The Effect of Public Social Housing on Households' Consumption in France

Journal of Housing Economics 10, 429–455 (2001) doi:10.1006/jhec.2001.0300, available online at http://www.idealibrary.com on

The Effect of Public Social Housing on Households’ Consumption in France1 David le Blanc2 Insee, CREST, J310, 15 Bd. G. Pe´ri, 92245, Malakoff cedex, France

and Anne Laferre`re3 Insee, division Logement, f330, 18 Bd. A. Pinard, 75675, Paris cedex 14, France Received May 16, 2000 The French public social housing sector offers rents which are more than 60% below market levels. The “loss” of the public sector landlords, estimated from the rent they could get for their apartments at market prices, amounts to 37 billion Francs per year for the 3 million public social apartments in France. This allows the social sector tenants to consume 10% more housing services and 11% more of other goods. The corresponding surplus gain is around 34 billion Francs. The surplus loss for the collectivity due to these transfers is thus 3 billion Francs, 8% of the transferred sums. As compared to personal housing subsidies, which represent half this amount for the same tenants, the surplus gains are much less concentrated on the poorest part of the population. 䉷 2001 Elsevier Science

1. INTRODUCTION The aim of this paper is to analyze the effect of public social housing (moderate rent habitations, habitations a` loyers mode´re´s, HLM in French) in terms of redistribution and welfare. French social housing started in the nineteenth century as a private initiative; the first local public housing agencies were created in 1894, but the substantive beginning occurred in 1928 and after the second World War, when the HLM were created in 1950 (Edou, 1998). The initial purpose of social housing was twofold. In terms of economic efficiency, the HLM companies were supposed to build new housing at a time of acute shortage, when poor 1

This project started with the work of Re´my Pigois, during his summer 1998 internship at Direction de la Pre´vision and INSEE. The authors thank the Editor and an anonymous referee for valuable comments and references. We also thank J. Me´litz for carefully reading the paper and suggesting improvements. 2 E-mail: [email protected]. 3 E-mail: [email protected]. 429 1051-1377/01 $35.00 䉷 2001 Elsevier Science All rights reserved.

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housing conditions were perceived to be hazardous to health and when private financing was lacking. In terms of redistribution, social housing was intended to help moderate-income families have access to decent housing. We do not address here the question of HLM companies’ efficiency in producing housing services. But we are interested in the redistributive and welfare consequences of social housing. What is the benefit of a below-market rent to a social housing tenant? How does a household living in public housing change its housing consumption and its consumption of other goods, as compared to the same household living in the private rental sector? Does public social housing benefit the poorest households? In the French case, it has often been noted that public housing did not accommodate the lowest income families but rather middle-class families, while it decreased the mobility of renters (Durif and Marchand, 1975). Around 1980 personal housing subsidies were extended on the basis of the idea that they would be more efficient than project-based assistance (“brick and mortar subsidies”). Since that time the composition of families in public housing has been modified: it now accommodates more of the low-income families than in the past. Half of social housing residents receive housing subsidies, in addition to the advantages of low rents. Tenant-based assistance is means-tested, and thus, together with social housing, constitutes a potential poverty trap which discourages the mobility of HLM tenants. This situation seems to resemble the British one where three quarters of social housing tenants receive housing subsidies (Maclennan et al., 1998). Our main aim in this paper is to describe the French public social sector and to estimate the order of magnitude of the transfers related to its existence. To our knowledge, this has not been done before, in contrast with many other countries such as the United States, where considerable work has been done. Thus, we do not introduce new methods for evaluating the efficiency of housing subsidies programs. Instead, our estimation procedures are straightforward applications of well-known methods. Without addressing directly the questions of mobility or poverty trap, we estimate the redistribution which takes place through the transfer from the social housing landlords to the tenants, in the form of low rents. The mean monthly surplus of social tenants is 934 Francs (142⫽), ( whereas the mean personal (cash) housing subsidy is only 450 Francs (69 ⫽ ( ). Thus, the transfer through public social housing is much larger on average. From a redistributive point of view, 95% of the housing subsidies go the poorer half of the population, whereas only 65% of the public housing surplus goes to the lower half. Personal housing subsidies are thus better targeted toward the poor. The paper is organized as follows. The French public social sector is described and compared to the private market rental sector in Section 2. The model is described in Section 3. Section 4 is devoted to the discussion of estimation procedures and econometric issues. The rent loss of social landlords is presented

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in Section 5; the gain of social tenants in nonhousing consumption is analyzed in Section 6. Section 7 discusses the collective surplus loss associated to the existence of HLM and considers the redistribution of the surplus in the population. Section 8 concludes.

2. THE FRENCH PUBLIC HOUSING SECTOR The French rental housing sector is divided into several subsectors, according to the type of contract between the landlord and the tenant (furnished or nonfurnished, let or sublet), the legal regime to which the rent is submitted, and the type of owner. We exclude here households who sublet or rent a furnished apartment (1.6% of all households in 19964). We also leave aside the households occupying 1948-type rent-controlled apartments (1.4% of households)5 whose number has been diminishing steadily. The two main rental groups are the private sector, where rent is considered to be largely market determined although regulated to some degree6 (see Section 3 for discussion of this issue), with 4.45 million tenants (19.1% of households), and the HLM sector, with 3.66 million households in 1996 (15.7%).7 The importance of the HLM sector has been increasing over time, both in absolute (1.93 million tenants in 1973, 4.45 in 1996) and relative terms (20.7% of the non-owneroccupiers in 1973, 29.7% in 1984, and 34.4% in 1996). This is the consequence of both new construction (62,000 units per year between 1980 and 1996), and the crisis of the private rental sector during the seventies and the eighties, which ended in the 1990s after some of the regulations protecting tenants had been removed. The French HLM system differs in some significant ways from public housing and subsidized new construction in the United States. In France, the State finances the construction of HLM units via low-interest loans and tax exemptions. The existing units, as a rule, remain in the HLM system forever. They are owned by companies operating at the local level (usually, there are only a few of them in each town or metropolitan unit). These companies are considered as private (they must make profit), but they have only limited power in attributing the dwellings. In fact, in every city, the municipality, the prefecture, and the social housing 4 All the data come from the National Housing Surveys conducted at INSEE (Institut National de la Statistique et des Etudes Economiques). 5 In 1948, a law was issued to gradually end the stringent rent control instituted since World War I. A few old dwellings are still submitted to that stringent rent control. 6 Rents are freely negotiated for new tenants. Their yearly evolution is bound by the construction cost index. Three or 6 year leases are compulsory and tenants cannot be evicted unless special circumstances specified by the law arise. 7 There also exists a small private social sector, subsidized by public funds, which currently houses less than 2% of the households, which we leave aside.

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committee, are all granted a certain quota of the vacated or newly built units, and may freely decide which households are to occupy those units. The system of admittance in HLM is quite intricate. To get a HLM, a household must first satisfy some “eligibility” criterion : its resources must be under a certain limit, varying with the geographical zone and the composition of the households. In 1994, this limit was such that around 60% of households were eligible (Pitrou, 1997). The household satisfying this condition and wanting to get a HLM must then register, either directly at the local HLM company, or at one of the organisms benefiting from quotas. The registered demand then follows a queuing process, which is totally opaque for the household, since there is no common criterion for admittance among organisms. The household must wait, usually several months, not unfrequently more than a year, before being offered a dwelling. The proposition consists of a particular dwelling (the size of which depends on the size of the household) at a particular monthly rent. The only degree of freedom of the household is to accept the dwelling or to refuse it and to go back into the line. In particular, the household does not have the choice of housing quantity, which turns out to be important for the economic analysis undertaken in this paper. The tenants of HLM are not on their demand curve: the only arbitrage for them is to compare their utility levels in the social sector (where the quantity is fixed but the rent is low) and in the market sector, where they are more able to adjust the quantity of housing service. As a consequence of the relatively loose resource criteria asked for admittance, only a small fraction of eligible households live in HLM. Conversely, the public sector houses many noneligible households. This is a consequence of another important feature of the French system : there is no legal possibility of eviction of a HLM tenant who has turned to be noneligible due to increased resources. Thus, many households enter HLM when relatively poor and stay there even after their income rose above the limit for admittance. We now briefly describe some features of the private and the HLM rental sectors. Since 87% of social tenants and 70% of private sector tenants live in flats, and because the factors influencing the level of rents are not the same for houses and apartments, we exclude houses from the study. The main characteristic of the social sector is low rents. Even if these rents have recently increased, they are still well below the market levels. They are also more concentrated (see Fig. 1). The maximum rents per square meter are set by law, according to geographical zones. They are allowed to be slightly higher in the Paris area than in the rest of France, one of the few concessions of the French legislator to free market logic. The evolution of the rents is regulated. Table I gives some descriptive statistics for the dwellings of the two sectors and the households occupying them. The HLM flats are usually more recent than private sector flats: 55% of apartments have been built between 1949 and 1974, and 38% since 1975 (the proportions are 30 and 25% in the private sector). They are also more comfortable. Originally built for families with children, HLM

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FIG. 1. The distribution of rents in the private and HLM sectors.

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LE BLANC AND LAFERRE`RE TABLE I Descriptive Statistics of Rented Apartments: Public (HLM) and Private Sector (%) HLM

Geographical distribution Rural areas Urban areas below 20,000 inhabitants Urban areas 20,000–100,000 inhabitants—downtown Urban areas 20,000–100,000 inhabitants—suburbs Urban areas 100,000–200,000 inhabitants—downtown Urban areas 100,000 to 200,000 inhabitants—suburbs Urban areas over 200,000 inhabitants—downtown Urban areas over 200,000 inhabitants—suburbs Paris area—outer suburbs Paris area—inner suburbs Paris city Total Age of dwellings Built before 1914 Built 1915–1948 Built 1949–1967 Built 1968–1974 Built 1975–1981 Built 1982–1989 Built 1990 and after Total 1 room 2 rooms 3 rooms 4 rooms 5 rooms or more No bathroom, no central heating No central heating Bathroom and central heating Mean surface in square meters Dwellers’ characteristics No family Woman alone Man alone Lone parent family Couple, man active, woman inactive Couple, man active, woman active Couple, man inactive, woman active Couple, man inactive, woman inactive Household head ⬍20 year old 20–29 years 30–39 years 40–49 years 50–59 years 60 years old and above Total (weighted) numbers of flats Source. INSEE, Enqueˆte Logement 1996–97.

Private sector

2 13 18 2 7 2 15 12 8 16 5 100

4 10 13 1 7 2 28 9 4 10 12 100

2 5 33 27 14 10 9 100 6 19 37 29 10 1 4 95 69

24 16 19 14 10 7 10 100 21 32 27 14 6 3 18 79 57

2 20 11 15 14 28 2 8 1 16 26 20 13 24 3,173,600

3 26 21 8 8 27 2 5 2 34 25 15 8 16 3,101,000

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TABLE II Selected Characteristics of the Weighted Sample: Tenants of an Apartment Less Than 120 m2, Not Housed by Their Employer Private sector Monthly rent ( ⫽) ( Monthly housing allowances ( ⫽) ( Rent per m2 ( ⫽) ( Age of Head Number of children Annual income ( ⫽) ( Number of active individuals

377 53 6.88 40.9 0.51 19,331 1.13

Public sector (HLM) 248 75 3.87 46.7 0.92 17,501 1.17

Source. INSEE, Enqueˆte Logement 1996–97.

apartments are larger on average than those in the private sector. Social housing tenants are less likely to live alone than tenants in the private sector and, when they do, they are older. Some entered the social sector when they were married and had children, and stayed there after their children left. Conversely, couples with children are overrepresented in HLM, and so are lone-parent families. The mean income of social tenants is lower than the income of private sector tenants (Table II). The length of tenancy of social housing tenants is increasing and is now of 9.4 years, as compared with declining tenancy in the private sector (5.3 years on average). Few households leave the public sector for owner occupation or the private rental sector, which makes access to the social sector difficult for younger generations. As a result, HLM tenants are older on average than private sector tenants and the age difference is increasing. To compare rents in the two sectors, the neighborhood characteristics must be taken into account. Public sector housing is often spatially concentrated. In the sixties or seventies some areas were entirely made up of social apartment buildings. Some HLM districts are mostly composed of blue-collar or employee population, with few executives and white-collar workers. We use an index computed at the district level as a proxy for neighborhood characteristics8 (Tabard, 1993), according to which, apartments in the private sector are on average in better locations than social sector apartments (see Table III). For HLM tenants, the index does not vary much with the tenants’ income for those under the 7th decile of income.9 However, for tenants whose income is above the 7th decile 8 This index is based on a factor analysis of the socioeconomic composition of communes at the 1990 Population Census. It reflects the social characteristics of the area, as well as the value of the public goods offered by the commune. 9 We use deciles of total pretax income of the household (excluding housing allowances but including most other public transfers) by consumption unit, i.e., equivalent income. We use OECD equivalence scale. Deciles are computed from the whole distribution of income, including owner-occupiers.

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(i.e., roughly, tenants above the eligibility limit), the index increases sharply. These tenants are thus living in better neighborhoods. At the same time, the length of tenancy in social housing increases with income (Table III). This is the effect of a filtering process: upper-class households, who could afford to live in the private sector, are more induced to leave the social sector if their apartment is located in a “bad” neighborhood, whereas they will stay in a well located apartment. Thus, public sector apartments that are freed and offered to new tenants are mainly located in the worst neighborhoods.

3. THE MODEL Rent control or public housing is generally analyzed within a partial equilibrium framework. Housing is exchanged either on the market (the free, uncontrolled sector), or in a sector where prices are controlled. In the context of a perfect uncontrolled market, rent controls lower the collective surplus (a good review can be found in Arnott, 1995). The issues are then to estimate the loss of landlords, and to identify the households that benefit from the controls. Here, we use the basic model developed by Olsen to study rent control in New York City (1972), then used by Murray (1975), Gyourko and Linneman (1989), and other studies on rent control. There are two goods, housing service and a composite good, assimilated to

TABLE III Tenancy, Socioeconomic Environment Index by Decile of Equivalent Income for HLM and Private Sector Tenants HLM

Private sector

Decile of equivalent income

% Tenants

Mean socioeconomic index

Mean length of tenancy in years

% Tenants

Mean socioeconomic index

Mean length of tenancy in years

1 2 3 4 5 6 7 8 9 10 Total

15 15 13 12 12 10 9 7 5 2 100

⫺0.03 ⫺0.02 0.01 ⫺0.01 0.03 0.03 0.14 0.17 0.23 0.26 0.04

7.4 8.6 9.4 9.2 10.3 10.1 10.1 10.6 11.4 12.1 9.4

15 10 9 9 8 9 9 9 10 11 100

0.16 0.14 0.11 0.08 0.13 0.18 0.17 0.18 0.31 0.54 0.20

3.7 5.5 6.5 5.1 5.7 5.3 5.8 4.7 5.1 6.0 5.3

Source. INSEE, Enqueˆte Logement 1996–97. Note. See footnote 8 for a definition of the socioeconomic index.

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the numeraire, which represents a bundle of all nonhousing goods. Housing service is an unobservable good emitted by each dwelling during each period of time. As is common in similar studies, we postulate that the housing service flow is proportional to the rent.10 There are three markets: the controlled market for housing services (the public sector), the free market sector for housing services, and the market for nonhousing goods (assimilated to the numeraire). The last two markets are assumed to be perfectly competitive and in the long run equilibrium. An important assumption of the model is that the existence of a social sector has no influence on the rents of the private sector. Put differently, it amounts to say that price of housing services in the free market is the same as the equilibrium price that would prevail if the social sector did not exist. This hypothesis may seem particularly strong in the French case, for at least two reasons. First of all, one may question the validity of the “free market” assumption in the private rental sector. In fact the private rental sector is submitted to a rent control that, following the U.S. terminology, can be labeled “second generation” rent control. Precisely, rents are freely set whenever a new tenant enters a flat, whereas annual rent changes are bound not to exceed a ceiling index during a lease. So, major changes in rents correspond to changes of tenants. This system is likely to generate complicated behavior of landlords and tenants. Knowing that future rent increases will be moderated, bargaining on the initial rent is likely to occur. Although we save further analysis of this issue for a subsequent paper, we are aware that this system has an effect on the rents of the private sector, which is our “free market” benchmark. Second, even in case of a really “free” sector, the quantitative importance of the public housing sector is likely to modify the rents in the free sector, due to changes in the demand for housing and spillovers from the controlled sector to the uncontrolled one. This issue has been dealt with by Marks (1984), and Fallis and Smith (1984, 1985). In the case of rent control, the latter authors show that the rents of the uncontrolled sector likely rise when rent control is introduced on a fraction of the housing stock.11 However, they emphasize that the nature of the mechanism of allocation of the flats in the controlled sector has to be precisely modeled, if one wants to assess the effect of the regulation on the uncontrolled sector rents. Empirically, Malpezzi (1993) gives results for several markets, indicating that the effects of controls on the uncontrolled rents are sometimes important, sometimes not. In the French case, as we have seen, the process of allocation of the HLM does not follow uniform rules. This precludes a precise modeling, at least in this paper. At the micro level in the Paris outskirts area, the presence of HLM seems to depress the free sector prices in the same 10

Thus a rent of 2000 Francs per month signals a quantity of housing services twice as large as one of 1000 Francs. 11 Two effects are acting in opposite directions: controls on rent changes in the private sector tend to lower rents, whereas the presence of the HLM is likely to drive them up. Our “free market” hypothesis amounts to say that the two effects approximately offset each other.

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area, through a “bad neighborhood effect” (OLAP, 1998), but no evidence exists on the overall effect of the HLM on the private sector rents. We are left to check empirical evidence that private sector rents in France are not “too high.” Indicators from Haffner and Dol (2000) show that rent-to-income ratios in the French private sector are comparable to those in similar european countries. We therefore argue that the “free market” hypothesis for the private rental sector is not unreasonable. At this stage, it is useful to introduce some notations. The price of the composite good is normalized to unity. Denote ps (respectively, pm) the unit price of housing service in the public sector (respectively, the unit price of housing service in the private sector). Suppose (as is empirically true) that ps ⬍ pm . A household living in the private sector consumes a quantity qm of housing service and a quantity cm of the composite good. Denoting x the household’s income, the corresponding budget constraint is x ⫽ cm ⫹ pmqm . In the same manner, a household living in the public sector consumes a quantity qs of housing service and a quantity cs of the composite good, with budget constraint x ⫽ cs ⫹ psqs . We assume that the household’s utility has a Cobb-Douglas form, v(c,q) ⫽ c␤ q1⫺␤. This is equivalent to assume that the price elasticity of housing demand is constant, equal to ⫺1.12 Comparing the situation of the public social sector renters with the situation of the private sector renters involves computing some measure of the surplus associated to each situation. The important point here is that a HLM tenant is not on his demand curve. The quantity of housing service and its price are imposed on him. Thus, all the comparisons must be made at the private sector price pm . The utility level in the HLM sector, us , is given by us ⫽ (cs) ␤ (qs)1⫺␤.

(1)

For a household renting in the private sector, housing quantity can be freely chosen, so that the household maximizes its utility subject to the budget constraint. This yields the marshallian demand functions cm ⫽ x␤, qm ⫽

x(1 ⫺ ␤ ) , pm

giving the household a utility level um . The “benefit” of HLM tenants can be computed in two different ways, analogous to the definition of the “equivalent variation” (EV) and the “compensating variation” (CV) in a perfect market (see for example Deaton and Muellbauer, 1980). The analogous of the compensating variation is the maximum amount 12

In many countries, there is evidence that the price elasticity of housing demand is less than unity, e.g., Ermisch (1995) for Great Britain, or Hanushek and Quigley (1980) for the United States. To our knowledge, no empirical evidence exists for France.

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FIGURE 2

that a HLM tenant would be willing to pay to avoid moving to the private market sector. Thus, it is defined implicitly by v(cs ⫺ A, qm) ⫽ um.

(2)

With Cobb-Douglas utility, (6) can be written as13

冋 册

um A ⫽ cs ⫺ (qs)1⫺␤

1/␤

冋

冢 冣册.

um ⫽ cs 1 ⫺ us

1 ␤

(3)

The analogous of the equivalent variation is the amount a private sector tenant would need to be as well off as a HLM tenant. If e denotes the expenditure function, it is defined by B ⫽ e(us, pm) ⫺ x. Now, the inefficiency arises from the fact that the HLM tenants are not on their demand curves. Figure 2 depicts the situation (see also Olsen and Barton, 1983). The private sector renter with income X is located at point E, the optimum. The HLM tenant gets a quantity of housing qs at price ps . He is located at point F 13 Equation (3) is still valid if situation 1 is not optimal. In this case, direct utility can be computed from (1).

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and reaches utility level us . For the HLM landlord, the loss resulting from renting the flat below the market price is equal to S ⫽ qs ( pm ⫺ ps). Were he given this sum in the form of a cash subsidy, the HLM tenant could reach utility u2 (point G). To reach the utility level us in the private sector, the household would only need the additional income B ⬍ S; he would then locate at point H. B is the equivalent variation. The welfare loss is then equal to S-B. Next, consider the point I, defined by the intersection of the vertical line of abscissa qs with the indifference curve um . The maximum amount the HLM tenant would be willing to pay to stay in the HLM sector, A, is given by the length of segment IF. Another reasonable way to deal with welfare issues is to use the marshallian surplus. In the present case, the demand curve for housing takes the form

p ⫽ D(q) ⫽

pmqm . q

The difference of marshallian surplus between the public sector and the private sector is then (Olsen, 1972)

qs

⌬S ⫽ pmqm ⫺ psqs ⫹

冮 D(q)dq ⫽ p q

m m

⫺ psqs ⫹ pmqm[log pmqs ⫺ log pmqm].

qm

(4)

In our empirical application, we use formula (4). We also compare the allocation of income between housing and nonhousing goods in the private sector and the HLM sector. Compared to a private sector tenant having the same income, the HLM tenant consumes a supplementary fraction of housing service equal to (qs ⫺ qm)/qm , as well as a supplementary fraction of other goods equal to cs ⫺ cm pmqm ⫺ psqs ⫽ . cm x ⫺ pmqm

For a sample of N households, with sampling weights (wi)1ⱕiⱕN, the changes in the quantity of housing service and of other goods are computed respectively as

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N

兺 wi (qs,i pm ⫺ qm,i pm) i⫽1 N

兺

(5)

wi qm,i pm

i⫽1

N

兺 wi (qm,i pm ⫺ qs,i ps) i⫽1 N

兺 wi (xi ⫺ qm,i pm)

.

(6)

i⫽1

4. ESTIMATION FROM SURVEY DATA In this section, we present the empirical procedures which we use to calculate the quantities introduced in the previous section. Examining formula (4), we see that the computation of the surplus for a HLM tenant involves a known quantity, the rent of the HLM flat occupied by the household, ps qs , and two unknown quantities, respectively the rent of the flat if it were to be rent in the private market, pmqs , and the rent the household would pay if it lived in the private rental sector, pmqm . Thus, we need two models: the first relates the market rents of dwellings to their characteristics, and the second relates the housing expenditure of households to their characteristics. The parameters of the first model will be used to compute a free market rent pmqs for each dwelling in the social sector. The parameters of the second model will be used to predict housing consumption for households living in the social sector, pmqm. We briefly discuss the econometric issues associated with the two models. First consider the estimation of the market rent equation. This equation links the market rent of the dwellings to their physical characteristics. To estimate this equation, one can simply apply OLS to the private sector flats in the sample. Alternatively, we could think of using the information contained in the rents of the HLM flats. For example, in the case of rent control, Caudill et al. (1989) make the hypothesis that the controlled rents are systematically below the market rents, and use this hypothesis in the estimation of the rent equation. More specifically, if the market rent is assumed to be a linear function of apartment characteristics, r *i ⫽ Xi␤ ⫹ ␧i, and the observed rent is ri , they assume that ri ⫽ r i* for uncontrolled units, and ri ⱕ r i* for controlled units. Assuming that the error terms are normally distributed, the parameter ␤ can be efficiently estimated by maximum likelihood in a straightforward manner. In our case, the hypothesis that the market rents of HLM units are always as least as great as their actual rent seems to be quite plausible on the view of the OLS results. So, both methods can be applied,

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as they give consistent estimates of the parameters.14 However, as the use of the private sector subsample is less demanding in terms of hypotheses, we stick to the OLS results. Then, consider the imputation of a market sector housing expenditure to HLM tenants. Our approach supposes that tenants in both sectors have the same preferences concerning housing services.15 In this case, applying OLS to the subsample of private sector tenants to estimate a housing expenditure equation is valid only if the selection of the households between the two sectors is random conditionally on their characteristics. In the French case, this is not likely to be the case. As already told, the selection process into the public social sector is very complicated. Nevertheless, denoting L ⫽ 1 if the household lives in the private sector, and L ⫽ 0 if it lives in the public sector, suppose that we can relate this variable to a latent variable L* such that L* ⫽ X2␦ ⫹ v L ⫽ 1 if L* ⱖ 0, L ⫽ 0 otherwise. Denote D* ⫽ X1␥ ⫹ u the housing demand function at market price. This variable is only observed for households living in the private sector. If the residuals u and v are correlated, the estimation of the housing expenditure equation by OLS on the subsample of private sector renters will lead to biased parameters. If we further assume that the disturbances u and v are jointly normal with correlation matrix

兺⫽

冋

␴ 21 ␳␴1

册

␳␴1 , 1

we obtain a generalized Tobit model. It can be estimated straightforwardly by maximum likelihood. The correct prediction of the housing expenditure for households living in the public sector is then E(D*/L ⫽ 0, X1, X2) ⫽ X1␥ ⫺ ␳␴1

␸ (X2␦ ) , 1 ⫺ ␾ (X2␦ )

where ␸ and ␾ are respectively the density function and the cumulative distribution function of the standard normal law. 14 Of course, this is the case only if there are no unobservable characteristics explaining both the level of the market rent and the fact that the dwelling is in the private or the public sector. 15 However, they could put a very different value on them. It is not easy to see in what direction the bias work (Olsen and Barton, 1983).

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We estimated both an OLS equation on the subsample of private sector renters and a selection model on the full sample of renters. The two procedures yielded very close predictions of housing expenditures for the households living in HLM. In this paper, we are not directly interested in the value of the parameter ␥. Thus we present here only the OLS results, which may be easier to compare to the results of other studies. However, we do not comment on the estimated value of the parameters, since they are not the true structural parameters. Having done so, we can compute the following : (i) the “loss” of the social landlord for a particular flat, as the difference between the actual rent and the imputed market rent; (ii) the differences in housing and nonhousing consumption between tenants in the private and the public sector, following formulas (5) and (6); (iii) the difference in marshallian surplus between those two sectors for a tenant; (iv) the total variation of welfare, which is simply the sum of the surplus gains of tenants of the social sector and of the landlords’ losses. Since the situation of reference is a perfect market, the landlords’ loss is larger than the surplus gain of consumers, and the total variation of welfare is negative. The data are drawn from the National Housing Survey conducted by INSEE in 1996–1997. A representative national sample of 29,000 households were interviewed, of which 15,400 rent their dwellings. We selected renters of apartments with a surface of less than 120 m2, who were not housed by their employers. Thus we obtain a sample of 7372 households, of which 3828 are in the social sector and 3544 live in the private sector. Those households represent a total population of about three millions of HLM tenants and as many private sector tenants.

5. MARKET RENT OF HLM To compute the market rent of social sector apartments, we use a hedonic type of model estimated on the private sector flats. The right-hand side variables include the characteristics of the dwelling, such as number of rooms and surface per room, date of building, plumbing conditions, neighborhood characteristics and size of town. The size of town is an index of the demand for land, and thus serves as a proxy for land price. The index of the quality of the neighborhood is obtained from a factor analysis of the socioeconomic characteristics of the town (Tabard, 1993). It acts as a proxy for the price of the public goods linked to the dwellings, which has a strong influence on rents. According to the central variant of the model presented in Table IV, the monthly rent for the average HLM flat on the free market would be 2640 Francs (402 ⫽), ( compared to an actual rent of 1630 Francs (248 ⫽), ( thus 62% higher. This difference of 1010 francs (154 ⫽) ( per month, as regards the 3 millions flats we study, represent a “gift” of 37 billions (5.6⫽) ( per year to social sector tenants. This amount cannot be interpreted in terms of net loss for the landlords, as in

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TABLE IV Model of Private Sector Rents as a Function of the Characteristics of the Dwelling Variable

Parameter

Standard error

Student T

Prob ⬎ 앚T앚

Constant Number of rooms Square meter per room Number of WC Lift Parking lot or garage Period of construction Before 1949 From 1949 to 1974 From 1975 to 1981 From 1982 to 1989 1990 and after Number of dwellings in the building Less than 20 From 20 to 39 40 and more Comfort of the dwelling No water or running water only Running water, no bathroom or no WC Bathroom and WC, no central heating All of above Location Rural area and urban area of less than 20,000 inhabitants Urban area, 20,000 to 100,000 inhab.—suburbs Urban area, 20,000 to 100,000 inhab.—center Urban area, 100,000 to 200,000 inhab.—suburbs Urban area, 100,000 to 200,000 inhab.—center Urban area, plus from 200,000 inhab.—suburbs Urban area, over 200,000 inhab.—Center Paris city Paris area—inner suburbs Paris area—outer suburbs Socioeconomic index

⫺240.33 528.43 34.71 506.70 245.81 118.83

115.12 14.88 2.52 72.69 37.23 35.07

⫺2.09 35.52 13.77 6.97 6.60 3.39

0.04 0.0001 0.0001 0.0001 0.0001 0.0007

⫺680.55 ⫺655.71 ⫺419.04 ⫺270.64 Reference

46.25 41.80 56.50 61.62 —

⫺14.71 ⫺15.69 ⫺7.42 ⫺4.40 —

0.0001 0.0001 0.0001 0.0001 —

142.54 Reference ⫺81.12

40.16 — 45.41

3.55 — ⫺1.79

0.0004 — 0.07

⫺302.38 ⫺130.90 ⫺112.13 Reference

158.75 119.22 37.82 —

⫺1.91 ⫺1.10 ⫺2.97 —

0.06 0.27 0.003 —

⫺30.47

52.12

⫺0.59

0.56

73.30

116.84

0.63

0.53

⫺14.08

50.20

⫺0.28

0.78

⫺10.83

94.96

⫺0.11

0.91

⫺47.02

56.23

⫺0.84

0.40

37.36

52.50

0.71

0.48

Reference 1178.68 748.04 865.20 1025.05

— 62.19 52.73 73.19 59.44

— 18.95 14.19 11.83 17.24

— 0.0001 0.0001 0.0001 0.0001

Note. Dependant variable: monthly rent in Francs, R2 ⫽ 0.56.

the case of rent control. The low rents in the social sector are the counterparts of government subsidies to construction (low interest rates, annual allowances, tax exemptions) and rehabilitation (low tax, exemption of property tax and of taxes on benefit, low rate of VAT). Those subsidies amounted to 14.5 billions

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FIG. 3. Ratio of imputed rents to actual rents in HLM flats by location.

Francs (2.2 billions ⫽ ( ) in 1995, according to the Direction de la Pre´vision. However, the annual loss computed here cannot be directly compared to those subsidies, which are perceived on an annual flow of new constructions The variations in the ratio of market rents to social rents based on the characteristics of the dwellings (location and size) can be interpreted as distortions in the HLM scale of rents. The ratio is larger, the more urbanized is the area (Fig. 3). This reflects the fact that HLM maximum rent scales depend very little on the location. In rural areas and urban units less than 100,000 inhabitants the difference is more pronounced for big apartments than for small ones; for example, free market rents are 20% higher (1 room) to 60% higher (5 rooms) in rural areas. In larger urban units, the ratio is the same regardless of the number of rooms. In the Paris area the order is reversed: the fewer rooms, the larger the ratio. Free market rents are between 100% (5 rooms) and 150% (1 room) higher than HLM rents in Paris.

6. HOUSING EXPENDITURE IN THE MARKET SECTOR We now turn to the prediction of a “free market” housing expenditure for the households living in HLM. As described in Section 4, we estimated an equation

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relating housing expenditures in the private sector to the characteristics of the households. We also estimated a model taking into account the selection of the households in the two sectors. The two specifications gave similar imputed housing expenditures for the social sector tenants. Once housing expenditure is predicted, the budget constraint gives nonhousing consumption (including savings). The variables included in the right-hand side of the expenditure equation are quite standard. However, two assumptions need some comments: they concern the treatment of space location variables and of the length of tenancy. How are location variables (size of city, environment) to be seen from the household’s point of view? A tenant does not devote the same part of his income to housing in the country, in a small town, or in Paris. In including the size of the city in the estimation of housing demand, we assume that HLM households would live in the same type of city, should they live in the private sector. On the contrary, we do not include the socioeconomic index of the district in the regression, thus assuming a certain freedom of choice for the household within a city type; this assumption seems realistic, since within a town, social and private sectors hardly spatially coincide.16 In the French private sector, the length of tenancy is a significant determinant of housing expenditure. The longer one stays in a flat, the lower the rent is ceteris paribus, since, as mentioned before, rent changes during a lease are controlled. The length of tenancy is thus included in the explanatory variables of the expenditure equation. However, tenants in HLM being less mobile than private sector tenants, using the HLM tenants’ length of tenancy to impute their spending in the private sector would underestimate this spending. To avoid this, we assume HLM tenants would have the same mobility as similar households living in the private sector. We estimate private sector tenancy as a function of tenants’ characteristics (age, sex, number of children, activity) (see Table V); this gives an imputed tenancy for social sector tenants; to impute their housing demand, we use the imputed tenancy as a right-hand side variable (some variants are in Table VII). According to the central variant presented in Table VI, social sector renters would spend 2410 Francs (367 ⫽) ( per month on rent if they lived in the market sector. This is to be compared to the estimated market rent of their flat, 2640 Francs (402 ⫽). ( Thus HLM tenants consume an average of 10% more housing services than they would if they were to look for an apartment on the market. This overconsumption of housing services, however, is more than balanced by the difference in rent levels between the two sectors, since the average rent in HLM is 1630 Francs (248 ⫽). ( As a consequence, HLM tenants are able to spend 16 There, one clearly sees the limit of this type of exercise. We abstract from general equilibrium effects, and at the same time do as if the public sector did not exist, which is quite antinomic.

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PUBLIC HOUSING IN FRANCE TABLE V Model: Tenancy as a Function of Tenant’s Characteristics

Standard error Student T Prob ⬎ 앚T앚

Variable

Parameter

Constant Location Rural area Urban area, less than 20,000 inhabitants Urban area, 20,000 to 100,000 inhabitants Urban area, more than 100,000 inhabitants Paris area Number of working persons of the household Number of children Age of Household Head Less than 30 years old From 30 to 39 years old From 40 to 49 years old From 50 to 59 years old From 60 to 69 years old 70 years and more Occupation of Household Head Working Unemployed Retired Housewife Other inactive Matrimonial status Single Unmarried couple Divorced Widow Married couple

0.22

0.09

2.29

⫺0.07 ⫺0.20 ⫺0.18 ⫺0.06 Reference 0.36 0.13

0.10 0.07 0.06 0.05 — 0.4 0.03

⫺0.66 ⫺2.88 ⫺2.90 ⫺1.30 — 9.00 4.51

0.51 0.004 0.004 0.61 — 0.0001 0.0001

⫺0.77 Reference 0.56 0.92 1.37 1.56

0.057 — 0.06 0.08 0.15 0.16

⫺14.54 — 8.80 10.87 9.39 9.86

0.0001 — 0.0001 0.0001 0.0001 0.0001

Reference ⫺0.08 0.30 ⫺0.16 0.24

— 0.07 0.14 0.25 0.13

— ⫺1.22 2.09 ⫺0.66 1.84

— 0.22 0.04 0.51 0.06

0.32 ⫺0.09 ⫺0.10 ⫺0.001 Reference

0.07 0.06 0.07 0.09 —

4.85 ⫺1.36 ⫺1.38 ⫺0.01 —

0.0001 0.17 0.17 0.99 —

0.02

Note. Dependant variable: log tenancy in years, R2 ⫽ 0.34.

a larger portion of their income (780 Francs, 119⫽) ( on average) on the consumption of nonhousing goods. This represents an average gain of 11% of nonhousing consumption for HLM tenants. On the whole, compared to a tenant in the private sector, a household living in HLM consumes 10% more housing services and 11% more other goods. According to a similar study on social housing in New York City in the sixties (Olsen and Barton, 1983), the corresponding gains were 66% in housing consumption and 17% in nonhousing consumption. Perhaps the best comparison to New York in France is the Paris metropolitan area, where the respective gains were 10 and 15% (see Table IX) (17 and 17% for the city of Paris itself). The differences with New York City may stem from different compositions of the concerned populations. In particular, the Parisian HLM residents are not particularly poor: 52% have an income that is above the median income of the whole French

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TABLE VI Model: Rent as a Function of Households’ Characteristics Variable Intercept Income Location Rural areas and urban units less than 20,000 inhabitants UU 20,000–100,000 inhabitants—suburds UU 20,000–100,000 inhabitants—downtown UU 100,000–200,000 inhabitants—suburbs UU 100,000–200,000 inhabitants—downtown UU over 200,000 inhabitants—suburbs UU over 200,000 inhabitants—downtown Paris City Paris area—outer suburbs Paris area—inner suburbs Number of non active persons in household Number of active persons in household Age of household head ⬍30 30 to 39 40 to 49 50 to 59 60 to 69 70 years old or more Head female Education level No diploma or primary level BEPC CAP, BEP Baccalaure´at, professional degree University 1st cycle University 2d or 3d cycle Social category of head Blue collar worker White collar employee Never employed Intermediary profession Farmer Craftman shopkeeper, self-employed Executive Imputed tenancy (in years)

Standard error

Student T

Prob ⬎ 앚T앚

88.76 0.002

15.75 30.29

0.0001 0.0001

⫺187.76

46.84

⫺4.01

0.0001

⫺203.58 ⫺280.25 ⫺87.40 ⫺110.72 47.81 Reference 979.99 522.45 809.05 184.24 35.87

116.59 47.86 95.56 56.47 53.53 — 52.74 53.70 74.41 16.00 31.36

⫺1.75 ⫺5.85 ⫺0.91 ⫺1.91 0.89 — 18.58 9.73 10.87 11.51 1.14

0.08 0.0001 0.36 0.05 0.37 — 0.0001 0.0001 0.0001 0.0001 0.25

Parameter 1398.34 0.073

⫺139.22 Reference 21.58 54.75 51.76 345.72 206.562

40.15 — 47.78 60.99 75.00 71.62 34.47014

⫺3.47 — 0.45 0.90 0.69 4.83 5.993

0.0005 — 0.65 0.37 0.49 0.0001 0.0001

⫺21.58 166.63 113.79 Reference 65.78 142.14

71.94 70.09 69.17 — 71.68 72.45

⫺0.30 2.38 1.65 — 0.92 1.96

0.76 0.02 0.10 — 0.36 0.05

⫺150.70 Reference ⫺65.03 25.81 ⫺465.51 309.94 166.05 ⫺180.44

44.94 — 57.45 49.00 204.99 71.99 57.78 11.53

⫺3.35 — ⫺1.13 0.53 ⫺2.27 4.30 2.87 ⫺15.65

Note. Dependent variable: monthly rent in Francs, R2 ⫽ 0.54.

0.0008 — 0.26 0.60 0.02 0.0001 0.004 0.0001

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PUBLIC HOUSING IN FRANCE TABLE VII Housing Expenditures of HLM Tenants in Francs: Rent, Imputed Rent with Different Assumptions Observed Rent

Predicted with imputed tenancy

Predicted without tenancy

Predicted with tenancy HLM

1628 1568 870 1248 2000 2824

2408 2276 1501 1904 2824 3679

2410 2279 1500 1905 2833 3678

2331 2215 1363 1798 2782 3598

Mean Median 5% Q1 Q3 95%

population. Now the relative gains are more important for the poorest households. In the Paris area again, the relative gains are of 21 and 49% for tenants in the lowest decile, 15 and 28% for the second, and 17 and 20% for the third decile. It is worth looking at the links between the consumption gains and the income level of HLM tenants. The gain in the quantity of housing services decreases progressively as income increases to reach zero at the ninth decile; it is negative for tenants in the highest decile. However, the relative gain in nonhousing consumption decreases only slowly with income; it is around 8% for the three highest deciles (see Table VIII). The collective transfer to households living in HLM, TABLE VIII Rents, Imputed Rents, Gains of Housing Service, Gains in Nonhousing Consumption of HLM Tenants by Decile of Income Mean actual Decile rent of (Francs) income* (1) 1 2 3 4 5 6 7 8 9 10 Total

1540 1540 1590 1570 1580 1610 1680 1780 2030 2420 1630

Mean Imputed housing market expenditure in price rent the private sector (Francs) (Francs) (2) (3) 2430 2460 2550 2580 2620 2680 2890 2980 3280 3350 2640

2070 2200 2260 2340 2370 2470 2640 2870 3170 3820 2410

Mean monthly income (Francs) (4)

Mean Mean gain of Mean gain in surplus housing non housing Gain per service consumption month (5) (6) (7)

4,590 6,700 8,260 9,090 10,230 11,140 12,480 14,760 17,410 24,130 9,730

18% 12% 13% 10% 10% 9% 10% 3% 0% ⫺12% 10%

21% 15% 11% 11% 10% 10% 9% 9% 8% 7% 11%

800 837 869 941 970 996 1139 1135 1092 752 934

* income by consumption unit, OECD equivalence scale. Note. The gains in housing and nonhousing consumption are computed as follows: (5) ⫽ 100.((2) ⫺ (3))/(3) (6) ⫽ 100.((3) ⫺ (1))/((4) ⫺ (3)). The surplus gain is computed using Eq. (4).

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TABLE IX Gains of Housing Service and of Nonhousing Consumption of HLM Tenants, by Income and Location Paris metropolitan area

Other areas

Decile of equivalent income

Gain of housing service

Gain of nonhousing consumption

Gain of housing service

Gain of nonhousing consumption

1 2 3 4 5 6 7 8 9 10 Total

21 15 17 13 12 11 14 5 2 ⫺7 10

49 28 20 18 19 16 14 12 10 8 15

18 12 12 9 9 6 3 0 ⫺7 ⫺26 9

15 12 9 8 8 7 7 7 5 5 9

through below-market rents, benefits the lowest income renters more (in relative values). Those in the first income decile gain 17% housing service and 21% consumption of non housing goods; up to the fifth decile, the consumption gains are above 10%, both for housing or nonhousing consumption. In that sense the public sector fulfills its role to help low resources households, allowing them to live in bigger flats than in the private sector, while consuming more of other goods. For the richest tenants, the only effect is to consume more of nonhousing goods. Households in the three upper deciles of income receive a mean monthly transfer of 1200 Francs (183 ⫽) ( and live in a dwelling equivalent to what they would choose in the private market sector. This gives them the opportunity to build up a downpayment to finance a home purchase in the future. The transfer is then antiredistributive in this case.

7. SURPLUS TRANSFERRED TO HLM TENANTS As mentioned before, two measures of surplus are computed: the marshallian surplus and the equivalent variation, EV. Both give similar results. Living in HLM generates a monthly surplus of 934 Francs (142 ⫽), ( about half the actual rent. Globally, the HLM tenants in our sample gain a surplus of 34 (5.2 ⫽ ( ) billions Francs. The loss of surplus to the taxpayer (estimated as the difference between the loss of rents in HLM, and the surplus gain of the HLM tenants), is around 80 Francs (12 ⫽ ( ) per household and per month, i.e., 3 billions Francs (0.4 billion ⫽ ( ) per year for the dwellings included in the study. This loss thus

PUBLIC HOUSING IN FRANCE

451

FIG. 4. Distribution of surplus and housing subsidies for HLM tenants (flats, less than 120 square meters, not accommodated by employer) by decile of equivalent income.

represents about 8% of the transfer operated by the State through the channel of public social housing. It is thus rather small. The surplus gains are more important in absolute value for the poorest population (see Fig. 4). However, 35% of the surplus goes to households belonging to the richest half of the population in terms of equivalent income. The redistributive effect of the HLM sector is not well targeted toward the lowest incomes. The distribution profile of surplus can be compared with personal housing allowances. Housing allowances distributed to tenants of HLM flats amount 18 billions Francs (2.7 billions ⫽ ( ) per year, half the amount of the surplus, but they are better targeted toward low-income tenants (Fig. 4): 95% of allowances go to households in the bottom half of the population, and 67% to the two lowest deciles. The main reason for this relatively poor targeting toward the poorest fraction of households is that the social sector houses wealthy households. This happens because the eviction of a HLM tenant is not possible, even when his economic situation improves and he is no longer eligible. High-income HLM tenants have no incentive to move; as a consequence, eligible households cannot enter the public housing sector. In comparison, personal housing subsidies have less adverse effects in terms of mobility, because they depend on the current resources of the households. In the beginning of the sixties, a law was issued, instituting a rent supplement (in French, supple´ment de loyer de solidarite´ SLS17) for households whose resources were above the limit. Until 1996, the HLM were free to apply 17

SLS is included in the rents used in the computations presented here.

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the SLS at the level they chose, or not to impose them.18 The HLM companies might be interested in keeping “rich” customers among their tenants, as an insurance against unpaid rents (rents payment incidents are twice to three times more frequent in HLM than in the private sector (Detour and Laferre`re, 1998)), or undermaintenance of dwellings. In addition, part of SLS was supposed to be paid back by the HLM company to the State, reducing the incentive to levy it (Edou, 1998). From the Government point of view, the risk of segregated neighborhood also weighs in the balance, due to the high spatial concentration of HLM dwellings. It excludes the wish of completely eliminating upper-class or upper middle-class households from HLM, if there is a collective value put on social diversity. All this explains why these rent supplements are levied on a small fraction of tenants, and why their levels are very low compared to the gains of the tenants. According to the 1996 INSEE National Housing Survey, less than 200,000 HLM tenants mentioned paying a SLS; only 20% of the tenants in the three upper deciles were paying them. From this survey, the total SLS amounted to 720 million Francs (110 million ⫽). ( According to our estimations, if it were decided to take away half of the surplus gain of HLM tenants belonging to the four highest deciles of income in the form of rent supplements, those would amount to 4.4 billions Francs (0.7 billion ⫽), ( six times the actual amount. It is thus highly probable that the rent supplements could be increased, and generalized, reducing the collective transfer to upper-class HLM tenants, without major risks for the social diversity of neighborhoods. Redistribution resulting from the existence of the HLM must also be considered from the point of view of horizontal equity. Some groups of the low-income households have easier access to the HLM sector than others. It is partly because most of the HLM were built in the sixties and seventies for families with children, who constituted the bulk of the low-income households. The existing stock of HLM is thus not well suited for a large part of the new low-income population, which frequently consists of single persons. Those households have to live in the private sector where rents are much higher. The gap between the poor households in the two sectors is further increased by the system of personal housing subsidies : housing subsidies are ceteris paribus more frequent and higher in the social sector than in the private sector (Clanche´ and le Blanc, 1999). 8. CONCLUSION This paper analyzes the effects of public social housing in France on redistribution and welfare. Using a simple economic model, we estimate the benefits of 18 Nowadays, the SLS are compulsory for the households whose resources exceed 40% of the eligibility limit, and remains optional if the eligibility limit is exceeded by between 10 and 40%. Exemption from SLS is still possible if the dwelling is located in certain “sensitive” zones, fixed by the law, where maintaining a social diversity of households is deemed important.

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453

social housing, in terms of consumption of housing service and nonhousing goods. The mean monthly surplus of social tenants amounts to 934 Francs (142 ⫽ ( ). Collective surplus losses are rather low, less than 10% of the total amount transferred. From a redistributive point of view, the transfers do not benefit only the less affluent households. Only 65% of the public housing surplus go the poorest half of the HLM tenants. In comparison, personal housing subsidies appear to be better targeted toward the poor. They also have fewer adverse effects on mobility. Other studies have tried to measure the effect of public housing on tenants’ welfare. As mentioned above, Olsen and Barton (1983) found a higher increase in housing consumption by public housing families in New York City in 1968 than we do for French social housing households, and an increase in consumption of other goods, which is more similar to what we find (17% compared to our 11%). Murray (1975) finds that the public housing program he studies increased the real income of participants by 35%. Mayo and Barnbrok (1985) compare the West German and U.S. situations around 1975. They find that in the United States, the benefits were of the same order of magnitude, whether the tenant was in a project-based program (public housing and the like) or received a tenantbased subsidy. The situation was very different in Germany, where tenant based subsidies (Wohngeld) were twice as high as the benefit from social housing. From our study, the distribution of benefits is reversed in France, where the average surplus of living in social housing is twice as large as the average benefit from tenant-based subsidy. All our results, however, must be taken only as rough estimates. The model relies on a number of simplifying assumptions, the most important of which is that the existence of a social sector has no influence on the rents of the private sector. As argued in Section 3, this hypothesis may seem particularly stringent in the French case, because of the quantitative importance of the public housing sector. One obvious extension to this preliminary work would be to check the validity of this assumption and to study the changes in the housing demand induced by the existence of the HLM, and the demand spillovers from the HLM sector to the private sector. Another simplification adopted here is to neglect the impact of the personal housing subsidies system on welfare in the two rental sectors. In reality, housing subsidies condition the behavior of households when they choose a dwelling, and of landlords, when they choose a tenant and set the rent. Two other potential issues related to welfare could be worth examining. The first is the efficiency of HLM companies in producing housing services. The second is the process of selection of tenants in the HLM, which might generate important welfare losses if the selected households are not those who value HLM most.19 19 The adverse consequences of the allocation process in the case of rent control are modeled in Glaeser (1996) and Glaeser and Luttmer (1997).

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Olsen, E. O., and Barton, D. M. (1983). “The Benefits and Costs of Public Housing in New York City,” J. Public Econ. 20, 299–332. Pitrou, L. (1997). “L’occupation du parc HLM”, in Les me´nages et leur logement: Analyse des enqueˆtes Logement de l’INSEE, Ministe`re de l’Equipement des Transports et du Logement, Collection Immobilier Finances, Economica 95–103. Tabard, N. (1993). “Des quartiers pauvres aux banlieues aise´es : Une repre´sentation sociale du territoire,” Econ. Statist. 270, 5–22.