QED Research Spotlight by JDI Research Associate Brock Mutic summarizes recent research by QED Professors Allen Head and Huw Lloyd-Ellis in collaboration with former PhD student Derek Stacey

Deciding whether to buy or rent a home is one of the largest financial decisions many people make. Across cities in the United States, however, this decision is not made equally, as the affordability of homeownership varies; in different cities, it is relatively more or less affordable to buy a home, compared with renting. Although economists hypothesize these differences are driven by local economic conditions, understanding which local factors are at play is no easy task: the effects in question lay submerged in the depths of the economic ocean, driven by the rough currents of the dynamic and complex housing market, and are not easily visible from the surface. Wading through the tide, and pulling the relevant effects up from below, is a task requiring a very precise net, and a very steady hand. 

Recognizing that the determinants of home affordability are relevant for millions of people however, as everyone needs a home, Queen’s Economics Department researchers Dr. Allen Head and Dr. Huw Lloyd-Ellis, in collaboration with Dr. Derek Stacey of the University of Waterloo, were undeterred by the waves. Setting their boat on the water, they engaged in research to study the question, in a paper recently published in International Economic Review. The team built a ‘frictional assignment’ model of the housing market to study the factors affecting inter-city home affordability, calibrated it, and tested it against observational data. Ultimately, they produced insightful results, with relevance for housing policy. 

At the centre of the research is a model in which the gears of the housing market turn. In any given period, a percentage of renters switch rental units as a result of random factors like eviction, and a percentage of homeowners put their homes up for sale, as a result of it no longer meeting their preferences or requirements.¹ New homes of various quality are also continuously built by a construction industry consisting of many firms and free market entry—who build homes for both ownership and rental markets as a result of free entry.  

As all households need a place to live, they are modelled as making the decision to either rent or buy a home and also as choosing their home’s quality. Households are assumed to prefer ownership to renting ceteris paribus, as owned homes can be customized to their liking; that is, there is an ownership surplus associated with owning a home, in comparison to renting—which, notably, is higher for houses of higher quality.² To purchase a home, households have to find one being offered by a seller which they can afford, and which meets their preferences. They search the ‘submarket’ of the available homes of a specific quality that are affordable to them to do so, but are only interested in purchasing specific units in such markets, due to their unique tastes. A household’s likelihood of being able to find a suitable home is affected by common ‘frictions’ that slow the gears of the market—like needed renovations—and also by the ‘tightness’ of the market—or by the number of buyers compared with the number of sellers—it ultimately depends on the actions of current owners too, who can choose to supply their units for rent or sale, and thus control availability. 

In the model’s equilibrium, conditions of free entry and the directed search of buyers adjust market conditions until the benefits buyers receive from purchasing a home—their ownership surplus—equals their willingness to pay the premium for it. Since higher-quality houses offer a greater ownership surplus for purchasing them, the owners of such units can sell them for higher prices, and thereby achieve higher returns. As such, in the model’s equilibrium, a greater number of houses at the higher-quality end of the spectrum are listed for sale, as opposed to being rented, relative to houses of lower quality. The result is that a greater percentage of relatively poor households rent—though they would prefer to own—because there are few houses being offered for sale that they can afford. In this way, the model’s equilibrium is consistent with the empirical finding that as the income of a household rises, it becomes much more likely, controlling for other variables, that they will own their home, and the finding that higher-value houses are more likely to be sold, as opposed to rented out.  

With their model built, the team calibrated it to match the housing market of an average US city, in terms of several key variables. In doing so, the model made several predictions of how the economy of such a city would respond to such variables changing. It predicted that: the rate of homeownership in a city would increase if the city’s average income rises, but would decline if inequality or the costs of construction rise; the affordability of owning a home, in comparison to renting, would decline, if a city’s average income, inequality levels, or construction costs, rise; and a higher proportion of owner-occupied housing would become vacant—which would increase the overall vacancy rate—if a city’s average income rises, but would decline if median age or construction costs do. The team also undertook an alternative calibration, and controlled for numerous possible confounding variables, and yielded similar results, indicating their predictions were robust.  

With their model’s predictions of the housing market’s dynamics, the research team turned to the data. They wanted to observe the actual dynamics of the housing market, to determine whether they matched the predictions; had they matched, Dr. Lloyd-Ellis, Dr. Head, and Dr. Stacey, would have had evidence that their model was accurately describing the operations of the US housing market, and accurately predicting key economic outcomes. Using data from the 2010 American Community Survey five-year estimates, the QED researchers computed the ownership rates, average price-rent ratios, vacancy rates, and inequality levels of 366 American cities. Overall, they found that the real dynamics of the housing market did indeed overlap with their model’s predictions. In particular, as they had predicted, homeownership rates were found to be positively associated with median income among the cities in their sample, and negatively associated with inequality and land price, while average home affordability (measured by price-rent ratios) was found to be positively associated with income, inequality, and land values, and vacancy rates positively with median incomes and land prices, and negatively with age.  

Since the team’s theoretical model of how they thought the housing market worked, once calibrated for real-world starting values, predicted outcomes that basically aligned with the observed housing market outcomes of the real world, the team had evidence, therefore, that their model may have been accurately describing the real American housing market, and capturing its key dynamics.  

As such, having ascertained the model’s accuracy, Dr. Lloyd-Ellis, Dr. Head, and Dr. Stacey were ready to put their model into action, and to use it to examine their main initial research question: namely, determining the factors that drive differences in home affordability, and make owning a home more or less affordable, in different cities. Turning to this question, the team inputted the real variances in city characteristics that exist across different US cities into the model.³ In doing so, the model predicted that in starting from differing economic fundamentals, different cities would obtain greatly varying economic outcomes—including differences in home affordability. Examining what was driving these differences in the model, the team uncovered that, interestingly, differences in income and age distributions across cities were in part driving the effect, in addition to differences in construction and land costs, and differences in city amenities. Notably, the model also found that having relatively less affordable housing in a city reduces the quality of housing for all households and, importantly, makes ownership less attainable for those with relatively low permanent incomes.  

Finally, after producing these results, the researchers turned to consider the policy implications of their findings and used their model to study the effects of increasing the progressivity of property taxes. Ultimately, the team showed that increasing the progressivity of property taxes improves the housing quality attainable by lower-income households, and thereby improves their well-being, relative to higher-incomes households. Moreover, it significantly increases homeownership, despite not targeting it directly. Households with high permanent income (who effectively bear the cost of the policy) continue to own at roughly the same rate but live in lower-quality houses. However, they were found to be able to offset this to a large extent by increasing their non-housing consumption. In this way, the research has relevance for current affairs, as many localities in the US and Canada are publicly debating the fairness of property taxes. For example, the newly-elected mayor of Toronto, Olivia Chow, has proposed raising property taxes, and the team’s research findings can inform such debates by offering empirical insights into the possible effects of such policies. 

Overall, the research published by Dr. Lloyd-Ellis, Dr. Head, and Dr. Stacey, produced informative findings and added to the housing literature in several ways. In addition to producing the notable findings that differences in land costs and city amenities may be driving differences in home affordability across cities, and making property taxes more progressive might plausibly benefit lower-income households, the research produced a novel model: whereas much of the previous macro housing literature focuses on the effect of downpayment requirements and household borrowing constraints in driving the distribution of households across rental and (relatively less-liquid) sale markets, the research produced by the team of QED economists highlighted that the optimal decisions made by buyers and sellers between such markets, based on numerous factors, including their preferences and financial constraints, can be highly influential in driving the composition of the housing stock, and should be considered in future research.  

Footnotes 

[1] To simplify, the team assumed that homeowners vacate their old houses and rent while they shop for a new house, so that only renters house shop, and listed houses are purely financial assets. However, this assumption was later relaxed, and doing so was shown to have no effect on any qualitative conclusions of the research. 

[2] This reflects the idea that the moral hazard of renting increases with house quality. 

[3] This was done using observational data, and by inferring values for differences across cities for various variables when data was not available. 

1. To simplify, the team assumed that homeowners vacate their old houses and rent while they shop for a new house, so that only renters house shop, and listed houses are purely financial assets. However, this assumption was later relaxed, and doing so was shown to have no effect on any qualitative conclusions of the research. ↩︎
2. This reflects the idea that the moral hazard of renting increases with house quality.  ↩︎
3. This was done using observational data, and by inferring values for differences across cities for various variables when data was not available.  ↩︎