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Homeowners' behavior model

Can we statistically estimate homeowners’ propensity to put a property for sale?

The number of transactions in the property market depends on many sectors of the economy. Fundamentals such as demographics, productivity, and income play a significant role in generating volatility in house prices. In general, transactions on the housing market are determined by how quickly houses are sold and at the same time how quickly appear on the market. How quickly houses come off in a sale the market depends on a process involving buyers and sellers. On the other hand, how quickly houses show up on the housing market depends on the decisions of homeowners to put a property for sale. Existing quantitative literature on housing markets has focused primarily on the demand and supply process that leads to sales of properties on the market. But how about the decisions of homeowners to put houses for sale on the market?  

Property viewing 

When potential buyers are interested in a house there is a friction that is related to the number of houses that buyers would need to view before a desirable property is found. Whether the property is suitable does not only depend on knowing objective features, for example the construction year of the property. What is desirable is a match between the buyers’ preferences and the characteristics that the property offers. A measure of the average number of viewings needed before a property can be sold is referred to viewings-per-transaction. Property Market Analytics Hometrack United Kingdom started a monthly survey regarding viewings-per-transaction in 2000. The survey was sent to real estate agents every month (June 2001 – July 2013). The figure below depicts results for all postcodes in England and Wales. On the y-axis one can observe viewings-per-transaction and on the x-axis the time measured in months is showed.

Correlation between the time-to-sell and the viewings per transaction (Brooks, C., & Tsolacos, S., 2010)

The figure shows that time-to-sell is correlated with viewings-per-transaction. So, time to sell is not entirely due to variation in the time that is taken to meet potential buyers. In other words, a viewing function alone is not sufficient as one can observe.


Homeowners’ behavior model

Therefore, it might be interesting to consider an alternative model, the homeowners’ behavior model. A key assumption of this model is that each property is occupied by a family and yields utility flow values. According to a study by Chris Brooks and Sotiris Tsolacos, authors of Real Estate Modelling and Forecasting, the dominant factor in explaining the number of properties appearing on the housing market is the decision of the homeowners. To understand the decision of the homeowners, the most important variable is their match quality ε, which will be compared with other owners in the market. Match quality is a utility flow value of an occupied property. In other words, if there is a high match quality the family finds the property appropriate An owner with match quality ε receives a utility flow of εξ while the property is occupied, where ξ denote a variable representing the economy level of demand. Moreover, homeowners incur a maintenance cost K regardless of whether houses are on the market for sale or houses are occupied.  So, housing demand ξ is common to all homeowners in the market, while ε is match specific.

A match quality ε for a property is a persistent subject to infrequent shocks that reduce match quality. These occasional shocks can be seen as life events that make a property less suitable to the family’s current circumstances.  The appearance of these shocks follows a Poisson process  A sequence of arrivals occurring at different points on a timeline, such that the number of arrivals in a particular interval of time has a Poisson distribution  with arrival rate a. When no shock occurs, the mathematical value remains the same. In case of a shock, match quality ε is narrowed from ε to δε, where δ denotes a parameter that defines the size of the particular shock (δ < 1). A desirable house has many quality parameters. Hence, not every aspect of a property can be affected by the so-called shocks. For instance, a new job might affect commuting time, but still leave other desirable aspects of a property unchanged.

In case of a shock, homeowners can decide to move or not. Those who move become property buyers and sellers at the same time. Moving is a process that is expected to deliver long-term benefits. Hence, moving is sensitive to macroeconomic and policy variables, for example taxes and interest rates that affect other investment decisions. On the other hand, the owners that do not experience a shock will observe a cost Z when the decision is to move properties. This cost Z represents the inertia to remain in the same property. To keep the equation simple, one assumes the equation is set up so that homeowners will not move (so Z → ∞). The value function for a homeowner when occupying a house with match quality epsilon at some time t is denoted by HO(t,ε). It follows that the equation for HO(t,ε) is:

rHO(t,ε) = εξ – K + a [max (HO(t(δε), Wt] – Ht(ε)

where r is denoted as the discount rate, and the sum of the values of owning a house for sale is denoted by Wt. The value function Ht(ε) is increasing in ε.


So, keep in mind when you are still waiting for an appropriate house that this does not only depend on the supply and demand in the housing market. Also, the homeowner behavior plays an important role in putting a house on sale or not. The claim that the moving rate amongst homeowners is important for house transactions can be understood using the homeowner’s behavior model.



Brooks, C., & Tsolacos, S. (2010). Real Estate Modelling and Forecasting (first edition). New York: Cambridge University Press.

Ngai, L., & Sheedy, D. (2016). The Decision to Move House and Aggregate Housing-Market Dynamics. From

This article is written by Moesen Tajik

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By Daniele Zedda • 18 February


By Daniele Zedda • 18 February

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