An income-distributional analysis of the rent control subsidy

Rent control measures are typically in place to assist low-income households and decrease segregation. Yet, there is little empirical research on the social impact of such policies and specifically the role of how rent-controlled apartments are allocated. This study analyzes the income-distributional effects of rent control with a novel dataset that includes characteristics of those who received rent-controlled apartments between 2011 and 2016 in central Stockholm, Sweden. Specifically, this paper provides analysis of the impact of allocating apartments through a centrally managed queue with apartments from both public and private landlords. To quantify the rent subsidy, we estimate hypothetical market rents by taking the owner-occupied market as a point of deviation. We find a positive relationship between the rent subsidy and time in que. Apartments in the fourth quartile of subsidy require on average 21 years in que, while those in the first quartile require 10 years on average. There is considerably heterogeneity in the level of rent subsidy, and tenant income. Even as allocating through queuing should benefit high-income households less than allocation based on landlord preferences, we find several regressive effects. Controlling for time in queue, we find that tenants in the fourth quartile of annual income receive monthly rent subsidies that are substantially higher than renters in the first quartile of income. Similarly, rental apartments in the fourth quartile of the subsidy have older tenants with substantially higher incomes compared to less subsidized apartments. The regressive effect is driven by high earners renting larger apartments with larger absolute subsidies and being able to wait longer in queue.


Introduction
Increasing residential rents and declining housing affordability have resulted in calls for rent controls across the globe (Slater, 2021).On a national level, Bernie Sanders and Jeremy Corbyn have called for rent control policies in the US and the UK, respectively.On a local level, New York and San Francisco are examples of cities in the U.S. that have adopted various forms of rent control.In Europe, Berlin has attempted to impose a moratorium on rents in 2020, and the mayor of London has signaled the necessity of similar measures.In short, rent control measures have become a popular policy to combat decreasing housing affordability.
The main arguments behind introducing and maintaining rent controls are typically based on keeping the housing stock affordable and accessible, also to households with lower incomes (Rajasekaran et al., 2019).As rent control will increase overall demand for housing and limit supply, landlords will have significant power over who has access to rental apartments.As landlord preferences tend to favor higher-income residents, the desired outcome of rent control may not be achieved.For rent control to act as a favorable re-distributional measure, the mechanism for allocation of rent-controlled apartments is important (Glaeser, 2003).One way of allocating rental apartments is through waiting lists (Lindsay and Feigelbaum, 1984), where the cost of housing is equal to the rent, plus the cost of waiting (Propper, 1995).Allocating rental apartments through queuing is applied in many different countries but can take different forms, such as public ques for a specific neighborhood or building (such as in New York) or be specific for public housing or a specific landlord (Van Ommeren & Van der Vlist, 2016).
The aim of this study is to analyze income-distributional effects of rent control in a setting where apartments are allocated through a centralized housing queue that encompasses many different buildings and neighborhoods, and where there are no specific requirements to enter the queue (such as income limitations for public housing).
We apply a novel dataset with characteristics of those who received rent-controlled apartments in Stockholm, Sweden, through a central queue.The queue mediates apartments from both public and private landlords.It is important to note that rent control covers all rental apartments, and that there is no social-housing sector with apartments designated for lowincome households in Sweden.Rental apartments mediated through the queue spans all neighborhoods and sizes, and tenants can have vastly different socio-economic status.In our analysis, we take the non-regulated owner-occupied market as a point of deviation to estimate hypothetical market rents for each rent-controlled apartment, as this allows us to explore the relationship between the rent subsidy, defined as the difference between market rent and regulated rents, and the socio-economic characteristics of those who receive rental apartments.
Although allocation through a central housing queue should favor high income households less, compared to allocation through connections with landlords or key money for instance, the possibility to gather waiting time may be skewed in favor of high-income households.The argument is simple, waiting for a decade for a rent subsidy demands an alternative housing solution in the meantime.Within the data in this study, the average time in queue among those who received a rental apartment in the attractive central parts of Stockholm is 14.8 years.This increases to 21 years for apartments in the fourth quartile of rent subsidy.Possibilities to arrange alternative housing solutions are naturally skewed in favor of high-income households, who can solve their housing needs on the ownership market.Lower-income households, who are likely to have a more immediate need for housing, are more likely to apply to a less subsidized apartment that requires less time in queue.
This paper adds to the existing literature in several ways.First provide an analysis of the income distributional effects of allocating rental apartments through waiting time.Second, we analyze a setting in which rental legislation is all-encompassing.This can be contrasted to studies of social housing (that is specifically targeted to low-income households) in otherwise free-market settings.
The remainder of this paper is structured as follows; a summary of previous literature is provided in Sect. 2. This is followed by a description of our data and the Swedish institutional setting in Sect.3. Section 4 covers our empirical strategy.Section 5 presents the results and Sect.6 concludes.

Literature review
From an income-distributional perspective, one of the earliest attempts to measure the impact of rent controls on different income-groups was Johnson (1951), who concludes that there is no evidence that rent control helps low-income households.Olsen (1972) provided one of the first econometric estimations of the consequences of New York rent control.He concludes that rent control benefits poorer households more than it benefits richer households.However, the allocation of benefits through rent control costs twice as much for landlords as the benefit received by tenants.
Gyourko and Linneman (1989) evaluated the impact of rent control in New York, across different socio-economic groups.The authors found that rent controls had little if any distributional impact due to inefficient targeting of benefits.While many low-income households benefit from rent control, many middle and high-income households do as well.
Inefficient matching between the housing benefit and recipients is a core cause of the distortions caused by rent control (Gyourko & Linneman, 1989;Van Ommeren & Van der Vlist, 2016).Thus, the ways in which rental apartments are allocated is closely related to how rent controls to achieve its stated goal of increasing affordability for low-income households (Glaeser, 1996(Glaeser, , 2003)).Arnott and Igarashi (2000) find that the mismatch costs increase as rent control policies becomes more severe.Glaeser and Luttmer (2003) empirically tested the misallocation of housing under rent control by comparing housing consumption across socio-economic sub-groups in New York, finding that an economically and statistically significant number of apartments are misallocated.
Misallocation of apartments can be exuberated by incentives for tenants to stay in subsidized apartments.Several studies have concluded that rent control reduces tenant mobility (Gyourko & Linneman, 1989;Ault et al., 1994;Simmons-Mosley & Malpezzi, 2006).Analyzing tenants in the Danish private rental sector, Munch and Svarer (2002) found that the typical tenant will have a tenancy duration more than six years longer if the apartment is among the 10% most subsidized apartments, compared to if the apartment belongs to the 10% least subsidized units.Diamond et al. (2019) analyzed the impact of rent control in San Francisco and noted that it has reduced tenant mobility by 20%.The longer-term effect of rent control is a reduction of rental supply by 15%, thus undermining the goals of the policy as market rents are driven upwards (Diamond et al., 2019).
This study is closely related to the strand of research that has analyzed allocation of rent-controlled apartments through queuing.Van Ommeren and Van der Vlist (2016) analyzed the welfare effects of allocating rent-controlled public housing in Amsterdam through queuing.The authors found no linkage between household income and market value of the apartment when analyzing a sub-sample of public housing apartments in Amsterdam with long queuing times.For apartments with short queuing time the authors found a positive relationship, where households with higher incomes receive apartments with higher market values.Another study in the Dutch setting is provided by Kattenberg and Hassink (2017), who found that renters of social housing with the 10% highest incomes, receive larger rent benefits than those renters with the 10% lowest incomes.The rent benefit results in higher income renters prolonging tenancy in social-housing.

Swedish rent control and the central stockholm housing queue
Sweden has had different types of rent control regimes since 1942.The current system of rent control was established in 1968 but has since undergone several changes (Andersson & Söderberg, 2012).The main result does however remain intact: rents lie far below market clearing levels, especially in Stockholm (Donner et al., 2017).
For most of the existing rental housing stock, rents are set through the user value system that was implemented in 1968 to ensure that apartments with similar characteristics would have similar rents.If a tenant and a landlord disagree regarding the rent, the rent can be tried in court, where the user value will be established through comparison with other apartments.Notably, the user value system does not consider location when determining rent, resulting in rents far below market clearing levels in attractive neighborhoods.
As the rent motivated by user value may not be high enough to cover building costs, a supplement to the rental legislation was introduced in 2006, that allows rents for newly constructed apartments to deviate from the user value, to cover expenses, for a period of 15 years.Thereafter, rents are to be tried against user values (Fritzon, 2020).
Prospective tenants can receive rental apartments in several ways.Connections and nepotism is one.Illustrative examples are the former social-democratic prime minister Göran Persson who received a rent-controlled apartment from a private landlord. 1The same goes for the current center-right prime minister, Ulf Kristersson.2Some landlords have their own waiting queues or allocation methods where they can choose between prospective tenants.The discrepancy between market rents and regulated rents also provides incentives for a black market (Malpezzi & Ball, 1991;Malpezzi, 1998).Black-market transactions of rental contracts are known to occur in Stockholm3 .
It is not a far stretch to suggest that black markets transactions and allocation through connections favor households with higher incomes.However, a portion of vacant rental apartments in Stockholm (approximately 20% according to Donner et al., 2017) are allocated through the central queuing system (Bostadsförmedlnignen i Stockholm, from here on referred to as the queue) that should benefit high-income households less.Both private and public landlords can post their apartments on the website of the queue.In our data set consisting of 9,943 mediated rental apartments for central Stockholm, we can identify 203 distinct landlords.
Queuing time starts upon registration in the queue.To register, the applicant needs to be 18 years of age and a legal resident of Sweden.There is an annual cost of 250 kronor ($29) to stay in the queue.An individual who has registered in the queue will start building waiting time, which is the currency with which an apartment can be acquired.An individual in the queue will never be offered an apartment, instead one must actively express interest in posted apartments on the website of the queue.
When the apartment has been posted and applicants have expressed their interest, several households, ordered from highest queuing times, are invited to view the apartment.After viewing, the household can decide whether they want the apartment.The individual with longest queuing time who wants the apartment and fulfills any income requirements set up by the landlord4 , can then sign a contract (Stockholm Housing Agency, 2022).Similar types of choice-based (i.e., that registered individuals may apply to any vacant apartment) queues have been applied in cities such as Amsterdam, London, and Toronto (Van Ommeren & Van der Vlist, 2016).
The number of queuing people is increasing at a rate faster than the number of mediated apartments.Average queuing times for mediated apartments exceeds 10 years and are approaching 20 years plus for apartments in the city center (Donner et al., 2017;Kopsch, 2019).In our data, the average queuing time is 14.8 years.

Data
To analyze the relationship between tenant characteristics and the rent control subsidy, we use three primary data sources which are described below.
First, a dataset of rental apartments that have been mediated through the central queue managed by the Stockholm Housing Agency.The dataset includes basic characteristics such as size, number of rooms and address.This data covers the period of 2011 to 2016 and includes apartments from both private and public landlords. 5econd, a dataset with nearly 40,000 arms-length sales of owner-occupied co-operative apartments6 sold through real estate agents during 2011 to 2016.The dataset is provided by the company Mäklarstatistik and has a market coverage of above 90%.We use this dataset to estimate an equation for market rents which is applied on our above-described dataset with rental apartments.The difference between the actual rent and the estimated market rent is the rent subsidy.
Third, we merge the rental data with information on all individuals who received a rental apartment.The data includes information about age, income, gender, and the postal area from which the individual moved.This data was also provided from the Stockholm Housing Agency.
Of 9,943 mediated rental apartments in central Stockholm during the period, we exclude short-term contracts and all special types of contracts (such as senior housing, student housing, housing specifically for youth and short-term contracts) to analyze what is typically considered a "normal" rental apartment by most individuals, i.e. with a right of tenancy and without special requirements.Our way of determining the sample follows previous research analyzing the Swedish rental market (Donner et al., 2017).We also exclude apartments in new development and renovations as these are subject to a different rent structure which allows for higher rents, closer to market rates.
Even though normal rental apartments constitute the vast majority of rental apartments in Stockholm, the remaining sample of mediated apartments numbers 2,375 (out of 9,943), illustrating that the turnover of rental apartments is much lower compared to other forms special rental contracts.This can be attributed to the shorter-term nature of special contracts (such as student housing), but also a consequence of a lock-in effect caused by low-rents (i.e., those with very subsidized apartments are unwilling to give up their contracts).
Table 1 below covers the basic characteristics of rental apartments and owner-occupied apartments used in our analysis.The statistics show us that rental apartments tend to be smaller (on average 57 square meters compared to 62 for co-operatives) and have fewer rooms (1.9 compared to 2.3).The data also tells us that the average transacted apartment sold for 4,427,017 Swedish Crowns (SEK) (approx.$511,794) with an average co-operative monthly fee of 2,888 ($334).This while the average mediated rental apartment has a monthly rent of 7,434 SEK ($859). 7e now shift our attention towards the characteristics of those who received rental apartments in central Stockholm through the queue between 2011 and 2016.
In addition to time in queue, Table 2 shows statistics on gender, age, income and if the renter was already living in central Stockholm.Information on annual income, time in queue and age is missing for 733 observations (notably time in queue which is missing for 541 observations).Therefore, our analysis covers the remaining 1,642 observations.8 The average individual who received a rental apartment is 43 years old and has an annual income of 487,761 Swedish Crowns (SEK) ($56,388).The median is 416,700 SEK or $48,173.The average time spent in queue was nearly 15 years (with a standard deviation of 6.2 years).There is a slight majority of women (56%), and about 46% was already living in the central parts of Stockholm that we are analyzing.The latter statistic is notable, as it shows that almost half of those who receive rent-controlled apartments already had some form of housing in the attractive city center.
The levels of income for those who received rent-controlled apartments are considerably higher than average incomes for Sweden and the greater Stockholm region (county).Based  Sweden, 2020).The average of averages for 2011 to 2016 is an annual income of 343,700 SEK ($39,734), which is 30% less than the average for those who received a rent-controlled apartments during the period.

The empirical strategy
Binding rent controls affects the price of rental housing, and results in prices that typically are below market clearing levels.Thus, implying a subsidy to the tenants living in rent-controlled apartments.In this paper we are interested in explaining and investigating whether socio-economic factors of renters can help explain the rent control subsidy.To achieve this, we need to quantify the subsidy.More specifically, the subsidy (S i ) is the amount of rent for apartment i that is not paid due to rent control.That is, the difference between the prevailing market level rent (h market i ) and the rent-controlled rent (h regulated i ).Or expressed mathematically: Regulated rents are observable in the Swedish context.But since the counterfactual market rents are unobservable, the true subsidy is unobservable.Therefore, we will have to provide an estimate of the subsidy ( si ).This demands an estimate of the counterfactual market rents.
Here, we follow the approach by Donner et al. (2017) of using transaction data of owneroccupied apartments to estimate hypothetical market rents for each rent-controlled apartment.In the below section, we cover each step of our analysis to estimate hypothetical market rents.

Estimation of market rents in a rent controlled setting
As previously described, the Swedish rent control policy is all-encompassing and applied to virtually all rental apartments (with some temporary market adjustments for new construction).The absence of an unregulated comparable rental sector prohibits estimation of market rents between sectors.Therefore, we will make use of the unregulated market for owner-occupied apartments.On a housing market without price controls, we would expect the monthly costs of apartments to converge with respect to tenancy form.We use information from the owner-occupied sector to estimate the household cost function of housing (c i ).This cost consists of two parts.First, the monthly fee, M i , that is paid to the housing co-operative to cover heating, maintenance and debt-maintenance if the co-operative holds debt.In Sweden, practically all owner-occupied apartments are in co-operative form, which is somewhat different in an international perspective.The monthly fee is included in our transaction data.Second, the cost of capital, which can be estimated from the transaction price, P i , assuming an annual cost of capital (r-g) 9 , where r denotes the annual interest rate and g the expected increase in apartment value.The total monthly cost of a co-operative apartment is therefore as shown in (3); In our dataset with co-operative apartment transactions, we can observe all components of (3) except for r-g, which we derive from a small sub-set of newly produced apartments with freely set rents s a point of reference.The estimation of r-g is detailed in the appendix (Sect.8).
The transaction data also includes apartment specific characteristics such as size and location.This allows us to estimate the housing cost function to provide an estimate of the individual cost components, such as size and location.That is, the monthly cost for apartment i is a function of the characteristics associated with that apartment: With  representing the physical characteristics of apartment . is a statistical error term that represents aspects that are important for the price of the apartment but that are not in our data set, and stochastic errors.This cost function would provide an estimation of market rents in a well-functioning rental market where the equilibrium is equal to the housing cost that a tenant is willing to pay.Expressed differently, the market rent (based on the market cost for owner-occupied apartments) is the sum of the estimated implicit cost of individual characteristics associated with the apartment.
To estimate hypothetical market rents, we run econometric models where the dependent variable is the monthly cost of an apartment which is the monthly fee, and the present value of the transaction price, M i + (r-g) P i /12.
The independent variables are apartment characteristics; the number of rooms, the living area (in square meters), the number of rooms multiplied with the living area, binary variables indicating neighborhood (parish) and time (quarterly).
As we found that the data is heteroskedastic, we do Box-Cox Transformations of the dependent and independent variables, following Halvorsen and Pollakowski (1981).The econometric specification is as below (5); Since we have stated that the free market outcome of both rents and monthly costs of owneroccupied apartments would result in equality between costs (h market i = c i ), we can use the implicit estimated costs ( f ) from (5) to impute market rents, such that: 9 See appendix Sect.8 for the approach of estimating r-g.
1 3 Since we can observe the same characteristics for rental apartments, i.e., size and location, as for owner-occupied apartments, this approach is possible.And thus, we can compute an estimate of the subsidy for each of the observed rental apartments, using (2).

Sources of potential bias for estimating market rents
Using estimated monthly costs of owner-occupied housing to estimate market rents may potentially result in biased results, for several reasons.For one, this approach assumes that rental housing and owner-occupied housing are perfect substitutes to each other.There are however some genuine differences between renting and owning, such as different service levels and different capital risks that speak to the fact that rents are likely to be slightly higher than monthly costs for similar owner-occupied apartments.Thus, market rents may be underestimated.
It is also likely that prices on the owner-occupied market are driven upwards due to the lack of supply of rental apartments and that a de-regulation of the rental market would have a depreciating impact on the owner-occupied market as supply of rental apartments increases.Thus, using prices of owner-occupied apartments as benchmark, may overestimate the market rent.In the longer-term, the subsidy is likely to be overstated as market rents would increase supply of rental apartments and thus drive down rents.Similarly, the current incentives to convert rental apartments to co-operatives that has decreased supply of rental apartment would also decrease (see Donner and Kopsch, 2018

for a review of this conversion process).
There is also a possibility that unobserved quality differences between rental apartments and owner-occupied apartments result in over-or underestimation of market rents.Economic theory typically points towards quality deterioration in presence of rent controls.Lind (2015) argues that the Swedish rent control policy may have the opposite impact, as landlords have an incentive to overinvest in quality as it allows for rent increases.We believe that unobserved quality differences are most likely to be small, and of limited importance.It is worth noting that a large part of the owner-occupied housing market in central Stockholm consists of tenure converted rentals (Donner & Kopsch, 2018).
Even as potential biases might impact the absolute magnitude of our estimated market rents, relative values are most important for the purpose of this study.Reassuringly, our estimated market rents, and corresponding rent subsidies, conforms with what we would expect from local market knowledge and behavior of market participants.Even as we cannot observe a household's willingness to pay for an apartment through price, the value of an apartment, at least relative to other apartments, is revealed by how long they are willing wait (Van Ommeren and Van Der Vlist, 2016).Our market rent estimates are supported by the observation that apartments in the fourth quartile of the estimated rent subsidy have an average waiting time that of 21 years compared to 10 years for apartments in the first quartile of the estimated subsidy.

Model specification for estimating the determinants of the rent subsidy
Section 4.1 above covers how we estimated market rents for all rent-controlled apartments by imputing the estimated equation from (5), and consequently the rent subsidy.
Our analysis therefore proceeds to estimate models that explain the rent subsidy as a function of the characteristics of the renter who received the apartment.
The independent variables are; gender, income (by quartiles), age (by brackets)10 , time in queue (in years), the square of time in queue (as we expect a non-linear relationship) and if the renter is from Stockholm.We also include binary variables controlling for location (parish) and time (year).
We run models with the dependent variable (the rent subsidy) based on discount rates of 2.65% and 3.0%.The absolute rent subsidy is estimated as shown in (7) below: It is likely that higher income individuals will demand larger and more expensive apartments, with a larger absolute subsidy.We therefore estimate a model where we control for apartment size (in square meters), the number of rooms, and the number of rooms multiplied with the living area.The econometric specification can be seen in ( 8):

Results
Our results will be presented in Sect.5.1 through 5.4.Section 5.1 briefly covers the results from our estimation of market rents and the rent subsidy, Sect.5.2 the impact of rent control across tenant income groups, and Sect.5.3 tenant characteristics by quartiles of the rent subsidy.Section 5.4 presents econometric models that explain the rent subsidy with renter characteristics.

Estimation of market rents and the rent subsidy
The output from the hedonic Box-Cox models (corresponding to Eq. 5 above) for estimating market rents is provided in Table 3.The dependent variables show their expected signs and are statistically significant (1%).These results provide us with an equation to estimate market rents.Our results from the analysis of the rent subsidy follows in Sect.5.2 through 5.3.
Binary variables indicating the year of sale and location (parish) are suppressed from the output to save space.
Table 4 shows the estimated market rents from applying the equation from Table 3.The average estimated monthly market rents are 10,818 SEK ($ 1,251) and 11,872 SEK ($ 1,372), depending on the applied discount rate.Estimated market rents and rent subsidies increase when a higher discount rate is applied, as it raises the cost-of-capital.
The average regulated rent is considerably lower at 7,434 SEK ($ 859). 11As seen in Table 4, the hypothetical market rents, and the estimated rent subsidy, increases when a higher discount rate is applied.
Regulated rents are significantly below market level across all neighborhoods in central Stockholm.As an example, the average rent in the Högalid neighborhood is 6,621 SEK ($765) while the average estimated market rents are 10,378 SEK ($1,200) and 11,396 SEK ($1,317), when applying discount rates of 2.65% and 3.0%, respectively.
Across all neighborhoods, we find average monthly rent subsidies of 3,384 SEK ($391) and 4,338 SEK ($502), when applying discount rates of 2.65% or 3%, respectively.There is considerable geographical spread of the rent subsidy.The neighborhood Gustav has the smallest difference between regulated rents and hypothetical market rents, and average subsidies of either 2,344 SEK ($271) or 3,602 SEK ($416).The Hedvig Eleonora neighborhood has the largest average subsidy, which is 5,961 SEK ($689) or 7,402 SEK ($856).

Breaking down the data by quartiles of tenant income
By breaking down the sample by quartiles of renter income, we can observe the level of subsidy that tenants with different levels of income receive.
Table 5 shows us tenant and apartment characteristics by quartiles of income.Tenants in the fourth quartile of income earn 836,008 SEK ($96,648) a year on average, while those in the first quartile on average earn 250,802 SEK ($28,994).This very large difference illustrates that the need, and ability to find housing at market clearing levels varies substantially among those who receive rent-controlled apartments.
11 Using an USD to SEK exchange rate of 8.65 (as of August 2020).1 3 Table 5 shows us that high earners tend to receive larger rent subsidies than low-earners.Tenants in the fourth quartile of income receives an average monthly subsidy of 3,309 SEK ($383), compared to 2,845 SEK ($329) for tenants in the first quartile of income, based on a discount rate of 2.65%.Tenants in the third quartile receive highest average subsidy when applying a discount rate of 2.65% at 3,402 SEK ($393).A 3% discount rate results in a higher estimated market rent and that tenants in the fourth quartile of income receives the highest average rent subsidy of 4,696 SEK ($543).
Even as the absolute rent subsidy is larger in higher income tenant groups, the percentage rent discount (i.e., market rent in relation to subsidized rent) is higher for lower income tenants.Tenants in the first quartile of income receives an average discount of 34% while tenants in the fourth quartile of income receive a 21.9% discount (at a 2.65% discount rate).We also find that the rent subsidy makes a considerably bigger impact on the financial wellbeing on low earners, with the rent subsidy on average being equal to 14.8% of income among those in the first quartile of income.For those in the fourth quartile of income (who receive a slightly larger subsidy in absolute terms), the subsidy only comprises 4.9% of their annual income.This tells us that even as the absolute subsidy is fairly stable across income groups (ranging from 2,845 SEK/$329 to 3,402 SEK/$393 at a 2.65% discount rate), low-income tenants are more likely to need the subsidy to afford their apartments.This while a substantial number of tenants with higher incomes can afford to pay hypothetical market rents.
As expected, higher earners consume more housing, with the average number of rooms and square meter size increasing with income -as an example, tenants in the fourth quartile of income have an average of 2.6 rooms on 75.5 square meters while those in the first quartile of income on average rent 1.3 rooms on 39.5 square meters.Lower income tenants cor- respondingly pay lower rents, on average 5,186 SEK ($600) in the first quartile of income and 10,814 SEK ($1,250) in the fourth quartile.
There is a substantial difference in estimated market rents across income groups, which is expected given the above-described differences in apartment characteristics.Those in the first quartile of income received apartments with an average estimated market rent of 8,031 SEK ($928).This while tenants in the fourth quartile of income rent apartments with an average estimated market rent of 14,123 SEK ($1,633).
Age, the fraction already living in central Stockholm before receiving a rental apartment, and time in queue shows little variation across income levels.

Breaking down the data by quartiles of rent subsidy
By breaking down the sample by quartiles of rent subsidy, we can observe the characteristics of those tenants that receive the most, and the least, subsidized apartments.Table 6 shows us tenant and apartment characteristics by quartiles of the rent subsidy.
Apartments in the first quartile of subsidy, based on a discount rate of 2.65%, have an average monthly subsidy of 804 SEK ($93), while the fourth quartile has an average monthly subsidy of 6,212 SEK ($718).The percentage rent discount also increases with the absolute subsidy, ranging from 10% in the first quartile to 43% in the fourth quartile.
One should keep in mind that the subsidy can be driven by either regulated rents or the estimated market rent.Some apartments with lower subsidies have comparably high regulated rents.Current, regulated, rents are on average 8,352 SEK ($966) in the first quartile of subsidy (based on a 2.65% discount rate), which is higher than in the second and third quartiles (6,802 SEK/$786 and 7,045 SEK/$814, respectively) and nearly at the same level as the most subsidized apartments in the fourth quartile (8,471 SEK/$979).
Given that the least subsidized apartments are also comparably expensive, it is no surprise that we also find a U-shaped relationship between income and the subsidy.We find that average tenant income is higher among those who received apartments in the first quartile of subsidy compared to the second and third quartiles.Highest average income is seen for those who receive the most subsidized apartments.
Tenant income varies considerably between the quartiles of rent subsidy.Average annual incomes are 519,065 SEK ($60,008), 434,571 SEK ($50,239),and 466,126 SEK ($53,887) for the first, second and third quartiles of subsidy, respectively.Apartments with the largest subsidies, in the fourth quartile, are mediated to tenants with an average annual income of 531,258 SEK ($61,417).
The most subsidized apartments are also those with the highest estimated average market rents (14,683 SEK/$1,697), which aligns with these apartments being larger in terms of the number of rooms and square meters (on average 74.6 square meters and 2.6 rooms, compared to 1.5 to 1.8 rooms and 47 to 52 square meters in the first, second and third quartiles).
Tenants that receive the most subsidized apartments tend to be older, on average 49.7 years in the fourth quartile of subsidy, compared to 37.3 years in the first quartile.This is expected as the average time in que also increases (on average 10 years in the first quartile and 21 years in the fourth).Older individuals and high earners are also more likely to have housing that fits their preferences and therefore be able to wait for a highly subsidized apartment, while low earners will have a more urgent need for housing, causing them to wait for shorter time-periods and receive a less subsidized apartment.More subsidized apartments have a slightly larger fraction of tenants who already were living in the attractive city center of Stockholm (50% in the fourth quartile compared to 45% in the first).That roughly half of all subsidized apartments are mediated to tenants who already were living in the attractive city center indicates that these tenants either already had a rent-controlled apartment or could afford housing at market clearing prices.As there are almost no rental apartments at market prices available, it is likely that a substantial fraction of these tenants owned an apartment while waiting in the housing queue until an attractive rental apartment became available.

Determinants of the rent subsidy
To further analyze the income-distributional effects of rent control, we run several models that explore the relationship between rent, estimated market rents, and rent subsidies, with tenant characteristics.These can be seen in Table 7.
Model 1 regresses regulated rent on tenant characteristics and provides us with insight into the process of how renters are sorted.The results tell us that higher earners are more likely spend more on rent, as the variables that indicate income in the second, third and fourth quartiles are all statistically significant.An individual in the fourth quartile of income will spend 4,999 SEK ($578) more a month in rent compared to someone in the first quartile of income, all else equal.Similarly, we find that renters already living in central Stockholm pay higher rents, paying 318 SEK ($37) more compared to those who are not, all else equal.We find that time in queue has a negative impact (with one additional year in queue reducing rent with 357 SEK/$41), and that this effect is diminishing (as queue 2 is positive).This supports that individuals wait to get cheaper apartments.Being under the age of 30 is also associated with lower rents (642 SEK/$74 lower, on average), as is to be expected as young people will have lower incomes and have a lower demand for larger, more expensive apartments.No effect on rent is found in terms of gender or other age brackets.The explanatory power is fairly high, with an R 2 of 0.52.
Models 2 and 3 provides us with insight into the sorting into apartments in respect to estimated market rents.One should keep in mind that the estimated market rent is not the rent paid, and that these models tell us which renters that end up in the most attractive apartments (rather than the most subsidized).Models 2 and 3 explain market rents using r-g of 2.65% and 3%, respectively.We find that income is positively correlated with market rents.The fourth quartile of tenant income is associated with 5,488 SEK (Model 2) or 6,033 SEK (Model 3) higher market rents compared to tenants in the first quartile of income.Already living in central Stockholm before receiving a rental apartment is associated with a higher estimated market rent -perhaps because those who already live in central Stockholm are comparably pickier and more interested in the most attractive apartments compared to those who don't already live in central Stockholm.Models 2 and 3 have R 2 values of 0.52.The core of our analysis comes from models 4 and 5, as we model the estimated absolute subsidy as a function of renter characteristics.Models 4 and 5 have R 2 values of 0.58 and 0.59, respectively, and tell us that renter income has a large role in determining the rent subsidy.
Time in queue is only significant at the 10% level in model 4, showing a marginally declining positive effect on the rent subsidy, as seen by the coefficient estimates for time in que and time in queue 2 (which is significant in both models).We find no statistically significant effect of age, gender or if the renter is from Stockholm, on the rent subsidy.
We find that income is significant and positively correlated with the rent subsidy.Renters in the fourth quartile of income receive monthly rent subsidies that are either 488 SEK ($56) or 1,034 SEK ($120) higher than those in the first quartile of income, all else equal (model 4 and 5, respectively).When looking at these numbers, one should keep in mind that the average incomes in the fourth and first quartiles of income are 836,008 SEK ($96,648) and 250,802 SEK ($28,994), respectively.
This effect of income also holds when comparing the third quartile of income with the first, showing a slightly smaller impact on the monthly subsidy, of 272 SEK ($31) or 535 SEK ($62) (model 4 and 5, respectively).
The results from models 4 and 5 show that higher income tenants receive larger absolute subsidies, while also controlling for time in queue, gender, age, location and time.It is interesting to see why this might be.Notably, if it is due to high income individuals consuming more housing (i.e., larger apartments) and therefore receive larger absolute subsidies, or if higher earners receive a larger subsidy even when renting apartments with similar characteristics as lower-income tenants.To test this, Models 6 and 7 add controls for apartment characteristics (apartment size and the number of rooms).
It is worth keeping in mind that regulated rent is set before the tenant moves in and without regard of who the tenant is -so any potential effect of tenant characteristics on the rent subsidy should be attributable to differences in apartment choice between groups of tenants.
Models 6 and 7 show no effect of income or gender on the rent subsidy, when controlling for apartment characteristics.An effect of being below 30 years of age is seen, with such tenants receiving slightly larger subsidies.
What models 6 and 7 tells us, when analyzed in conjunction with models 4 and 5, is that the fact that higher income tenants receive larger absolute subsidies is driven by such tenants preferring larger and more expensive apartments, which in turn are more subsidized.
Heteroscedasticity robust standard errors are estimated.T-values are shown in parenthesis below the coefficient estimates.Time fixed effects are binary variables indicating the year of the rental contract and location fixed effects are defined as parish.

Conclusion
We apply a framework for estimating hypothetical market rents in a setting with regulated rents below market clearing levels and no ability to observe market rents.We also provide an empirical analysis of the income-distributional effects of rent control in a setting where subsidized rental apartments are allocated through queuing.
We find that low-income households benefit from the rent subsidy and this benefit is likely to allow them to afford housing that they would not afford at market rents.Thus, we find that rent control will decrease segregation and mitigate displacement.However, we do find several regressive effects.Notably, when we compare renter groups by quartiles of income, we find that high income tenants on average receive larger absolute rent subsidies than lowincome tenants.This tells us that a large fraction of the total rent control subsidy goes to individuals that can afford to pay market rents.We also find that apartments in the fourth quartile of subsidy have older tenants with higher incomes compared to less subsidized apartments.
Tenants wait for on average nearly 15 years to receive a rental apartment in the attractive city center of Stockholm, Sweden.We find the expected a positive relationship between the rent subsidy and time in que.Apartments in the fourth quartile of the subsidy require 21 years in que on average, while those in the first quartile require on average 10 years in que.Long que requirements benefit higher income individuals who either owns housing or already has a rental apartment, as they can wait until a subsidized rental apartment becomes available.This while lower-income households with more immediate housing needs are likely to choose less subsidized apartments that require less time in que.
Controlling for time in queue (and other characteristics such as age and gender), our econometric models find that tenants in the fourth quartile of income (who on average earn 836,008 SEK/$96,648) receive monthly rent subsidies that are 488 SEK ($56) to 1,034 SEK ($120) higher than renters in the first quartile of income (who on average earn 250,802 SEK/$28,994).
7 Appendix: Determining the cost of capital, r-g.
As noted above, estimating (4) & (5) requires information on the cost of capital, r-g.We estimate an appropriate level for r-g by using the relatively freely set rents of a small number of newly produced apartments as a point of reference -these are referred to as presumption rents and is a segment of the market where rent control is less strict for a period of 15 years after construction.
Consequently, we estimate (5) at various levels of r-g and use values that minimizes the forecast error when we apply the equation to a subset of our data that covers of new construction with presumption rents.We apply two measures of forecast error; the root mean square error (RMSE), and the median absolute forecast error (MAPE).
We find that RMSE is minimized at r-g = 2.65% and MAPE is minimized at r-g = 3%.
on official statistics, the average income for the metropolitan area was 323,300 SEK for all individuals between 20 and 64 years of age in 2011 (the median was 290.000SEK), with the equivalent value for 2016 being 367,200 SEK (with a median of 331,300 SEK) (Statistics

Table 4
Estimated Market Rents and Current Rent Controlled Rents by Zip Codes in Central Stockholm.

Table 5
Apartment and Tenant Characteristics by Quartiles of Tenant Income.Mean Values with Standard

Table 6
Apartment and Tenant Characteristics by Quartiles of the Apartment Rent Subsidy.Mean Values with Standard Deviations in Parenthesis

Table 7
Regression Results.Dependent variables are rent, market rent, and rent subsidy.Coefficient Estimates with T-values Parenthesis