Heterogeneous Agents Models in Economics, Summaries of Business

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Why Heterogeneous Agents Models?

Jes´us Fern´andez-Villaverde^1 April 12, 2022 (^1) University of Pennsylvania

Models with heterogeneous agents

• Economic (individuals, firms, ...) agents are heterogeneous along important dimensions:
  1. Age.
  2. Locations (spatial or economical).
  3. Productivity.
  4. Wealth.
  5. Information.
  6. Beliefs and expectations.
  7. ....
• Even within narrowly defined subgroups, we observe large individual heterogeneity in behavior (unobserved heterogeneity emphasized by Heckman and Wolpin).

Income and Wealth Inequality from Kuhn et al. (2018)

from Kuhn et al. (2018)historical data. The observed long-run trends are clearly statistically significant. America is considerably more unequal today than it was in the 1970s, with respect to both income and wealth. Figure 5: Gini coefficients with confidence bands

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1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

90% confidence intervals Gini coefficient

(a) Income

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1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

90% confidence intervals Gini coefficient

(b) Wealth

Notes: Gini coefficient of income (panel (a)) and wealth (panel (b)) with 90% confidence bands. Confidence bands are shown as gray areas, and point estimates are connected by lines. Confidence bands are boot- strapped using 999 different replicate weights constructed from a geographically stratified sample of the final dataset. 3

Figure 2. The correlation between financial wealth and its return

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0 20 40 60 80 100 Percentile of the financial wealth distribution Average return Median return

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1968 1972 1976 1980 1984 1988 1992 1996 2000 2004

T ot al^ De b t

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C on s u m er R (^) e volvin g

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1983 1986 1989 1992 1995 1998

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When is heterogeneity important? II

• Questions about aggregation bias:
  1. Does heterogeneity matter for aggregate quantities and prices along the balanced growth path?
  2. Does heterogeneity matter for aggregate quantities and prices over the business cycles?
  3. And for the welfare cost of business cycles?
  4. What is the relation of heterogeneity and asset prices?
  5. What are the (aggregate and distributional) effects of temporary tax cuts?
  6. What are the (aggregate and distributional) effects of monetary policy?
  7. How does price stickiness matter for the business cycle?
  8. What is the relation of wealth inequality and financial frictions?
  9. Political-economy of all previous questions.

Implications

• Relation of this class of models with empirical micro, especially labor economics, industrial organization, and international trade.
• Thus, fruitful area for cross-fertilization.
• Plenty of work to be done:
  1. Substantive questions.
  2. Solution methods.
  3. Taking the models to the data.

A short history

• Early start in the 1980s.
• Relation with micro data revolution.
• Certain disappointment in the early 2000s.
• Revival during the last decade.
• Why?
  1. New solution methods.
  2. Better computers and parallelization.
  3. “Everything is data”: (plain text, library records, parish and probate records, GIS data, electricity consumption, satellite imagery, web scraping, network structure, social media, ...).

Parish and probate data

Cell phone usage

Type of models with heterogeneous agents, I

• Number of agents:
  1. Two (or a few agents): asset pricing, monetary economics.
  2. Several agents: OLG, networks, regions, industry dynamics, international trade.
  3. Continuum of agents: households, firms, ....
• We will focus on models with a continuum of agents. Why?
• I will make some references to models with several agents, as I believe there will be a fruitful area of research during the next decade.

Type of models with heterogeneous agents, III

• Convex vs. non-convex problems.
• Ex ante vs. ex post heterogeneity.
• Discrete vs. continuous time.
• HA models vs. ABE.

Computation of heterogenous agent models

• The big bottleneck for the practical implementation of models with heterogeneous agents is computation.
• While usually we do not even have many theoretical results, lack of quantitative results make the model close to useless.
• There are many aspects of the computation of models with heterogeneous agents, but I will focus on the issues most specific to the field.
• I will explain why I find machine learning a promising approach to solve models with heterogeneous agents.