital stock

Notebook: KrusellSmith.ipynb

#### 5.6 The Micro Steady State and Macro Fluctuations

A problem with solving methods using the original Krusell Smith method is that the computational challenge was so great that only the simplest such models could be solved, and the ability to construct standard tools like impulse response functions to aggregate shocks was very limited.

Reiter (2009) showed how to solve such problems several orders of magnitude faster; the essence of his idea was to solve the micro problem for the steady-state distribution, and then capture business cycle fluctuations by figuring out how to perturb the decision rules and the distribution appropriately.

Building on his work, the last few years have seen great further strides in speed and power of such tools.

References:

- Reiter (2009)
- Boppart, Krusell, and Mitman (2018)
- Ahn, Kaplan, Moll, Winberry, and Wolf (2017)
- Bayer and Luetticke (2018)

#### 5.7 The Bayer-Luetticke Method

#### 5.8 Other Literature

References:

- Monetary Policy Transmission with Many Agents, Crawley and Lee (2019)
- Macroprudential Policies in a Heterogeneous Agent Model of Housing Default, Khan (2019)
- Redistribution, risk premia, and the macroeconomy, Kekre and Lenel (2019)
- The Missing Intercept: A Sufficient Statistics Approach to General Equilibrium Effects, Wolf (2019)

## Disclaimer

This is an excerpt from the complete course description for the course. If you are an active student at BI, you can find the complete course descriptions with information on eg. learning goals, learning process, curriculum and exam at portal.bi.no. We reserve the right to make changes to this description.