Finding a job, a partner, and a house are three of life’s big decisions. All involve searching because what is a good match for one person need not be so good for another. A basic lesson of search theory holds that a person should stop searching when a ‘good enough’ match is found. The better the match, the more likely a person is to remain longer in the match. But circumstances change, and sometimes it is best to search again for a new match.
Search and matching models
‘Search and matching’ models building on these ideas have long been used to understand turnover rates and dynamics in the labour market, and even the ‘marriage market’. But the application of these ideas to housing markets is relatively recent (starting from Wheaton 1990). In the labour market, the difficulty of the search process is manifested in the considerable time taken for job seekers to find jobs and firms to fill vacancies, in spite of there being simultaneously many unemployed workers and many vacancies. Evidence of the difficulty of search in the housing market is similarly found in the number of weeks taken on average to sell a house, as plotted in Figure 1. A substantial amount of time is typically needed to sell, and the amount varies considerably between the years.
Source: Genesove and Han (2012).
Conceptually, the source of the time taken to sell a house can be broken down into two difficulties in the search process. First, the time needed for buyers to locate potentially desirable houses to view. Second, the fact that many houses viewed will actually prove to be unsuitable to particular buyers once their characteristics have been made clear by the viewing. In other words, the same house has a wide range of ‘match qualities’ for different potential buyers. Evidence on the importance of the second difficulty of search, not knowing match quality before a viewing, is provided by the large number of viewings that are required on average to sell a house, as shown in Figure 1. The mere fact that average viewings per sale are far above one indicates the role of a range of match qualities across different potential buyers in explaining the rate at which houses are sold.
A key insight of our recent research (Ngai and Sheedy 2015) is that match quality is important in understanding not only the time taken to sell a house, but also how long, on average, homeowners will live in the new house before their next move. Just as match quality must be good enough when a house is bought, if circumstances change and match quality deteriorates, those for whom it is no longer good enough choose to move house. Search theory provides a guide to how what is considered ‘good enough’ is determined by market conditions, interest rates, incomes, and the costs associated with moving house. Changes in the average time homeowners live in the same house can then be understood through the lens of changes in what match quality is good enough.
We present new evidence that changes in the average time between homeowners’ moves is crucial for explaining housing-market dynamics. It is well known that there is considerable variation over time in the number of houses that are sold. What is less well understood is that these fluctuations are overwhelmingly driven by changes in the duration of time between homeowners’ moves rather than by changes in how long it takes to sell houses once they are on the market. We calculate moving rates for homeowners (inversely related to the average time between moves) and selling rates for houses on the market (inversely related to the average time taken to sell a house). Both rates vary considerably over time, but changes in the moving rate account for almost all of the changes in the number of houses sold.
What lies behind this finding is that the average time between moves (more than a decade) is around 30 times longer than the average time taken to sell a house (a few months), implying that the stock of houses on the market is typically 30 times smaller than the stock of all houses. This means that an increase in the selling rate quickly depletes the stock on the market and has little lasting impact on the volume of house sales. On the other hand, even a small change in the number of houses put up for sale has a disproportionate impact on the stock for sale, and the numbers of houses subsequently sold.
To understand why the moving rate changes over time, we apply search theory to the decision to move house. Existing research (for a survey, see Lu and Strange 2015) has focused on the determinants of the selling rate for houses already on the market, treating the moving rate as an unexplained and fixed number. This, however, is problematic when the moving rate turns out to be the much more important of the two rates in understanding overall housing-market activity.
Our approach is to think about moving house as an investment in improving match quality. Moving is best thought of as an investment because of its large upfront costs coupled with the expectation of long-lasting gains. As such, moving is influenced by factors that are common to many investment decisions, such as interest rates, taxes, and the size of the upfront costs themselves. These factors influence the threshold for acceptable match quality and thus the number of homeowners whose current match quality falls below the acceptable minimum. While the moving decision for an individual homeowner is typically driven by a particular change in circumstances that worsens current match quality, at the level of the whole housing market what matters is changes in the match quality threshold for the marginal homeowner who is contemplating moving.
One application of our model is to study the boom in housing-market activity in the US between 1995 and 2004. We show that developments during this period such as the fall in mortgage interest rates, the spread of internet-based property search, and the rise of incomes owing to the productivity boom all provided incentives for homeowners to upgrade match quality by moving more frequently. Quantitatively, these factors alone can account for approximately half of the increase in listings and sales of houses during that period.
On the other side of the Atlantic, many UK commentators (for example, the Financial Times) have pointed to the dramatic decline in housing ‘turnover’ (sales of houses relative to the stock of all houses) in recent decades. This is the flip side of the rise in the average time between homeowners’ moves from approximately eight years in the 1980s to more than 20 years by 2015. Increases in stamp duty (a tax on house purchases) are often suggested as one factor that contributed to this trend.
Recent reforms with the goal of improving the functioning of the housing market have reduced the rate of stamp duty on the median house by 1.5% (HM Treasury 2014, Table 1.9). Our framework can be used to estimate the likely impact on housing turnover and the welfare of homeowners. A uniform reduction of 1.5% in the tax burden of buying a house is predicted to increase turnover by around 8%, suggesting that decisions to move house are very sensitive to tax incentives. Greater turnover also has the benefit of improving homeowners’ average match quality by reallocating houses to those for whom they are currently best suited. This indirect benefit is estimated to be approximately the same size as the reduction in tax revenue. Our findings thus suggest that tax distortions to moving house can have very substantial effects on welfare.
Financial Times (2015), “Average home sells just once every 23 years”, 10 April.
Han, L and Strange, W C (2015), “The microstructure of housing markets: Search, bargaining, and brokerage", in G Duranton, J V Henderson and W C Strange (eds.) Handbook of Regional And Urban Economics, volume five.
HM Treasury (2014), “Autumn Statement 2014”.
Ngai, L R and Sheedy, K D (2015), “Moving house", CEPR Discussion Paper 10346.
Wheaton, W C (1990), “Vacancy, search, and prices in a housing market matching model", Journal of Political Economy 98(6): 1270-1292.