Demand for Rent-Regulated Apartments: the Case of Sweden

Demand for rent-regulated apartments: The case of Sweden

Mats Wilhelmsson

Working Paper 2021:4

Division of Real Estate Economics and Finance Division of Real Estate Business and Financial Systems Department of Real Estate and Construction Management School of Architecture and the Built Environment KTH Royal Institute of Technology Demand for rent-regulated apartments: The case of Sweden

Mats Wilhelmsson

Division of Real Estate Economics and Finance Department of Real Estate and Construction Management Royal Institute of Technology, Stockholm, Sweden

Email: [email protected]

Abstract:

The Swedish rental housing market is characterised by, among other things, a form of rent control in which rents remain lower than market rate. This means that distribution of rental apartments is not based on the tenants' willingness to pay for a specific apartment. Instead, in most cases, distribution is based on a person's position in the housing agency queue. In Stockholm, many public and private housing rental contracts are set up via a common queue administered by the municipal housing agency. Individuals with much time in the queue can access a more extensive selection of rental apartments. The purpose of the following study is to estimate the demand for rent-regulated apartments. We do so by investigating the relationship between queue time and apartment attributes. A so-called hedonic waiting time equation will be estimated. The implicit prices of the rental apartment will be related to the tenant's income, and income elasticity will be estimated in a second step. The results indicate a significant willingness to pay for rent-regulated apartments, and that the demand for rental apartments can partly be explained by regulated rents, and partly by tenants' income.

Keywords: Rental housing market, Queuing time, Waiting list, Excess demand, Controlled rents

JEL-codes: R21, R23, R31

Acknowledgement: We thank the research project Housing 2.0 (Bostad 2.0) for financial support, and the housing agency of Stockholm (Bostadsförmedlingen) for data.

1. Introduction

The Swedish residential rental market is characterised by lower rents than the equilibrium rents in many local housing markets, although the reverse can also be found. As a result, apartments are not distributed based on households' willingness to pay, but mainly according to how long the household or individual has been in line for an apartment. The value of standing in line is high, and the individual will have many opportunities to choose an apartment with different characteristics, rents, locations, and landlords. Even if there is an income test, it will probably not be binding for individuals with a long queue time. The question is how the individual uses the value created by their time in line. As Willis (1984) points out, there is no opportunity cost connected with standing in line. It does not displace either income or leisure time. This is not to say that there is no cost for the individual in connection with waiting, and a loss of welfare for the society when we have a situation where the marginal willingness to pay far exceeds the marginal cost of the quantity offered (Andersson and Söderberg, 2012).

There are two reasons why rent control is introduced in housing markets (Haffner et al., 2008). It can be justified based on a redistributive policy goal, or an increase in the market's socio-economic efficiency. The former is, of course, a politically motivated measure that we as researchers have little to say about, except possibly the degree of effectiveness of the measure to achieve the political goal (Haffner et al., 2008). Ellingsen and Englund (2003) believe that there are no efficiency reasons for having a rent regulation system, but its occurrence must be regarded as a "political victory of tenants over landlords".

Increasing socio-economic efficiency is based on the fact that there are market imperfections in the rental market, and rent regulation can be a suitable tool for correcting these. The market failures that can be anticipated are in part asymmetrical information between tenant and landlord, and in part shortcomings in market competition. Housing is a very heterogeneous product, with long durability and high moving costs (Smith et al., 1988). This can create a situation of monopolistic competition, which can mean that the landlord can charge higher rents than justified by socio-economic efficiency (Lind, 2001). The rent regulation can protect the tenant against lower apartment quality and that the landlord charging too high rents in the future (Lind, 2001).

Moreover, as a commodity, housing is characterised by high transaction costs in the form of search and relocation costs. These leads to a mismatch between tenants and dwellings. This mismatch causes a welfare loss, where the existence of housing agencies has an important role to play. For example, Anas (1997) shows that a regulated market can reduce the degree of mismatch, but only if rents are higher than the market rent, it stimulates rental apartments and reduces the search cost and queue time. However, Sieg and Yoon (2020) find significant transaction costs and higher search costs in a regulated housing rental market that create friction in the rental market, which is also a welfare loss.

An effect of below-market rents is that new private landlords will gradually fail to enter the market (Haffner et al., 2008). The rental market will shrink, and only public actors will operate in the market. However, another effect of rent regulation is that it reduces mobility in the housing market, which can also be to the advantage of landlords by reducing the cost associated with a high turnover of tenants. (Turner and Malpezzi, 2003).

One consequence of below-market rents is that the production of new apartments decreases. According to Lind (2003), this can happen through three channels: decreasing the rent level, increasing the risk that the rental system may change, and by the pricing vulnerability of new housing stock in the event of a reduction in demand and vacancies. However, Lind (2003) argues that the connection between the construction of rental apartments and rents is weak. Andersson and Söderberg (2012) argue that the loss of welfare of rent regulation is significant, and moving to a system of market rents will generate welfare gains both in the existing stock and new production.

Since many rental markets are not in equilibrium, we cannot relate the rents with different characteristics of the apartment as in a traditional hedonic model. The Swedish housing rental market is an example of a housing market characterised by relatively 'tough' rental regulation. The rent regulation applies to both old and new tenants and applies indefinitely. The objective is that all citizens should have access to and afford a good quality apartment (Lind, 2001). Moreover, Lind (2001) believes that the regulation is comparable to rent regulations in Austria and New York, which are somewhat stricter than those in the Netherlands and Germany.

Analysing the rental market is important, as the willingness to pay for many different types and amenities and disamenities is based on owner-occupied housing in the property market. We know very little about the tenants' willingness to pay. Evaluating the queuing system and queuing time more carefully makes it possible to better account for tenants' willingness to pay for various housing policies and urban development projects (Willis, 1984).

The present paper aims to estimate the demand for rent-regulated (subsidised) apartments and estimate income elasticity using information about waiting times and waiting lists. To analyse the relationship between individuals' queue times and apartment attributes, we can analyse what the individuals use their queue time for. Do they buy size, location, or low regulated rent? The implicit prices can then be related to characteristics of the tenant, such as age and income. In this way, it is possible to estimate income elasticity. The problem, however, is that the estimated marginal willingness to pay and the elasticity of income are based on a model that assumes equilibrium in the market, which is not the case here. The ambition is to be able to use the result to evaluate different development plans for rental apartments even though market equilibrium rents do not exist.

Surprisingly, relatively few studies analyse queue times in a regulated housing market, even though many countries have rent regulation of varying degrees (Kettunen and Ruonavaara, 2020). One exception is Van Ommeren and Van der Vlist (2016), where they estimate a so-called hedonic waiting equation. The article has a theoretical and empirical approach that is close to what we are trying to achieve. By analysing more than 700 leases in the public rental market in Amsterdam, they conclude that both the rent level and the apartment's implicit market value impact the length of the queue period. Moreover, they estimate a positive income elasticity on demand for a subsidised rental apartment, indicating a smaller mismatch between tenants' preferences and dwelling characteristics than expected.

Our contribution mainly provides another example of empirical analysis within a relatively small research area. We have access to a rich geocoded dataset from a rental housing market considered to have a relatively strict rental regulation system. Unlike Van Ommeren and Van der Vlist (2016), we have access to significantly more rental contracts over a longer period. We also have contracts from both the private and the public rental market. In addition, there are some institutional differences between the rental market in Amsterdam and Stockholm. For example, rental contracts with reduced rent in Amsterdam entail an income ceiling, while similar contracts entail an income minimum in Stockholm. This means that rent regulation in Stockholm can be considered more general than those in Amsterdam. There are also some exceptions to rent regulations in Stockholm, such as rent in new production buildings, which means that different segments of the rental housing market are more in balance (tending towards equilibrium) than others. We also have access to information on how many people are interested in specific vacant apartments, which enables us to estimate the hedonic waiting time equation as well as the hedonic waiting list equation.

The article is organised as follows: Section 2 will briefly present the theoretical framework and the chosen estimation method. In Section 3, the case study of Stockholm will be presented. The data will be introduced in Section 4, and the results from the econometric modelling will be presented in Section 5. The article concludes with Section 6.

2. Theoretical framework and methodology

The theoretical framework is the classic hedonic price model, with the difference that it does not include equilibrium prices related to value-affecting attributes of the product housing (Rosen, 1974). Instead, we will relate queue time to different value-influencing characteristics of the apartment and the area. However, the queue time is not the "natural" queue time in equilibrium, as the natural vacancy rate, but the queue time we analyse results from excess demand, as contract rents are lower than the equilibrium rents. In order to be able to interpret estimated coefficients as marginal willingness to pay, we need to be able to assume that the market is in equilibrium. Thus, in general, we cannot do this for the rental

market, even if the rents can be regarded as equilibrium rents in certain areas and newly built rental apartments.

Anas and Eum (1984) develop the classic hedonic approach by assuming that the market is not in equilibrium. They do this by explicitly including a price adjustment mechanism in the hedonic price equation with cross-sectional data. The methodology has similarities with an error correction representation in time series analysis. We cannot use a similar approach here, as their model assumes that we are moving towards equilibrium, which is not the case in a regulated rental housing market.

Instead, we take as a theoretical starting point that the demand for rental housing (QD) is a function of the housing rent (R) and the apartment's characteristics (X) as well as household income (I) and other socio-economic attributes (Y). The supply of rental housing (QS) is also a function of the dwelling's rent and its characteristics, as well as landlord-specific characteristics (Z). In equilibrium, we have that QD * = QS, and in the reduced form, we have that the equilibrium rent (R ) is a function of the dwelling, household, and landlord characteristics. However, the rental housing market is not in equilibrium, but * the regulated rent (RC) is lower than R , which generates a demand surplus (QD> QS). This means that

* we now have a situation where R -RC = λ (QD-QS).

However, the demand surplus at RC is not directly observable; instead, as an approximation of the demand surplus, we have the number of individuals registered with the housing agency on a waiting list for specific apartments that interest the person. The number of individuals on the waiting list, or the time on the waiting list, can be interpreted as a measure of excess demand. R* is also not observable but is possible to estimate approximately from the condominium market, i.e., it is possible to estimate the market value (MV*) of rent-regulated apartments if they had been sold in the condominium market. MV* can be estimated according to the equation:

= + (1) ∗ 𝑀𝑀𝑀𝑀 𝛼𝛼 − 𝛽𝛽1𝜌𝜌𝜌𝜌 𝛽𝛽2𝑋𝑋 where α and β have been estimated from a hedonic price model applied to the condominium market. The parameter ρ is an adjustment factor, making the monthly fee in the condominium market comparable to the rent in the tenant-ownership market. If we assume a log-linear utility function in X and R, we can now describe the demand surplus equation as:

= + + + + (2) ∗ 𝑊𝑊𝑊𝑊 𝑜𝑜𝑜𝑜 𝑊𝑊𝑊𝑊 𝛾𝛾0 𝛾𝛾1𝑀𝑀𝑀𝑀 − 𝛾𝛾2𝑅𝑅 𝛾𝛾3𝑌𝑌 𝛾𝛾3𝑍𝑍 𝜀𝜀 where WT is equal to the waiting time and WL is equal to the waiting list. The parameter estimate γ1 is equal to the implicit price of a rental apartment with subsidised rent. The estimate is expected to be positive, as there is a willingness-to-pay to get a rental apartment. The parameter estimate γ1 is the inverse implicit price of the controlled rent. Higher rent is expected to decrease waiting time and waiting

lists. The estimated models have similarities to the hedonic waiting function that Van Ommeren and Van der Vlist (2016) estimate. Equation 2 can also approximately be expressed as a function of the characteristics (X) of the apartment instead of MV*, combining Equation 1 and 2.

= + + + + (3)

𝑊𝑊𝑊𝑊 𝑜𝑜𝑜𝑜 𝑊𝑊𝑊𝑊 𝛾𝛾0 𝛾𝛾1𝑋𝑋 − 𝛾𝛾2𝑅𝑅 𝛾𝛾3𝑌𝑌 𝛾𝛾3𝑍𝑍 𝜀𝜀 In step 2, we relate the estimated market value of the tenancy with the implicit price of MV* and RC together with the household's income:

= + + + (4) ∗ 𝑀𝑀𝑀𝑀 𝛿𝛿0 𝛿𝛿1𝛾𝛾1 𝛿𝛿2𝐼𝐼 𝜔𝜔 Where all δ are estimated, and γ1 is the implicit price of MV from equation 2.

As a valuation system, the queuing time differs from the price of a condominium to the extent that the household can sell the home and recover parts of the capital when buying a home. This is not the case with queue time, as it can be used once, and then it is consumed. There is an option value embedded in the queue time, as the household can save it and use the queue time in the future for something that better corresponds to the household preferences. However, if the household chooses to use its queue time, it can be used to exchange an apartment with another tenant.

There is a risk that the rent in the hedonic waiting equation is endogenous due to the housing company's setting lower rents in less attractive areas. We argue, however, that rents are sticky for reductions. Even in times of crisis, landlords are reluctant to lower rents. Empirically, Genesove (2003), among others, has found a significant rigidity of apartment rents, and theoretically, the issue has been analysed recently by Gallin and Verbrugge (2019). Of course, the endogeneity may also be caused by the lack of relevant variables in the model. In order to address some of the endogeneity issues, we have also included fixed area effects (the parameter γ1,j in Equation 3 where j is equal to separate residential areas within the housing market) to capture the possible bias that omitted variables can cause.

3. The case of Stockholm, Sweden

We will use the Swedish rental market in Stockholm as a case study. Housing policy in Sweden, which addresses all types of households and all segments of the housing market, is general compared to, for example, housing policy in Finland, which is more selective and targets low-income households.

The population of the city of Stockholm in 2019 amounted to 974,073 people. In the same year, the number of dwellings in the City of Stockholm was 471,455. Hence, the average number of persons per dwelling was approximately two persons. This is a proportion that has remained relatively constant since the 1970s. Of the total number of dwellings, approximately 40,000 were owner-occupied dwellings and 240,000 condominiums. Thus, the number of rental housing units amounted to approximately 185,000, of which approximately 40 percent consists of public rental housing. The three largest municipal housing 7

companies are Stockholms Hem, Svenska Bostäder and Familjebostäder (source: Statistics Sweden). As in many other countries in Europe (e.g., the Netherlands, Spain, and the U.K.), the rental market as a share of the total housing market has declined from just over half, in the 1950s to just under a fifth in the early 2000s (Haffner et al., 2008).

Rent regulation is a tool used in housing policy. Sweden is one of six countries in Europe with relatively strict rent regulation (Lind, 2001; Kettunan and Ruonavaara, 2020). From the post-war rent regulations, there has been a shift to softer rent regulation in many countries (including Sweden) and to free rental markets in others (e.g., Finland). Following Arnott's (2003) terminology, Sweden has second-generation rent regulation together with, e.g., Denmark, while many other countries have third-generation rent regulation, such as, e.g., Norway. Following Lind (2001), the Swedish residential rental market is Type E, a market that intends to protect all tenants against various rent increases.

The Swedish rent regulation was introduced in 1942 and was originally used to prevent rent increases during times of crisis. It was phased out during the 1970s, and replaced by today's so-called use value system, usually referred to as rent regulation. The regulation refers to a public system of rules for determining and controlling rents. Rent regulation in Sweden is based on costs, a so-called cost-price regulation that applies to new and existing contracts. This regulation is cost-based, but simultaneously a result of negotiations between the local tenants' association and the municipal housing companies (Lind, 2001). Moreover, the rents of private landlords cannot exceed the rent of the municipal housing company for a comparable apartment.

The rent in new multifamily houses is usually not negotiated between the tenants' association and the housing company. Instead, it is negotiated directly with the tenant, or a so-called 'presumptive rent' is used. If the rent has been negotiated with the tenant directly, the tenant has the right to have their rent tested after six months to assess whether it is reasonable, i.e., whether it is comparable with the rent for equivalent apartments nearby. The 'presumption rent' was introduced in 2006 and gave the housing company the right to set a higher rent than that based on the value in use. The presumption rent is valid for a maximum of 15 years, during which time the housing company cannot increase the rent for renovations and standard increases by more than the average rent development in the area. Moreover, since the rents in newly produced apartments are closer to market rents, these apartments will be relatively less attractive for an exchange of rental apartments between tenants.

Despite the existence of presumption rents, according to Lind (2001), Haffner et al. (2008) and Kettunan and Ruonavaara (2020), Sweden has the strictest regulatory system compared to Germany, the Netherlands, Spain, the U.K., or France. However, large regional variation exists within Sweden regarding how the rental system is implemented (Björklund and Klingborg, 2005; Lind and Hellström, 2006).

If market rents are not what governs the allocation of apartments among the tenants, then there must exist an alternative system. An alternative system is a housing agency where you can register yourself on a waiting list for an apartment in the future. More than 700,000 people are in the housing queue in Stockholm, i.e., the number registered in the housing queue. The housing agency distributes approximately 10,000 rental apartments per year. This means that there is a relatively large imbalance between those in the queue and the distributed apartments. This imbalance is likely to occur because as the number of apartments distributed via the queuing system increase, the queue will normally also increase (Willis, 1984).

Once a person is on the waiting list, it is their responsibility to apply for and register their interest when vacant apartments are advertised. The advertising takes place on the housing agency's website. This means that they form a separate waiting list for each apartment that is advertised as vacant. If the individual is one of those with the longest queue time, the process continues with a viewing of the apartment. After a viewing, the individual must again make a decision. If they are interested, they must provide a certificate of income, their current residence, and how many people are in their household. If the housing company approves them, they sign a long-term contract with the security of tenure and with rent regulated through lease negotiations.

4. Data

We have used geocoded data regarding first-hand contracts for rental apartments, primarily in Stockholm and some surrounding municipalities around Stockholm. In total, we have access to 40,000 contracts with information about the apartment, location, housing company, and tenant. All data has been geocoded, which has made it possible for us to merge the data with other types of geocoded data. The source of the data used is the housing agency in the city of Stockholm. Table 1 shows the variables used in the empirical analysis. Descriptive statistics refer to mean and standard deviation.

Table 1. Descriptive statistics (2014–2020).

Variables Abbreviation Average Standard deviation

Apartment

Rent R 8,470.513 2,902.503

Market value* MV 2,515,530 1,300,689

Size S 62.211 18.916

Rooms RS 2.323 0.897

Floor F 2.599 2.416

New N 0.293 0.455

Renovated RE 0.026 0.159

Existing market EM 0.681 0.466

Neighbourhood

Distance to CBD CBD 12.895 10.926

Distance to a Metro station M 4.719 9.023

Distance to a shopping mall SM 3.884 6.550

Tenant

Age A 39.144 12.023

Income I 478,743 2,541,761

Landlord

Private PR 0.619 0.486

Public PU 0.381 0.486

Intermediation

Waiting time WT 9.496 4.460

Waiting list WL 282.806 320.037

Number of rental contracts 35,075

* Estimated market value using information from the condominium market.

Around 35,000 leases were included with complete information in the analysis (approximately 5,000 contracts were incomplete). The material covers 2014–2020, i.e., seven years, although 2020 was incomplete. The average monthly rent is just under SEK 8,500, which corresponds to approximately USD 850. The standard deviation is relatively high (almost 3,000 SEK). The average size is about 62 square meters, divided into 2.3 rooms (as well as a kitchen). The standard deviation is relatively high, which indicates that we have both large and small apartments in the sample. Just under 30 percent of the

contracts relate to newly produced dwellings, and the rest consist mainly of apartments in the existing housing stock market. A relatively small number refer to renovated rental apartments.

On average, the apartments are just over 12 kilometres from the central business district (CBD), but variation is large. The average distances to the metro station and shopping mall are 4.7 and 3.9 kilometres, respectively. Just under 62 percent are apartments with private landlords. Tenants are on average 39 years old when contracts are signed, and have an average annual income of SEK 478,000 (here, the standard deviation is large, and there are some outliers with remarkably high incomes, which increases the average income). On average, tenants have been in a queue for almost ten years for the apartment they have signed a contract for, and which they have received in competition with an average of 280 people, i.e., the average number of people in queue per apartment.

We have estimated the market value (Equation 1) of a rental apartment using information about transactions in the condominium market. The model specification uses the same variables that we have available in the rental market. It consists of information about size in terms of living space and number of rooms, location in terms of distance to the CBD, subway station, and proximity to a shopping mall. The hedonic price equation also includes information about the monthly fee. However, it is important to note that the monthly fee in a tenant-owner association cannot be directly compared with the rent in a rental apartment, as it is normally higher, all else being equal. If we compare the data on condominium transactions and rental apartment contracts, we can observe that the rent for a rental apartment is normally 2/3 higher than the corresponding monthly fee to the tenant-owner association; ρ in Equation 1 is estimated to be 2/3. The result from the hedonic price equation is presented in the appendix.

Figure 1 illustrates so-called heat maps where we have rent per square meter (Rsq) on the vertical axis, and on the horizontal, we have (a) waiting time (WT) and (b) waiting list (WL), respectively. The colour reflects the degree of public versus private landlords.

Figure 1. Private and public landlord (rent per square meter, waiting time and waiting list) 350 Public 350 Public .975 .975 .925 .925 300 .875 300 .875 .825 .825 .775 .775 .725 .725 250 .675 250 .675 .625 .625 .575 .575 .525 .525 200 200 Rsq Rsq .475 .475 .425 .425 .375 .375 .325 .325 150 150 .275 .275 .225 .225 .175 .175 100 .125 100 .125 .075 .075 .025 .025 50 50 0 10 20 30 40 0 1000 2000 3000 4000 WT WL

(a) (b)

The private (red) and the public (green) landlords are found in all rental segments. We can observe that the private landlords are found in segments where the time in the queue is shorter than segments where public landlords are found. This is probably a consequence of the fact that the private landlords are the ones who produce new tenancies, which means that the rents in this segment are more expensive, on average smaller, and further from the CBD. In the segments where a slightly longer queue time is required, the private landlords are found in the medium-expensive rental segments, while the public landlords are found in the less expensive segments. For apartments where a long queue time is required, public landlords dominate. The pattern is almost the same for the waiting list relations in Panel b, although it is even more clear that private landlords have shorter waiting lists and that this is especially clear in the higher rental segments.

Table 2 shows the average rent, size, and distance to the CBD, as well as the share in the existing housing stock market divided into different intervals (percentile 0.25, 0.5, 0.75) of waiting time. We can note that it does not differ much, perhaps significantly less than expected for the average rent. The differences are not statistically significant. It was expected that people with long queues would buy low rents, but this is not the case on average. However, apartments with a shorter waiting time (fewer than seven years) have significantly higher rents than apartments where a longer waiting time is required. A contributing reason for this may be that the rent distance gradient within the city of Stockholm is weak. The rents in the inner city do not differ much from those observed in the outer city.

Regarding the size of the apartment, we can observe a weak positive relationship between size and queue time. Individuals with long queue time tend to sign contracts for larger apartments. The most obvious

pattern is that individuals with a long queue time use it to get a lease in the existing housing stock market and locations closer to the CBD.

Table 2. Waiting time

WT<6.9 6.911.2

R 9159.5 8263.8 8042.8 8452.2

(2647.4) (2818.7) (2757.6) (3212.6)

S 62.6 59.3 61.2 65.7

(19.6) (17.8) (17.5) (20.0)

EM 0.415 0.657 0.778 0.856

(0.49) (0.48) (0.41) (0.35)

CBD 21.9 13.3 9.9 7.16

(14.8) (8.7) (6.1) (5.64)

Number 8532 8441 8474 9192

Table 3 shows the correlation matrix for all the variables included in the study. Stronger colour intensity indicates a clearer relationship between the two variables. Blue indicates a negative association and red positive association.

Table 3. Correlation matrix

WT -0.063

WL -0.400 0.614

S 0.666 0.094 0.008

RS 0.677 0.064 -0.014 0.909

F 0.187 -0.005 -0.107 0.061 0.080

EM -0.419 0.323 0.537 0.042 -0.057 -0.164

CBD -0.149 -0.469 -0.249 0.012 -0.001 -0.067 0.031

SM -0.063 -0.296 -0.179 0.007 0.000 -0.095 0.025 0.839

M -0.044 -0.366 -0.250 0.017 0.002 -0.085 0.002 0.928 0.934

R WT WL S RS F EM CBD SM

The rent level is mainly negatively correlated with the existing housing stock market (new production has higher rents) and waiting line (more people put themselves on the queue list if the rent is lower), while we have a positive relationship between rent and size (larger apartments measured in square meters and number of rooms have a higher rent). Other variables have a weaker correlation with rent. We can also observe that there is a significant correlation between some of the other variables. Of course, housing size in square meters is highly correlated with the number of rooms, and we can also note that apartments far from the CBD are also further away from the metro station and shopping mall. Waiting time is negatively correlated with the CBD (and metro station and shopping mall) and positively correlated with the number of people who register themselves on the waiting list for a specific vacant apartment. We can also observe that more individuals sign up on the waiting list for not newly produced dwellings.

5. Econometric Analysis

The econometric analysis will take place in two steps following Rosen's (1974) two-step procedure. We will estimate the hedonic rental equation, which implicitly assumes that the rental market is in equilibrium, and then estimates the hedonic waiting time and waiting list equations. This will be done by including value-affecting apartment attributes or including the estimated market value for the rental apartment. The market value has been estimated based on transactions from the condominium market. We will also analyse whether there is any difference between the public and the private rental housing market. In the second step, we will estimate the demand for rent-regulated rental apartments by relating

the estimated market value of each apartment to the implicit price of the rental apartment and the tenant's income and age.

The hedonic rent and waiting equations

Table 4 shows the estimates for the hedonic equations: rent (column 1), waiting time (columns 2 and 3), and waiting list (columns 4 and 5). Box-Cox transformation suggests that a log-linear relationship cannot be ruled out. Therefore, we have estimated all models where the dependent variable and the continuous independent variables have been transformed with a natural logarithm. The interpretation is, therefore, in the form of elasticity.

The result from the rent equation is interesting. In total, the independent variables can explain almost 78 percent of the variation in rents. All estimated parameters are statistically significant and have expected signs. Furthermore, and unsurprisingly, larger apartments have higher rent. As expected, rents are higher in new production apartments (lower in the existing housing stock market), which is reasonable given presumptive rents and regulated rents based on user value. The rents in the public housing market have an average of 13 percent lower rents, all else being constant. The results also suggest that the rents near metro stations and the shopping mall are lower, while rents in the more central locations are higher than in the suburbs. This means that there is a rental distance gradient, but it is relatively weak. If the distance from the CBD increases by another percent, the rent is 0.15 percent lower.

The result from the hedonic waiting time equation has a significantly lower degree of explanation; the independent variables can explain only 39 and 50 percent of the variation in waiting time. The model with market value included in the specification has a lower degree of explanation than the specification with the apartment attributes. The model in column 2 estimates Equation 2 presented earlier, i.e., where the value of rental housing is a function of, among other things, the estimated market value.

Table 4. Hedonic rent, waiting time/waiting list equation

(1) (2) (3) (4) (5) Rent Waiting time Waiting time Waiting list Waiting list

R -0.382*** -0.664*** -1.265*** -2.462*** (-42.93) (-50.00) (-45.96) (-56.79)

MV 0.326*** 0.446*** (83.89) (37.10)

S 0.589*** 0.321*** 1.072*** (96.99) (18.86) (19.29)

RS 0.141*** 0.143*** 0.504*** (29.93) (12.01) (12.99)

EM -0.285*** 0.255*** 0.180*** 4.515*** 4.134*** (-146.51) (44.50) (29.28) (255.13) (206.17)

PU -0.135*** 0.249*** 0.149*** 0.569*** 0.332*** (-68.38) (48.33) (28.65) (35.78) (19.48)

SM 0.00552*** -0.0425*** -0.0620*** (5.02) (-15.53) (-6.95)

M 0.0302*** 0.0177*** -0.00446 (36.86) (8.51) (-0.66)

CBD -0.150*** -0.404*** -0.489*** (-95.33) (-92.31) (-34.21)

Time 0.0000726*** 0.000164*** 0.000216*** 0.0000355*** 0.000184*** (60.64) (49.82) (69.00) (3.50) (18.02)

Constant 3.926*** -6.475*** -1.836*** 4.029*** 11.63*** (68.64) (-43.02) (-12.12) (8.66) (23.52)

N 35075 33969 35070 33974 35075 R2 0.776 0.389 0.504 0.759 0.767 AIC -27987.3 39909.7 35890.5 116571.7 118916.8 t statistics in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001 Fixed effects are included in all models.

The parameter estimate is positive, which means that the queue time is expected to increase by 0.3 percent with a 1 percent increase in market value. This means that the willingness to pay (measured in time) to get a lease is highest, where the difference between the equilibrium market rent and controlled rent is greatest. The controlled rent has an expected negative effect on the waiting time. If the rent increases by one percent, the waiting time is expected to increase by almost 0.4 percent. The model in column 3 shows that what primarily increases the waiting time is if the apartment is larger, older, has a public landlord and is relatively close to central Stockholm. The estimated impact of distance to CBD is much higher in the waiting time model than in the rent model, indicating that the rent distance gradient is relatively flat.

The degree of explanation in the model that explains the variation in waiting lists is significantly greater than the model that explains waiting time. The independent variables can explain just over 75 percent of the variation in the waiting list. Hence, rent is an important aspect in how many individuals register themselves on the queue list for a specific apartment. The higher the rent, the shorter the list. It is also clear that newly constructed dwellings and dwellings with private landlords have shorter queues. The higher the estimated market value is, the longer the queue, which is primarily driven by the size of the apartment (the larger, the more on the list) and where the apartment is located (the further out from the city, the shorter the queue list). The impact of distance to CBD is higher in the waiting list model than in the waiting time model. If the distance to CBD increase by 1 percent, the waiting list is expected to decrease by 0.5 percent.

Parameter heterogeneity

The possibility of higher rents in newly constructed dwellings means that the contracted rent is closer to the unregulated market rent. The controlled rental distance gradient is relatively flat, which means that the regulated rents in the more peripheral locations are closer to a market rent than those in the more central parts of the city. This means that the segment of new rental housing and dwellings in the suburbs have a smaller gap between market rents and controlled rents. Whether there are also differences between the private and the public rental market that cannot be linked to quality differences is analysed in this section. Hence, we will analyse the difference in estimated parameters between older and new apartments (Table 5) and the difference in estimated parameters between private and public landlords (Table 6).

Table 5. Existing housing stock and new apartments.

Waiting time Waiting list EM NEW EM NEW R -0.379*** -0.387*** -1.622*** -0.502*** (-45.30) (-15.69) (-66.21) (-6.79)

MV 0.473*** 0.366*** 0.872*** 0.337*** (98.45) (35.63) (62.09) (10.98)

Time 0.000154*** 0.000275*** 0.0000568*** 0.000133*** (43.02) (35.13) (5.44) (5.68)

Constant -7.940*** -11.69*** 4.666*** -5.405*** (-48.52) (-30.20) (9.75) (-4.67) N 23580 10608 23582 10611 R2 0.337 0.177 0.217 0.013 AIC 23412.4 18087.2 74046.7 41344.7 t statistics in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001 Fixed effects are included in all models.

If we divide the material into two submarkets, one for existing housing stock market and another submarket for newly produced dwellings, the results indicate that most contracts have been for older apartments in the existing housing market (23.000 compared to 10.000). The results also suggest that the degree of explanation is greater in that market. This is especially clear in the hedonic waiting list equation. In the model for waiting time, we can note that the effect of rent is about the same in both markets. On the other hand, the effect of estimated market value is somewhat greater in the market for the existing housing stock, which may result from the estimated market value of market rents being relatively in line with the regulated rents. In the waiting list model, the difference between the estimated parameters is greater. An increase in rent in the existing housing market reduces the number in the queue significantly more than in the market for newly produced. The effect of estimated market value also significantly impacts the number of people in the queue in the existing housing market than for newly produced apartments. 17

Table 6. Public and private landlords

Waiting time Waiting line Public Private Public Private R -0.0867*** -0.537*** -0.795*** -1.437*** (-9.00) (-40.28) (-17.93) (-41.30)

MV* 0.406*** 0.371*** 0.804*** 0.572*** (47.68) (64.73) (20.54) (38.26)

EM 0.132*** 0.176*** 4.972*** 4.122*** (16.80) (21.48) (137.11) (192.48)

Time 0.000143*** 0.000224*** 0.0000310* 0.0000921*** (42.25) (44.75) (1.99) (7.06)

Constant -9.121*** -8.281*** -5.161*** 1.521* (-52.10) (-36.29) (-6.41) (2.55) N 13353 20835 13353 20840 R2 0.298 0.292 0.746 0.736 AIC 4169.8 31531.5 44928.3 71546.9 t statistics in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001 Fixed effects are included in all models.

If we divide the material by landlord instead, it is clear in the hedonic waiting time model that a rent change in the public rental stock has a relatively small impact on the waiting time, while the same rent change has a significantly greater effect on private housing stock. As for the effect of the estimated market value, it is at approximately the same level independent of the landlord. The same applies if it concerns the existing housing stock market or the market for newly produced apartments. Concerning the number who queue for a specific apartment, we can observe that the rent has a different impact depending on whether it is a private or public landlord. A change in rent affects the waiting line in the private rental housing stock more significantly than in the public one. The estimated market value also differs between landlords (greater sensitivity to stock changes in public housing than private).

A large part of the differences in effects comes from the fact that the public landlords, to a greater extent, own homes in the older housing stock in more peripheral locations and that the private landlords are found in the newly produced housing stock, which is also found in the more peripheral locations. In the older housing stock, private landlords have more apartments in the more central locations.

The estimation of the demand for rental apartments

In step two, we have estimated the demand for tenancies with regulated rent. The quantity demanded consists of the estimated market value of the tenancy. Independent variables include, among other things, the implicit price of waiting time, the tenant's income, and the control variables existing housing stock market and period for contract writing. We have estimated a demand function (Equation 4) for public landlords (column 1) and private landlords (column 2). The results are exhibited in Table 7.

Table 7. The demand for rental housing, MV*.

(1) (2) Public Private Implicit price MV* -0.547*** -0.574*** (-84.18) (-116.18)

Income 0.156*** 0.289*** (34.00) (32.73)

EM 0.162*** 0.351*** (28.06) (49.74)

Time 0.0000960*** 0.0000930*** (29.92) (19.52)

Constant 1.256*** -1.213*** (6.88) (-5.24) N 13217 20829 R2 0.427 0.491 AIC 1769.8 29218.2 t statistics in parentheses * p < 0.05, ** p < 0.01, *** p < 0.001

The demand for rental-regulated rental apartments is explained by the implicit price of the market value and income as well as a binary variable that indicates whether it is the existing housing stock market or not. The results indicate that the higher the implicit price of the market value, the lower the demand for tenancies. The effect of the implicit price on the market value is the same regardless of whether the landlord is private or public. The tenant's income has a significant effect on demand. Households with higher incomes show higher demand (positive income elasticity). We expect this in a market where the rent is determined by demand and supply, i.e., where we have market rents, but not in a regulated housing market. A regulated rental market with queuing time is considered by many to be neutral and fair (Willis, 1984). If this is the case, the demand for tenancy with regulated rent should not be a function of income, as we find on the rental market in Stockholm.

The fact that we can observe a positive and statistically significant income elasticity (between 0.15 and 0.30) means that rental apartments characteristics are not distributed completely randomly and that the mismatch between the tenant's preferences and the apartment is less than anticipated, as previous research has indicated (Von Ommeren and Van der Vlist, 2016). This mismatch means that those with a long queue time consume significantly larger apartments and in a better location than what is effective from a welfare theoretical perspective, i.e., the regulation provides incentives for overconsumption of housing.

However, compared with the ownership market, the income elasticity is relatively low. The estimation method is not entirely comparable with Von Ommeren and Van der Vlist (2016), but our results indicate that income elasticity is slightly higher in Stockholm's rental market than Amsterdam. In Wilhelmsson (2002), for example, the income elasticity of the single-family home market in Stockholm is estimated

at approximately 0.5 (compared with around 0.15–0.30 in this study). Hence, income elasticity is lower in the rent-regulated rental apartment market than in the unregulated owner-occupied single-family housing market.

What is also worth noting is that there is a significant difference between public and private landlords. Income elasticity is significantly higher among private landlords than public landlords. This may be due to a certain selection of biases by tenants, but it may also be due to private landlords applying a stricter income assessment of their tenants.

6. Conclusion

Decisions about urban development are often made based on information from the homeownership market. Housing prices can measure how attractive different residential areas are, and they can also be used to evaluate, for example, changes in land use. However, this may not be relevant to housing markets where the rental market is regulated. The tenants' willingness to pay for amenities and willingness to accept disamenities is much more difficult to obtain. The rent cannot be used directly in a hedonic rent equation.

Nevertheless, even a regulated rental market has information that can be used better to make informed decisions about land use in general, and above all, when it comes to decisions about policies that depend on the rental market and its functioning. If the rent is not the allocation mechanism of apartments between tenants, this allocation must be done by some other means. A common way is to distribute rental apartments via a queuing system administered by a housing agency. This means that information about queue times as well as interest in individual apartments, based on the number of individuals on the waiting list to apply to rent them, can be used.

We have used information about the waiting time and waiting list to estimate a hedonic waiting time equation and a hedonic waiting list equation because the rental housing market is in disequilibrium. Moreover, we have estimated an alternative of the hedonic price equation where the estimated market value of the tenancy is included (to correct for disequilibrium) in the model specification. The models enable us to estimate the demand for rent-regulated tenancies. Our results indicate that there is a significant willingness to pay for subsidised rental apartments. Since the market value of the tenancy is a function of size and location, the willingness to pay will be higher for larger homes in better locations but, above all, apartments with lower regulated rent.

The income elasticity is positive, which indicates that the demand for rental apartments increases with higher incomes. In a completely random distribution of apartments, we would expect income not to affect housing choice. The mismatch between tenant and apartment is smaller than it would have been

if the distribution had been completely random. However, income elasticity is lower than in an apartment market with ownership.

One policy implication is that willingness to pay for tenancy can be estimated even when regulations maintain below-market rents. Information about waiting times and waiting lists is important to understand tenants' willingness to pay for different apartment and residential area value-affecting attributes.

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Appendix

Estimation of the market value of the rental apartment

Price

Monthly fee -585.1*** (-164.57)

Living area 58306.9*** (166.10)

Number of rooms 202046.9*** (34.20)

Distance CBD -184952.2*** (-199.21)

Distance shopping mall -4948.7*** (-3.53)

Distance subway station 147743.4*** (86.51)

Date 201.8*** (23.96)

Constant -6219161.3*** (-16.93) N 103406 R2 0.611 AIC 3185980.3