The neighbor is king: customer discrimination in the housing market

Transcription

1 The neighbor is king: customer discrimination in the housing market Pierre-Philippe Combes y Bruno Decreuse z Benoît Schmutz x{ Alain Trannoy k March 19, 2010 Abstract This paper provides a way of detecting customer-based discrimination in the housing market using survey data. We build a matching model with ethnic externalities where landlords di er in the number of housing units they own within the same neighborhood. In the event of customers prejudice against the minority group, landlords who own several apartments discriminate more often than single-dwelling landlords because they internalize a higher negative externality on their probability to ll their other vacancies. Using the French National Housing Survey, we show that tenants with non-european origin are less likely to rent from a multiple-dwelling landlord than other tenants. We then show that the proportion of multiple-dwelling landlords at the local level is positively correlated with the probability of non-europeans to be living in public housing while this is not the case of other ethnic groups. Keywords: Customer Discrimination, Neighborhood Externalities, Housing Market JEL Classi cation: R21, J71 This paper has bene ted from discussions with Pierre Cahuc, Jan Eeckhout, Cecilia Garcia-Peñalosa, and Morgane Laouénan. We also wish to thank seminar participants at CREST, Insee, Paris School of Economics and University of Aix-Marseilles, as well as participants to the Journées d Economie Spatiale conference in Dijon. Data was made available by the Centre Maurice Halbwachs. This research was partly funded by the Direction de l Animation de la Recherche, des Etudes et des Statistiques (Dares). The usual caveat applies. y Greqam, CNRS, ppcombes@univmed.fr, z Greqam, University of Aix-Marseilles, decreuse@univmed.fr, x Greqam, University of Aix-Marseilles, benoit.schmutz@gmail.com, { Corresponding author k Greqam, EHESS, alain.trannoy@univmed.fr, 1

2 1 Introduction If discrimination in the housing market happens to be the main driving force behind urban patterns, this could dramatically a ect the design of any public policy geared towards improving the life of urban minorities (Zenou, 2009). For example, fair housing legislation could then become a useful tool against spatial mismatch on the labor market. That said, providing conclusive evidence of housing market discrimination remains a challenging empirical enterprise (Dymski, 2006). It either requires very detailed datasets (to estimate credible hedonic prices) or the conduct of randomized experiments (Yinger, 1986). Moreover, most research on housing market discrimination has not yet bene ted as much as it could have from Becker s (1957) theoretical insights on the rationale for customer discrimination, even though the housing market is the quintessential customer market (Lang, 2007) and it is now agreed that "most discriminatory behavior in the housing market is founded upon either the personal prejudices of agents or their belief that it is in their nancial interest to cater to the presumed prejudices of their Anglo customers" (quoted in Farley et al, 1994). In particular, the respective roles played by landlords and tenants prejudice in the discrimination process are seldom clearly disentangled, even though the parallel is easily drawn between landlords and employers and between customers and tenants (or home buyers). This paper addresses both the theoretical and empirical challenges: to our knowledge, it provides the rst theoretical model of customer discrimination in the housing market, which then paves the way to a simple test for customer discrimination. Becker s model of customer discrimination focuses on the labor market. In Becker (1957), rms do not hire black applicants for jobs in contact with customers because white customers racial prejudice lowers the productivity of black employees. Transposed to the housing market, Becker s reasoning means that tenants utility depends on the ethnic composition of the neighborhood. Prejudiced applicants care about the racial makeup of the neighborhood and they refuse to move in next to a neighbor whose ethnic type they dislike. Landlords know that and it may a ect their decision to accept a minority tenant regardless of their own prejudice. However, and unlike the clients of a particular rm, the ats and houses in a given neighborhood do not necessarily belong to the same owner. Accepting a minority tenant creates a negative externality at the neighborhood level. How landlords react to prejudiced whites depends on their ability to internalize the externality, which in turn depends on the number of apartments they own within the same neighborhood. Namely, the more apartments they own, the more sensitive to applicants prejudice and the more often they discriminate. In this paper, the negative externality created by a minority tenant takes place at the building level. We focus on the rental market and model landlords decision-making process in a dynamic framework with ethnic heterogeneity and matching frictions. 1 Rents are xed and some Whites are prejudiced against 1 Matching frictions are taken into account because the vacancy rate is generally quite high in the housing market. For 2

3 black tenants. Landlords have to choose whether they accept an applicant or not. We demonstrate that they may gain from refusing some types of applicants, even if this increases the mean delay to ll the dwelling. Our model gives a rationale for customer discrimination by showing that, provided enough applicants are prejudiced against another group of applicants, any landlord can nd himself in a situation where he would gain from refusing access to the members of this group. This result cannot be directly tested since both tenants and landlords may be prejudiced against the same group of applicants. To come up with an identi cation strategy between tenants and landlords prejudice, we go one step further and consider the situation where landlords are in fact heterogenous with respect to the number of housing units they own within the same building. Our model predicts that landlords who own several contiguous apartments discriminate more often than those who only own one apartment: indeed, the latter only care about the impact of their selection decision on their ability to rent out the same apartment again in the future, while the former also care about the impact of their decision on their current ability to rent out their other vacant lots. This leads to the prediction that, in the event of customer-based discrimination against black applicants, black tenants should less often have landlords who own several housing units within the same neighborhood. This prediction is testable on regular survey data and constitutes a direct test for the presence of customer-based discriminatory practices in the housing market. We then provide an empirical application on French data. The French case is relevant for two reasons. First, the di cult integration of ethnic minorities is a major public policy concern. The urban riots of Fall 2005, where more than nine thousand vehicles were arsoned in three weeks (with a climax of almost four thousand in three nights), showed the entire world that France also had race-relation issues, even though the mere possibility of a speci cally racial problem had long been denied by French political philosophy, intentionally color-blind. We argue that some of the di culties experienced by ethnic minorities in France may be attributed to housing market discrimination and its consequences, segregation and unemployment. The second reason for picking France is that there is little legal room for price discrimination in the French rental market, which ts well our xed-price model. Contrary to what happens on the home-sale market, the asked rent is posted on the ads and landlords are not allowed to increase it unilaterally before signing the lease. Moreover, a set of laws and regulatory practices prevents them from xing prices at their will on many segments of the private rental market. Price discrimination must be covert: it may involve the amount of the security deposit, or temporary discounts in exchange for improving the quality of the dwelling, but this cannot be the sole force behind the di erential treatment of undesired ethnic groups and most discrimination, if any, has to come through quantity rationing. First, we conduct a direct empirical test of the theory. This test lays on the assumption that, conditional on all other observable characteristics of the dwelling, applicants do not observe or do not care about their future landlord s type (whether she owns several contiguous apartments or not). In other instance, it is about 8% in France. 3

4 words, search is random. Under this assumption, the conditional allocation of tenants across landlords types can be interpreted as the result of a natural experiment, which only re ects the supply side of the market and does not raise any of the usual selection issues regarding the choice of residence. Using data from the French National Housing Survey, we show that rst-generation immigrants of non-european origin who live in privately-rented apartments are less likely to have a landlord who owns the entire building. In the absence of any conclusive alternative explanation, this result is interpreted as the expression of a supply constraint exerted by multiple-dwelling landlords upon minority applicants and constitutes a strong indication of customer-based discriminatory practices in the French private rental market. In a second stage, we make advantage of the fact that, unlike audit data, the National Housing Survey makes it possible to extend the analysis to the macroscopic consequences of customer discrimination on the housing consumption patterns of ethnic minorities. In particular, their overrepresentation in public housing has generally been accounted for, either by ethnic-speci c preferences, or by the history of immigration. We here provide an alternative explanation of such "social housing magnet" (Verdugo, 2009) where customer discrimination plays a key role. In that purpose, since housing consumption stems from a complex nexus of decisions about many possible outcomes, we restrict ourselves to a very simpli ed dual rental market where some segments are privately-rented by potentially discriminating landlords and the rest is administered by a supposedly color-blind public authority. Then, using a methodology derived from the empirical literature on spatial mismatch on the labor market, we construct a zone variable which de nes the relative weight of multiple-dwelling landlords in each local housing market. We nally show that the probability of tenants of non-european origin to be living in public housing is positively correlated with this zone variable, whereas the correlation does not stand for any other ethnic group. This second result gives valuable information regarding the impact of customer discrimination on the residential location of ethnic minorities. The direct test is a new way to provide empirical evidence on housing market discrimination. So far, two interesting methodologies have been developed in order to detect discrimination in consumer markets but both are subject to criticism (Yinger, 1998). The rst is to make use of available survey data and to look for the e ect of the ethnic status of consumers on the characteristics of the goods which they have access to. This is done to answer the following question: everything else equal, do minorities have to resort to lower quality goods and/or pay higher prices than other consumers? In the US, price discrimination in the housing market has been studied since the 1960s, when the growing expansion of the Afro-American and Hispanic middle class was starting to modify the racial makeup of Suburbia (Rapkin, 1966, King et al, 1973). Numerous studies based on hedonic methodology and geographical discontinuities show that Blacks often have to pay a premium to enter formerly all-white neighborhoods (Yinger, 1997). The use of large-scale representative surveys is very interesting from a policy-oriented viewpoint since it gives an idea of the aggregate impact of discrimination. However, this methodology requires to dispose of very 4

5 detailed information in order to minimize the risk that the observed pattern might be due to a third factor, either from the consumers side or from the suppliers side. This condition is even harder to meet when one thinks that tastes, which are largely unobservable, are likely to be partially ethnic-speci c. Moreover, this methodology does not provide evidence on discrimination in the making: how and why agents discriminate remains unknown and the phenomenon of discrimination, if attested, remains a black box. For all these reasons, most empirical evidence have come from pair-based audits, which highlight the role played by realtors. Many such audits have been conducted in the US since the late 1970s. For instance, using the results from an audit conducted in 1981 in Boston, Yinger (1986) shows that black applicants are o ered up to 30% fewer opportunities to visit housing units: two decades later, this gap has narrowed but has not closed and by far (Ondrich et al, 2006). Another example could be found in the Housing Discrimination Study of 1989, where a series of audits on 25 US metropolitan areas leads to another wave of evaluations. In one of them, Ondrich et al. (1999) explicitly distinguish between three possible causes of discrimination: agents prejudice, customers prejudice and agents misperception of Blacks preferences. As for the customer prejudice hypothesis, it is tested through three di erent channels. First, the authors look at the impact of the individual characteristics of black applicants that prejudiced neighbors are most likely to care about. Second, they identify the characteristics of the neighborhood which should in theory impact customer discrimination as well. Finally, they argue that a larger agency, which bene ts from a broader client base, may discriminate less. Although the research strategy is plausible, those three di erent channels can be criticized on the basis that one may come up with alternative interpretations for each variable. In order to capture the sole e ect of customer discrimination, we argue that one needs a variable which speci cally takes into account the impact of the neighborhood externality on realtors decision-making process. In addition, while similar audits should be conducted in France, they are costly 2 and their partial equilibrium framework makes their results di cult to interpret. To paraphrase Yinger (1998), an audit study only indicates the discrimination that occurs during certain phases of a market transaction when minority customers visit a random sample of rms and are quali ed to buy what the rm is o ering, not the average discrimination faced by an average minority customer. In other words, audits give causes, but not results. Our methodology borrows from both kinds of studies. We go back to the theory of discrimination and we extract one speci c rationale for discrimination out of the black box. We then derive an identi cation strategy which relies on fairly weak assumptions regarding consumers and suppliers tastes. Thanks to the use of an original variable on the geography of landlords real estate portfolios, we are able to isolate more precisely the impact of 2 Recently, eld experiments using newly available matching techniques, such as the Internet, have been conducted. In particular, Ahmed et al (2008) have provided strong evidence for gender and ethnic discrimination in the Swedish rental market, by looking at the reaction of landlords who had posted an ad on the web and were contacted by ctitious applicants with distinctively ethnic and gender names. 5

6 customer discrimination. Then, we make use of large-scale, easily available survey data, which allows us to pursue analyses at the aggregate level as well. Both aspects constitute a breakthrough in the literature on housing market discrimination. The paper is organized as follows: section 2 presents a matching model of landlord behavior with prejudiced tenants and its predictions in terms of discrimination. Section 3 tests these predictions on French data. Section 4 makes use of the previous results to propose a novel explanation of why ethnic minorities are overrepresented in public housing. Section 5 concludes. 2 Customer discrimination in the housing market: theory We consider a matching model of the rental market with ethnic heterogeneity and multiple-dwelling landlords. Landlords want to ll their vacancies and decide whether they screen some types of applicants or not. The systematic refusal of one type of applicant is called discrimination. We show that landlords who own several apartments in the same neighborhood are more likely to discriminate against black applicants. In other words, they are better o discriminating under a wider range of circumstances. These circumstances are de ned by the characteristics of the local housing markets: the matching and separation rates, and also the ethnic composition and the tastes of the population of applicants. 2.1 Set-up The city is made of identical buildings, each composed of two identical apartments. These buildings de ne the scale of the neighborhood externality: even if it is very small, it is not unrealistic, since many background e ects only take place within the same building (Goux et al, 2007). All apartments are rented out by landlords who live elsewhere. Landlords are heterogenous with respect to the number of apartments they own, which de nes their type k (k = 1; 2): type-2 landlords own an entire building, type- 1 only own one apartment. 3 However, a tenant is strictly indi erent between the two types. Applicants do not choose their location according to how likely they are to be matched with one type or another. Applicants are either white, in proportion p, or black. Prejudice is one-sided: a xed fraction of the population of Whites is prejudiced against Blacks, but Blacks are never prejudiced against anybody. 4 If they are matched with a black neighbor, prejudiced Whites refuse their match and keep searching. However, they do not move out if a black tenant moves in next to them. 5 Otherwise, applicants do not 3 We do not account for heterogeneity in the number of buildings owned by type-2 landlords. In that case, their strategy set would become much more complex. 4 US studies show that more than 70% of whites are not willing to move into a neighborhood which is more than 50% Afro-American, whereas more than 80% of Afro-Americans are willing to move into a neighborhood with only a few black neighbors (Farley et al, 1994). 5 From her observation of current trends in American neighborhoods, Ellen (2000) draws a two-sided conclusion. On the 6

7 behave strategically. They are not time-constrained and their decision to refuse a match is costless. Matching is random. Applicants do not observe the landlord s type, and cannot direct their search towards a particular type as a result. A given dwelling receives applications from potential tenants at rate. From landlords perspective, the parameter measures the e ciency of the housing market. It does neither depend on the applicant s race, nor on the landlord s type. When a match is completed, landlords receive a rent R, net of maintenance cost. The rent is ethnic-dependent, with R w R b. As all individuals pay the same price, this leaves the possibility that unobservable characteristics correlated with ethnicity make Blacks more likely to deteriorate the dwelling. Landlords may discriminate against Blacks for this reason, even though white tenants are not prejudiced. Sometimes, the tenant will leave his apartment. Separation follows a Poisson Law of parameter q. Finally, r is the discount rate. 2.2 Value functions Every apartment is de ned by the type of the tenant who lives inside it. It is either vacant (v), occupied by a white tenant (w) or occupied by a black tenant (b). We note ij k the expected pro t of a type-k landlord who owns a type-i (i = v; w; b) apartment, located in a building where the other apartment is type-j (j = v; w; b). A landlord k accepts any applicant i (i = b; w) given a neighbor j (j = v; w; b) if and only if ij k functions 1 (ij) k The ij k vj k. We simplify the notation of this acceptance condition and de ne the following dummy as: 8 < 8 (i; j) 2 fb; wg fb; w; vg ; 1 (ij) k = : 1 if ij k vj k 0 otherwise are de ned by two systems of steady-state equations, one for each type of landlord. The system for type-1 landlords gains puts together nine independent equations, one for each couple (i; j) 2 fv; w; bg 2. As for the type-2 landlords, the system for their gains is reduced to six equations, given the identity ij 2 ji 2. Let b =, w = 0 and i; j = b; w. With these notation conventions, we can write a simpli ed version one hand, white willingness to move into a neighborhood really seems to be a ected by the presence of African Americans; on the other hand, white willingness to remain in their current neighborhood is not clearly a ected by African Americans moving in. According to Ellen, this means that Whites use racial composition to stereotype neighborhoods, while they do not necessarily prefer to reside in all white neighborhoods. A more simple interpretation would be to assume that moving costs, which are already paid by prospective tenants, override the neighborhood externaliy. (1) 7

8 of these two systems. For a type-1 landlord, one gets: nh r ij 1 = R i + q vj h i r vj 1 = q vv 1 vj 1 1 ij 1 i 8 < + : h io + iv 1 ij 1 h 1 (1 j ) p 1 (wj) 8 r iv 1 = R i + q vv 1 iv < 1 + : r vv 8 < 1 = : +1 (bj) 1 (1 p) wj 1 vj 1 h bj 1 vj 1 1 (wi) 1 (1 i ) p iw +1 (bi) 1 (1 p) ib 1 (wv) 1 p [( wv 1 vv 1 ) + ( vw +1 (bv) 1 (1 p) bv 1 vv 1 1 )] + vb 1 vv 1 1 vv i i 9 = ; 1 iv 1 1 iv 1 9 = ; 9 = ; (2) (3) (4) (5) For a type-2 landlord, one gets: nh r ij 2 = R i + R j + q vj h i r vj 2 = R j + q vv 2 vj 2 2 ij 2 i 8 < + : h io + vi 2 ij 2 h 1 (wj) 2 p (1 j ) +1 (bj) 2 (1 p) wj 2 vj 2 h bj 2 vj 2 n r vv 2 = 2 1 (wv) 2 p [ vw 2 vv 2 ] + 1 (bv) 2 (1 p) vb 2 vv 2 To solve these systems, we rst assume values for the di erent dummies 1 (ij) k i i 9 = ; (6) (7) o (8) and then we check if the solutions we derive are compatible with these hypothetical values. If this is the case, it means we nd the set of optimal strategies. De nition 1. An optimal strategy is a couple of vectors n o i=b;w;j=b;w;v n 1 (ij) k ; solving equations (1), (2)-(5), and (6)-(8). k=1;2 ij k o i;j=b;w;v k=1;2 A discrimination strategy is de ned by the neighbor s and the applicant s types. For each type of landlord, there are sixty-four di erent cases to look after. 6 However, as long as R w > 0, a landlord is always better o with a white tenant than with a vacant unit. This leaves us with eight cases, for each type of landlord: one case when no applicant is ever refused, and seven cases when a black applicant might be discriminated against and be denied access to a housing unit. 2.3 Results Landlords may dispose of eight di erent strategies. First of all, accepting anyone remains a dominant strategy in many cases, because it does not require to keep one s unit vacant when it could have been 6 Let I = fb; wg and J = fb; w; vg. Then Card [I P (J)] = 64. 8

9 rented out. As for the seven strategies which involve some degree of discrimination, they are de ned by the type of neighbor who occupies the apartment nearby the one they are putting on the market. Precisely, these seven strategies are the following: I prefer keeping a vacant unit rather than renting it to a black applicant if the neighboring apartment is (1) occupied by a white tenant; (2) occupied by a black tenant; (3) vacant; (4) occupied by a black tenant or by a white tenant; (5) occupied by a black tenant or vacant; (6) occupied by a white tenant or vacant; (7) regardless of the situation of the neighboring apartment. Among those seven strategies, we distinguish two types of discrimination. Strong discrimination refers to cases where the landlord always discriminates. Weak discrimination corresponds to the case where the landlord only discriminates when the other dwelling is vacant. Proposition 1. Properties of optimal strategies (i) For all k = 1; 2, bb k < vb k ) bw k < vw k ) bv k < vv k (9) (ii) For all j = v; b; w, bj 1 < vj 1 ) bj 2 < vj 2 (10) Proposition 1 restricts the number of possible optimal strategies. Doing so, it sheds light on the various externalities involved by customer discrimination with multiple dwellings. Refusing a black tenant features an option value. In turn, this option value depends on the arrival rate of potential tenants, on the proportion of prejudiced customers, on whether the other dwelling is lled or not, and on whether it is rented to a black tenant or not. The larger the option value, the higher the risk of discrimination. Part (i) ranks option values and shows that there are only four possible optimal strategies for each type of landlord: they never discriminate, or they only discriminate when the other dwelling is vacant, or when the other dwelling is vacant or occupied by a white tenant, or they always discriminate. For instance, owing to customer discrimination, the value of a vacant dwelling is relatively low when the other dwelling is occupied by a black tenant. Indeed, prejudiced Whites will refuse to move in, thereby increasing the probability that the dwelling will stay un lled. So, if landlords discriminate in such a case, they always discriminate. Part (i) means that strong discrimination implies weak discrimination. Part (ii) reveals a fundamental property: given the other tenant, the fact that a type-1 landlord discriminates implies that a type-2 landlord discriminates. Customer discrimination implies that accepting a black tenant entails two externalities. The rst externality is static. Indeed, having a black tenant today reduces the chances that the other dwelling will be rented out by a white tenant. So the value of the other dwelling goes down. Type-1 landlords do not take this e ect into account. The second externality 9

10 is dynamic. Accepting a black tenant today a ects the future composition of the building. In turn, this composition may alter the chances to nd another tenant in case of separation. Both types of landlords face the dynamic externality, whereas only type-2 landlords internalize the static externality. They are more likely to discriminate as a result. We now emphasize the roles played by customer discrimination and market frictions. Proposition 2. Limit properties (i) If = 0, then type-1 landlords discriminate if and only if type-2 landlords discriminate, that is bj 1 < vj 1, bj 2 < vj 2 for all j = b; w; v (11) (ii) If tends to 0, landlords never discriminate, that is lim!0 bj k > lim!0 vj k for all j = b; w; v and k = 1; 2 Part (i) shows that type-1 and type-2 landlords behave similarly when there is no customer discrimination. In that case, the only reason why Blacks may be discriminated against is that the e ective rent (net of maintenance costs) is lower. Statistical discrimination becomes equally likely for both types of landlords. This result provides a simple strategy to test for the presence of customer discrimination on the rental market. If Blacks are discriminated against by multiple-dwelling landlords and not by singledwelling landlords, then it means that there are prejudiced tenants (Whites) and that landlords take them into account prior to renting the apartment to a black tenant. Part (ii) shows that discrimination requires market power. Landlords cannot discriminate when they have no chance of nding another tenant. Rejecting an application is a costly strategy as the corresponding option value is nil. To go beyond the limit properties of equilibrium strategies, we consider a parameterization of the model. We abstract from statistical discrimination and assume that R w = R b = 1. As for r and q, dynamic simulations were completed for a large range of values: between 0.1% and 1% for r (monthly interest rate) and between 0.01 and 0.1 for q, which corresponds to an average stay between 100 and 10 months. Both r and q act as deterrents against discrimination: if r is high, landlords care too much about current vacancy to discriminate; if q is high, accepting a black applicant has a limited impact on pro t, since the landlord is not stuck with a particular tenant for a long time. These two parameters are important, but they should not vary a lot across local housing markets. As a consequence, we focus on the other three parameters p, and, which are likely to drive most of the heterogeneity. Figure 1 draws the solids for which discrimination is a dominant strategy in the space (p; ; ) when landlords are unprejudiced. The results are displayed for an annual interest rate of 5% and for an average stay of 6 years (both values were chosen to be as close to our data as possible). 10

11 Figure 1: Triplets fp; ; g for which discrimination is a dominant strategy. The other parameters are R w = R b = 1, q = 1=6 and r = 5%. Figure 1 illustrates several features of the model. What strikes rst is that discrimination is often a dominated strategy. If Whites are locally outnumbered (p. 1=2) or if enough of them are unprejudiced (. 0:4), no unprejudiced landlord will ever discriminate. The same happens in the event of a completely frozen rental market (. 0:05). However, these threshold values would decrease with the addition of a pecuniary motive to discriminate. We also check that type-2 landlords always discriminate when type-1 landlords discriminate; and when both types discriminate, type-1 never discriminate more strongly than type-2. The main e ect of each of the three parameters goes in the expected direction: a higher p, a higher and a higher make it more pro table to discriminate. The e ect of and is unambiguous: if white applicants are more prejudiced, customer discrimination increases and, similarly, a more uid market makes it less risky to discriminate by ensuring that other applicants will be met shortly. In almost all cases, an increase in p also leads to an increase in discrimination: if more applicants are white, accepting a black applicant is more costly since it will be di cult to meet another black applicant in the future. However, when p gets close to 1, its e ect becomes ambiguous, especially for type-1 landlords. This re ects the fact that the dynamic externality is no longer a concern: if almost all applicants are white (and provided there still are some white applicants who are not prejudiced), accepting a black applicant will not increase the probability that the other apartment will be occupied by a black tenant when the landlord has to nd another tenant. 11

12 2.4 Testable prediction The model leads to an empirical strategy to test for the presence of customer discrimination in the housing market. Single- and multiple-dwelling landlords behave similarly when there are no prejudiced white tenants. By contrast, multiple-dwelling landlords are more prone to discrimination when there are prejudiced white tenants. Focusing on the tenant population and examining landlord s type provide a simple way to detect consumer discrimination. Prediction 1. If black tenants are less likely to have a type-2 landlord than white tenants, then there are prejudiced Whites in the rental market. The model predicts the distribution of landlord s type by ethnic group of tenants. In the absence of prejudiced Whites, black and white tenants are equally likely to have a multiple-dwelling landlord. The probability is equal to the proportion of dwellings owned by multiple-dwelling landlords. When there are prejudiced Whites, multiple-dwelling landlords may discriminate more than single-dwelling landlords. In that case, Black tenants are less likely to have a multiple-dwelling landlord. There may be up to three di erent situations which enable to identify the role of the landlord s type on the probability of Blacks to access the rental market: when type-2 landlords weakly discriminate and type-1 landlords do not discriminate at all, when type-2 landlords strongly discriminate and type-1 landlords still do not discriminate, and when type-2 landlords strongly discriminate and type-1 landlords also discriminate, but weakly. As long as one of these situations at least has an empirical counterpart, Blacks should be less likely to have a type-2 landlord. 2.5 Discussions In this subsection, we discuss the theoretical robustness of our test strategy to detect customer discrimination in the housing market. We introduce landlord s taste for discrimination and pecuniary externalities at the building level, and we discuss various ways to enrich the model Taste-based discrimination and statistical discrimination Introducing taste-based discrimination does not alter the working of the model. Suppose that a non-trivial proportion of landlords systematically refuse to rent their apartment to a black tenant. As far as this proportion is broadly the same among type-1 and type-2 landlords, the fact that landlords have a taste for discrimination does not a ect the theoretical prediction according to which black tenants should be less likely to have a multiple-dwelling landlord. Actually, the same remark holds for statistical discrimination. Our model assumes that the potentially negative e ects that Blacks may have on landlord s pro ts do 12

13 not change with landlord s type. Put otherwise, the test strategy is robust to various omitted factors provided that such factors are not correlated with landlord s type. However, the test strategy is not robust to omitted externalities at the building level. Consider the case of pecuniary externalities. Suppose that the rent net of maintenance costs is R b < R w in both apartments once a black tenant has been accepted in the building. It may be so if unobservable characteristics correlated with ethnicity make Blacks more likely to deteriorate the common property of the building. Accepting a black tenant in one of the two apartments lowers the value of the entire building. Type-1 landlords do not internalize this externality, while type-2 do. Therefore, Blacks could be less likely to have a type-2 landlord, even though there is no customer discrimination. However, such externalities are very associated with the formation of white prejudice. If black tenants deteriorate the common parts of the building, white tenants are likely to avoid black neighbors. From this perspective, the consideration of omitted externalities at the building level has more to do with the origins of racial prejudice than with a competitive theory for the underrepresentation of Blacks in rentals owned by multiple-dwelling landlords Endogenization of the parameters Many parameters of the model can be made endogenous. The parameter may depend on the proportion of black applicants and on ethnic-speci c rents net of maintenance costs. This would require specifying a matching function and the supply of buildings. Prejudice may also depend on the ethnic make-up of the population. Moreover, the proportion of black applicants may respond to discriminatory behavior. In particular, if p were made endogenous, discrimination might lead to segregation through the constitution of a dual housing market where landlords would specialize in one type of tenant or another. Those various extensions would enrich the theoretical model and help understand discrimination issues better. However, they would not a ect the test strategy that relies on individual discriminatory behavior. Optimal tenant acceptance or rejection, as described by Proposition 1, do not depend on the particular way to close the model. Rents could also be made endogenous in our framework. For instance, they could be bargained between the tenant and the landlord. Bargaining requires to set an outside option for the potential tenant. In case of agreement, the bargained rent would imply that tenant s utility ends up between the reservation utility and the highest level compatible with landlord s acceptance. As the latter utility level must be lower for a black tenant than for a white tenant, black tenants would pay higher rents at given reservation utility. When match surplus becomes negative, there is no rent compatible with landlord s acceptance and black applications get rejected. Assuming that match surplus is larger with white than with black tenants (that condition does not seem too demanding, but it depends on reservation utility that may vary across ethnic groups), the test strategy would be una ected. Indeed, multiple-dwelling 13

14 landlords would still account for the negative externality that a black tenant originates. Match surplus would be lower for those landlords than for single-dwelling landlords. In other words, multiple-dwelling landlords would reject black applicants more often than single-dwelling landlords. We do not elaborate more on this extension, since statistical regressions presented in the next section do not conclude that minority tenants pay higher rents, regardless of landlord s type A stronger de nition of prejudice We could add the possibility of a white ight, with prejudiced Whites moving out as soon as they have a black neighbor. How this stronger prejudice would a ect landlords behavior would depend on whether tenants prejudice is observable or not. However, in both cases, type-2 landlords will keep on discriminating more. For instance, in case prejudice is observable on tenants, type-2 landlords with a prejudiced white tenant in their other apartment will always reject black applicants, no matter what. Type-1 landlords, on the other hand, might care about knowing that they are about to make the neighbor move out, but this will not always prevent them from accepting a black applicant. In case prejudice is unobservable, both types will discriminate more often than with the previous de nition of prejudice. However, type-1 landlords still do not care as much as type-2 landlords about the impact of their acceptance decision on the probability that the other tenant might leave as the result Heterogeneity in building size and collusion behavior The discrimination strategies we depict have consequences in terms of long-run patterns of segregation: under weak discrimination, Blacks are underrepresented in the rental market; under strong discrimination, they are completely barred from it. However, if the goal of the model were to predict the allocation of tenants across types according to ethnicity, many other factors should be included, such as the history of ownership in the building and the heterogeneity of the housing supply with respect to the number of apartments within each building. This is not the purpose of the model, which only aims to identify individually optimal strategies and derive a prediction out of them. In that sense, the assumption of homogeneity of building size is justi ed. 7 The main theoretical drawback of a framework with only two apartments in the building is that it makes it di cult to rule out the possibility of collusion between the two type-1 landlords of the same building: if both landlords cooperate, they can no longer be distinguished from a type-2 landlord. Both features (heterogeneity in building size and the possibility of collusion between type-1 landlords), if included in the model, would decrease the probability to observe prediction 1 in the data. However, since the bias may only be downward, this does not a ect the relevance of the 7 The next section will show that using real data implies to compare type-n landlords (n 2), who own the entire building, to type-k landlords (k 2 f1; :::; n 1g), who do not. For a given building of size n, former type-1 landlords may then greatly di er from one another. The same is true across buildings, between former type-2 landlords. 14

15 test The home-sale market The separation parameter q is what mostly distinguishes our framework from a model of the home-sale market, given the one-shot dimension of a sale. Once the lot is sold, the seller is no longer interested in its future evolution, hence q = 0. Otherwise, the modelling of the home-sale market does not require many additional changes. We still consider a city of identical buildings with two identical apartments. These apartments belong to unprejudiced owners and they are for sale, for a lump-sum price. We distinguish between type-1 sellers, who only sell one apartment, and type-2 sellers, who sell both apartments simultaneously yet in two separate lots. Here, type-1 sellers will never discriminate out of the prejudice of white buyers. On the contrary, if the sale process is sequential and if applicants observe the type of their potentially future neighbor before accepting to buy the apartment, type-2 sellers may discriminate against Blacks who apply for the rst of their two apartments (once they have sold one apartment, type-2 sellers become type-1 and they stop discriminating). We do not elaborate more on this extension since we lack critical information regarding the type of seller homeowners have bought their dwelling from in the dataset we use. 3 Detecting customer discrimination This section tests for the presence of customer discrimination in the French housing market. We describe our dataset and notably the fact that tenants declare whether their landlord owns the entire building or not. The main test consists in confronting Prediction 1 to data. The test shows that tenants with non-european origin are less likely to rent from a landlord who owns the entire building. We then check that this result is robust to several possible issues. 3.1 Data Our dataset consists in the pooling of the last three 8 waves (1996, 2002 and 2006) of the French national housing survey ("Enquête Nationale Logement", henceforth ENL). The ENL is a very detailed crosssectional survey on a nationally-representative sample of around thirty thousand households, thirty- ve thousand dwellings and seventy- ve thousand individuals. The main drawback of the ENL is inherited from a French political tradition, which makes it still very controversial to collect racial or ethnic statistics. Consequently, we isolate a group of "Blacks" who are in fact rst-generation immigrants of non-european origin: both non-european citizens and people 8 Previous waves lack critical information about the origin of the respondent. 15

16 born out of Europe and not French at birth. Three quarters of them come from Africa, and most of the quarter left come from South and Southeast Asia. This measure of ethnicity misses a large number of people, because of colonial history (people born in the colonies were given French citizenship at birth), of French West Indies and of the increasing number of second, third and even fourth-generation immigrants of non-european origin in France. Moreover, it does not clearly disentangle ethnicity and immigration status. We address this issue in two ways: rst, we always consider the group of "European origin" (both non-french European citizens and people born out of France, in Europe and not French at birth) as a second control group, intermediate between "the French" and "non-europeans". This group should be subject to the same di culties as all immigrants, but its members are not expected to be discriminated against out of race. Second, we drop from our sample all the households whose respondent was not living in France or was living at someone else s place four years before. By doing so, we focus on immigrants who are really settled in France and may have started to integrate in the labor market. Each one of these two groups of not-too-recent rst-generation European and non-european immigrants represents around 4.5% of the population of households whose respondent had a place of her own four years before the survey. As shown in Table B1 (cf. Appendix B), non-europeans are overrepresented, both in the private rental market and in the market of apartments (broadly de ned here as dwellings which share a building with another dwelling). As a consequence, the share of non-european immigrants in the population of tenants in privately-rented apartments is twice as high as their share in the total population. Within this sub-population of tenants, Tables B2 and B3 (cf. Appendix B) show that non-european households are poorer and larger. Apart from individual characteristics, the ENL provides a lot of information about the comfort of the dwelling and about the tenure status. Most notably, it includes a dummy variable which indicates whether the apartment is located in a building owned by a single landlord or not. This variable is speci c to the ENL. It does not come from a scal le nor a cadastre. It is informed by the respondent himself or, if he does not know, by his neighbors or by the caretaker of the building. Even if this variable cannot be used to identify all the intermediate cases when a landlord owns several units within the building, but not the entire building, it gives an idea of the magnitude of this phenomenon of multiple ownership. According to our sample, about 40% of privately-rented apartments correspond to this type of multiple ownership. This rate is surprisingly high and varies a lot across regions and cities. It is partly inherited from local history of rms and families. It is also related to current economic conditions, and especially to the local price of land and real estate. From now on, a "multiple-dwelling landlord" is a landlord who owns an entire building, while a "single landlord" does not. Tables B4 and B5 (cf. Appendix B) show that both types of apartments are similar in terms of size and comfort. However, rents are somewhat lower and buildings are both older and smaller in case of multiple-dwelling landlords. Figures B1, B2 and B3 (cf. Appendix B) also show that multiple-dwelling landlords are not randomly allocated across 16

17 France: for instance, they are fewer in large cities and more generally, in populated areas. Moreover, their local importance is correlated with other characteristics of the local population, such as the rate of single-parent families. All these features will be accounted for in the speci cation used to test for customer discrimination in the next subsection. 3.2 Test of the main prediction Prediction 1 of our model states that there is evidence of consumer-based discrimination in the rental market if black tenants less often have a landlord who owns several apartments within the same building. In order to test this prediction, we use the subsample of tenants in a privately-rented apartment to estimate a probit model of the probability to have a landlord who owns the entire building. We regress this probability on a dummy variable which indicates whether the respondent is of non-european origin or not. If the coe cient on this variable is negative, there is consumer-based discrimination. As already mentioned, this variable of multiple ownership does not identify all the intermediate cases where landlords own several apartments but not the entire building. Similarly, the non-european variable misses many racial minority households who are not rst-generation immigrants. Both measurement issues are expected to lead to a downward bias on the coe cient on the origin of the tenant. Table 1 shows that the coe cient associated to non-european origin remains signi cantly negative, regardless of the speci cation. In particular, it does not decrease when we control for every available characteristic of the apartment itself (column 5): non-europeans remain less likely to have a landlord who owns the entire building by 4% and probably by more, since the coe cient is likely to be underestimated. We can interpret this negative coe cient in terms of customer discrimination if we are con dent that the other variables included in the regression control adequately for the main di erences in the housing supply and the marketing process of both types of landlords. In this perspective, it is interesting to see how the coe cient varies with the set of controls. Column 2 controls for individual characteristics and the coe cient goes up. As explained before, Non-European households are poorer and larger, while housing units owned by multiple-dwelling landlords are typically cheaper and contain more rooms. Non- Europeans should be overrepresented in housing units owned by a multiple-dwelling landlord as a result. On the contrary, controlling for département (district) xed e ects and city size in columns 3 and 4 reduces the coe cient. It is due to the fact that multiple-dwelling landlords are overrepresented in small cities and rural areas, while Non-European tenants, for many di erent reasons, mostly live in big cities. Finally, column 5 controls for dwelling characteristics. This does not substantially a ect the coe cient, which remains very similar to the raw e ect displayed in column 1. 17

18 Table 1: Probability to have a landlord who owns the entire building (1) (2) (3) (4) (5) Non-European origin ** ** ** ** *** (0.021) (0.020) (0.015) (0.018) (0.014) European origin (0.031) (0.035) (0.035) (0.035) (0.037) Individual characteristics X X X X district (département) xed e ects X X X City size X X Housing characteristics X Trend X X X X X N Pseudo-R Sample: all private tenants in a collective building, who had a place of their own in France four years before the survey Housing characteristics: comfort and size of the dwelling, rent by squared meters, age and size of the building, recent deterioration of common property (cf. Appendix A) Individual characteristics: age, gender and education of the respondent, household size, number of children, household income by consumption unit (2006 euros), year of arrival in the dwelling Standard errors are clustered by region-year Marginal e ects of a probit model Coe cient signi cance: *** : 1%, ** : 5%, * : 10% Source : Insee, ENL 1996, 2002 and Discussions Quality and price discrimination Both types of landlords should provide a similar good, so that all kinds of applicants are indi erently looking across both types. The set of controls makes it unlikely that the characteristics of the dwelling itself might be su ciently di erent between the two types of landlords to explain the exclusion of non- Europeans by di erences in tastes with respect to housing. Similarly, di erent prices between the two types of landlords should not play a large role in this phenomenon, since the last speci cation displayed in column 5 of Table 1 includes the level of rent among the right-hand side variables: even if the price elasticity of non-europeans demand for housing was di erent because of unobservable characteristics correlated with ethnicity, this last speci cation should take it into account. This addresses the concern that, compared to smaller landlords, multiple-dwelling landlords might behave as local price makers, which would enable the prejudiced fraction of them to set higher rents in order to impede the arrival of non-european applicants. In that case, regressions displayed in Table 1 would rather be a test of 18

19 market power than a test of customer discrimination. However, two arguments seriously challenge this interpretation. First, the regression results presented in Table C1 (cf. Appendix C) constitute a strong indication that, according to the ENL, non-european tenants do not seem to pay any kind of racial premium, either from single- or from multiple-dwelling landlords. Second, in spite of recent liberalization trends, the French private rental market remains very regulated Taste-based discrimination Second, one must be con dent that, in the absence of applicants prejudice, both types of landlords would equally provide their apartments to all kinds of applicants. However, racial preferences might be correlated with landlord s type. For instance, multiple-dwelling landlords seldom are immigrants and they are wealthier, hence more conservative. Both features make them more likely to be racially prejudiced and no data is available to control for it. However, personal prejudice should be playing a more important role if the landlord (or the real estate agent, in case the landlord is a rm) also lived in the neighborhood. While our data does not indicate when the landlord also lives in the building, it has been shown that this situation is largely restricted to small buildings of two or three apartments (Bessière et al, 2002), often located in rural areas and involving intergenerational coresidence. This speci city of the housing supply of multiple-dwelling landlords could explain a large part of our result, but Table 2a shows that this is not the case, since the e ect of being of non-european origin does not decrease with the size of the building The nature of the landlord: individuals and rms Another argument against the taste-based discrimination hypothesis relates to the nature of multipledwelling landlords: according to the ENL, a quarter of them are not individuals, but rms or public agencies, whereas this is only the case for 6% of single landlords. While it could make sense that prejudiced individual landlords seek to impose their tastes upon their realtors and impact the whole 9 Di erent laws and regulations circumscribe the level of freedom granted to private landlords, which depends on the type of dwelling they put on the market. For example, the law n de nes a set of restrictive constraints regarding the xing the rent of unfurnished dwellings. Until 1997, most of non new rentals had to be priced according to the current level of rent in the neighborhood. Rents are now xed freely before the arrival of a new tenant. However, once the lease is signed, the evolution of the rent is strictly regulated. During the time span of the lease, it is bounded by a quarterly index which is computed by the French National Institute of Statistics. When the lease has to be renewed, any larger increase must be justi ed by the landlord, who has to provide evidence supporting that the housing unit is notably underpriced. On a separate yet related subject, the profession of realtor is also quite regulated in France. For example, a ministerial order from June stipulates that realtors must clearly placard their fees within the premises: as a consequence, any attempt to practice price discrimination on the entry fee is a risky strategy, since they may be barred from the profession as a result. Finally, and perhaps most importantly, any signi cant increase between posted price (on the ad) and asked price (before signing the lease) may be considered as an expression of misleading advertising and, as such, be prohibited by article of the French Consumer Code. Prospective tenants can go to court to enforce this rule. 19

20 acceptance decision, in the case of the rm, the management of the housing stock is more likely to be delegated to several agents, some of whom will be prejudiced whereas others will not. Table 2a: Variations of column (5) in Table 1 by building size n 2 n 5 n 10 n 15 n 20 n 30 n 50 (1) (2) (3) (4) (5) (6) (7) Non-European origin *** *** *** *** *** *** ** (0.014) (0.01) (0.012) (0.015) (0.016) (0.028) European origin * (0.037) (0.036) (0.031) (0.038) (0.04) (0.06) (0.076) Controls X X X X X X X N Pseudo-R Sample: all private tenants in a collective building, who had a place of their own in France four years before the survey n refers to the number of apartments within the building Column (1) reproduces column (5) of Table 1 Controls: all controls included in the speci cation displayed in column (5) of Table 1 Standard errors are clustered by region-year Marginal e ects of a probit model Coe cient signi cance: *** : 1%, ** : 5%, * : 10% Source : Insee, ENL 1996, 2002 and 2006 However, rms may still discriminate, for at least two reasons. First, they are likely to have access to a larger information set on the key parameters of the real estate market, which should increase their propensity to engage in customer discrimination. Second, one may also assume that when rms are not reported as multiple-dwelling landlords because they do not own the entire building, they are nonetheless more likely to own more than just one apartment in the building, thanks to their greater nancial ability to engage in massive real estate investments. For these two reasons, the binary variable which indicates that the landlord is a rm may also be considered as a proxy for being a type-2 landlord. Compared to the multiple-dwelling landlord variable, its main advantage relates to the fact that it captures intermediate situations where the rm owns several apartments, yet not the entire building. On the other hand, being a rm probably impacts the matching process in many di erent ways. For example, it may be more easily observed by the applicant than being a multiple-dwelling landlord, which contravenes the random search assumption. Similarly, since rm landlords are also employers, their housing supply may not be available to the whole pool of applicants. Table 2b replicates the results displayed in Column (5) of Table 1 for variants of the dependent variable which account for the nature of the landlord. If we still think that, despite its limitations, the rm landlord dummy remains a valid proxy for landlord s type, we expect non-european tenants to be 20

21 less likely to have a rm landlord. Column (2) shows that this is actually the case. Conversely, columns (3) and (4) show the estimation results if the dependent variable depends on the realization of one of the two situations, at the exclusion of the other (in column (3), the landlord is not a rm but owns the entire building; in column (4), the landlord is a rm which does not own the entire building). In both cases, this characterization of the dependent variable implies to leave too many cases aside where non-europeans may still be discriminated against, hence the unsigni cant (column (3)) or very small (column (4)) coe cients. In addition, one may wonder whether the e ect found in Table 1 is not only driven by the behavior of those multiple-dwelling landlords which also are rms. If it were the case, we would expect non-europeans to be even more underrepresented within this smaller group of multiple rm landlords. Column (5), which displays the estimation results for the probability to have a landlord combining the two features, shows that this is not the case: the coe cient on non-european origin is signi cantly reduced. Moreover, there is no longer any observable di erence in the treatment of non- European and European immigrants. Finally, column (6) displays the estimation results for a dependent variable which indicates that the landlord either owns the whole building, or is a rm. Once again, the result con rms that both features make the landlord more likely to deny access to non-european applicants. However, since the coe cient is not signi cantly larger than the one we found in Table 1, and given the uncertainty regarding the relevance of the rm dummy, we think it is better to keep focusing on our initial variable of multiple ownership. 21

22 Table 2b: Variations of column (5) in Table 1: accounting for the nature of the landlord in the dependent variable Multiple Firm Multiple Firm non Multiple Multiple landlord landlord non rm multiple and rm or rm (1) (2) (3) (4) (5) (6) Non-European origin *** ** ** ** *** (0.014) (0.013) (0.017) (0.003) (0.010) (0.017) European origin * *** (0.037) (0.013) (0.031) (0.008) (0.007) (0.042) Controls X X X X X X N Pseudo-R Sample: all private tenants in a collective building, who had a place of their own in France four years before the survey Column (1) reproduces column (5) of Table 1 Controls: all controls included in the speci cation displayed in column (5) of Table 1 Standard errors are clustered by region-year Marginal e ects of a probit model Coe cient signi cance: *** : 1%, ** : 5%, * : 10% Source : Insee, ENL 1996, 2002 and Statistical discrimination On the matter of statistical discrimination, it has already been mentioned that the test strategy is not robust to omitted externalities at the building level. If unobservable characteristics correlated with origin make non-european tenants more likely to cause damages to common property in the building, multipledwelling landlords will be more likely to internalize this externality, regardless of tenants prejudice. This eventuality is partly taken into account in the last speci cation of Table 1, which controls for whether the respondent complains about recent deterioration of common property of the building. Moreover, if housing characteristics are adequately controlled for, non-european tenants are as likely as the other tenants to have witnessed this kind of deterioration in their building (regression results not shown here). However, both arguments are not compelling. A more clear-cut test of statistical discrimination would consist in replicating the test of the tenant model prediction on the market of privately-rented houses, where common property does not matter as much. Provided prejudiced applicants also care about their neighbors when they look for a house, this new test would enable us to assess the respective importance of the two e ects. Unfortunately, it is not possible with the ENL, which does not indicate landlord s type when the rental is not located in a collective building. 22

23 3.3.5 Could search be directed by heterogenous marketing channels? A last possible issue involves the di erences between the marketing process of both types of landlords. For example, single landlords may be more likely to use non-standardized advertising, where social networks help applicants be noti ed of a new vacancy. If, at the same time, non-european applicants are more likely to mobilize social networks when they search, they will more often be matched with single landlords. This may be due to ethnic-speci c search behavior, but also be endogenously exacerbated by discrimination in the more standardized segments of the market. This story can be tested with the ENL, which provides information on the way private tenants who have moved in for less than four years had heard about the place they currently occupy. According to the ENL, non-european applicants do mobilize social networks more frequently: on average during the decade , 33% of non-european private tenants who had recently moved in a new apartment had heard about it from a friend or a relative, while this was only the case of 22% of the other private tenants in apartments. However, multiple-dwelling landlords also seem to be largely bene ting from such informal networks. If anything, they bene t from them even more than single landlords, since, among all the tenants who had recently moved in their apartment, 27% of those with a multiple-dwelling landlord had heard about their apartment from a friend or a relative, while this was only the case of 20% of the tenants facing a single landlord. 10 Finally, Table 2c reproduces the estimation results of column (5) in Table 1 for this sample of recent tenants. Column (1) shows that the impact of being of non-european origin remains unchanged. When we control for the information channel, whether we only distinguish between social and institutional networks (column (2)) or also between di erent kinds of institutional networks (column (3)), this impact is not altered either. 10 Both di erences are signi cant at the 1% con dence level. 23

24 Table 2c: Variations of column (5) in Table 1: controlling for the information channel (1) (2) (3) Non-European origin ** ** ** (0.019) (0.020) (0.022) European origin (0.036) (0.036) (0.041) Friends or relatives X X Other Information channels X Controls X X X N Pseudo-R Sample: all private tenants in a collective building, who had a place of their own in France four years before the survey and who have moved in for less than four years Friends or relatives: binary variable equal to 1 if the current dwelling was found through friends or relatives All information channels: set of binary variables equal to 1 if the current dwelling was found through an ad, a rental agency, the employer, a public agency, or another channel Controls: all controls included in the speci cation displayed in column (5) of Table 1 Standard errors are clustered by region-year Marginal e ects of a probit model Coe cient signi cance: *** : 1%, ** : 5%, * : 10% Source : Insee, ENL 1996, 2002 and 2006 All things considered, we believe that the result displayed in Table 1 is robust enough to all these issues to constitute a strong indication that ethnic minorities su er from customer-based discriminatory practices in the French private rental market. 4 Discrimination and public housing ghettos In this section, we turn to the macroscopic implications of customer discrimination in the housing market. We show that the proportion of apartments owned by multiple-dwelling landlords is positively correlated with the probability to live in public housing for non-european immigrants, while this correlation does not stand for the French-born and the other immigrants. Provided this probability re ects, at least partly, the di culty to access the private rental market, this result gives valuable information regarding the impact of customer discrimination on the residential location of ethnic minorities. Given the high level 24

25 of concentration and isolation of the French public housing market, this result can even be considered as providing an alternative explanation of the existence of public housing ghettos in France. This explanation neither involves a magnetic e ect of the public housing supply on immigrants location decision (Verdugo, 2009), nor the aggregate e ect of preference-based tipping mechanisms (Card et al, 2008). Whether housing discrimination still is a major factor behind the persistent racial segregation found in U.S. metropolitan areas today is a fairly controversial subject (Ross, 2008), but as far as France is concerned, this result gives some ground to the "collective action racism" theory, according to which "ghettos are the result of collective action taken by whites to enforce separation from blacks" (Cutler et al, 1999). 4.1 The French public housing market: magnet or last resort? In France, public housing is a very large and old public program which dates back to the 1920s. Publiclysubsidized, rent-controlled housing units represent 40% of the rental market, 15% of the total stock of main homes. It is generally denoted by the acronym HLM, which stands for "Habitations à Loyer Modéré". Even if the HLM constellation is very diverse, in terms of quality, location and inhabitants, most of the HLM supply is located in derelict, suburban areas which have become ethnic ghettos along the past thirty- ve years (Laferrère et al, 2006). Non-European immigrants are notably overrepresented in the HLM complex: according to the ENL, more than 40% of non-european immigrants live in HLM, compared to about 15% of European immigrants and people of French origin. After controlling for di erences in socioeconomic characteristics, this gap is narrowed, but remains very high. It has been argued that this situation partly re ects the historical speci city of non-europeans housing demand. For instance, Verdugo (2009) nds some evidence of a causal relationship between HLM supply at the city level and the location decision of immigrants when they rst arrived in France, for a few non- European ethnic groups. From this starting point, one can imagine how HLM ethnic communities arose and have kept reinforcing ever since, sometimes with the direct help from the HLM agencies themselves, which practiced ethnic matching. However, this story does not explain why the overrepresentation of non-european immigrants is also true in ows, both within and into the HLM market. Table 4 displays the raw transition rates between households tenancy status. The time span is four years and we restrict the sample to households who have moved out at least once during these four years: it shows that non-european immigrants who were not initially living in HLM are more likely by more than 10 percentage points to end up living in one: 23% (28%) of non European homeowners (resp. private tenants) move back to a HLM, whereas it is only the case of 9% (resp. 18%) of European homeowners (resp. private tenants) and 10% (resp. 14%) of French-born homeowners (resp. private tenants). As for the group who was initially living in HLM, non-european immigrants are more likely by more than 20% to end up living in another HLM (69% against 41% of European HLM tenants and 44% of French-born HLM 25

26 tenants). These large di erences are not driven by di erences in socioeconomic characteristics, as shown by the last matrix ("French-born weighted"), which gives the mobility pattern of a counterfactual group of people of French origin, whose characteristics were matched to the characteristics of non-european immigrants. 11 In Appendix C, Table C2 displays the results of a test of likelihood ratio that shows that the residential mobility pattern of non-european immigrants remains di erent from any other group, which is not the case of European immigrants. Table 4 : Transition matrix of residential mobility by tenancy status for households who have moved out in the past four years Previous Status Current Status N Hom. sd HLM sd Priv. T. sd Total 7314 Homeowners 0.62 (0.49) 0.10 (0.30) 0.28 (0.45) Pop HLM 0.30 (0.46) 0.46 (0.50) 0.23 (0.42) Private Tenants 0.34 (0.47) 0.15 (0.36) 0.51 (0.50) N Hom. sd HLM sd Priv. T. sd French-born 6739 Homeowners 0.62 (0.49) 0.10 (0.30) 0.29 (0.45) 4010 HLM 0.31 (0.46) 0.44 (0.50) 0.25 (0.43) Private Tenants 0.35 (0.48) 0.14 (0.35) 0.51 (0.50) N Hom. sd HLM sd Priv. T. sd Non-European 314 Homeowners 0.44 (0.50) 0.23 (0.42) 0.33 (0.47) origin 609 HLM 0.20 (0.40) 0.69 (0.46) 0.10 (0.30) 1225 Private Tenants 0.17 (0.37) 0.28 (0.44) 0.56 (0.50) N Hom. sd HLM sd Priv. T. sd European 261 Homeowners 0.69 (0.46) 0.09 (0.29) 0.21 (0.41) origin 130 HLM 0.41 (0.49) 0.41 (0.49) 0.17 (0.38) 393 Private Tenants 0.39 (0.49) 0.18 (0.38) 0.44 (0.50) N Hom. sd HLM sd Priv. T. sd French-born 6601 Homeowners 0.64 (0.48) 0.09 (0.29) 0.26 (0.44) weighted 3930 HLM 0.36 ( (0.49) 0.22 (0.42) Private tenants 0.40 (0.49) 0.15 (0.36) 0.45 (0.50) Sample : all households who had a place of their own in France four years before the survey and who have moved out during these four years. Example: among the 4010 households of French origin who where living in HLM four years before the survey and have moved in the past four years, 31% have become homeowners, 44% still live in a HLM and 25% are now renting a place on the private rental market. Source : INSEE, ENL, 1996, 2002 and These characteristics are: age, gender, education and employment status of the respondent, total household size and number of children in the household. The employment status corresponds to the situation of the respondent four years before the survey. It was grouped into four categories: employed, unemployed or inactive, retired, student or in the military. 26

27 Moreover, if HLMs were speci cally chosen by non-europeans for cultural reasons, they should be enjoyed more by non-europeans than by other tenants, whereas our data seems to indicate that the opposite is actually true: if anything, non-european HLM tenants are less satis ed with their dwelling than other HLM tenants. Even after controlling for any observable characteristic of the dwelling, a non- European HLM tenant is still 5% more likely to declare that he would move out if he could than his French or European counterparts (cf. Table C3, Appendix C). 4.2 Discrimination with public housing as outside option We argue that the overrepresentation of non-europeans in a type of housing that they do not particularly like but where they are more easily accepted partly re ects customer discrimination on the private housing market. People make residential choices, even HLM tenants. Notably, they choose whether trying to rent a place in the private market, or staying in HLM. Each option has expected gains net of costs, and individuals compare the gains attached to each option prior to selecting one of them. Discrimination in the private rental market alters residential choices through two e ects, one direct e ect and an indirect e ect. First, if some groups of HLM tenants are barred from some segments of the private rental market, they will need more time to nd a place, hence they will automatically stay longer in HLM. This is the direct e ect. Second, the value of search in the private rental market is lower, which deters HLM tenants from even trying their luck. This is the indirect e ect. Its magnitude depends on how people react to what they perceive of their opportunity set. Multiplicative e ects may explain why a small di erence in individual treatment can lead to a large di erence in aggregate outcomes. We provide a simple framework to illustrate how these two e ects may come in play. We consider a tenant of ethnic group i = w; b who has two choose whether to stay in HLM or search for a place in the private rental market. Tenants from both ethnic groups are exactly alike, apart from their probability x i to be accepted by a private landlord whom they have been matched with. They compare their utility level in HLM, U HLM i to their utility level in a private rental, Ui P R. We normalize the instant utility people derive from living in HLM to zero and let a be the corresponding utility in a private rental. We assume that the supply of public housing is not a source of concern for anybody. Reality is more complicated, given the diversity within the HLM complex, but it is a reasonable rst approximation. Here, public housing acts as a complete safety net: people always have immediate access to a HLM and once inside, HLM tenants cannot be evicted. On the contrary, they have to search for a private rental, with no guarantee of success. The search cost is c and matching occurs at rate : A match between a private landlord and a type-i tenant is completed with probabiliy x i. Moreover, private tenants are never secured in their dwelling. With rate, which may for example relate to a drop in income, they will have to depart and go back to a HLM. Finally, r is the discount rate. 27

28 The value functions U HLM i and U P R i are given by the following equations: rui HLM = max 0; c + x i U P R i rui P R = a + Ui HLM U P R i Ui HLM (12) (13) An HLM tenant will enter search if and only if c=a x i = (r + ) Let c=a follow the distribution. The proportion of HLM tenants ready to enter search is equal to (x i = (r + )). If we note HLM i the long-run probability of a tenant i to be living in HLM, we now have: HLM i = + x i (x i = (r + )) (14) The probability HLM i is an increasing function of the return rate and a decreasing function of the matching parameter and the acceptance parameter x i : Since the probability to be discriminated against is simply equal to (1 x i ), the expression x i (x i = (r + )) captures both the direct and the indirect e ects of discrimination: x i is the probability of success given that people search and (x i = (r + )) indicates how likely people are to start searching. We now specify x i. We still consider a framework where only blacks may be discriminated against. Consequently, x w = 1. We then draw from the results of Section 3 to write an expression of x b which depends on the probability for an applicant to meet a multiple-dwelling landlord. We have: x b = (1 ) Share I MD + (1 Share) I SD (15) where Share is the proportion of multiple-dwelling landlords in the local market of privately-rented apartments, is the proportion of prejudiced landlords who will refuse black applicants regardless of whether it is a dominant strategy or not and I MD (resp. I SD ) is the probability for a black applicant to be accepted by an unprejudiced multiple-dwelling (resp. single-dwelling) landlord. The e ect of Share on HLM b is equal to: 0 dhlm b dshare = (HLM b) xb r+ A 41 + x r + xb r+ xb r+ 13 A5 (1 ) I SD I MD (16) where (:) = 0 (:). Equation (16) shows that, if (x i = (r + )) is very large, then the e ect of Share is much larger than the sole e ect of customer discrimination as measured by I SD I MD. This is the case if c=a is closely distributed around x i = (r + ). There are other multiplicative e ects which have not been taken into account here. For example, the ethnic composition of the di erent segments of the rental market (HLM, private with single-dwelling landlord, private with multiple-dwelling landlord) should also impact white willingness to come and live in one of them. Another important issue concerns homeownership. Since Blacks, for many reasons which are not documented here, are also largely excluded from the home-sale market, prejudiced Whites may use 28

29 homeownership to enter homeowners neighborhood and avoid black neighbors as a result. All these issues aside, we at least know that if there is customer discrimination, then I SD I MD, hence dx b =dshare 0 and dhlm b =dshare 0: On the contrary, since dx w =dshare = 0, then dhlmw=dshare = 0. This allows us to establish the following prediction: Prediction 2. If there is customer discrimination in the private rental market, then the probability for black tenants to be living in public housing is positively correlated with the proportion of multiple-dwelling landlords in the private rental market. This is not the case for white tenants. Prediction 2 can be tested empirically using the same data as in Section Empirical Strategy We focus on the subsample of tenants in the public and private market. Given our theoretical framework, we expect non-europeans to be more excluded from the private rental market in the places where more landlords own entire buildings (Share high), whereas this local rate of multiple-dwelling landlords should not have any impact on the probability of the other tenants to enter the private rental market. For each household (i), living in area z (i), we construct the zone variable Share z(i) as the proportion of multiple-dwelling landlords in the market of privately-rented apartments in area z (i). Then, we regress the probability for the household to be living in HLM on this zone variable. The use of local averages as explanatory variables has been largely used in the spatial mismatch literature on the labor market. For instance, Hellerstein et al. (2008) regress the probability for Afro-Americans to be unemployed on very local employment rates (computed for the census track), controlling for MSA xed e ects. Our approach deals with much larger geographical units, since we compute Share z(i) at the département level and control for region xed e ects. However, a focus on very small spatial units would not t our purpose as well: while Hellerstein et al. take residential location as given and look at its impact on employment, we are interested in the residential location process itself. Along this process, households must generally be considering a wider range of location opportunities than the small census track. For each group of tenants, we consider the following equation of the probability to be living in public housing: 8e (i) 2 ff; E; NEg ; Pr (HLM i ) = e(i) Share z(i) + X i e(i) + W z(i) e(i) + " i (17) where a household i of ethnic group e (i) is either French (F ), of European origin (E) or of non-european origin (NE). Each household has individual characteristics X i and shares other zone characteristics W z(i) with others. The X i are usual sociodemographic variables, including the level of income by consumption unit. The W z(i) are region-year xed e ects and city size-year xed e ects: 12 they are included to account 12 There are 22 regions and 9 di erent categories in the city size variable we use. 29

30 for the e ects of the local HLM supply-demand equilibrium, and, more generally, for any contextual e ects. As for the variable Share z(i), it is computed, for each wave, at a smaller scale than the region: the "département", equivalent to a district. 13 Consequently, the measured impact of Share z(i) is identi ed by its variations at the département level within cities of a speci c size in a speci c region, at a given time. Prediction 2 can be rewritten as: 4.4 Results 8 < : F = E = 0 NE > 0 We estimate a probit model of Pr (HLM i ) on ve di erent samples of tenants: total population, Frenchborn, immigrants, European immigrants and non-european immigrants. Table 6 displays the estimation results of the marginal e ect of Share and household income. 13 There are 96 départements in France, on the mainland. We do not claim that each value of Share we compute is perfectly representative of the housing market of the département. However, this could just lead to more noise and bias our estimates downwards. Moreover, we follow in that respect the methodology used in Hellerstein et al (2008), who compute local unemployment rates on any neighborhood provided it is the place of residence of at least one individual. Figures B2, B3 in Appendix B show that the variable Share takes on many di erent values. Figures B4 shows that the distribution of Share on the total population is almost normally distributed, yet somewhat skewed to the right. (18) 30

31 Table 6: Probability to be living in HLM : the role of the Variable Share Total French- All French- European Non-European pop. born immigrants born immigrants immigrants (1) (2) (3) (4) (5) (6) Share *** *** (0.06) (0.05) (0.103) (0.05) (0.129) (0.104) Household income -5.75*** -7.39*** *** -7.74*** 2.2 (1.75) (0.96) (1.72) (0.96) (2.11) (3.04) Other controls X X X X X X N Pseudo-R Sample: tenants who had a place of their own in France four years before the survey Each column displays the estimation results on a di erent sample, except (2) and (4) Household income by consumption unit (millions of 2006 euros) Other controls include: individual characteristics, city size-year xed e ects, region-year xed e ects,and a trend. Individual characteristics: gender, age and education of the respondent, household size and number of children Standard errors are clustered by region-year Marginal e ects of a probit model Coe cient signi cance: *** : 1%, ** : 5%, * : 10% Source : Insee, ENL 1996, 2002 and 2006 Results strongly match prediction (18). The variable Share is not correlated with the probability of French-born to be living in HLM (column 2) whereas its associated coe cient is positive and signi cant on the probability of immigrants (column 3). However, if we break the sample of immigrants into Europeans and non-europeans, we observe that this positive coe cient is only due to the e ect on non-europeans (column 5 and 6). Another interesting feature of these results concerns the coe cient on income, which varies a lot according to the population of interest: it is unsurprisingly large and negative if we consider all tenants (column 1), non-immigrants (column 2) or European immigrants (column 5). On the contrary, it becomes completely unsigni cant for the non-european sample (column 6): we think this re ects the degree of constraint experienced by this group, where people are not able to sort between public and private rental markets according to their level of income. 14 This result is robust to numerous speci cation and sampling variations. Table 7a shows that it is not driven by the xed e ects speci cation (line b), nor by a spurious correlation of Share with the level of the local HLM supply, i.e. the proportion of HLMs in the total housing market of the département, as measured in the 1990 French Census (line c). The correlation 14 However, this interpretation is weakened by the fact that non-european tenants are less heterogenous with respect to household income. Indeed, the standard deviation of this income variable is 30% lower for this group. 31

32 remains stable if we control for an indicator of quality (or attractiveness) of this HLM supply, measured by the vacancy rate within the local HLM stock (line d). 15 Finally, it is not a ected if we control for the local proportion of non-european immigrants and of European immigrants, as measured in the 1990 French census as well (line e). Table7a: The marginal e ect of Share on the probability to be living in HLM: Speci cation variations Total French- All French- European Non-European pop. born immigrants born immigrants immigrants (1) (2) (3) (4) (5) (6) Table *** *** (0.06) (0.05) (0.103) (0.05) (0.129) (0.104) (a) N Pseudo-R No Control for city size * *** (0.067) (0.051) (0.12) (0.051) (0.122) (0.118) (b) N Pseudo-R Control for the HLM supply * ** at the district level (0.038) (0.035) (0.130) (0.035) (0.125) (0.164) (c) N Pseudo-R Control for the HLM vacancy *** *** rate at the district level (0.065) (0.054) (0.105) (0.054) (0.134) (0.102) (d) N Pseudo-R Control for the proportion of ** *** the two groups of immigrants (0.052) (0.047) (0.095) (0.047) (0.127) (0.092) at the district level (e) N Pseudo-R (a) reproduces the rst two and the last two lines of Table 6. (b) to (d) display the results for these four lines in case of a change in the speci cation Source : Insee, ENL 1996, 2002 and 2006; Census 1990; Enquête Parc Locatif Social, 1996 Table 7b shows that the result remains almost unchanged if we include in the sample anyone who did not live in France or did not have a place of his own four years before the survey (line b) or if 15 We use a speci c survey entitled "Enquête Parc Locatif Social" (EPLS) from 1996 to compute these vacancy rates. 32

33 we restrict the sample to the population who lives in a département which is important enough in the survey to compute Share on at least 30 observations (line c). Finally, it is also robust to the inclusion of homeowners in the sample (line d). In this last case, the estimated coe cient on Share is much lower, which con rms our assumption regarding the separation of the rental market and the home-sale market. Table 7b: The marginal e ect of Share on the probability to be living in HLM: Sampling variations Total French- All French- European Non-European pop. born immigrants born immigrants immigrants (1) (2) (3) (4) (5) (6) Table *** *** (0.06) (0.05) (0.103) (0.05) (0.129) (0.104) (a) N Pseudo-R Including the households who *** *** did not have a place of their own in (0.059) (0.047) (0.101) (0.054) (0.121) (0.098) France four years before the survey (b) N Pseudo-R Only in départements where Share 0.19* *** *** is computed on at least 30 (0.111) (0.101) (0.084) (0.101) (0.193) (0.074) observations (c) N Pseudo-R Including homeowners * *** (0.017) (0.016) (0.053) (0.016) (0.045) (0.059) (d) N Pseudo-R (a) reproduces the rst two and the last two lines of Table 6 (b) to (d) display the results for these four lines in case of a change in the speci cation Source : Insee, ENL 1996, 2002 and 2006 The estimated coe cient is high compared to the estimation results of Section 3, which suggests that large multiplicative e ects of customer discrimination probably come in play. However, if we think that its magnitude is correct, this means that an increase in one standard deviation in Share increases by 6% (resp. 3.5%) the probability of non-european tenants (resp. households) to be living in public housing. This result can contribute to a more general theory aiming at explaining the existence of ethnic enclaves in public housing. For now, it stems from a reduced-form speci cation, mixing together both the direct 33

34 e ect of customer discrimination and an indirect e ect where discrimination eventually discourages non- European households from trying to enter the private housing market. The respective importance of these two e ects should be empirically evaluated. We leave this for future work. 5 Conclusion The nature of the links between discrimination and urban patterns has long been argued about. However, most works on the subject miss the role played by the structure of real estate ownership, although it is a key background factor for apprehending the diversity of urban patterns. This paper is an attempt to illustrate why ownership structure matters, both theoretically and empirically. We construct a matching model with ethnic externalities where landlords are heterogeneous with respect to the number of housing units they own within the same neighborhood. We show that, regardless of their own preferences, landlords who own several units are more likely to discriminate against ethnic minorities if these minorities are subject to the prejudice of a fraction of the population of mainstream tenants. This prediction and its implications are then tested and never rejected on French data, which con rms the existence of customerbased discriminatory practices against immigrants of non-european origin on the French housing market. However, we believe that our empirical investigation could fruitfully be adapted to other countries as well. Moreover, a slightly similar framework could be applied to the detection of coworker discrimination in the labor market. In particular, it would be interesting to compare the hiring patterns of very small rms who already employ someone, to independents who hire their rst employee, in case a fraction of the labor force is racially prejudiced. Housing market discrimination hinders the residential mobility of ethnic minorities. In France, it certainly is one of the main reasons why non-european immigrants, and especially African immigrants, remain stuck in the HLM complex, a fact we also largely document. As a consequence, these populations cannot easily take advantage of employment opportunities when those are located in another city or region and they su er from a situation of regional or even national spatial mismatch, which should account for at least part of their much higher unemployment rate. The social consequences of housing market discrimination are therefore so negative that they justify the intervention of policymakers. Two kinds of policies may be implemented. First, one should take advantage of the fact that larger landlords can be more easily monitored. Therefore, it should not be impossible to impose ethnic quotas upon them, particularly when they are not individuals, but rms. This is currently starting to happen on the French labor market and could be replicated on at least some portions of the housing market. Second, it is possible to think of a taxation design which would incite multiple-dwelling landlords to scatter their real estate portfolio: for instance, as soon as two of their apartments are registered at the same address, landlords could be submitted to a higher tax rate. 34

35 A Proofs of propositions 1 and 2 Forthcoming B Descriptive Statistics Table B1: tenure status by immigration status French European Non-European origin origin origin Private rental (0.396) (0.390) (0.453) Apartment (0.482) (0.494) (0.425) Privately-rented apartment (0.326) (0.335) (0.431) N Sample: all households who had a place of their own in France four years before the survey Source : Insee, ENL 1996, 2002 and 2006 Table B2: respondent characteristics of the population of tenants in apartments (by immigration status) Respondent French European Non-European origin origin origin Woman (0.493) (0.485) (0.433) Age (17.80) (18.18) (13.75) Middle school degree (0.462) (0.419) (0.375) High school degree (0.306) (0.204) (0.270) University degree (0.476) (0.410) (0.444) N Sample: all tenants in privately-rented apartments who had a place of their own in France four years before the survey Source : Insee, ENL 1996, 2002 and

36 Table B3: household characteristics of the population of tenants in apartments (by immigration status) Household French European Non-European origin origin origin Household income* ( ) ( ) ( ) Household size (1.079) (1.189) (1.685) Number of children (0.780) (0.825) (1.331) Year of arrival in the dwelling (11.1) (11.3) (8.6) N *Income by consumption unit (2006 euros) Sample: all tenants in privately-rented apartments who had a place of their own in France four years before the survey Source : Insee, ENL 1996, 2002 and

37 Table B4: Characteristics of the apartment (by landlord s type) Table B5: Characteristics of the building (by landlord s type) Apartment Multiple Single Building Multiple Single landlord landlord landlord landlord Number of rooms (log) Number of levels (0.465) (0.485) (2.908) (3.726) Area (log) Number of apartments (0.447) (0.463) (27.31) (43.88) Rent by sq. meter Built in (in 2006 euros) (4.296) (4.980) (0.435) (0.487) Balcony Built after (0.454) (0.499) (0.390) (0.459) Private outdoor space Recent deterioration (0.280) (0.189) of common property (0.352) (0.389) Large bathtub N (0.494) (0.462) Sample: all private tenants in privately-rented Safety device apartments who had a place of their own (0.462) (0.493) in France years before the survey Parking space Source : Insee, ENL 1996, 2002 and 2006 (0.448) (0.483) Tenant su ers from cold (0.382) (0.364) Tenant su ers from noise (0.499) (0.497) N Sample: all private tenants in privately-rented apartments who had a place of their own in France years before the survey Source : Insee, ENL 1996, 2002 and

38 1 Fraction of multiple landlords 0,75 0,5 0,25 0 Rural Less than 5,000 inh. 5,000 to 10,000 inh. 10,000 to 20,000 inh. 20,000 to 50,000 inh. 50,000 to 100,000 inh. 100,000 to 200,000 inh. 200,000 to 2,000,000 inh. Paris region City size Figure B1: City size and fraction of multiple landlords in the private market of apartments 38

39 1 Fraction of multiple landlords by département (National Housing Survey 1996, 2002 and 2006) 0,75 0,5 0, Population in the département (Census 1990) Figure B2: Total population of the département and fraction of multiple landlords in the private market of apartments 39

40 1 Fraction of multiple landlords by département (National Housing Survey 1996, 2002 and 2006) 0,75 0,5 0,25 0 0,06 0,07 0,08 0,09 0,1 0,11 0,12 0,13 0,14 0,15 Fraction of single parent families by département (Census 1990) Figure B3: Fraction of single-parent families and fraction of multiple landlords in the private market of apartments 40

41 Figure B4: The distribution of Share in the total population Figure A4 shows that the variable Share is almost normally distributed, yet somewhat skewed to the right. The normal distribution its distribution is closest to has mean 0.46 and standard deviation