Revealing social discrimination is crucial for public policy. Surveys based on self-reporting can help identify the discriminatory behaviours that individuals feel they have experienced. Other methods measure this phenomenon by creating profiles of fictitious applicants and submitting their applications to employers, for example. This testing method has uncovered clear evidence of job discrimination based on origin. In this article, the authors use this method to measure the obstacles certain family types encounter in renting private housing in Paris. Do lone-parent families, more often lone mothers with fewer resources, face greater discrimination than others as a result?
1Lone-parent families [1] are increasingly common in France, especially in Paris. According to the 2014 census, they account for 30% of households in the city, one of the highest proportions in metropolitan France. Women are the household head in 85% of these families, although the share of fathers is increasing slowly (from 11% in 1990 to 15% in 2011; Acs et al., 2015). Lone mothers are more economically active than women in couples and more often unemployed, with twice as many affected by poverty as partnered women (Drieux et al., 2016). Lone parenthood is most often the consequence of a separation or a death. In the life trajectory of lone mothers with children, finding a place to live on the private rental market after separation is a major challenge, particularly in Paris where such families are less frequently homeowners or social-housing tenants than elsewhere (Decondé et al., 2013). However, while extensive research on discrimination has been conducted in France since the early 2000s, only a limited range of causes (sex, origin, and place of residence) and markets (mainly the labour market) have been covered. Discrimination based on family status is one of the 25 forms of discrimination prohibited by the penal code and the labour code which provide a legal definition of direct discrimination (Défenseur des droits, 2018), yet few studies focus on access to housing, and none take family status into account. This knowledge gap needs to be filled.
2This study uses an experimental protocol to measure discrimination based on family status in access to private rental accommodation in Paris. Four fictitious profiles of rental applicants were constructed. One corresponds to a couple with two children, and the other three to lone parents, one man and two women. One of the lone mothers has a secure job and income as a civil servant. Between early December 2017 and late March 2018, four inquiries including a request for an appointment to visit were sent in response to 791 advertisements for apartments to rent, i.e. 3,164 messages (791 × 4). Our study is a statistical analysis of the answers to these inquiries. We distinguish between the advertisements placed by private landlords and those published by letting agents so that any specific characteristics of housing-market intermediaries and their propensity, or otherwise, to mitigate discrimination can be identified.
3The Paris housing market is well suited for this study because it involves a very large number of transactions, and the proportion of lone-parent families is high. It is not unusual for several lone parents to apply for the same apartment, so a testing experiment on housing discrimination is likely to go undetected. This market is also very tight, a situation liable to foster discrimination. Like all measures of discrimination based on testing campaigns, our study provides no more than a partial snapshot of the local situation at a particular moment. It is a first attempt to measure direct and objective discrimination in access to the Parisian private housing market on grounds of family status.
4The article is organized as follows. Section I reviews the literature on the housing situation of lone-parent families. Section II describes the different testing methods and Section III the protocol used for our study. The main descriptive statistics and the test results are detailed in Section IV, and Section V presents an econometric analysis. The scope and the limitations of our study are given in the conclusion.
I – The housing situation of lone-parent families
5While the classic model of the nuclear family remains dominant in France, new family types such as lone-parent families and stepfamilies are becoming increasingly frequent. Since the 1960s, the share of lone-parent families has increased steadily as parental unions have become more unstable. In 2009, 21% of children were living in a dwelling with just one enumerated parent, compared with 8% in 1968 and 11% in 1990 (Chardon et al., 2008). This demographic trend is observed throughout Europe (Keilman, 1987), with variations across countries or regions (Chambaz, 2001). Of course, the proportion of lone parents remains low in absolute terms. According to the 2009 census, 6.13% of women were lone mothers, and just 1.28% of men were lone fathers. These figures have more than doubled in 30 years, however. In the 1982 census, the proportions were 3.04% for women and 0.54% for men (Toulemon, 2012).
1 – Lone parents in Paris
6Lone-parent families are especially numerous in Paris. According to 2014 census data, they represent 18.4% of Parisian households and 32.3% of households with children. This is the second highest proportion in all the departments of metropolitan France (after Pyrénées-Orientales). A study by the Paris Urbanism Agency (Atelier parisien d’urbanisme), using data from the 2011 national family and households survey (Famille et logements), counted 78,200 lone-parent households with at least one child aged under 25. Under this definition, these households represented 28% of Parisian families, a higher proportion than elsewhere in the Paris region (23%) and in all metropolitan France (22%).
7Who are these lone-parent households? They do not form a clearly defined social category or a homogeneous social group. The situations of the youngest, least educated mothers affected by high levels of unemployment are very different from those of older mothers or lone fathers (Algava, 2002). They do share some common traits, though. First, because children in lone-parent families are most often cared for by the mother, most lone parents are women. In the year following parental separation, 76% of minor children are cared for by the mother only and 9% by the father only. The remaining 15% are in alternating custody (Bonnet et al., 2015), an increasingly frequent arrangement, especially for high-earning parents (Algava et al., 2019). Moreover, while the living standard of lone-parent families varies considerably across households, it is generally lower than that of couples with children. Families with three or more children are under-represented in lone-parent households, and the share of these households decreases sharply with the number of children. In Paris, 57% of lone-parent households have one child (vs. 41% of two-parent families and 28% of stepfamilies), 32% have two children (vs. 38% of two-parent families and 44% of stepfamilies), and 11% have three or more (vs. 21% and 28%). Their exposure to poverty increases with the number of children (Bargain et al., 2017).
8Family policy at the national level and welfare policies in Paris have been addressing this problem for many years, providing targeted support for lone parents through public transport subsidies and preschool childcare support via specific cash or non-cash benefits. Lone-parent families remain socially vulnerable nonetheless. Only half of lone mothers have a full-time job, despite typically being the household’s main earner (Chardon et al., 2008). More generally, one-parent families have less favourable and less stable housing conditions than couples with children. Given their low standard of living and the high level of housing demand, it is often difficult for these families to find a place to live or to obtain a home that corresponds to their needs.
2 – The key role of the private rental sector
9Finding a home in the private rental sector is a milestone in the life course of lone parents. The separation that leads to the formation of a lone-parent family represents an upheaval in the residential trajectory associated with family formation, with its initial period of home rental when the couple first moves in together, followed by a home purchase when the children are born. Becoming a homeowner provides security for couples whose relationship stands the test of time (Bonvalet and Bringé, 2016). Those who separate, on the other hand, experience residential disruption, often involving a return to the social-housing or private rental sector after selling the family home to pay off the mortgage (Bonvalet, 2005; Pirus, 2005). This is why, at the national level, lone mothers with children less often live in suburban houses and more often in city-centre apartments (63% of lone-parent families live in an apartment vs. 31% of couples with children). In the Paris region (Île-de-France), only 27% of lone-parent families are homeowners versus 57% of couples (Drieux et al., 2016).
10Lone parents are nonetheless a priority group for the social-housing sector, whose purpose is to provide homes for low-income households. Bonnal et al. (2012) estimate that for lone-parent families, the waiting time for social housing is around half as long as for couples, all other things being equal, notably after controlling for income. This is less true in Paris, however, where proportionally fewer lone parents obtain social housing than in other French departments (Decondé et al., 2013). Moreover, as property prices are high, they are less frequently homeowners; 21.5% of lone parents own their home versus 25% in the rest of the Paris region (Drieux et al., 2016). This explains why a relatively large share of lone parents in Paris live in private rented accommodation: 35% compared to 30% in metropolitan France as a whole (Decondé et al., 2013). That said, lone mothers with severe financial difficulties also have priority access to emergency accommodation. Using data from two qualitative surveys of rehoused individuals and of the housing support organizations that help them, Lanzaro (2018) shows that emergency housing provision is governed by both compassion and the goal of maximizing the likelihood of successful reintegration. Both factors weigh in favour of lone mothers.
II – The hypothesis of discrimination against lone parents
11Matched-pair audit testing is the most widely used method in the international literature to measure housing discrimination. It has been applied many times in the United States since the 1970s (Yinger, 1986; Page, 1995; Choi et al., 2005; Hanson and Hawley, 2011) and, more recently, in several European countries (Ahmed et al., 2008; Ahmed and Hammarstedt, 2010; Bengtsson et al., 2012; Bosch et al., 2010, for Spain; Baldini and Federici, 2011, for Italy; Drydakis, 2011, for Greece; Carlsson and Eriksson, 2014, for Sweden; Van den Broeck and Heylen, 2015, for Belgium) but rarely in France, where only four studies have used an experimental approach to measure housing discrimination. Bonnet et al. (2016) analysed the responses received by fictitious applicants who enquired about homes for rent in the Paris region in spring 2009. They answered 250 advertisements and revealed personal details to the landlords in accordance with a pre-established protocol. Acolin et al. (2016) responded by email to online rental advertisements over a 2-month period between April and May 2014, sending 1,800 messages across the whole of France. Both studies found strong evidence of ethnicity-based housing discrimination but were unable to capture the spatial dimension or to interpret the causes of this discrimination. The authors observed that levels of discrimination vary across the French regions, but they did not give more specific information about the municipalities or neighbourhoods concerned. Bunel et al. (2017) measured origin-based discrimination on the Parisian private rental market by answering 504 advertisements. They found strong discrimination against the fictitious applicant of North African origin. Le Gallo et al. (2017) analysed responses to 5,000 rental advertisements gathered via a nationwide audit covering the 50 largest urban areas in France, to measure ethnicity-based housing discrimination and map its spatial disparities. Discrimination of this kind was detected in numerous urban areas.
12No studies have so far explored the role of family status in France, although being a lone parent was one of the criteria included in a study by the Asdo research and consulting agency for the anti-discrimination authority, Haute Autorité de lutte contre les discriminations et pour l’égalité (HALDE), published in 2006. They found no differences of treatment based on this criterion, but the study included a sample of just 126 rental advertisements answered by fictitious applicants who did not all respond to the same ones, and the statistical analysis was incomplete.
13International studies examining the role of family status in access to housing are also quite scarce. Galster and Constantine (1991) were the first to test housing discrimination against women with or without children. They conducted a paired audit in Ohio in January 1985 that combined telephone inquiries and in-person visits to apartments and found evidence of discrimination against lone mothers with children. The analysis was based on just 11 observations, however, well below the standard number used for audit studies, which generally include hundreds or even thousands of observations. An experiment in Vancouver showed that lone parents are less fairly treated than two-parent families on the housing market, and likewise for same-sex couples with children (Lauster and Easterbook, 2011). Conversely, another study in Belgium by Van den Broeck and Heylen (2015) found no evidence of discrimination against lone parents. Lone parents were not the only group tested, however. A paired audit method was used, with real applicants and a limited sample of 30 applicant pairs. But above all, the control group comprised men only, while the test group included lone mothers with children, so the study could not distinguish between the effect of lone-parent status and that of the parent’s sex.
14Against this backdrop, our study applies a testing method to measure discrimination against lone parents on the Paris rental housing market and uses a protocol that enables us to interpret its causes. More exactly, we want to determine whether refusing to rent a home to a lone parent reflects a ‘pure aversion’ to the applicant’s family status—independently of their presumed financial stability or of statistical discrimination—linked to a belief that he or she may be unable to pay the rent. Two approaches are often contrasted in the literature on discrimination economics. The first corresponds to Becker’s model (1957) in which discrimination is linked to suppliers’ preferences. The second is based on the models of Phelps (1972) and Arrow (1973) in which discrimination is explained by the information about applicants available to landlords.
III – Testing and data collection protocol
15We tested for the existence of housing discrimination against lone-parent families looking for a home on the Parisian private rental market. More specifically, are the rental offers received from landlords by a woman with a partner and two children equivalent to those received by a lone mother with two children, all other things being equal? [2] If not, then the difference in treatment is based on an illegal criterion, that of family status, and therefore constitutes discrimination. Consistent with Becker’s models (1957, 1971), discrimination may result from exogenous preferences or an individual aversion to one or other of an applicant’s demographic characteristics. These may be preferences or stereotypes about lone-parent families on the part of letting agents, their landlord clients, or residents. It may also arise from statistical discrimination, which, in a situation of imperfect information (about the applicant’s potential ability to afford the rent, for example) is based on the supplier’s knowledge, actual or presumed, about the mean and the dispersion of this characteristic among the subpopulation to which the applicant belongs (here, lone-parent families), consistent with the models of Arrow (1973) and Phelps (1972). To assess the explanatory power of this second hypothesis, we examine the effect of reported financial stability on the likelihood for a lone mother with two children of being invited to visit an apartment for rent. This is the strategy used in all audit studies aiming to interpret the causes of housing discrimination. Flage (2018) shows that studies on ethnicity-based discrimination and on gender generally find evidence of both aversion and statistical discrimination.
16Four messages were sent by fictitious individuals in response to each rental advertisement. Four profiles were invented for the controlled experiment:
- a woman with a male partner and two children living in the household (Sandrine Leroy);
- a lone mother with two dependent children (Nathalie Legrand);
- a lone father with two dependent children (Sébastien Moreau);
- a lone mother with two dependent children who reports being a tenured civil servant (Isabelle Petit).
17The four individuals sent similar short email messages in response to a property rental advertisement, in which they enquire about visiting the property and about the supporting documents needed for the rental contract. Their distinctive characteristic is identifiable either via their first name (gender) or the message content (family status, occupation).
18Inquiries were sent by the four fictitious individuals in response to the same advertisements, several hours apart and on the first day they appeared online. Box 1 shows the content of the messages sent.
Box 1. Identities and messages of the four fictitious individuals
Hello,
My partner and I are looking for a home to rent with our two children, and the flat shown in this advertisement seems to fit the bill. Would it be possible to visit the flat? What supporting documents are needed for the rental contract?
With thanks,
Sandrine Leroy
Hello,
I am looking for a flat in this neighbourhood, and the property shown in this advertisement looks like a good size for three people (myself and my two children). Could I arrange a visit? Could you also tell me what documents I need to give you?
Best regards,
Nathalie Legrand
Dear Sir or Madam,
I live alone with my two children, and the flat advertised here corresponds to what I am looking for. Would it be possible to organize a visit? I would also like to prepare the rental application. Could you send me a list of the documents you require?
Thank you in advance,
Sébastien Moreau
Hello,
I am a tenured civil servant and have recently moved to Paris with my two children, who I am raising alone. I am looking for a flat in this neighbourhood, and I am interested in the property advertised here. Could I arrange a visit? Could you give me a list of the documents needed for the rental contract?
Kind regards,
Isabelle Petit
19To limit the risk of a message wording that gives an advantage to a fictitious applicant independently of his or her distinctive features, the messages were regularly switched around, two by two (Legrand vs. Moreau and Leroy vs. Petit, with minor changes to include their distinctive characteristic). [3] In addition, the messages sent in response to the same advertisement were dispatched in random order; for all the advertisements tested, each message was sent in first place a comparable number of times.
20By comparing the answers given by agencies and landlords to these four fictitious people, considered two by two, we can look for evidence of housing discrimination against lone mothers with children versus mothers with a partner. Next, among lone-parent families, we can test for the existence of gender discrimination (lone mother vs. lone father). Last, we can assess the effect of the agency’s uncertainty about the presumed long-term ability of a lone mother with two children to pay the rent (lone mother with unknown employment status vs. civil servant lone mother). Figure 1 shows the comparisons made to identify these effects.
Figure 1: The profiles compared and the effects revealed

Figure 1: The profiles compared and the effects revealed
21Advertisements placed by letting agents and private landlords were tested. While each agency was tested just once, some companies with multiple branches were tested several times via different agencies.
22The main French property websites were consulted for this study: À vendre à louer, Bien ici, Logic-immo, ParuVendu, SeLoger, Louer vite, PAP, and Le bon coin. On each site, applicants contact the letting agent or landlord via an online form; they enter their inquiry, giving their first and last names, phone number, and email address. Letting agents or landlords can reply directly by phone or email. Each of the four fictitious individuals had an email address and a mobile phone number to receive the letting agents’ and landlords’ replies, but there was no additional follow-up to the answers obtained.
23The selected rental properties, located in all 20 arrondissements of Paris, varied in floor space, number of rooms (one to three bedrooms), and rental price.
24A reply to the inquiry was considered negative when the agency or landlord did not reply or gave an explicit refusal (for example, because the apartment was no longer available). In all other cases, the reply was non-negative and labelled a ‘positive answer’. An agreement in principle by the agency or landlord to arrange a visit to the apartment was the second, more restrictive indicator of success. All the results are classified according to these ‘positive answer’ and ‘agreement in principle’ indicators.
25Between December 2017 and March 2018, 791 property rental advertisements were tested (642 posted by agencies and 149 by private landlords), and 3,164 (791 × 4) inquiries were sent.
IV – Evidence of discrimination
26Not all agencies and landlords replied, even to the initial message, doubtless because of the large number of inquiries received. For 42.7% of advertisements, none of the four inquiries sent by the fictitious applicants received a reply (Table 1A). For the other 57.3%, a reply was sent to at least one applicant, and in more than half of these cases (58.1%) a reply was sent to all four. The frequency of non-response was greater for private landlords than agencies, with a difference of around 15 percentage points (Tables 1B and 1C).
27Some applicants were more likely to receive a positive answer than others, a finding that suggests the decision to reply is not distributed randomly across different personal profiles. These differences are evidence of discrimination. When receiving multiple inquiries about the same property, an agent or landlord is not necessarily able to show it to everyone interested. Applicants are not randomly selected, however. For many of the advertisements tested, the likelihood of receiving a positive answer varied considerably from one profile to another (Table 2).
28The profile with the fewest positive answers overall was that of the lone mother with children (44.1%); and the one with the most was that of the civil servant mother with children, followed by that of the lone father with children. This ranking is the same for the advertisements posted by letting agents. For those posted by private landlords, it differs slightly, but again, the civil servant mother received more positive answers (Appendix Table A.2). Agents or landlords who replied to just one inquiry gave priority to the civil servant mother in 32.8% of cases or the lone father with children (31%). For agreements in principle, these same two profiles were most successful, but with the lone father (34.8%) ahead of the civil servant mother (27.5%).
Table 1
Number of positive answers and agreements in principle to visit per advertisement
A: All advertisements (N = 791)

A: All advertisements (N = 791)
B: Advertisements posted by letting agents (n = 642)

B: Advertisements posted by letting agents (n = 642)
C: Advertisements posted by a private landlord (n = 149)

C: Advertisements posted by a private landlord (n = 149)
Table 1
Number of positive answers and agreements in principle to visit per advertisement
Interpretation: In this test, inquiries were sent for 791 advertisements, 641 posted by an agency and 149 by a private landlord. For each advertisement, four inquiries were sent. A total of 338 inquiries (in response to 256 advertisements posted by agencies, 82 by landlords), were not answered, 58 received one positive answer, 54 received two, 78 received three, and 263 received four.29The interesting point in this study is the difference of treatment between the lone mother with children and the partnered mother with children. In Table 2, which covers all advertisements, the proportion of positive answers is slightly higher (+0.8 points) for mothers with a partner. When the advertisement is posted by a private landlord, the proportion of positive answers for lone mothers is 3.3 points higher than for partnered mothers. However, the tests on private landlords are not significant (tests presented in Section V). When the advertisement is posted by a letting agency, the proportion of positive answers for lone mothers is 1.7 points lower than for partnered mothers. These findings suggest that letting agents are discriminating against lone mothers or protecting owners from lone mothers with presumed insecure employment status, and this will be confirmed by the tests described in the following Section.
Table 2: Proportion of positive answers and agreements in principle to visit by applicant’s profile (all advertisements; N = 791)

Table 2: Proportion of positive answers and agreements in principle to visit by applicant’s profile (all advertisements; N = 791)
30The differences are relatively small, however. Between a lone mother and a partnered mother, the difference in the proportion of positive answers is significant but small, to the advantage of the latter, but only for large apartments (Appendix Table B.1). The differences are an order of magnitude higher in studies of discrimination by origin. In the overview by Flage (2018) covering 29 correspondence tests conducted in 15 different countries, applicants whose surname sounded foreign were half as likely to be invited to visit a home for rent than those from the majority population. In the study by Brunel et al. (2017) on housing discrimination in Paris, applicants with a North African-sounding forename and surname were one-third less likely to be invited to visit an apartment to rent.
31The proportion of positive answers is very sensitive to apartment size. It is lower for small one-bedroom apartments (between 32% and 37% depending on the individuals) and higher for two- and three-bedroom apartments (between 54% and 58% across the different profiles). The applicant rankings also vary by apartment size. For the agency advertisements (Appendix Table B), a lone mother has the lowest proportion of positive answers for two- and three-bedroom apartments (53.1%), while a mother who is a civil servant or in a couple has the highest (57.3%). For one-bedroom apartments, the partnered mother has the lowest proportion of positive answers (35.4%), while the lone father has the highest (41.3%). The differences between these positive response rates are systematically tested in Appendix Tables B and C, using the three tests shown in Figure 2 to determine the probability that the differences are due simply to chance.
32We performed Fisher’s tests for differences of proportion, the standard tests used for this type of comparison, with a statistical inference based on a bootstrap procedure, which is more accurate when samples are small. The results are summarized in Figure 2. On the tested advertisements from agencies and landlords (total sample), no effect of being a lone parent and no advantage for a mother with a partner are observed. A financial stability effect is observed, however, for both agencies and private landlords. For lone mothers with children, being a civil servant increases the likelihood of a positive answer. Last, lone fathers have more success than lone mothers, a finding that suggests a gender effect. For all advertisements placed by letting agents, the chances of receiving a positive answer are significantly lower for the lone mother than for the civil servant lone mother and the lone father. No significant difference is observed, however, between the couple and the lone mother. These differences only become significant when the analysis is limited to large two- and three-bedroom apartments, for which there is a difference of 4.23 percentage points. Based on the standard significance levels used, this cannot be attributable to chance. Apartment size is thus decisive for analysing discrimination by family status. The existence of gender discrimination, between lone mother and lone father, is only confirmed for small, one-bedroom apartments.
33These results can be interpreted as a form of ‘matching’ behaviour on the part of letting agencies, who aim to match the presented characteristics of the property for rent with those of the applicant to increase the chances of a successful transaction. This behaviour has been identified by sociologists of the real estate industry (Bonneval, 2011; Bernard, 2017). They show that to achieve a deal, the letting agent adjusts and reframes the demands and preferences of both landlord and applicant to achieve a match between the two. The presumed beliefs of the landlord (resp. applicant) about the social characteristics of the applicant (resp. landlord) guide the letting agent in the search for a successful match. Hence, a large apartment may be more suitable for a family with more members, i.e. the couple with children, relative to the lone parent with children. A larger home also means a higher rent, so the civil servant lone mother has an advantage over the other lone mother. Gender discrimination for smaller apartments may reflect statistical discrimination (higher presumed income and lower unemployment risk for a man) or agencies’ preferences (or the presumed preferences of their clients).
Figure 2: Differences in proportion of positive answers by characteristics of the applicant and the property for rent

Figure 2: Differences in proportion of positive answers by characteristics of the applicant and the property for rent
General interpretation: The graph shows the absolute difference in the proportions of positive answers received by each applicant, relative to the reference applicant, for the same apartment, depending on its characteristics.Interpretation of top graph: For the full set of tested advertisements (N = 791), there are no differences for any applicant with respect to the reference applicant, be it for all advertisements or those posted by agencies only. For two- and three-bedroom apartments, the number of positive answers received by women with a partner is 4.23 percentage points higher than for a lone mother (effect of lone-parent status) when only agency advertisements are considered (n = 354). The difference is 3.43 points for the full set of tested advertisements, including both agencies private landlords (n = 408).
34The same type of analysis was performed for advertisements posted by private landlords, for which the proportion of positive answers was generally lower, especially for one-bedroom apartments (between 21% and 26% across the categories versus 50% to 59% for two- and three-bedroom apartments). Overall, out of the 149 private landlord advertisements tested, there was no significant difference between the four fictitious individuals in the likelihood of receiving a positive answer, whatever the apartment size.
V – An econometric analysis confirms these findings
35These findings must be confirmed by econometric analysis. In the experiment, the applicants’ characteristics are fully controlled for, since constructed artificially, while those of the advertisements and the advertisers are not. We can estimate a model to check that the results are not due to composition effects linked to the characteristics of the advertisement and/or agencies and landlords.
36The observations correspond to the answers to 3,164 inquiries sent by the four fictitious applicants in response to 791 advertisements. We estimate an explanatory model of the probability of receiving an agreement in principle for a visit to the property. In practice, these data can be used to construct two complementary indicators of a successful inquiry: a positive answer and, more specifically, an agreement in principle for a visit. These two indicators are variables with values of 0 or 1. A probit model is estimated for each type of indicator. The independent variables are the type of advertiser (private landlord or agency, taken as reference), apartment size (two and three bedrooms, or one-bedroom as reference), applicant’s profile (lone mother as reference), website where advertisement was posted, rental price per square metre, furnished or unfurnished, and sending order among the four inquiries sent. Differences in message wording are also controlled for (see Note 3) via dummy variables named Set A, Set B, and Set C.
37The models are estimated with a location fixed effect (arrondissement of property address) and an ‘inquiry month’ fixed effect to control for unobservable differences across time and space. The standard deviations are estimated using a robust statistical inference method. To take account of potential correlations between arrondissements, and because observations are replicated for each advertisement, they are doubly clustered at arrondissement and property/advertisement levels.
38Table 3 shows the probability of receiving a positive answer, for all advertisements (Models 1 to 3) and for agencies only (Models 4 to 6). [4] The first model (Columns 1 and 4) includes all the independent variables presented above. The second model (Columns 2 and 5) adds interaction terms between the applicant profile and the apartment size. The third model (Columns 3 and 6) adds interaction terms between the applicant profile and the rental price.
39The central effect of this analysis is given by the coefficient of the ‘mother with a partner’ variable, which measures the difference in percentage points of probability between a couple and a lone mother (reference situation). This difference is not significant in the models. Regarding the selection of applicants who receive a positive answer, there is generally no discrimination against lone mothers on the Parisian housing rental market. However, the interaction term with a two- or three-bedroom apartment is significant in Model 2 (all advertisements) and Model 5 (agencies only). The hypothesis of discrimination against lone mothers is thus confirmed, all other things being equal, for larger apartments, even though the landlord/agency has no information on the applicant’s income. The estimates also confirm that the signal of financial stability (‘civil servant lone mother’ category) significantly increases the likelihood for a lone mother of receiving an agreement in principle to visit the property, suggesting that discrimination against lone mothers corresponds to statistical discrimination based on a presumed inability to afford the rent. [5] This effect is not significant in the interaction models, however, so its robustness is not confirmed.
40These results are obtained with a model that explains the probability of receiving an agreement in principle to visit the property. They are also verified for a model in which the dependent variable is the probability of obtaining an agreement in principle. [6]
41The models do not confirm the existence of gender discrimination, however. Although the lone father variable appears to be significant in the first model, suggesting the existence of discrimination against women, it is non-significant in the others. This result is not robust to the indicator considered or to inclusion of the interaction terms.
Table 3: Probability of receiving a positive answer (probit model)

Table 3: Probability of receiving a positive answer (probit model)

Note: Robust standard deviations in parentheses.
Conclusion
42Statistical measures of housing discrimination in France are scarce. This study has aimed to fill this knowledge gap by measuring discrimination against lone parents on the private rental market in Paris using a paired audit method. We wanted to determine whether refusing to rent a home to a lone parent corresponds to statistical discrimination based on presumptions about rent non-payment or a ‘pure aversion’ to the applicant’s family status, independently of their presumed financial stability.
43Our main findings were as follows. First, in most cases, not all agencies and landlords reply to all inquiries, or even to the initial message. This selectivity is doubtless linked to the large numbers of inquiries received. Second, the inquiries that do receive a reply are not chosen randomly and are sometimes discriminatory. For certain types of property, applicants are significantly less likely to receive a positive answer if they indicate that they are raising their children alone. For larger two- and three-bedroom apartments advertised by letting agencies, our analysis confirms the existence of discrimination against lone parents (Figure 2). The differences in the treatment of lone parents and couples with two children provide evidence of housing discrimination. This difference narrows when the lone mother signals financial stability by mentioning in her inquiry that she is a civil servant. This corresponds to information-based discrimination, consistent with the models of Arrow and Phelps.
44We interpret this as a form of ‘matching’ behaviour on the part of letting agencies, who seek to match the rental property’s characteristics with the actual or presumed characteristics of the applicant to increase the chances of a successful transaction; they may presume that a larger two- or three-bedroom apartment is more suitable for a family with more members, i.e. a couple with children rather than a lone parent with children. A larger home also means higher rent, so the civil servant lone mother signalling financial stability has an advantage over the other lone mother.
45Several limitations of this study should be highlighted. First, its scope is limited to Paris; it would be useful to see if similar conclusions can be drawn for other cities. We tested 791 advertisements, posted by both letting agencies (n = 642) and private landlords (n = 149). Like all testing experiments, the results are partial and limited to a particular point in time and space, which may explain the limited significance of the effects. The Parisian property rental market is very tight, and lone-parent families are strongly over-represented. This situation may foster housing discrimination against lone parents or, on the contrary, greater tolerance of a common family type. We also tested the effects of being in a couple, of financial stability, and of gender relative to a lone mother with children, without the cross effects of these characteristics or the effects observed by changing the reference profile. The intersection of lone-parent status with other discrimination criteria, such as country of origin, was not explored. To do so would have called for a different protocol, with applicant profiles different from the ones tested. Last, a different signal of financial stability could have been used for the lone mother, while for the potentially dual-earner couple, a signal of financial insecurity could have been tested. These limitations highlight the need for further research based on paired audit testing, using different protocols applied to other fields of investigation.
Acknowledgements
This study received funding from the city of Paris as part of the PIRATE project (Parent isolé recherche appartement: un test et une évaluation [Lone parent seeks apartment: a test and an assessment]). We are grateful to the steering committee for their comments. We also thank the members of the RECI network (Ressources pour l’égalité des chances et l’intégration) for their remarks when the study was presented in April 2019. This paper was reviewed anonymously by three Population referees. We would also like to thank them, along with the Editorial Board and the three journal editors.Appendix
Table A
Proportion of positive answers and agreements in principle by inquirer’s profile
A1: Advertisements posted by letting agents (n = 642)

A1: Advertisements posted by letting agents (n = 642)

Table A
Proportion of positive answers and agreements in principle by inquirer’s profile
Table B
Results of difference tests for positive answers



Table B
Results of difference tests for positive answers
*Significant difference at 10% level, **at 5% level, ***at 1% level.Table C
Results of difference tests for agreements in principle to visit



Table C
Results of difference tests for agreements in principle to visit
*Significant difference at 10% level, **at 5% level, ***at 1% level.

Notes
-
[1]
A lone-parent family comprises a lone parent without a cohabiting partner, living with one or more single children of any age (who have no children of their own). The child or children generally spend some of the time (half at most) with the other parent.
-
[2]
That is to say, controlling for all characteristics of both the housing unit and the tenant.
-
[3]
In addition to switching around the messages as described in Box 1, the wording ‘my two children, who I am raising alone’ was sometimes replaced by ‘my two children with whom I live alone’. The former may suggest that the mother receives no child support from the father, and hence that her income is lower.
-
[4]
Appendix Table D shows the probability of receiving an agreement in principle for a visit.
-
[5]
The coefficients of the interactions between family status and rent are not significant.
-
[6]
Results are shown in Appendix Table D.