Impact of Right to Buy Policy on Low Income Households & Council Housing Quality, Study notes of Construction

Download Impact of Right to Buy Policy on Low Income Households & Council Housing Quality and more Study notes Construction in PDF only on Docsity! The right to buy public housing in Britain: a welfare analysis IFS Working Paper W15/05 Richard Disney Guannan Luo The Institute for Fiscal Studies (IFS) is an independent research institute whose remit is to carry out rigorous economic research into public policy and to disseminate the findings of this research. IFS receives generous support from the Economic and Social Research Council, in particular via the ESRC Centre for the Microeconomic Analysis of Public Policy (CPP). The content of our working papers is the work of their authors and does not necessarily represent the views of IFS research staff or affiliates. to the RTB policy: (i) imposing resale restrictions on RTB properties; (ii) reducing the discounts on RTB sales; and (iii) using the resulting proceeds to build new public properties. We show that some of these policies are only effective under certain conditions (primarily, again, the quality of the existing council housing stock). Section 6 concludes the paper. Graphs of evidences and proofs of propositions are provided in appendices. 1.1 Background: Council housing and the development of ‘Right to Buy’ ‘Council housing’ (the term for public housing constructed by local government authorities in the United Kingdom), was a policy developed from the 1920s onwards in order to re-house low income families in subsidized housing. The need to re-house families arose from an ongoing policy of slum clearance in the 1920s and 1930s; a need heightened from the 1940s onwards because 4 million UK houses were seriously damaged or destroyed by bombing between 1939 and 1945. Aided by the 1946 Land Acquisitions Act, which allowed local authorities to acquire land for construction, and by direct subsidies from central government, council house building accelerated after 1945 and continued well into the 1970s. By 1979, around 32% of all dwellings in Britain were council houses, totaling some 6.5 million properties - a far greater share of the total housing stock than that of public housing in, for example, the United States.2 Council housing is normally allocated to families by a simple queuing mechanism with priority given to families with special housing needs (state of existing accommodation, severe health problems, eviction unrelated to personal behavior, homelessness, etc) but also more generally to those with low incomes and/or observed proxies for low income such as family size and employment status. For those without priority needs, waiting times could be as long as several years or indeed indefinite, although in the heyday of council housing a local authority could usually offer a property of some kind within a shorter period. For tenants, the attractiveness of council housing is that rents are usually significantly lower than those for comparative-sized privately-owned properties. Maintenance costs are in general covered by local authorities. This was made possible in part by direct subsidies for construction from central government and the development of low-cost system building methods, which, how- ever, subsequently sometimes led to higher maintenance costs falling on the local authority. As a relatively cheap solution to a major social problem, council housing was generally regarded as a major success story in public housing policy in the United Kingdom. However, the policy had obvious costs. Rents were subsidized and did not cover full economic cost, so local authorities bore a burden that was partly subsidized by block grants from central government. Because council housing was subsidized, generally excess demand prevailed. Families who got on a council house waiting list had no incentive to remove themselves from their list; indeed, even if families’ economic conditions improved, there was no incentive to exit the council house sector at all. This, it was suggested, reduced the flexibility of the labour market (e.g. Hughes and McCormick, 1981). And as the criteria for council house priority shifted from slum clearance to family ‘need’, there were strong incentives for families to assume the characteristics (lack of job, large number of children, partnership dissolution) that increased eligibility. As real incomes increased, the need for further council house building seemed less clear 2Jones and Murie (2006) Table 2.2. and p.52. 3 cut. Although significant council house building continued into the late 1970s, the building program peaked in the early 1950s. A succession of Conservative governments began to emphasize home ownership as a means of distributing wealth more widely; hence some Con- servative local authorities began to see their council housing stock both as a burden on local taxpayers (subsidized rents and maintenance costs) but also as a potential means of widening asset ownership in their local communities with the potential for externalities arising from a better social mix of residents. There was strong pressure on national government from these local authorities to permit a policy of subsidized selling of the existing council house stock (albeit with equal resistance from the Labour Party and the architects of post-war housing policy). It was the arrival of the Conservative central government under Margaret Thatcher with a large majority in Parliament in 1979, however, that provided the key impetus for a national Right to Buy policy. 1.2 Evolution of Right to Buy The Housing Act of 1980 introduced a statutory right to buy for council tenants with at least three years’ tenure in their council house - ‘statutory’ in the sense that the policy should be implemented in all local authorities and not just voluntarily by a few Conservative councils. Discounts on the sale price relative to the market value of the property ranged from 33% for council house tenants with three years’ residence through to a maximum of 50% after twenty years’ residence. Local authorities were also required to make mortgages available to would-be purchasers albeit subject to standard age limits and income multiples. The discount would be repayable if the property was sold within five years of a RTB purchase and there was a floor price such that recently constructed properties should not be sold at less than the cost of construction. Subsequent legislation in the 1980s relaxed the conditions still further – for example by increasing the discounts for owners of apartments and relaxing the cost floor condition. Graph 1 shows clear peaks in council house sales arising from the 1980 Act and the lib- eralization of eligibility conditions and increased discounts in the mid-1980s. Note that new council house builds almost disappeared after the introduction of RTB although construction of other forms of social housing (around 20,000 new builds a year) continued. Nevertheless, although sales were at a lower level after these spikes associated with policy changes and the general decumulation of the council housing stock, they continued into the mid-2000s at a significant level for two reasons. First, new tenants became eligible by attaining residency requirements and increasingly took advantage of the relatively low interest rates through much of the later period. Second, because of residual opposition to the policy from some Labour councils, the process and speed of sales varied from local authority to local authority. For example, some councils opposed to the policy initially attempted to evade the statutory provisions to facilitate sales by handing all or most of their council house stock over to com- munity or social housing associations where conditions for sale were considerably stricter until these were liberalised in the mid-2000s – hence the further upsurge in RTB sales in the early-2000s. These policies delayed the peak of sales in some localities. By the mid-2000s, around 2.8 million council houses had been sold in the United Kingdom – almost half the total stock and indeed greater than half in areas such as Scotland which had seen high rates of council house sales in the previous period (Jones and Murie, 2006). However the rate of RTB sales has slowed considerably for reasons to be described shortly. Who were the gainers and losers from this policy? The clear winners from the policy were 4 those tenants who had been able to purchase relatively desirable properties at subsidized prices. Central government also gained because the bulk of receipts from council house sales were offset by a reduction in central grants to local authorities - that is, receipts were mostly transferred to central government. After 1990, local authorities normally had access to 25% of the capital receipts with the remaining 75% treated as ‘reserved receipts’ which could not be utilized for general funding of local services (including replacement house building). The sale of council houses was the ‘largest privatization’ undertaken in Britain in this period in terms of raising revenue for central government, exceeding the proceeds from the sale of any of the major public utilities throughout the late 1980s and early 1990s (House of Commons, 1999, p.11). In contrast, the losers were, arguably, those tenants of public housing who were unable or unwilling to buy their council house or apartment because they had low incomes and/or a less desirable property. Apart from any sense of ‘relative deprivation’, there was an increasing risk of the public housing sector becoming over time a residual of the lowest quality housing inhabited by the lowest income groups – a process of ‘ghettoization’ at odds with the ideals of some founders of ‘garden city’ public housing built for the working poor in 1930s. For local authorities, too, sales were a mixed blessing. Whilst reducing the need for covering maintenance costs and subsidized rents, they had received little of the receipts from the council house sale programme and still had a statutory duty to rehouse the homeless and those with pressing housing needs. Malpass and Murie (1999) point out that subsidies paid by local authorities to cover council house tenants had fallen (in nominal terms) from £2.1 billion in 1980 to £1.2 billion by 1990 – a clear saving. Nevertheless, as those authors note, the total number of homeless families more than doubled over the same period, from 63,000 to 146,000. By being forced to house homeless families in unsuitable or more expensive housing (e.g. private tenancies or even hotels), the savings from council house sales were rapidly eroded. The incoming Labour government in 1997 decided to tighten up the rules for selling council houses. A series of measures between 1998 and 2004 were designed to tighten eli- gibility, reduce discounts, to limit access to public mortgages and to reduce the capacity of RTB owners to resell their properties within a short period at a profit. It should be noted, however, that this was a period when private mortgages were relatively easily accessed, and when house prices and private house building were both increasing. Of particular interest were changes that came into effect in 1999. Until this point, there was a national maximum discount of £50,000. Clearly, since some regions (notably London) had higher house prices (and house price increases) than others, the effective subsidy was thereby of different value across the country. In 1999, ceilings were reduced and applied differentially across regions, with the highest ceiling in London (£38,000) and the lowest in northern England (£22,000). Subsequently, in 2003, the policy was changed such that ceilings could be reduced where there was clear evidence of public housing shortages (as evidenced by homelessness and queues for public housing). This led to further reductions in ceilings - not in the low housing cost areas such as the north, but in areas of greatest pressure on available public housing - namely London and the South East. In nine local authorities in the south east and all but two London boroughs, the maximum ceiling was reduced to £16,000 (Jones and Murie, 2006. p.40; House of Commons, 2012). Subsequently, for similar reasons, the national government in Scotland ceased council house sales altogether. However, in the same period the Right to Acquire (a policy similar to RTB that allows housing association tenants to buy their home at a discount) was introduced for tenants of many housing associations, thus ending the 5 The private housing market is competitive. The profit of constructing a property and selling it is zero. The housing price equals the construction cost of the house, which is assumed fixed over time for simplicity. Let P be the per unit housing price in the private housing market. There are sufficient exogenous funds available to finance households’ home ownership. The gross interest rate on mortgages equals 1+r. There is a fixed adjustment cost (FC) of purchasing a house, which is incurred when a tenant switches to home ownership. Mortgages are paid at the beginning of each period and amortized to infinity. Define M as the per period mortgage payment per quality of housing, then M = r 1+r P . In the private housing rental market, suppose that there are competitive landlords that offer private rental properties. Define R as the equilibrium housing rent. By assumption there is a maintenance cost, δ, already defined. The housing rent is determined by the equivalence of the current cost and discounted payoff of leasing a house, then R = δ+r 1+r P . Having paid the fixed cost (FC) at the moment of purchasing a property, a homeowner pays the mortgage plus the discounted maintenance cost of the house. The per-period payment equals the equilibrium rent, Then the discounted cost of the owned property equals the mortgage payment plus maintenance cost, which equals the competitive private rent, R. The homeowner loses the house if he or she fails to pay R. He or she will however prefer to own rather than rent so long as the payment is made because of the disutility of renting, φ. To ensure that every household lives in a property, assume that household incomes (either low or high) are greater than the equilibrium housing rent. The lump sum fixed cost of purchasing a property for new homeowners is large such that low income households cannot afford to purchase a private property. Only high income households can afford private properties. Assumption 1 The equilibrium housing rent, housing price, lump sum fixed cost for new homeowners, and household incomes satisfy: R < Y L < R + FC < Y H < P . In the private housing market, households either rent, purchase (new ownership), or own (retained ownership) private properties. If a household rents or owns a house at time t, it pays the housing rent each period, so its consumption is Ct = Yt − R. A household can purchase a house only if it receives the high income. Its consumption at the time of a new purchase is Ct = Y H − R − FC. Because of the disutility of renting relative to owning houses, private housing owners always prefer continuing living in their own properties to rented properties. The value of owning a property for a low or middle wealth household is: V i o (Yt) = Cα t + (1 + r)−1Et [ V i o (Yt+1) ] , i ∈ {l,m} , = (Yt −R)α + r−1 ( λi ( Y H −R )α + ( 1− λi ) ( Y L −R )α) , (2) where Yt ∈ { Y H , Y L } . Only high income households can afford the fixed cost of purchasing houses. The state variables of a household’s optimization problem at time t are its current income, Yt, and whether it purchased or owned a house in the previous period, ψt−1 = I[own a house at time t−1]. If the household owns a house, its value function equals the value of continuing living in the house; otherwise, it decides whether to purchase a house whenever it receives the high income. Then a household’s value function at time t is: V i(Yt, ψt−1) = max ψt∈{0,1} { ψt−1V i o (Yt) + (1− ψt−1) ( V i r (Yt) + ψtI[Yt=Y H ] ( V i p − V i r (Y H) ))} . where V i r and V i p are the household’s values of renting and purchasing a private house, respectively. When the probability of receiving the high income is not too large, households 8 prefer renting to owing private houses when they receive the high income. To obtain the cutoff point, we solve the households’ optimization problem recursively as described in Appendix B.1, to derive the following proposition: Proposition 1 A high income household prefers renting to owning a private house if and only if its probability of getting the high income is not too large such that λi < λ̄, where: λ̄ = r ( (1− φ)1−α − ( 1− FC Y H−R )α)− ( 1− (1− φ)1−α) ( Y L−R Y H−R )α ( 1− (1− φ)1−α) ( 1− ( Y L−R Y H−R )α) . (3) Our analysis focuses on the households which are interested in public housing. They usually have relatively low wealth. They prefer renting to purchasing private houses even if they receive the high income occasionally. We now make the following assumption: Assumption 2 Middle wealth households’ probability of receiving the high income is not too high such that: λm < λ̄. However, it is large relative to either the disutility of renting houses or low wealth households’ probability of receiving the high income, and the number of middle wealth households is relatively small compared to that of low wealth households such that: λm − ( 1− (1− φ)1−α) λm − λl > ( 1 + (1− λm) Nm (1− λl) N l )−1 > 1− λl. Then λl < λm < λ̄. In these circumstance, both low and middle wealth households prefer renting to purchasing private properties even when they receive the high income on occasions. The intuition is as follows. Low wealth households have a high probability of receiving low income. Even when they receive the high income, the high probability of later low income outcomes raises the possibility of costly future housing tenure changes. So they are not likely to purchase a private property even if they receive a high income for a period sufficient to overcome the initial fixed cost of purchasing a property. The same story is likely to hold for middle wealth households’ incomes. Although their incomes are more volatile, meaning they are often in a position to buy a property at market prices, risk-averse households may prefer not to buy when receiving a high income because they are trading the disutility of renting (versus owning) against the potential transactions and search costs arising from selling properties and finding alternative accommodation in the face of future income volatility. This accords with the existing literature on choice of housing tenure. As we shall see, however, subsidizing purchase through RTB may changes the value function of middle wealth households considerably. We now extend the model to an additional form of tenure: public (‘council’) housing. In the following sections we first set up the optimal council housing system without RTB policy, then compare low and middle wealth households’ welfare before and after the RTB policy (without resale restriction) was introduced. After that, we investigate how imposing resale restrictions on RTB in recent decades changes the social welfare. 3 Equilibrium of Housing Tenure with Council Hous- ing We now incorporate a council house sector (public housing) into the model. The rationale for, and mechanisms for allocating, council housing were described in Section 1. In this 9 section we examine the individual household’s decision as to whether or not to apply for a council house. We also examine the local authority’s decision as to what quantity of council houses to provide, and of what quality. Initially, we examine a setting where there is no ‘Right to Buy’. We assume that the local authority’s key observable of ‘need’, other than obvious factors such as family composition, is current income. The council housing rental system comprises two components: existing tenancies and a waiting list. The local authority can verify that an applicant applying to join the waiting list for a council house has a low income. Note our presumption that a high wealth household (i.e. a household with a sequence of high incomes) will never be on the waiting list and is unlikely currently to be living in a council house. We assumed that lifetime permanent income or wealth is private information to the individual applicant i.e. the local authority only observes ‘high’ income Y H or ‘low’ income Y L. Thus the local authority will be faced with two kinds of applicants in our model: those with almost permanently low incomes (low wealth households), and those with low outcomes from a more volatile income process (middle wealth households). It is reasonable to assume that the local authorities’ first priority would be to house those with almost permanently low incomes, although they will have a degree of legal responsibility, resources permitting, to house anyone who would otherwise be homeless. Local authorities might try to differentiate between the two types of households by further investigation: for example the simplest device for revealing information on income trajectories is through a queuing system: households may have several income realizations before they reach the top of the waiting list, and some of those with only temporary low incomes may be sifted out by requiring households that receive a high income are required to leave the council housing queue. However, a certain fraction of those with volatile incomes may thereby still obtain council houses, and will want to do so insofar as risk aversion (and subsidized rentals) leads them to prefer council house tenancy to either private ownership or private renting. However, another solution to this rationing and selection problem is to limit the de- mand for council housing by ensuring that the council house stock is of lower quality than equivalently-sized privately-owned properties, thereby reducing the demand for council houses and increasing the supply available within a fixed budget. Consequently, when the share of expenditure on high quality private housing rental is large for low income house- holds, the local authorities are able to provide council housing of lower quality than private houses such that low income households are better off renting council houses, but high in- come (middle wealth) households are not so interested in public rentals even when they have low income realizations. Assumption 3 Low income households have too low income to benefit from renting private housing: Y L < Ȳ , where Ȳ solves Ȳ − r 1+r FC − ( Ȳ−R α )α ( R 1−α )1−α = 0. The supply of council houses is determined as follows: local authorities borrow money up to a given constraint from the central government in order to build houses. Over time, the local authorities can endogenize the quality of council housing to optimize their objective function subject to their initial capital budget constraint for housing, defined as B. As mentioned in Section 1, when RTB was introduced, the central government did not allow the local authorities to keep the bulk of their proceeds from council house sales to build replacement dwellings. Thus, B is assumed to remain fixed over time. Combining the budget constraint with the measure of quality chosen by the local authority gives the stock 10 house sale price given the council housing quality, η.3 For simplicity, assume that the annu- itized discount on the sale price (and therefore mortgage reduction) is equal to the original discount of rental payment. In addition, the RTB policy may alleviate the initial payment constraint because tenants may now be given access to mortgages (or greater mortgages) than they would have otherwise had. By this simplifying assumption, the required mort- gage payment for a RTB-purchased house is the same as the cost of renting a council house but the flow of utility generated by the property increases because the disutility of renting relative to owning houses is removed. RTB is therefore attractive to council tenants for two reasons. First, it reduces the price of home ownership by discounting the sale price. This is especially attractive to volatile income (middle wealth) households for several reasons: (i) if they subsequently have a series of low income, their recurrent cost is no higher than renting a council house; (ii) if they have a subsequent sequence of high incomes and have held the house for a minimum period, they can rent the RTB house out to a private tenant and rent elsewhere; or (iii) they have the possibility of selling the RTB house at market price and purchasing a different house. Thus, even the most risk averse middle wealth households might want to exploit RTB. In theory, the relaxation of the initial payment restriction and the lower sale price also potentially makes RTB attractive to low income households although accumulating enough capital to afford the down payment on even the subsidized purchase price may prove an insuperable problem. RTB is in principle attractive to low income tenants whether they are middle or low wealth households, since their utility is increased by owning instead of renting a council house. Indeed, without restrictions on RTB eligibility, households prefer to purchase council houses to renting either council or private houses. This has an important consequence, however. Low and middle wealth households that do not have council houses but rent privately have an incentive to join the waiting list for council housing with a view to purchasing a council house at a later date. In the short run, therefore, the demand for council housing may even increase. The effect of this additional incentive on the size of the queue for council houses and, therefore, the potential effect on the quality of council housing in the future (given the fixed budget for council house construction) will depend on the priority criteria for RTB purchase established by the RTB policy (for example, priority or higher subsidies for long-duration tenants). While it is costless for private tenants to join the queue for council houses, if offered a council house, they are trading the lower quality of the public rented property relative to the private rental for the future possibility of obtaining a subsidized house purchase. 4.2 Equilibrium with Unrestricted RTB We now consider the issue of whether a homeowner who has exercised RTB will resell their properties if permitted, which we term ‘unrestricted RTB’. We show that this decision will depend on the quality of the RTB-purchased property (hence we shall also show that any restriction on resale may affect the quality of properties sold). The next issue that arises is as to who would repurchase a property originally obtained under RTB. An important 3The discount rate may vary across local authorities but is set by central government, albeit sometimes amended as a result of lobbying by individual authorities (see the discussion in Section 1 of the period from 1997 onwards). However, to our knowledge, the actual discount rates and ceilings on subsidies chosen by the central government were not based on any explicit welfare analysis. 13 effect of the RTB policy, by our earlier assumptions, is to put properties with a different distribution of qualities onto the private housing market, whether for outright ownership or rental. Hence there will be some, primarily lower quality, properties on the private market as a result of RTB that might prove attractive to, for example, low wealth households which, for whatever reason, have not been in the council rental sector at the time that the RTB policy was implemented. Depending on these factors, we will demonstrate that resale restrictions may or may not increase overall welfare. We assume that the average quality of council houses within any local authority available for RTB purchase is determined by the budget constraint, as illustrated previously, and varies across local authorities. If the average quality of council house properties available for RTB purchase in a particular locality is ‘high’, then middle wealth households will continue to wish to live in their RTB-purchased properties in the future. However, if the quality of council properties available for RTB is relatively low, middle wealth households who have exercised RTB might prefer to resell the RTB purchase and rent privately. Post-RTB tenure transitions may then arise since some lower wealth households who were not in the council house sector but were renting privately are able to purchase the lower quality property privately. To consider these post-RTB tenure transitions, we can consider a simple model along the lines of Wheaton (1990). Renting or reselling RTB properties is subject to search frictions and delays in finding a suitable match. The search cost arises because in general RTB properties are of different (on average, lower) qualities than private houses and also the supply of RTB properties of given quality may be spatially distributed unevenly in the housing market as a whole. Hence we assume that homeowners continue to live in their RTB properties until a match is formed. The match surplus is then shared by both parties in relation to the bargaining power of the initial homeowner. Assume this bargaining power equals β where 0 ≤ β ≤ 1 and that the matching function between RTB owners and ‘searchers’ follows a standard functional form such as Cobb-Douglas. RTB rental or resale contracts are signed at the beginning of each period before household incomes are realized. The duration of RTB rental contract is one period. When a match of renting RTB housing is formed, the searcher rents the RTB house for one period and has to return the house to its initial owner afterward. He/she has to search again if (s)he wants to continue renting a RTB house. As the quality of council houses is lower than private ones, the marginal utility of renting a RTB house is strictly decreasing in the household’s income. Because low wealth households have a higher probability of getting the low income, they have higher utility from renting RTB houses than middle wealth households. Moreover, because of the disutility of renting relative to owning RTB properties, households having the same level of wealth will not form a profitable match. Hence the only profitable match on renting RTB houses is that middle wealth RTB homeowners rent out their RTB properties to low wealth households. In contrast, when a match of reselling RTB housing is formed, the searcher purchases a RTB house and can continue living in it indefinitely. Low wealth households generate greater total welfare from owning RTB houses than middle wealth households, and middle wealth RTB homeowners may be interested in selling their RTB houses to low wealth searchers. Whether middle wealth RTB purchasers continue living in their RTB properties or sell them and rent (or ultimately purchase other) private housing therefore depends on the quality of their RTB property. If the quality of RTB properties is high, middle wealth RTB purchasers continue living in their properties whatever income they receive in the future. However, if the quality of their RTB properties is low, they will seek to resell their houses to the households 14 that have low wealth. The disutility of renting relative to owning houses also affects the RTB rental and resale decision. If the disutility of renting is extremely high, all RTB homeowners will prefer living in their properties than renting out or selling their houses to private parties. Then there is no second market for RTB houses. At the other extreme, if the disutility of renting is extremely low, no initial council housing tenant is interested in purchasing the house he lives in under RTB. The equilibrium is then the same as that with the option of renting council houses discussed in the previous section. It seems highly likely that preferences are such that an intermediate setting, which generates both a RTB market and resale market, will exist in practice. Hence the issues of resale and resale restrictions are important components of the RTB policy. Assumption 5 The disutility of renting relative to owning a house is moderate such that: ( Y H − (1− α)Y L )α − ( αY L )α (Y H −R)α − (Y L −R)α < ( (1− φ) R (1− α)Y L )1−α < ( Y H − (1− α)Y L )α (Y H−R)α−(Y L−R)α ( (1−α)Y L R )1−α + (αY L)α . The total surplus of either renting or reselling a RTB property from middle wealth house- holds to low wealth households is strictly decreasing in the quality of initial council houses sold under RTB. Under Assumptions 4 and 5, middle wealth RTB homeowners sell instead of renting out their properties to low wealth households when they prefer renting private housing to owning RTB housing. Further, the difference between the increment in utility of renting RTB housing relative to private housing between the low and high income house- holds is negative. It is greater than the surplus of a match on renting a RTB house, which equals the searcher’s gain minus the provider’s loss in current utility. Middle wealth RTB homeowners are not interested in renting out their houses to low wealth households because the surplus from the match is negative when the quality of council housing is less than that of private one. The surplus of a RTB housing resale at equilibrium, S, equals the searcher’s gain minus the provider’s cost in utility, which satisfies: rS(η) λm − λl = ( α 1− α R )α η − (1− φ)1−α ( Y L −R )α − (( Y H − Y L η + α 1− α R )α η − (1− φ)1−α ( Y H −R )α ) . (8) At equilibrium, the value of owning a RTB house, V i RTB, and renting a private house, V i r , for a household of type i, i ∈ {l,m} (low or middle wealth), satisfy, respectively: rV i RTB = ( λi ( Y H − Y L η + α 1− α R )α + ( 1− λi ) ( α 1− α R )α) η; (9) rV i r = (1− φ)1−α ( λi ( Y H −R )α + ( 1− λi ) ( Y L −R )α) . (10) The effect of Right-to-Buy on the welfare of eligible council house tenants, when the quality of council houses is low, can be summarized in the following proposition, the proof of which is given in Appendix B.3. 15 5.1 Right-to-Buy with Resale Restrictions A natural policy reform to consider is to impose some form of resale restriction (indeed just such a policy reform was introduced introduced to the RTB policy in its later years – see Section 1). However, the welfare effect of such a policy depends on the parameters described previously since, as we described, the probability of a right to resale being exercised depends on several factors: the wealth of the RTB household, the quality of the RTB house, and the household’s disutility of renting. We pursue further in this section by considering a variant of a resale restriction policy: one in which owners of RTB properties have to sell their properties back to the local authority from which they purchased it at the original (real) price if they move to another private property. We also assume, to avoid gaming the system, that RTB purchasers are not eligible for either renting council houses or exercising RTB in the future. The effect of these restrictions is that RTB property owners receive no future benefit from selling the property as they have to rent privately afterwards irrespective of whether they receive a high or low income. Comparing the difference in utility between owning a RTB property and renting privately, the cutoff quality of RTB properties that attracts a middle or low wealth homeowner to continue living in the property, η̃i, solves: ( α 1− α R )α η̃i − λirS(η̃i) λm − λl = (1− φ)1−α ( Y L −R )α , where i ∈ {m, l} . (13) With resale restrictions, the cutoff quality of RTB properties above which middle or low homeowners prefer continue living in the property rather than renting privately satisfies: η̃l < η̃m < η̄, where η̄ is the cutoff quality of RTB houses above which middle wealth homeowners prefer continue living in their properties to resale without restrictions, that is, the surplus of RTB resale without restrictions is zero, S(η̄) = 0, where S is given in equation (8). In contrast, low wealth households are more interested in owning RTB houses than middle wealth households with resale restrictions. The quality of council housing at equilibrium is always larger than low wealth households’ reserve quality of participation, that is, η > η̃l. Middle wealth RTB homeowners continue living in their houses if the quality of council housing is high such that η > η̃m; otherwise, they sell their houses back to local authorities and rent privately. With resale restrictions imposed, the change in welfare only happens when the quality of RTB housing is low such that middle wealth RTB homeowners want but are not able to sell their houses to low wealth households: η < η̄. Then they either hold on to their houses (when η > η̃m) or sell them back to the local authorities (when η < η̃m). The results are given in the following proposition, the detailed proof of which is provided in Appendix B.4. Proposition 4 Imposing resale restrictions on RTB houses improve the aggregate welfare of low income households if and only if the quality of RTB houses is low such that η < η̃m. It can decreases the welfare if the quality of RTB houses is relatively high such that η ∈ (η̃m, η̄). Resale restrictions have no effect on the choice of whether or not to exercise RTB when middle wealth households prefer owning council houses to reselling their houses to low wealth households. This happens when the quality of council houses is high, or equivalently, the 18 original government budget on council housing is relatively unconstrained. In these circum- stances, introducing RTB generates a waiting list for new council housing applicants. Low wealth households have a greater welfare loss than middle wealth households when they are not able to get council houses and if they bear some of the burden from renting privately at higher cost. Over time, however, the composition of tenants of low quality council houses shifts from both middle and low wealth households that receive low income to predominantly low wealth households. Resale restrictions on RTB could even have a negative net welfare effect when the quality of RTB houses is not too high but middle wealth households prefer owning council houses to renting private houses. Relatively high quality council houses are more attractive to middle wealth households that temporarily have low incomes, since they are better off owning high quality council housing than renting a private house even when they fall back into poverty in the future. The local authorities lose more potential benefit to low wealth households from imposing resale restrictions on relatively high quality RTB houses because middle wealth RTB homeowners retain their houses. The potential redistribution of surplus arising from RTB housing resale from middle to low wealth households vanishes. In contrast, when the quality of RTB houses is low such that middle wealth RTB home- owners prefer renting private housing to continuing living in their own RTB purchases, resale restrictions can help to improve the housing condition of low wealth households without giv- ing too much benefit to the medium wealth households. Middle wealth households sell their RTB houses back to the local authorities, which can then provide these properties to future council housing applicants either for rent or for sale under RTB. Middle wealth households are not interested in purchasing these low quality RTB houses even if they rent them when they receive the low income. They will move out of the council house sector and rent private housing once they receive a high income in the future. In contrast low wealth council housing tenants are interested in purchasing the low quality council houses that they live in under RTB. So at equilibrium, all council houses that are purchased are occupied by low wealth households. Hence, resale restrictions are practical reforms where potential RTB properties are of low quality. Overall, imposing resale restrictions on RTB houses works for a low quality council hous- ing stock but not for a high quality stock, leaving more low quality council houses to the low wealth households that need help in the future. The original losses from sale of high quality council housing under RTB cannot be recouped from imposing resale restrictions. The local authorities should not have get rid of high quality council houses through selling them under RTB. Finally, since the quality of council houses is strictly increasing in the local authorities’ budget, B, introducing RTB helps to improve the aggregate welfare of households in poverty while reducing the budget only if the original budget under council housing rental system is low. When the local authorities’ budget under the original council housing rental system is high, council housing quality is high. RTB on high quality houses is not optimal for the local authorities. Otherwise, the budget deficit is reduced at the cost of a welfare loss. 5.2 RTB with Reduced Discount In the previous analysis, we assumed that the discounts on RTB sales given by local au- thorities equalled the rent subsidies implicit in the council house rent. In this subsection, we study whether social welfare is increased when the discounts that local authorities can 19 offer on RTB sales are reduced. The required mortgage payment for a RTB house increases as the subsidy on purchasing a council house decreases. The utility of owning a council house is strictly decreasing in the required payment rate. It decreases faster for low income households than for high income households. A low income household prefers owning a RTB property than renting it under the initial rental system if and only if the required payment under RTB is less than or equal to τ̂ , where: τ̂ = τ + ( 1− (1− φ) 1−α α ) α 1− α , (14) and the required payment rate for renting council housing, τ , is given by (7). To insure that RTB policies improve the welfare of low income households relative to the initial council housing rental system, a necessary condition is that the discount on RTB sales is not too low such that the require payment is less than or equal to τ̂ . The surplus of a RTB housing resale at equilibrium is strictly decreasing in the required payment on the property. For a high quality council property with quality greater than η̄, where η̄ solves S(η̄) = 0 with S(η̄) given in (8), the government can reduce the discount so that high income households are not interested in living in the property. The required payment is set such that the surplus from RTB resale is nonnegative. Then at equilibrium, any low income household can own a council property, purchasing from either the local authority, or from a high income RTB homeowner, who sold his/her property because (s)he preferred renting private housing to owning the council property given the lower discount. However, because of the necessary condition on the upper bound of the required payment, τ̂ , the reduced-discount adjustment works only when the quality of council housing is not too high such that η ≤ η̄, where η̄ solves S(η̄, τ̂) = 0, where S(η, τ̂) increases in either η or τ̂ and is given by: rS(η, τ̂) λm − λl = ( Y L − τ̂Rη )α η1−α − (1− φ)1−α ( Y L −R )α − (( Y H − τ̂Rη )α η1−α − (1− φ)1−α ( Y H −R )α) . (15) Thus, introducing RTB to relatively high quality council housing (η > η̄) with reduced discounts relative to renting council housing can help to improve the welfare of the low income households only if the quality of the RTB houses is not too high (η ≤ η̄). 5.3 RTB with New Construction Until now, we assumed no new council housing is constructed using the receipts of RTB. This accords with the evidence presented in the discussion in Section 1 and the evidence in Graph 1. In this subsection, we investigate how social welfare changes if the local authorities use the proceeds of high quality (η > η̄, where solves S(η̄) = 0 with S(η̄) given in (8)) RTB houses to build new council houses. This is done within a balanced budget setting; hence the government reduces discounts on RTB sales and the local authority increases the number of council properties within the fixed budget on council housing, B. We focus on high quality RTB housing in our investigation here. As shown in the results of the previous subsection, reducing the discount on RTB sales of high quality council housing can improve the welfare of the low income households only if the quality of RTB properties is not too high such that η ≤ η̄, where η ≤ η̄ solves S(η̄, τ̂) = 0 with S(η, τ̂) given in (15). We will explore in the following analysis whether using the proceeds from RTB sales 20 A Graphs Number 180000 160000 140000 120000 100000 80000 60000 4c00c0 20000 1960 Graph 1: New builds and RTB sales of public housing 1980-81 to 2012-13 Source: Department of Communities and Local Government Housing Statistics Tables 244, 678 ay BP me ONT Oa GH GEubrRRE AR KR & w& AARARAARAA A SaaS R3RSRR SAS ocal authority + social housing RTB sales 2 1984 3 1990 1992 1994 1996 1998 2000 2002 2004 2006 Local authority+ social housing builds 2008 2010 2012 60% 55% 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% O% Graph 2A: Average discount on RTB sales as % of purchase price, England average and selected regions a 2 a a ca st w 2 tS 2 Q Ss g < = 2 g g 2 LS os a S a a oO + wo S i a a S e 2 S Se 3 S Ss a a S S S S S S S S a a a a a a a a a a —®— England —@®—London ——-—NorthWest ----- East Source: DCLG: Table 643, Social Housing Sales: Financial Statistics 2008/09 Graphs 2B: Number of RTB sales by selected regions in England: 1998-99 to 2008-09 16,000 14,000 12,000 10,000 8,000 6,000 4,000 2,000 6 = aD 2 ot a 2 st ry) rr) om x a D 2 S S S S =] S Ss S 2 oe oS S a a a + a wo YF os D a 3 2 o o 3 S 3 So 3 a a eS S eS S S S 3S eS 3S a a a a a a aq aq a a a —@— london ——-—NorthWest ----- East South West Source: DCLG: Table 643, Social Housing Sales: Financial Statistics same as with private housing except that they rent council houses instead of private ones when they receive the low income. The optimal number of council houses offered is: N = N̄ = ( 1− λl ) N l + (1− λm) Nm, where N l is the number of low wealth households (with probability 1−λl in poverty) and Nm is the number of middle wealth households (with probability 1− λm in poverty). Therefore, the aggregate welfare of all low income households (either of low or middle wealth) is rWc = N̄ ( Y L − τRη )α η1−α (1− φ)1−α = N̄ (1− φ)1−α ( α 1− α R )α η. B.3 Proof of Proposition 3 Take the derivative of the surplus of RTB housing resale as shown in equation (8) with respective to the RTB housing quality, η, get dS dη has the same sign as: ( 1 κ + 1 )α − 1 + ακ κ + 1 , where κ ≡ (1− α) ( Y H − Y L ) αRη > Y H − Y L αY L . The derivative of it is α ( 1 κ+1 )2−α ( 1 κ+1 )α+1 , which is negative. So the expression is strictly decreasing in κ. Also Y H−Y L αY L is strictly increasing in Y H and Y H > Y L. Therefore, dS dη < 0. The surplus of RTB housing resale is positive if and only if η > η̄, where η̄ solves S = 0. Middle wealth RTB homeowners continue living in their houses if the quality of the RTB houses is high such that η > η̄; otherwise, they sell their houses to low wealth households and rent private housing. In the first case, no further council housing is available for future generations. A RTB homeowner’s value equals that when he lives in the RTB house forever. From Proposition 2, among the initial RTB housing owners, there are ( 1− λl ) N l low wealth households and (1− λm) Nm middle wealth households. When the quality of RTB houses is high such that η > η̄, RTB homeowners live in their houses and other households rent private houses. The aggregate welfare of low income households when η > η̄ is: rW (η) = (( 1− λl )2 N l + (1− λm)2 Nm ) ( α 1− α R )α η + (( 1− λl ) λlN l + (1− λm) λmNm ) (1− φ)1−α ( Y L −R )α . The second case is when the quality of council houses is low, which happens when the local authorities’ budget on council housing is tightly limited. Without resale restriction on RTB houses, house tenants will choose to exercise their right-to-buy but then sell the RTB house and rent privately when they receive the high income in the future. Under Assumption 2, N l > N̄ . That is, there are more low wealth households than RTB houses. Then all RTB houses are occupied by all low wealth households and some low wealth households have to rent private housing. The aggregate welfare of low income households when η < η̄ is: rW (η) = (( 1− λl )2 N l + (1− λm)2 Nm ) ( α 1− α R )α η + (( 1− λl ) λlN l + (1− λm) λmNm ) (1− φ)1−α ( Y L −R )α + ( (1− β) ( 1− λl ) + β (1− λm) ) (1− λm) NmrS(η). 28 Comparing the aggregate welfare of low income households with and that without RTB as shown in Proposition 2, the difference between the two satisfies: rW (η)− rWc(η) N̄ (1− φ)1−α ( α 1−α R )α = ( 1− λl − Λ (1− φ)1−α − 1 ) η + ( λl + Λ ) ( Y L −R α 1−α R )α + ( 1− λl λm − λl − β ) rS(η)I[η<η̄]. where Λ is the difference in the fraction of high income RTB homeowners between whether the RTB houses initially owned by middle wealth households are resold to low wealth households: Λ ≡ ( λm − λl ) (1− λm) Nm N̄ = ( λm − λl ) ( 1− ( 1 + (1− λm) Nm (1− λl) N l )−1 ) . Under Assumption 2, the difference between the aggregate welfare of low income households with and without RTB is strictly decreasing in the quality of RTB houses η. Let: η ≡ ( 1− 1− λl − Λ (1− φ)1−α )−1 ( λl + Λ ) ( Y L −R α 1−α R )α . If the cutoff quality of positive surplus from RTB resale is low such that η̄ < η, RTB without restriction on resale improve the aggregate welfare of the low income households if and only if the quality of RTB houses is not too high such that η < η. Middle wealth RTB homeowners continue living in their houses when the quality is high such that η ∈ ( η̄, η ) but resell their houses to low wealth households when the quality is low such that η < η̄. Otherwise, if the cutoff quality of positive surplus from RTB resale is high such that η̄ > η, RTB without restriction on resale improve the aggregate welfare of the low income households if and only if the quality of RTB houses is not too high such that η < η̂, where: ( 1− 1− λl − Λ (1− φ)1−α ) η̂ − ( 1− λl λm − λl − β ) rS(η̂) = ( λl + Λ ) ( Y L −R α 1−α R )α , η < η̂ < η̄. Middle wealth RTB homeowners resell their houses to low wealth households at equilibrium. B.4 Proof of Proposition 4 If the quality of council houses is high such that η > η̄, all RTB homeowners continue living in their houses either with or without restrictions on resale. The aggregate welfare of low income households stays the same when the resale restrictions are imposed on RTB houses. If the quality of council houses is not too high such that η̃m < η < η̄, middle wealth RTB homeowners who would resell their houses to low wealth households without resale restriction now continue living in their houses. The aggregate welfare of low income households becomes: rW̃ (η) = (( 1− λl )2 N l + (1− λm)2 Nm ) ( α 1− α R )α η + (( 1− λl ) λlN l + (1− λm) λmNm ) (1− φ)1−α ( Y L −R )α . 29 If the quality of council houses is not too high such that η < η̃m, middle wealth RTB homeowners who would resell their houses to low wealth households without resale restriction now sell their houses back to local authorities and rent privately. The local authorities either rent out these houses or sell them again under RTB to future council housing applicants. At equilibrium, middle wealth households are not interested in purchasing these low quality council houses under RTB, but low wealth households are. So at equilibrium, all RTB houses are resold to low wealth households. The final outcome is the same as a special case without resale restrictions when low wealth households have bargaining power equal to one, 1−β = 1. Thus, the aggregate welfare of low income households becomes: rW̃ (η) = (( 1− λl )2 N l + (1− λm)2 Nm ) ( α 1− α R )α η + ( 1− λl ) (1− λm) NmrS(η) + (( 1− λl ) λlN l + (1− λm) λmNm ) (1− φ)1−α ( Y L −R )α . Comparing the aggregate welfare of low income households under RTB with and that without resale restrictions as shown in Proposition 3, the difference between the two satisfies: rW̃ (η)− rW (η) N̄ (1− φ)1−α ( α 1−α R )α = βrS(η)I[η<η̃m] − ( 1− λl λm − λl − β ) rS(η)I[η̃m<η<η̄]. Therefore, imposing resale restrictions on RTB houses improve the aggregate welfare of low income households if and only if the quality of the RTB houses is low such that η < η̃m, where η̃m solves equation (13) and η̃m < η̄. It even has negative effect on the welfare if the quality of RTB houses is relatively high such that η ∈ (η̃m, η̄). 30