Abstract
Following the evidence that housing costs may impair the proper functioning of the labour market, this paper develops a search and matching model where trading frictions in the mortgage, housing and labour markets interact with each other. Precisely, the employment status affects the probability to get a mortgage. In turn, the granting or not of the mortgage affects the housing tenure choice (tenancy or owner occupancy). Finally, the housing tenure choice affects the unemployment rate. It will show that tenants generate a greater effort in searching for a job than homeowners, since employed workers have a greater chance of getting a mortgage to buy a home. As a result, the positive correlation between the homeownership and unemployment rates emerges as quite consistent with the evidence that homeowners tend to be unemployed less often than tenants.
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Notes
In this specific instance, it needs to pay attention to the use of positive or negative relationship. A positive relationship between homeownership and unemployment implies that an increase (decrease) in the homeownership rate leads to worse (better) labour market outcomes, since unemployment is a “bad phenomenon”.
The dependent variable of the model is the (natural logarithm of the) state unemployment rate. The coefficients of interest are the homeownership rates in previous years. The size of the coefficient on lagged homeownership rate (always statistically significant) becomes stronger as one goes backwards in time.
Head and Lloyd-Ellis (2012), for example, show that while homeowners are less mobile than renters, the impact of homeownership on unemployment is quantitatively small.
The main difference is that job mobility in a local labour market does not involve a change of residence, while a change of residence would be necessary before accepting a job in a non-local labour market.
The results that homeownership have higher wages, shorter unemployment spells and a lower unemployment risk are also found by Coulson and Fisher (2002).
Probably, also because of the presence, in some markets, of a large share of tax evasion.
Heston and Nakamura (2009) find that for similar housing features, owner occupied housing would rent for about 14 % above market rents. A large part of this premium may be attributed to the so-called “owner pride”.
The percentage of new houses sold by cash in one of the richest countries (i.e. the United States) is never exceeds 10 %. Thus, the main type of financing to buy a house is the mortgage: more than 90 % considering the Conventional, VA and FHA loans (source: http://www.mortgagenewsdaily.com/data/financing-type.aspx).
Note that this type of home seeker does not coincide with the outright owners. The outright owners are not necessarily wealthy people that can buy a house with their own equity. In effect, in many cases, outright owners have obtained their own dwelling through a hereditary legacy. Also, the analysis focuses on the home seekers while the outright owners are people that already have a home.
Precisely, the matching function (1) assumes that: (i) With a rise in only one of two inputs (b or t), holding the other fixed, the number of trades increases but at decreasing rates due to negative congestion externalities (the hypothesis of diminishing productivity in the matching function with respect to each input); (ii) Also, with an increase in b, holding t fixed, the matching probability increases for tenants and decreases for banks (the inverse is true when t increases but b remains fixed); (iii) With an identical rise in both the inputs, for example with a doubling in both b and t, the matching function increases at the same rate, i.e. it doubles (the hypothesis of constant returns to scale in the matching function).
Standard technical assumptions are also employed, namely: \( \underset{\theta_{m\to o}}{ \lim }{m}_m\left(1,\ {\theta_m}^{-1}\right)=\underset{\theta_{m\to \infty }}{ \lim }{m}_m\left({\theta}_m,1\right)=\infty \); \( \underset{\theta_{m\to \infty }}{ \lim }{m}_m\left(1,\ {\theta_m}^{-1}\right)=\underset{\theta_{m\to 0}}{ \lim }{m}_m\left({\theta}_m,1\right)=0 \).
Basically, there are no restrictions on the number of mortgages granted, since the granting of a mortgage does not deprive the bank of the chance to grant a mortgage to another client who may apply for it.
An asterisk above the variable denotes the steady state equilibrium value.
Actually, the rates δ m and ρ m refer to the condition of owners with a mortgage, i.e. home seekers (tenants) that have already obtained a mortgage.
We assume that m(v m , t) has the usual properties, i.e. constant returns to scale.
Actually, the selling price is the outcome of a bargaining between seller and buyer. Properly speaking, therefore, the amount of mortgage payments \( \overline{x} \) depends on the sale price P.
New buildings are usually put on sale and thus the entry of new vacant houses is realistic in the homeownership market. However, one can assume that a portion of them is subsequently rented.
In equilibrium, the value of a further vacancy must be equal to zero.
The cost of search could increase with z, in the sense that it could become more expensive when z increases, since the latter includes the value of leisure and the search implies the forgoing of leisure.
To ensure that production takes place we also assume that (1 − β) · y > k.
Hence, \( Y\equiv \frac{\overline{x}}{\beta \cdotp y} \) is the maximum payment to income ratio for employed workers and \( Y\equiv \frac{\overline{x}}{\left[z-c\left({s}_t,z\right)\right]} \) is instead the maximum payment to income ratio for unemployed workers.
Hence, we are implicitly assuming that \( G\equiv {m}_m\left({\theta}_m,1\right)\cdotp \left[1-F\left(\overline{x}\right)\right]\cong 0 \) for unemployed/tenants since it is very likely that \( \overline{x}>\left[z-c\left({s}_t,z\right)\right] \).
They are behavioural equations for search intensity. By using the Nash bargaining rule, Pissarides (Chapter 5, 2000) derives a very simplified equilibrium relation between search intensity and market tightness. In the specific instance, however, it is more useful to use the behavioural equations. Also, the standard Nash bargaining solution for the wage determination is not used in this model.
Economically, in fact, there may be more than one equilibrium solution (see Pissarides 2000). This could occur if many job vacancies come into the market (in the case of positive economic shocks) and, thus, unemployed search more intensely and firms open additional job vacancies. As a result, both search intensity and market tightness increase faster. Suppose, for example, that the curves s(θ) and θ(s) are increasing and convex functions. Obviously, if s(θ) is an increasing and convex function, it becomes an increasing and concave function in the space (θ, s) when the variable of search intensity is represented in the horizontal axis as in Fig. 1. Thus, a second intersection (a second equilibrium solution) is possible. Note that the same result (more than one equilibrium solution) may occur also if less job vacancies come into the market. Formally, it is possible to obtain multiple equilibria with increasing returns in the matching function. However, it is a necessary but not sufficient condition (see again Pissarides 2000).
Very intuitively, a decrease in the rental price or in the costs of housing searching has the same effects of an increase in the mortgage payments, namely G · [W o − W t ] is lower.
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Acknowledgments
The author wishes to thank the anonymous referees for the helpful comments and suggestions. A previous version of this paper appeared in the Ivie working papers (AD series).
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Lisi, G. Mortgage Market, Housing Tenure Choice and Unemployment. J Real Estate Finan Econ 53, 472–493 (2016). https://doi.org/10.1007/s11146-015-9533-0
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DOI: https://doi.org/10.1007/s11146-015-9533-0
Keywords
- Search and matching frictions
- Mortgage market
- Housing costs
- Housing tenure choice
- Search intensity
- Unemployment