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Agent-Based Model of the Housing Bubble

posted Dec 15, 2010, 2:02 AM by Olaf Bochmann

This article outlines an approach in agent-based computational economics to build a macroeconomic model of the recent housing bubble. The goal of this effort is to gain a better understanding of it's causes and to formulate policy prescriptions. The common view of economists with respect to the housing bubble causes is that the Federal Reserve policies and measures that started in 1993 with respect to interest rates has led to the current crisis. This hypothesis needs to be verified (by observing some emergent properties). This is a model where we observe patterns of development out of the individual interactions of agents qualitatively and try to match them with the empirical data.

In contrast to the conventional approach that produces quantitative house price projections based on trends in incomes, interest rates and housing supply and demand, the agent-based approach simulates the interaction of individual agents who seek to buy and sell properties. House prices emerge from this market process.

Model Definition

According to McMahon et. all (2009) the main actors in the housing market (people, banks) and the components (houses, mortgages) are modelled as agents. People are either renters or owners of one or more houses. Mortgages are Adjustable Rate Mortgages (ARMs) based on interest rate. Each house is associated with zero or one mortgage that is owned by a bank.
The prices of the houses and the mortgages are determined endogenously by the interacting agents. Disturbances are induced only by controlling for the interest rates exogenously.

People

People have a fixed income that follows a uniform distribution within some range. They may relocate, which in turn requires to rent or own houses. This decision requires the evaluation of the financial situation with respect to the rent or ownership situation. House owner may evaluate the decision to buy an extra house for investment and rent it out to other people. House owner may decide to sell a house.

Houses

Houses can be rented or owned. Initial house prices follow a uniform distribution within some range. Houses are foreclosed, due to insufficient funds to pay mortgages or rents.

Mortgages

The mortgage is owned by a bank, and is associated with a particular person and a house. Mortgage payments are adjusted to represent the notion of ARMs, possible with some time lag.

Banks

Banks maintain a balance sheet to keep track of their assets (mortgage payments) and liabilities (mortgage value of the houses owned by the bank).

Model initialization

Houses are created at a certain density (patchDensity) on the map. Each house is then assigned a price. A fraction of houses are assigned as rentals (rentalDensity) and some percentage is occupied (occupiedPerc) by people. Each person is then assigned an income and People are assigned to houses according to matching income - rental/ownership costs. The parameter patchDensity, rentalDensity, and occupiedPerc can be calibrated to empirical data. 
The model generates the following output: average house Price, average mortgage cost, number of owned vs. rented houses, banks balance sheet, and percentage of bankrupt people, and average location of houses.

First Results

With the Axtell & Epstein (1994) model, we can observe patterns of development out of the individual interactions of agents qualitatively and try to test them with the empirical data. Using the actual interest rate scenario 1993-2009 a big drop in the banks balance sheets can be observed, that corresponds to the decrease in the house prices and the increase in the average mortgage rates. A policy of controlling exogenously for the interest rates leads to the emergence of bubbles and foreclosures.

Things to do

As first results have shown, an exogenous control for the interest rates was one of the factors that led to the housing crisis. However, this is considered to be a necessity, but not a sufficiency condition: Future models should link the subprime crisis to the housing market. The model can be further enhanced by including the supply side of the market represented by the construction companies, in order to refine the endogenous emergence of the house prices.

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