Clémence Berson
email: clemence.berson@univ-paris1.fr

Does Competition Induce Hiring Equity? *

Keywords: J71, C93 Discrimination, hiring, competition Mots clés: Discrimination, embauche, concurrence

This paper tests the impact of competition on the hiring process in the French retail sector. Following the Becker's theory, higher the competition, lower is discrimination. Using local Herfindhal-Hirschman indexes, a correspondence study ensures to observe how competition affects discrimination. A strong employment gap is observable between French natives and second generation immigrants. Concerning gender, women are favored as cashiers. The impact of competition depends on the target population: competition reinforces preference for women, whereas discrimination due to origin is follows the Becker's theory. However, increasing competition to fight against discrimination is not a solution, as it will enhance bad condition of women in the labor market and an increase of awareness of human resources department to equality of treatment is more efficient.

Résumé

Une large littérature s'accorde sur un effet de la concurrence sur le marché des biens sur la discrimination. Mais l'ensemble de ces études se focalisent sur les salaires et les postes, sans s'intéresser à l'embauche. Cet article teste l'impact de la concurrence sur le processus d'embauche et ses conséquences sur les écarts d'emploi. Deux types de discrimination sont étudiés : le genre et l'origine. Le secteur choisi est celui de la grande distribution. En utilisant des niveaux locaux de concurrence, un testing permet d'observer comment la concurrence affecte la discrimination. Les résultats montrent que la concurrence peut accentuer la discrimination statistique dans le cas du genre. De plus, elle n'est pas forcément un bon outil pour lutter contre la discrimination, le cas de l'origine montrant un impact plus fort de la centralisation du recrutement et de la sensibilisation des recruteurs.

Introduction

The presence of discrimination on the labor market is now well documented [START_REF] Altonji | Race and Gender in the Labor Market[END_REF]). Studies on wage differentials, glass ceilings and employment access in many countries point out a persistent discrimination against women and ethnic minorities. Discrimination against sexual minorities or disables is yet observed in spite of a lack of data. More attention is now paid to the mechanims and how to disentangle different types of discrimination to lead fitted policies. In order to test the Becker's theory, researchers analyze the impact of competition on discrimination and results tend to confirm the theory. However, these studies focus on labor outcomes on the job. This article aims at filling out the literature by testing the impact of competition on hiring discrimination.

Discrimination is introduced in economics by [START_REF] Becker | The Economics of Discrimination[END_REF]. He defines discrimination as the result of a taste. Some employers, coworkers or consumers do not want to employ, work with or buy something to an individual belonging to a particular group. It induces a different treatment of these workers from the others, in spite of identical observable productive characteristics. However, in the case of employers, satisfying their taste for discrimination is costly, as it reduces the pool of applicants for the firm, and workers belonging to the group discriminated against receive a lower wage because of the psychological cost of their employer. In a competitive market, prejudiced firms are less efficient than the others and will be drive out of the market. Arguments are relatively similar in the case of prejudiced co-workers and rational employers hire only one type of workers in order to obtain the largest productivity of workers. The steady state is a perfect segregation, which is not realistic. The case of prejudiced consumers is the only stable case. Indeed, employers increase their profit when they answer to the taste of customers for discrimination. However, it concerns only jobs, which implicate a direct contact with customers. In order to explain a persistence of discrimination, [START_REF] Arrow | The Theory of Discrimination[END_REF] and [START_REF] Phelps | The Statistical Theory of Racism and Sexism[END_REF] enhance this theory by developing the concept of statistical discrimination. In this case, discrimination does not result from a particular taste but from imperfect information and beliefs of employers. These formers are assumed to know the true 3 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19 productivity level of workers belonging to her group and ignore the productivity of workers belonging to another group. To set the wage of workers of the minority, they also use the expectancy of the average estimated productivity of this group. Generally, individuals of the majority believe that workers of the minority are less productive in average and the wage offered to them is lower than the wage offered to workers of the majority. However, a phenomenon of learning makes it disappear. In both theories, discrimination does not have to persist. This explains that a lot of empirical studies aim at outstanding the role of competition in the phenomenon of discrimination in the labor market.

Empirically, most of studies focus on discrimination on the job. They first compare wage gap and employment rate in differently concentrated sectors [START_REF] Comanor | Racial Discrimination in American Industry[END_REF], [START_REF] Hellerstein | Market Forces and Sex Discrimination[END_REF]). However the comparison of distinct sectors induces biases due to their unobservable characteristics. To avoid them, [START_REF] Peoples | Trucking Deregulation and the Black/White Wage Gap[END_REF], [START_REF] Heywood | Deregulation and the Prevalence of Black Truck Drivers[END_REF] and [START_REF] Black | The Division of Spoils: Rent-Sharing and Discrimination in a Regulated Industry[END_REF] used external shocks of competition within a sector in order to observe its consequences on wage gap, employment rate and occupations. [START_REF] Ashenfelter | Sex Discrimination and Product Market Competition: The Case of the Banking Industry[END_REF] slightly differed in their method as they determine the impact of competition on labor market output thanks to the diversity of local competition in the US banking sector. A third way to study the impact of competition is to observe variations due to globalization of trade. [START_REF] Black | Importing equality? The impact of globalization on gender discrimination[END_REF] show that competition decreases wage differentials between men and women, improves job attainment and the rate of workers discriminated against in the sector. However, no study focuses explicitly on the hiring process, because of the lack of data concerning employment. This is an important issue, particularly, in a period of large unemployment, where discrimination will be revealed more in the hiring process than in wages. This article offers to complete the literature by leading a field experiment in areas with different level of competition. Correspondence studies underline discrimination in the hiring process against women ethnic minorities across a large set of countries and ethnicities. Existence of discrimination against this population allows me to focus on the topic of this article: the impact of competition on the discrimination due to origin and gender. In order to easily measure the level of competition, the tested sector is the French retail sector. Indeed, databases on strategic data are available and the local competition varies sharply across regions. A correspondence study gives the data on discrimination and a matching with competition databases allow me to study how competition affects discrimination during the hiring process.

Main results are that women are favored and discrimination is observable against second generation immigrants. The impact of competition on employment varies according to the type of discrimination: A less competitive environment leads to a higher equity between men and women, showing the particular condition of women in this job, whereas the impact of competition is more standard concerning origin. Discrimination against men seems to be a statistical discrimination as when competition is sharper, employers favor women. This mirrors the study of [START_REF] Askenazy | Travail et salariés dans la grande distribution[END_REF] on the French retail sector, where women are said more susceptible to work in bad condition. The type of discrimination against second generation immigrants is not straightforward. A part is clearly due to a taste of employers. However, the other part could be due to customers' taste or to statistical discrimination. This paper is organized as follows. The design of the experimentation is presented in Section 2. The Section 3 gives the empirical results and robustness checks are described in Section 4. Finally, Section 5 concludes.

Experimental Design

A correspondence study is a field experiment aiming at measuring discrimination in the hiring process among a particular characteristic such as gender, ethnicity, nationality and so on. Two similar resumes are spontaneously sent to a large number of firms or in order to answer to an ad. The only significant difference between both resumes is the characteristic researcher wants to test. This experiment can be extended by an audit but it induces biases because of unobservable characteristics of fictious applicants. Moreover I consider that an interview is costly for the firm and the selection due to discriminatory criteria is often done during the resume step. In order to find a more precise argumentation, see [START_REF] Bertrand | Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination[END_REF]. Thereafter, an econometric study of the likelihood of callback of each candidate measures discrimination. 5 Documents de Travail du Centre d'Economie de la Sorbonne -2012. 19 Riach & Rich (2002) surveyed audit and correspondence studies and listed them by country and methodology. The first correspondence study was done by [START_REF] Jowell | Racial Discrimination and White-Collar Workers in Britain[END_REF] in Great Britain. This experiment concerned discrimination against non-white looking for white-collar jobs. They aimed at distinguishing between discrimination due to 'color' and discrimination due to 'foreignness' by using different origins, and they found evidence on a greater disadvantage for the colored immigrant group than for the white immigrant group. Other field experiments followed in a large set of countries like Australia, the United-States, Canada, the United-Kingdom and France. International economic reviews began to publish correspondence studies in the 1980s and this procedure is now well-known as an objective measure of discrimination in the hiring process by researchers in economics. The correspondence study of [START_REF] Bertrand | Are Emily and Greg More Employable Than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination[END_REF] on racial discrimination in Boston and Chicago is now the reference of field experiment on discrimination. They tested the impact of a sounding African-American name in the labor market. They found a significant discrimination against African-American workers, which seems to be due to some tastes of employers because a better quality of resume does not improve the number of callbacks of this minority. with the creation of the fictious resumes. The last one describes the timeline.

Sector selection

The retail sector is highly regulated in France. The official aim of these policies is to protect traditional groceries from a sharp competition of supermarkets and megastores. A first law is voted in 1973 and made compulsory for new entrant to apply for an authorization to build a new store (or just to enlarge an existing one) if the surface area is larger than 1000m 2 in a small city or than 1500m 2 in a large city. The regional board charged to study the application is composed of local elected members, store owners already established and representatives of consumers. This regional zoning board created a barrier to enter the market and only few new stores have been authorized to set up. [START_REF] Bertrand | Does entry regulation hinder job creation? Evidence from the French retail Industry[END_REF] studied the impact of the Royer law and found that stronger deterrence of entry by local boards increased retailer concentration. Besides, the concentration ratio in the retail sector has a negative impact on employment, in the retail sector and in the economy. On the contrary, the number of approvals by the regional zoning board has a positive effect. It suggests that the zoning regulation introduced in France in the early 1970s to restrain the development of large stores has an impact on the whole economy.

Moreover, this law explains a part of geographical discrepencies in competition as some boards were more favorable than others. [START_REF] Askenazy | Travail et salariés dans la grande distribution[END_REF] point out this heterogeneity throughout the country as stores are unequally distributed. Some stores are in a monopolistic situation, often in rural areas, and others are surrounded by stores belonging to other groups and competition is sharper.

In 1996, two other laws restricted the competition: The Galland and Raffarin laws, both applied in 1997. The Galland law consists in forbidding stores to pass on individually negotiated discounts to consumers. This is equivalent to allowing industry-wide price floors. [START_REF] Biscourp | The Effects of Retail Regulations on Prices: Evidence from the Loi Galland[END_REF] and [START_REF] Allain | La loi Galland sur les Relations Commerciales : jusqu'où la réformer ? Editions rue d'ulm[END_REF] show that it induced an increase in prices and a decrease in the level of competition of the retail sector. The Raffarin law reinforced the Royer law of 1973 by generalizing the necessity of approval to enlarge or establish a large store. The new threshold dramatically decreased to 300m 2 . Both Galland and Raffarin acts strengthened the regulation of the market. Recent laws relaxed both acts (Dutreil in 2003 andChatel in 2008 for the Galland law and LME in 2008 for the Raffarin law). In spite of these amendments, aiming at increasing competition, the French retail sector remains highly concentrated. In a report of 2009, the French Competition Authority (Autorité de la concurrence) notes that the French retail sector is very concentrated, really similar to an oligopoly. Indeed, this sector is essentially composed of six main companies, which represent 85% of the sector in terms of market share in 2009. Companies are organizes in two different ways: One half is cooperative and the other half is integrated. This distinction will be useful in order to identify discrimination due to employer taste. Indeed, on the one hand, managers are owners of their store and are only member of the brand. On the other hand, managers are wage-earning and receive a profit-share as branch store or franchise. In the second case, the employer taste for discrimination would be more difficult to express. Another useful remark concerns the way of recruitment. One of these six companies centralizes its hiring process. Stores, which serache applicants for a job or receive resumes, have to contact the centralized human resources department. Then, two or three applicants are proposed to each vacant post. This policy aims at reducing costs and discrimination. The company increases workers of the human resources department awareness of diversity and equity during the hiring process. However, results show that all stores of this company do not use this procedure and recruit themselves. They probably want to choose applicants corresponding to their taste. A dummy, called central recruitment, captures this effect in probit estimations.

Areas selection and competition

The second step of this experiment is to locate favorable places to do the test and to measure competition. The Herfindahl-Hirschmann Index (HHI) is an adequate measure of competition in our context. Indeed, the index has a large scale and disentangle uncompetitive areas even if there are only few stores in the area. HHI is the sum of the squares of the market shares of each chain of retail. The data base I use contains an exhaustive list of the retail stores in March 2011, with precise information on location, phone number, surface area and number of cash desks. Consequently, it is possible to precisely calculate HHI at a local level. Thereafter, measures will be more precise, using a smaller geographical scale.

Employment areas are break down in three categories: competitive, uncompetitive and highly uncompetitive. The index goes from less than 1000 to more than 6000. An industry is usually considered as competitive when the HHI is less than 1000, uncompetitive between 1000 and 2000 and highly uncompeti- third of the total of employment areas without Corsica, which is very particular.

An area is considered as competitive under 2404, uncompetitive between 2404 and 3045 and highly uncompetitive above. Figure 4 shows that the density of HHI of the selected zones is similar to the whole employment areas.

A merge with data from INSEE of 2007, on characteristics of employment areas and competition data enables to summarize their characteristics. The selected areas try to be representative of each category but could be various in term of demographic characteristics like the concentration of immigrants (Figure 3) or population density. A special attention is paid to equilibrate these characteristics in each competition category. Table 1 summarizes the characteristics of the selected employment areas. The French territory is break down in more than 2,000 PCA, urban and rural.

By construction, PCA are relatively similar to customer catchment areas of retail stores, as number of retail stores is a large weight of the competitive facilities index. Table 2 summarizes, their characteristics depending on their situation: HHI less than 4,000, HHI between 4,000 and 10,000 and PCA in monopoly.

For each category, the first line is the mean and in brackets are the standard deviation coefficients.

population and surface area are both variables, which vary with HHI. However, their correlation with HHI is weak (-0.21 and -0.14 respectively). women job, both genders are tested in order to detect a self-selection of women or a discrimination against men in this sector.

Types of job and applicants

Resumes creation

The fourth step of the design is to create appropriated resumes. In order to make credible templates, a human resources manager of a retail store has given some accepted CVs. The characteristics of applicants are inspired from these true CVs. To keep a usual framework, biographies are designed with templates of the word processor. Four different one are used to be sure that a firm does not received resumes with an identical shape.

The applicants are 20, obtained a vocational high school degree in trade on the level of competition. Finally, the last paragraph estimates the likelihood to be called back and points out the impact of competition. In this article, I consider that there is discrimination when the rate of positive return for a type of candidate is higher than another type. A positive return is a call back or an e-mail asking more information on the candidate or offering an interview. Moreover, the sample is bootstrapped in order to have robust results. The number of replications is 10,000 in the t tests and in the probit estimations.

Is there a gender/origin gap in callbacks?

First, Table 4 Keeping this definition induces that equal treatment is essentially composed of no callback. In order to better annalyse results, this category is dropped of tables. As it will be discussed in the Section 4, taking them into account induces an under-estimation of discrimination. First, Table 5 shows that women and men are not treated even if a man slightly receives less callbacks in average.

The t test points out that the averages of stores favoring men and women are significantly different at 99%. In other words, it means that women are preferred by employers. It reinforces assessments of [START_REF] Askenazy | Travail et salariés dans la grande distribution[END_REF] that employers want to hire women more than men because of a statistical discrimination:

women are said to better accept bad condition than men, which should decrease the large turnover. Table 6 shows a preference for French origin applicants. difference is highly significant and no symmetry is also observed in the favoring of workers with French sounding name and workers with Moroccan sounding name. The ratio is yet one fourteenth, which confirms Table 4 figures and the strong discrimination against second generation immigrants from Morocco.

Does discrimination vary according to competition?

Discrimination against men and especially against applicants with Moroccan origin is well established by the previous section. This part aims at observing a statistical difference between population catchment areas (PCA) with various levels of competition.

First, Table 7 and Table 9 tabulate the average callback rates by gender and HHI category, and by origin of names and HHI category, respectively. These tables give an overlook of some variations of discrimination depending on the level of competition of the PCA. It is worth observing that the percentage of callbacks for an interview decreases with the level of competition whatever the gender and the origin of the applicant. This is consistent with the fact that a more competitive environment induces a tighter labor market. However, monopolistic areas have the same callback rate than competitive areas. Tables 8 and10 show the same analysis at store level instead of candidate level. For each category, the first lines are the percentage of callbacks.

As has already been pointed out, men and women are differently treated in average. A difference in favor of women is observed and is statistically significant. Table 7 shows that the variation of the degree of competition has no impact on the gender gap of interview. The ratio of answers of men and women is about 77 in the three cases. Tests of Hotelling show that higher the competition, less an equality of means could be accepted. In other words, lower is the level of competition, the more a significantly different treatment is observable between men and women. At first thought, we can assume that men may be discriminated against in uncompetitive employment areas. A possible interpretation is that, in a more competitive framework, it is costly for stores to favor women as cashier. However, these results have to be confirmed ceteris paribus and not only be observed in descriptive statistics. A comparison by For each category, the first line is the percentage of stores corresponding to the title and in brackets is the number of stores. For instance, 10.30% of stores located in a competitive employment area favored women, which is equivalent to 45 stores.

store gives a slightly different analysis. Indeed, if men are favored in the same proportion whatever the degree of competition, women are less preferred when competition increases. In the case of a discrimination of employers à la Becker, competition increases expression of preferences for the population discriminated against and/or decreases expression of preferences for the population favored, as discrimination or nepotism are costly. Women should be in the second case.

Table 9 gives the distribution of callbacks by origin and level of competition of the employment area. The percentage of callbacks is lower for young workers with Moroccan sounding name and this gap is significant whatever the level of competition. However, the results do not seem to depend on competition.

The ratio of positive answer to workers of Moroccan origin on workers of French origin is relatively stable and reaches 0.25 At first sight, the prediction of Becker For each category, the first lines are the percentage of callbacks.

the discrimination against second generation immigrants on the labor market. For each category, the first line is the percentage of stores corresponding to the title and in brackets is the number of stores. For instance, 21.06% of stores located in a competitive employment area favored French origin, which is equivalent to 92 stores.

Table 10 studies by HHI category how employers favor some applicants.

Whatever the level of competition, employers favor workers with French sounding names. The difference in callbacks for an interview between both origins is statistically significant and the null hypothesis of equality of means between both groups is rejected. However, as in the previous table, there is no strong evidence of an impact of competition in this difference. To confirm this conclusion, the next section presents an econometric study taking into account observable characteristics of employment areas.

To summarize, descriptive statistics does not show a disappearance of discrimination with competition. Concerning gender, the gap is only significant when competition is high. The taste of employers for a discrimination against 21 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

men is rejected. The study of [START_REF] Askenazy | Travail et salariés dans la grande distribution[END_REF] on the French retail sector explains that employers prefer hiring women suffering fragile economic condition in order to decrease the turnover of employees. This explanation suggests that there is a correlation between a competitive market of retail and a tight labor market. Concerning applicants with Moroccan origin, discrimination seems to be due to a taste of customers. Indeed, the level of discrimination does not vary with competition. In the study of [START_REF] Askenazy | Travail et salariés dans la grande distribution[END_REF], employers admit a discrimination against workers of foreign origin supposedly to answer of customers' taste. In this case, a higher competition will not have any impact of discrimination because the cost is borne by consumers. The next part aims at controlling other characteristics of areas in order to disentangle the real impact of competition from other causes of discrimination.

What is the influence of competition on discrimination?

In order to study the impact of competition on the hiring process ceteris paribus, the probability to have an interview is estimated by a probit model. The explanatory equation of a callback is the following:

Callback * i = X ′ i δ i + X ′ j δ j + X ′ EA γ EA + X ′ P CA γ P CA + ν i (1)
where Callback * is latent variable, X i the vector of characteristics of applicant i, X j the one of the firm, X EA the one of employment area EA and X P CA the one of population catchment area PCA, δ and γ the coefficient to be estimated and ν the error term. The latent variable is not observable and an index-function is used:

Callback i = 1 if Callback * i > 0 Callback i = 0 if Callback * i ≤ 0
where Callback i = 1 indicates that the applicant received a callback and Callback i = 0 that she does not. The effect of competition index is significant. In order to allow non-linear effect, HHI is linear and squared. Moreover, to make reading easier, the index is divided by hundred. Results show that the more competitive the area, lower is the probability to obtain an interview. However, the negative impact decreases ployment rate stands for controlling economic circumstances of the employment area. It impacts negatively the probability to have an interview as cashier. The interpretation is intuitive: In a high unemployment place, it would be more difficult to find a job than in another place because of a queue phenomenon.

The density, which has to control for rural location of EA, has a positive but insignificant effect. The white and blue collars rate in the population aims at controlling for the local composition of working population. Its effect is negative: A higher rate suggests more competition between applicants as cashiers.

However, this impact is not significant. In all cases, the impact of the HHI and the gender and origin gaps do not vary with the introduction of other variables.

Tables 12 and13 show the results concerning the estimation of the likelihood to be called back, where variables are interacted with gender and origin, respectively. Concerning gender, the constant term is positive and significant.

A preference for women is clearly observed in this job, as the likelihood to receive a callback is 47% higher when the applicant is a woman. Moreover, interacted terms between other variables and women are not significant, except some regions where the gender preference is lower. In other words, explanatory variables have no influence on gender gap. However, signs of coefficients give an intuition of the situation. First, competition seems to reinforce the gender gap, which contradicts the employer taste theory. In a competitive PCA, women are more favored than in a less competitive one. Consequently, probit estimation of the likelihood to be called back points out a discrimination à la Becker against women. Indeed, these coefficients are significant for women and the negative effect is stronger for women than for men. Results are probably not significant for men because of fewer answers. The fact that a weaker competition induces a lower likelihood for women to be called back compared to men, can be interpreted in this way: when employers have a higher rent, they can spend more time and money to search an applicant corresponding to their taste and hire a man. Moreover, the population composition has no impact on women whereas a larger pool of blue and white collars significantly decreases the probability to obtain an interview for male applicants. These results are in keeping with women because their turn over is lower and they accept harder tasks and part time contracts. Coefficients of unemployment rate reinforce this interpretation as increasing unemployment rate impacts more sharply women than men. In other words, when the labor market is more tight, employers prefer women than men, ceteris paribus. To summarize, the lower probability of men to obtain an interview is less due to a discrimination against them than the results of women condition on the labor market and beliefs of employers concerning their vulnerability.

Besides, variables are further interacted with a dummy variable for whether the applicant has a Moroccan or a French sounding name. Dummies on immigration rate are added in regression in order to control for a negative reaction to a higher immigration rate. Results are summarized in the Table 13. The coefficients of interacted terms are only significant concerning immigration and unemployment rate, way of management and Northern France. As regards immigration rate, simple and interacted coefficients cancel each other. It means that the probability of an applicant with a Moroccan sounding name to obtain an interview does not vary with the immigration rate. On the contrary, an applicant with a French sounding name has a better chance to be called back if the number of immigrants is high in the local labor market. Moreover, the impact of immigration rate is only significant when more than 9.5% of population is immigrant. As in the gender case, the tightness of the labor market has not the same impact for both origins. A significant difference of almost 3 percentage points is observable in favor of the French origin. In other words, an increase of unemployment rate has a stronger impact on the Moroccan origin than on the French one. When the pool of applicants is larger, employers prefer the ethnic majority. Concerning competition, coefficients are not significant but signs comply with the Becker's theory of employer taste for discrimination. icant. In short, a part of origin gap is due to employers and another could be due to customers' taste because of the impact of immigration rate.

Results point out two different conclusions. First, it is worth to identify the type of discrimination before using competition to decrease discrimination.

In the gender case, competition reinforces bad work condition of women and induces more segregation than equality. Second, to incite companies to increase awareness of human resources manager seems to be a better policy to fight discrimination than to improve competition.

Robustness checks

Experimental design The experimental design aims at controlling all applicants' characteristics. However, some templates for resumes may be better than others, or a specific name may have more callbacks due to a less typical feeling.

Resumes are sent in a randomize order. However, to be sent first could have a positive effect on callbacks. In this section, the effect of applicants' characteristics and resumes is estimated on the likelihood of callback to confirm neutrality of the design. Table 14 summarizes the results. As none coefficients of 'CV' is significant, templates of resumes are equivalent, even if CV4 has a negative coefficient and CV2 and CV3 a positive one. Moreover, order of sending is not significant even if the first intuition is confirmed as to be sent first or second has a positive impact on the likelihood to be called back. Finally, names are relatively equivalent as no coefficient is significant, except the second Moroccan female name of "Aïda Djalouzi", which has a positive and significant impact on the likelihood to obtain an interview. Note that nul coefficients come from gender and origin dummies and those results are similar without any control variables. According to the results, the experimental design of this correspondence study is relatively neutral.

Answering stores As the main point of this paper is the impact of competition on discrimination, it could be interesting to restrict the sample to stores, which answer to, at least, one applicant. Indeed, stores, which did not answer, Men have a higher probability to be favored when competition decreases and signs of coefficients are similar to previous regressions. The third regression concerns origin and all variables are interacted with origin. Applicants with a

Moroccan sounding name increase their chance to have an interview when competition goes down. Only two coefficients remain significant: unemployment rate and the way of management. The first one has a negative effect on the probability of Moroccan origin applicants to obtain an interview, the second has a negative impact on the likelihood to obtain an interview for applicants with a French origin. This results mirror the previous one.

Preferences In order to better explain discrimination as a preference, an ordered probit model of the likelihood to favor an origin or a gender is estimated.

Results basically mirror our previous findings (Table 16) but are not significant, certainly due to a lack of data. Concerning gender, men have a higher probability to be favored when competition decreases. In the second estimation, applicants with a Moroccan sounding name increase their chance to have an interview when competition goes down. Only two coefficients remain significant:

unemployement rate and the way of management. The first one has a positive effect on the probability of French origin applicants to obtain an interview, the second a negative one. This confirms former findings.

Conclusion

This article uses an original way to study the impact of competition on labor market outcomes. This experiment adds to the literature on the consequences of a variation of competition. The hiring process has never been studied and this correspondence study in the French retail sector allows us to measure the effect of competition on hiring. The population tested is young French applicants with Moroccan sounding names, male and female. Results show that men do not face discrimination, contrary to what one may think at first sight. On the contrary, their callbacks decrease with competition, showing that if employers have a rent, they prefer hiring men. This shows that experiment studies do not always point out discrimination. A deeper analysis of descriptive statistics is necessary to correctly interpret reults. Concerning origin, a large and significant difference of callbacks for an interview underlines discrimination against the second generation immigrants from North Africa in France. The level of competition has a positive impact on the number of callbacks whatever the origin of the applicant.

Nevertheless there is no evidence for a stronger effect concerning the population discriminated against. Becker's theory could be applied in this case as employers seems to have a taste for discrimination. However, higher competition is less efficient to reduce discrimination than a consciousness rising of human resources managers to discrimination. Concerning gender, the interest variable is null when no preferences are revealed, -1 when women are favored and 1 when men are favored. Concerning origin, the interest variable is null when no preferences are revealed, -1 when Moroccan origin is favored and 1 when French origin is favored. In estimations (2) and (4), the sample only contains stores which call back at least one applicant. Estimations are controlled for regions. EA stands for employment area. 2), the interest variable is worth 1 if women/men are favored, 0 otherwise. In estimation (3), the interest variable is worth 1 if there is any favor (women and men) and 0 in case of equal treatment. Estimations are controlled for regions. EA stands for employment area.

Documents de

  During the 1990s and 2000s decades, these experiments gain an official recognition. The International Labor Office (LBO) commissioned audit and corresponding studies in European countries to deeply observe the phenomenon of discrimination on the labor market in Europe. Studies were executed in the Nederland, Germany, Spain, Belgium and, later, Italy, Sweden and France. This commission legitimated this kind of experimentation to measure discrimination on the labor market in the political sphere. Some countries, like France in 2004, legalized this practice in order to fight against discrimination. As regards the aim of this article, a correspondence study is well-adapted to measure discrimination in the hiring process. Local variations of competition in the selected sector allow observing their impact on discrimination. The experimental design is described in five paragraphs. The first one explains how the retail sector has been selected. The second paragraph concerns geographical areas where the correspondence study takes place. The third part points out jobs and type of applicants targeted by the experiment. The fifth section deals 6 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

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Figure 1 :

 1 Figure 1: Herfinhal-Hirschmann Index by employment area

  tive for more than 2000. The local retail sectors are highly uncompetitive and the bounds used in the article are slightly different. Each category contains one 9 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

Figure 2 :

 2 Figure 2: Herfinhal-Hirschmann Index by life pool

  125 PCA contain only one retail store. Degree of competition is various and 11 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

  The target job is cashier in retail stores. The study of[START_REF] Askenazy | Travail et salariés dans la grande distribution[END_REF] show a large turnover of almost 80% between 2003 and 2005 in the sector and it seems that this particular job is only a spell before a better one. The main modes of application are network, ad in the store or spontaneous applications. It does not need particular abilities even if a vocational education in trade practice is welcome. The training last two days when the worker has no experience but only half a day if she already worked as cashier. It is predominantly a women's job in France. As note Askenazy et al. (2009), cashiers are not unionized (only 2%), are often part time workers and are mainly vulnerable individuals. Employers admit that they favor single mothers because they need to keep their job in spite of low wages and the severity of working condition. Moreover, they recognize to hire less foreigners and colored people, supposedly to answer to consumers' taste. The third step of this correspondence study is to choose the target popula-12 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

Figure 3 :

 3 Figure 3: Proportion of immigrants in the total population by employment area in 2007 Source : INSEE

  practice and have some work experience by trainings and student job during holydays. Student job is cashier in discounted retail establishments in order to have an experience in the job. Trainings concern other trade sector, like clothing salesperson or salesperson in a DIY shop. She has basic computer skills and practices sport. The resumes are adapted to the location and firms used for training are national firms present in all regions. Each applicant has an e-mail address, a phone number and a postal address. Fictious e-mail addresses are created for each applicant, made up of her name and surname. Applicants in each origin/gender cell have the same phone number. The phone lines have only a voice mailbox attached to them. A similar outgoing message is recorded on each of the voice mailbox but each message is recorded by someone of the appropriate gender and without any accent, which can indicate a foreign origin. Since the same phone number is allocated for applicants with different names, the outgoing message contains only the phone number and no person name. Concerning postal addresses, fictious addresses are determined in burgs when the employment area is rural and in the center of the city when the employment area is urban. This strategy allows avoiding districts with bad connotations. Origins are suggested by the name and surname of the candidate. The French nationality is clearly written on resumes and typical Moroccan-sounding or French-sounding name and surname informs of the origin of the applicant. Each tested type has four possible names to be sure that one of the chosen names does not affect the results. In order to select names of candidates, the 14 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

19

  Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

  is not validated by this experiment. A higher competition level does not decrease 20 Documents de Travail du Centre d'Economie de laSorbonne -2012.19

  with concentration. Intuition suggests that competition is synonymous of a larger number of stores and also a larger number of jobs and we have to purge competition of these effects. Furthermore, a monopolistic firm can easier secure loyalty of employees. Consequently, estimation (2) uses other competition variables and estimation (3) introduces some characteristics of the labor market in order to disentangle the role of competition.The second estimation shows that the size of stores has a positive impact on the probability to be called back. Retail companies have two different mode of governance. Half of them manage their stores by franchise or branch stores and the other half are composed of individual owners, who are signatory of the company's charter. In the first case, managers are not owners and, even if they are profit-sharing, the prediction of Becker concerning taste of employers should be less observed than in stores, where the manager is the owner. The probability to receive a call back decrease of 13.25 percentage points when the manager is not owner of the store. Central recruitment does not impact the probability. The third estimation takes into account labor market characteristics and economic situation. Three variables are introduced: unemployment rate and density of employment area and the composition of the labor force of PCA. The unem-

  statistical discrimination described by Askenazy et al. (2009): employers prefer 25 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

  Travail du Centre d'Economie de la Sorbonne -2012.19

Figure 4 :

 4 Figure 4: Density of the HHI by employment area.

37

  Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

Table 1 :

 1 Average characteristics of selected employment areas

		Competitive Uncompetitive	Highly
				uncompetitive
	# observations	12	21	21
	Population	384,465	248,367	127,583
		(331,571)	(257,579)	(86,993)
	Density	0.28	0.28	0.28
	(inhab./km 2 )	(0.02)	(0.05)	(0.07)
	Immigration rate	0.07	0.06	0.08
		(0.02)	(0.03)	(0.05)
	Unemployment rate	11.3	10.8	9.15
		(2.11)	(2.20)	(2.99)
	Surface area	103,490	63,124	36,164
	(km 2 )	(84,734)	(52,143)	(23,555)
	HHI	2,148	2,705	3,987
		(156.98)	(205.2)	(1061.1)

For each category, the first line is the mean and in brackets are the standard deviation coefficients. Employment areas are too large to approximately fit customer catchment areas of stores. A second zoning is necessary to better approximate the local level of competition. Population catchment areas (PCA), "bassin de vie" in the INSEE nomenclature, are the smallest areas, where inhabitants can access to current facilities and employment. The aggregate measure of facilities contains an index on competitive facilities (retail, stores, bank...), non-competitive 10 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

Table 2 :

 2 Characteristics of selected population catchment areas

		Competitive Uncompetitive Monopolistic
	# observations	14	161	121
	Population	447,801	29,249	8,680
		(469,553)	(37,809)	(3,772)
	Surface area	1,142	330	138
	(km 2 )	(691)	(310)	(114)
	Density	438	330	138
	(inhab./km 2 )	(490)	(310)	(318)
	Immigration rate	0.07	0.06	0.05
		(0.02)	(0.03)	(0.03)
	Unemployment rate	10.7	10.0	10.1
		(1.8)	(2.2)	(2.5)
	# stores	38.9	3.5	1.0
		(35.4)	(3.0)	(0)
	HHI	2,393	4,947	10,000
		(377)	(983)

Table 3 :

 3 Names used in experiment by gender and origin

		Gender
		Women	Men
		Naïma Jlassi	Ahmed Charbit
	Moroccan	Aïda Djalouzi	Mounir Benzekri
		Fadela Khalis	Mehdi Brahimi
	Origin	Soraya Haddad	Selim Belkacem
		Gaëlle Dupuis	Pascal Martin
	French	Justine Bonnet	Nicolas Leroux
		Claire Dufour	Sébastien Rivière
		Stéphanie Masson	Vincent Dubois

correspondence study of

[START_REF] Duguet | Are Young French Jobseekers of Ethnis Immigrant Origin Discriminated Against[END_REF]

is used. They choose usual Moroccan surnames and first names are Moroccan usual names of this generation.

Concerning French-sounding names, first names are the most common in the eighties and family names are the most current ones in France (Table

3

). In both cases, names unambiguously sound Moroccan or French. Applicants' gender is clearly indicated on resumes and cover letters by the name of applicants and adjectives and nouns agreements.

Timeline

The experiment was carried out from April to July and from September to November 2011. The one-month break is due to annual closing of administrative service in August. An applicant name of each type is associated with a random chosen type of resume. By origin and gender, a resume with a motivation letter is sent to each store of the employment area. The sending order is random and two applications are sent with an interval of 15 days. 1250 supermarkets and large stores have been targeted in 54 employment areas, which is equivalent to 5000 resumes sent. 15 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

Table 4 :

 4 summarizes the callbacks for interview by origin and gender. 391 applicants received a callback from 274 stores. Women have 8.80 percent chance Callbacks by origin and gender Documents de Travail du Centre d'Economie de la Sorbonne -2012.19gender is higher and more significant amongst workers with a Moroccan origin than workers with a French-sounding name.Concerning origin, resumes with French sounding names have a 12.48 percent chance of having an interview. Equivalent resumes with Moroccan sounding names only have 3.16 percent chance of having a callback. The probability that a worker with Moroccan origin receives a callback is almost 4 times less than the probability for an applicant with a French sounding name. This difference of 9.32 percentage points is highly significant. Since names are randomly assigned during the experimental design, this difference can only be attributed to the name manipulation. This result is consistent with the findings of[START_REF] Duguet | Are Young French Jobseekers of Ethnis Immigrant Origin Discriminated Against[END_REF] that a significant discrimination against workers of Moroccan origin during the hiring process is observed in France. Dividing the sample by gender, a larger gap is observed for men than for women. In both cases, the null hypothesis of an equality of means is rejected.

		Moroccan French	Total
		[79]	[312]	[391]
	Women	3.92	13.68	8.80
	[220]
	Men	2.40	11.28	6.84
	[171]
	Total	3.16	12.48	7.82
	[391]
	H 0 : Men=Women		p=0.0098
	By origin:	Moroccan		p=0.0298
		French		p=0.0695
	H 0 : Moroccan=French		p=0.0000
	By gender:	Women		p=0.0000
		Men		p=0.0000
	For each category, the first line is the percentage of callbacks
	and in brackets is the number of callbacks. Each applicant
	sent 1250 resumes and motivation letters.
	of being called back. Equivalent resumes of male applicants have a 6.84 percent
	chance of receiving a callback. This represents a difference in callback rate of
	1.96 percentages points, which is significant at 99%. Whereas this is a women's
	job in France, it seems to be partly due to a self-selection of women, the other
	part coming from discrimination. Indeed, men receive a significant number of
	callbacks when they applicate. Breaking results by origin, the difference by
		16

Table 5 :

 5 Distribution of callbacks by store and genderRather than studying the number of callbacks by applicant type, one can use the distribution of callback at the store level. This allows observing a preference for one type of applicant or another, which better fit discrimination definition. Tables5 and 6reports three different treatments of applicants by employers. The first two lines count when there is a preference. The type A 17 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19is favored in three cases: when an A applicant and none B applicant receive a callback, when both A applicants and none B applicant are called back and when both A applicants and only one B applicant receive a callback. In the last line, both types of applicants (Moroccan/French origin, men/women) are equally treated. It occurs when no applicant is called back, or one applicant of each type receives a callback, or all four applicants are asked for an interview.

	Men Favored:	0Wo+1Me 0Wo+2Me 1Wo+2Me
	6.6	6.2	0.2	0.2
	[83]
	Women Favored: 1Wo+0Me 2Wo+0Me 2Wo+1Me
	9.9	8.3	0.9	0.7
	[124]
	Equal treatment: 1Wo+1Me 2Wo+2Me
	5.4	4.8	0.6
	[67]
	# stores	1250
	H 0 : Men=Women	p=0.002

M e stands for M en and W o for W omen. For each category, the first line is the percentage of stores corresponding to the title and in brackets is the number of store. For instance, 2W o + 1M e means that both women and one man received a callback.

Table 6 :

 6 Distribution of callbacks by store and origin o stands for M oroccan and F r for F rench. For each category, the first line is the percentage of stores corresponding to the title and in brackets is the number of store. For instance, 2M o + 1F r means that both applicants with a Moroccan sounding name and one applicant with a French sounding name received a callback.

	French Favored:	0Mo+1Fr 0Mo+2Fr 1Mo+2Fr
	17.2	12.3	4.1	0.8
	[215]
	Moroccan Favored:	1Mo+0Fr 2Mo+0Fr 2Mo+1Fr
	2.5	2.2	0.2	0.1
	[31]
	Equal treatment:	1Mo+1Fr 2Mo+2Fr
	2.2	1.7	0.6
	[28]
	# stores	1250
	H 0 : Moroccan=French p=0.000
	They are favored by 17.2 percentage points of employers whereas only 2.48
	percents of employers prefer applicants with a Moroccan sounding name. This

M 18 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

Table 7 :

 7 Callbacks by gender and HHI category

		Competitive Uncompetitive	Monopolistic
	Women	9.4	7.2	9.6
	Men	7.3	5.6	7.2
	# applications	1,542	708	250
	Men/women	0.78	0.78	0.75
	H 0 : Men=Women	p=0.037	p=0.233	p=0.334

Table 8 :

 8 Distribution of callbacks by gender and store

		Competitive Uncompetitive Monopolistic
	Women Favored	43.6	47.7	50.0
	Men Favored	29.6	32.3	30.0
	Equal treatment	26.8	20.0	20.0
	# answering stores	179	65	30
	# stores	771	354	125
	H 0 : Women=Men	p=0.012	p=0.159	p=0.222

Table 9 :

 9 Callbacks by origin and HHI category

		Competitive Uncompetitive Monopolistic
	Moroccan	3.4	2.5	3.6
	French	13.4	10.3	13.2
	# applications	1,542	708	250
	Moroccan/French	0.25	0.25	0.27
	H 0 : Mo=Fr	p=0.000	p=0.000	p=0.000

Table 10 :

 10 Distribution of callbacks by origin and store

		Competitive Uncompetitive Monopolistic
	# stores	[771]	[354]	[125]
	French Favored	77.6	80.0	80.0
	Moroccan Favored	11.2	7.7	20.0
	Equal treatment	11.2	12.3	0
	# answering stores	179	65	30
	H 0 : Moroccan=French	p=0.000	p=0.000	p=0.000

  The error term of the equation is normally distributed with mean 0 and variance σ ν . As every other characteristics are identical, variables of X i are origin and gender. X j is composed of the number of cash desk and 22 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19 the nature of the owner. X EA contains unemployment rate, the density of the area, region and immigration rate concerning origin. X P CA comprises the rate of blue and white collar in the population, if there is a central city in the PCA and the variable of interest, the HHI.

	Table 11 reports the impact of control variables on the likelihood to receive
	a callback for an interview. Estimation (1) contains only individual character-
	istics, competition index and geographical data such as region and rural/urban
	location of the PCA. To be a woman increases the probability to be called back
	by 5.6%. The likelihood for an applicant with a Moroccan sounding name to
	obtain an interview is lower by roughly 30% percentage points than likelihood
	of other applicants. These results are consistent with previous observations.

Table 11 :

 11 Estimation of the probability to obtain an interview.

		(1)	(2)	(3)
		Callback	Callback	Callback
	Woman	0.14***	0.14***	0.14***
		(0.05)	(0.05)	(0.05)
	Moroccan	-0.74***	-0.74***	-0.75***
	origin	(0.06)	(0.06)	(0.06)
	HHI	-0.035*** -0.035*** -0.035***
	(*0.01, by PCA)	(0.011)	(0.012)	(0.012)
	HHI squared	0.0002*** 0.0002*** 0.0002***
	(*0.01, by PCA)	(0.0001)	(0.0001)	(0.0001)
	Unemployment			-0.074***
	rate (by EA)			(0.021)
	Density			0.07
	(inhab./km 2 , by EA)			(0.06)
	White and blue collars			-0.63
	rate (by PCA)			(0.49)
	# cashdesks		0.005**	0.005**
			(0.002)	(0.002)
	Franchise/branch		-0.31***	-0.32***
			(0.09)	(0.09)
	Central recruitment		-0.03	-0.03
			(0.10)	(0.10)
	Ile-de-France	-	-	-
	Ile-de-France periphery	-0.17	-0.21	0.13
		(0.13)	(0.13)	(0.16)
	North	-0.51***	-0.57***	-0.20
		(0.13)	(0.13)	(0.16)
	South West	0.13	0.07	0.27**
		(0.10)	(0.10)	(0.11)
	South East	-0.18*	-0.21**	0.11
		(0.10)	(0.10)	(0.14)
	PCA with a city	-	-	-
	of more than 30,000 inhab.
	PCA without a city	0.23	0.21	0.25
	of 30,000 inhab.	(0.14)	(0.14)	(0.15)
	PCA in the periphery of a city	-0.04	-0.08	-0.07
	of more than 30,000 inhab.	(0.17)	(0.16)	(0.17)
	Constant	-0.35	-0.21	0.16
		(0.25)	(0.25)	(0.38)
	Observations	5,000	5,000	5,000
	Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
	PCA stands for population catchment area, EA for employment area.

24 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

Table 12 :

 12 Estimation of the probability to obtain an interview by gender.

	(1)
	Callback
	Interacted
	with woman

Table 13 :

 13 Estimation of the probability to obtain an interview by origin.

	(1)
	Callback
	Interacted
	with origin

28 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

29

  Documents de Travail du Centre d'Economie de laSorbonne -2012.19 cannot be classified as prejudiced or not. Table15summarizes results of the probit regression of the likelihood to be called back. The few number of observations decreases the significance of coefficients. First column is the basic estimation of the probability to be called back. Only gender and origin and Southwestern France are significant. It is worth to notice that gender coefficient is lower and the origin one is larger than in previous estimations. It suggests that discrimination against applicants with a Moroccan sounding name is underestimated and women preference overestimated. The second column contains results of the probit regression where all variables are interacted with gender.

Table 17

 17

	sums up the results of a probit regression of the likelihood to pre-
	fer one category of applicants. Coefficients are consistent with former results
	on the probability to obtain an interview. Concerning gender, coefficients are
	not significant except concerning geographical location. However, it confirms

30 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

Table 14 :

 14 Effect of application characteristics on likelihood to receive a callback Estimation is controlled for gender, origin, competition, regions, unemployment rate and density of the employment area, the number of cashdesks in the store and its way of managment, composition of population and type of PCA. Wf stands for women with a French sounded name, Wm for women with a Moroccan sounded name, MF stands for men with a French sounded name and Mm for men with a Moroccan sounded name.

			Interview
	Name Mf 1		Name Mm 1	-0.36	CV 2	0.06
				(0.28)		(0.07)
	Name Mf 2	0.18	Name Mm 2 0.051 CV 3	0.06
		(0.14)		(0.23)		(0.07)
	Name Mf 3	0.18	Name Mm 3	0.28	CV 4	-0.15
		(0.14)		(0.22)		(0.12)
	Name Mf 4	0.10	Name Mm 4	0	Second	0.05
		(0.14)		(0)		(0.07)
	Name Wf 1	0.23	Name Wm 1	0.13	Third	-0.02
		(0.26)		(0.22)		(0.07)
	Name Wf 2	0.19	Name Wm 2 0.47** Fourth	-0.06
		(0.27)		(0.20)		(0.08)
	Name Wf 3	0.18	Name Wm 3	0.26	Constant	-0.63*
		(0.27)		(0.21)		(0.34)
	Name Wf 4	0.17	Name Wm 4	0
		(0.28)		(0)
	Observations		5,000
	Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1.

Table 15 :

 15 Estimation of the likelihood to obtain an interview, limited sample.Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1. PCA stands for population catchment area and EA for employment area.

		(1)	(2)		(3)
		Callback	Callback	Callback
	Moroccan	-1.26*** -1.29***	0.02
	origin	(0.10)	(0.14)	(0.18)
	Woman	0.29***			0.28**	0.04
		(0.09)			(0.125)	(0.182)
	HHI	-0.014	0.010	-0.046	-0.005	-0.040
	(*100, by PCA)	(0.013)	(0.025)	(0.041)	(0.016)	(0.044)
	HHI squared	0.0001	-0.0001	0.0003	0.00003	0.0003
	(*100, by PCA)	(0.0001) (0.0002) (0.0003) (0.0001) (0.0003)
	Immigration rate				-0.11	-0.24
	0.065<0.095				(0.15)	(0.29)
	Immigration rate				0.04	-0.55
	>0.095				(0.19)	(0.42)
	Unemployment	-0.011	-0.009	-0.006	0.020	-0.121*
	rate (by EA)	(0.022)	(0.043)	(0.072)	(0.033)	(0.071)
	Density	-0.02	0.04	-0.11	0.04	-0.14
	(inhab./km 2 , by EA)	(0.06)	(0.10)	(0.17)	(0.09)	(0.18)
	White and blue collars	0.007	-1.075	1.815	-0.073	0.107
	rate (by PCA)	(0.502)	(1.166)	(1.498)	(0.722)	(1.913)
	# cashdesks	0.0004	0.004	-0.008	-0.001	0.003
		(0.003)	(0.005)	(0.009)	(0.003)	(0.007)
	Franchise/branch	-0.07	0.11	-0.36	-0.25**	0.44
		(0.08)	(0.16)	(0.27)	(0.12)	(0.27)
	Central recruitment	-0.03	-0.12	0.17	0.04	-0.12
		(0.09)	(0.19)	(0.32)	(0.16)	(0.33)
	Ile-de-France	-	-	-	-	-
	Ile-de-France periphery	0.09	0.57**	-0.88*	0.23	-0.33
		(0.15)	(0.27)	(0.49)	(0.31)	(0.65)
	North	-0.01	0.56*	-1.07*	0.33	-1.06*
		(0.17)	(0.33)	(0.56)	(0.29)	(0.58)
	South West	0.19*	0.48**	-0.55	0.31	-0.19
		(0.11)	(0.22)	(0.34)	(0.21)	(0.49)
	South East	-0.03	0.11	-0.25	0.01	0.16
		(0.14)	(0.32)	(0.54)	(0.26)	(0.61)
	PCA >30,000 inhab.	-	-	-	-	-
	PCA without	0.15	0.01	0.26	-0.04	0.60
	city> 30,000 inhab.	(0.16)	(0.31)	(0.51)	(0.20)	(0.48)
	PCA periphery	0.01	0.15	-0.29	0.23	-0.77*
	city>30,000 inhab.	(0.15)	(0.33)	(0.50)	(0.24)	(0.40)
	Constant	0.51	-0.37	2.01*	-0.14	1.35
		(0.37)	(0.71)	(1.18)	(0.63)	(1.47)
	Observations	1,096	1,096	1,096

36 Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

Table 16 :

 16 Estimation of the likelihood to favor a gender/origin by an ordered probit.

	(1)	(2)
	Gender preferences Origin preferences

Table 17 :

 17 Estimation of the likelihood to be preferred by gender and origin.Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 The sample only contains stores which call back at least one applicant. In estimations (1) and (

		(1)	(2)	(3)	(4)
		Women	Men	Fr. origin	Mo. origin
		favored	favored	favored	favored
	HHI	-0.009	0.043	0.057	-0.059
	(*100, by PCA)	(0.030)	(0.030)	(0.039)	(0.045)
	HHI squared	-0.0001	-0.0003	-0.0004	0.0005
	(*100, by PCA)	(0.0002) (0.0002)	(0.0003)	(0.0003)
	Immigration rate			0.25	0.23
	0.065<0.095			(0.29)	(0.39)
	Immigration rate			0.37	-0.22
	>0.095			(0.40)	(0.49)
	Unemployment	0.012	-0.018	0.150**	-0.125
	rate (by EA)	(0.053)	(0.055)	(0.066)	(0.082)
	Density	-0.20	-0.37	-4.56**	1.99
	(inhab./km 2 , by EA)	(1.89)	(2.07)	(2.27)	(2.617)
	White and blue collars	1.69	-1.24	-0.10	-1.18
	rate (by PCA)	(1.50)	(1.59)	(1.33)	(1.82)
	# cashdesks	-0.003	0.008	0.0005	0.006
		(0.00596) (0.006)	(0.007)	(0.008)
	Franchise/branch	-0.21	0.36*	-0.56**	0.37
		(0.21)	(0.22)	(0.24)	(0.28)
	Central recruitment	0.13	-0.26	0.10	0.16
		(0.25)	(0.26)	(0.27)	(0.31)
	Ile-de-France	-	-	-	-
	Ile-de-France periphery	-0.84**	0.71*	-0.07	-0.28
		(0.39)	(0.40)	(0.54)	(0.62)
	North	-0.96**	0.90**	0	0
		(0.44)	(0.45)	(0)	(0)
	South West	-0.56**	0.40	-0.28	-0.43
		(0.27)	(0.29)	(0.46)	(0.53)
	South East	-0.37	0.36	-0.68	0.60
		(0.40)	(0.42)	(0.52)	(0.60)
	PCA (city >30,000 inhab.)	-	-	-	-
	PCA without a city	0.09	-0.21	-0.68	0.46
	of 30,000 inhab.	(0.36)	(0.36)	(0.45)	(0.53)
	PCA in the periphery of	-0.052	0.07	0.96	0
	a city>30,000 inhab.	(0.36)	(0.39)	(0.59)	(0)
	Constant	0.14	-1.52	-0.32	0.46
		(0.89)	(0.93)	(1.22)	(1.42)
	Observations	274	274	253	239

Documents de Travail du Centre d'Economie de la Sorbonne -2012.19

* I gratefully acknowledge financial support from the Fonds d'expérimentation pour la jeunesse of the French Ministère de l'Emploi et de la Solidarité and from the Paris School of Economics.


Fabien Leurent
email: fabien.leurent@enpc.fr.

Vincent Benezech

François Combes

A stochastic model of passenger generalized time along a transit line

Keywords: Vehicle load, Headway rank, Passenger exposure, Wait time, Run time, Journey time

Along a transit line, vehicle traffic and passenger traffic are jointly subject to variability in travel time and vehicle load hence crowding. The paper provides a stochastic model of passenger physical time and generalized time, including waiting on platform and in-vehicle run time from access to egress station. Five sources of variability are addressed: (i) vehicle headway which can vary between the stations provided that each service run maintains its rank throughout the local distributions of headways; (ii) vehicle order in the schedule of operations; (iii) vehicle capacity; (iv) passenger arrival time; (v) passenger sensitivity to quality of service. The perspective of the operator, which pertains to vehicle runs, is distinguished from the user's one at the disaggregate level of the individual trip, as in survival theory. Analytical properties are established that link the distributions of vehicle headways, vehicle run times, passenger wait times, passenger travel times, and their counterparts in generalized time, in terms of distribution functions, mean, variance and covariance. Many of them stem from Gaussian and log-normal approximations.

Introduction

Background. The operations of a transit line, and even more of a network of lines, are submitted to variability in a number of ways. On the operator side, vehicle type may not be homogeneous, the passenger load depends on the service schedule and varies along the route, traffic disruptions arise due to causes either internal (such as human error, material incident, passenger incident or accident…) or external (such as adverse weather, malevolent intrusion, conflict with another flow…). On the demand side, the passenger experiences travel conditions along his trip, from service waiting and platform occupancy at the access station up to station egress passing by vehicle occupancy and its journey time, which vary according to the occurrence of the trip in a series of reiterations and also between passengers on a given occurrence. A major issue pertains to service reliability: any disruption causing a large delay induces a significant loss in quality of service, and the frequent reiteration of such events will make the passenger reconsider his travel decision of network route and even of transportation mode. Stated Preferences surveys have shown that frequent significant delays amount to additional travel time in a more than proportional way: for instance, the factor of proportionality was estimated to 1.5 for delays of more than 10 minutes occurring three out of 20 times in Paris suburban railways [START_REF] Kroes | On the value of punctuality on suburban trains to and from Paris[END_REF]. Such behavioral patterns must be Objective. The paper's objective is to provide a stochastic model of traffic variability and passenger exposure along a transit route. The model is designed as a sophisticated time-flow relationship at the level of the service route, in a matrix form between the stations of access and egress; thus it can be used as a component in a passenger traffic assignment model to a transit network. On the supply side, the model assumptions involve the statistical distribution of the local vehicle headways at station nodes and of the local run times along inter-station links, together with the distribution of vehicle capacity in terms of seated and standing passengers. On the demand side, a spatial pattern is assumed for the access-egress matrix of passenger flows, together with a statistical distribution (temporal pattern say on a day-to-day basis) of a volume index.

The model yields the following outcomes: (i) the distribution of vehicle journey times by pair of access-egress stations, together with the distribution of passenger loading ; (ii) the distribution of passenger physical time by access-egress pair ; (iii) the distribution of passenger generalized time by access-egress pair, assuming that crowding density adds discomfort cost to travel times. Thus the interplay of operations variability with the spatial pattern and temporal distribution of passenger flows is captured in an explicit and consistent framework.

Approach. The paper deals with the physics of traffic operations and passenger exposure to travel conditions both of service operations and vehicle load. The main variables of vehicle traffic, passenger traffic and passenger travel are cast into a probabilistic framework in the form of random variables. Variability sources are identified, among which the major one is the heterogeneity of vehicle headways. Analytical properties are established between the main model variables, in the form of functional relationships linking the CDF, PDF, mean and variance of them. This is achieved by making convenient specific assumptions: noteworthy assumptions include the conservation of headway rank by service run, normal approximations for headways and vehicle loads, or alternatively log-normal approximations when the interest lies in a product rather than in a sum of variables. Overall, the paper blends up probabilistic analysis taken mostly from the theory of renewal and survival, with traffic analysis at the two levels of transit vehicles and passengers, respectively. Previous analytical work along that line has addressed vehicle traffic only (e.g. [START_REF] Carey | Stochastic approximation to the effects of headways on knock-on delays of trains[END_REF][START_REF] Meester | Stochastic delay propagation in railway networks and phase-type distributions[END_REF] or passenger traffic restricted to the issue of passenger waiting at a platform station, as in [START_REF] Bowman | Service frequency, schedule reliability and passenger wait times at transit stops[END_REF]. Our specific assumptions extend the scope to a "transit leg" that includes the in-vehicle journey from access to egress station as well as waiting on the access platform. Recent work has shown the distribution of travel conditions and the distinction between the operator and user perspectives: [START_REF] Islam | Impact of Occupancy Profile for Waiting Time of Bus Transit Users[END_REF] on the basis of micro-simulation and Yuan et al (2011) on the basis of traffic observations. Structure. The rest of the paper is organized in five sections. Vehicle traffic is considered first, by focusing on headways and deriving some consequences on journey times by pair of entry-exit stations (Section 2). Then, passenger load by vehicle is characterized with respect to headway rank and the index of demand volume (Section 3). Next, we turn our attention to passenger exposure to in-vehicle crowding, wait time and travel time (Section 4). The consequences of service irregularity and other variations affect not only the physical times but also the "generalized time" which takes into account the discomfort of specific travel states (Section 5). Lastly, the conclusion points to the model scope, limitations and potential developments (Section 6).

Paper submitted to EWGT XV, 2012, Paris 3/14

On vehicle headways and journey times

In this paper, a transit line operated along a single service route in a single direction is considered. The stations are indexed by M m ∈ and the sections or links between adjacent stations by A a ∈ . Each vehicle run is characterized by a trajectory in space and time. The journey time is made up of the run times on the sections plus the dwell times at the stations.

The objective of this section is to model the statistical distribution of vehicle run times between station pairs along the line. The statistical population of interest is the set of runs during a reference period, for instance the morning peak hour of working days.

First, we shall model the distribution of vehicle headways ( § 2.1). Second, their propagation between stations is addressed in § 2.2. Then, a postulate is made about the "conservation of headway rank" ( § 2.3), which entails specific properties for the distribution of vehicle headways ( § 2.4) and that of journey times ( § 2.5).

On vehicle headways

] /E[ ] [ ] [ m m m η η σ = η γ .
Assuming that the incoming passengers at station m arrive independently from one another and from service schedule, their arrivals can be modeled as a Poisson process and, if the process intensity is medium or high, then it can be safely assumed that the number of passengers waiting for a given vehicle is proportional to the headway (neglecting any capacity constraint). Furthermore, the distribution of passenger waiting times at m stems from that of vehicle headway in a specific way (see Section 4).

Spatial propagation

The instant of departure of vehicle i from station m , ) (i h m , is separated from that of the next station, ) ( 1 i h m+ , by the run time along section

) 1 , ( + ≈ m m a plus the stop time at 1 + m , altogether denoted as ) (i t a : ) ( ) ( ) ( 1 i t i h i h a m m + = + .
(2.1)

Note that we also have:

) ( ) ( ) ( 1 i h i h i m m m - - = η .
So that from vehicle 1 i to vehicle i , the headways at service stations satisfy:

) ( ) ( ) ( 1 i i i a m m τ + η = η - , (2.2) wherein ) 1 ( ) ( ) ( - - = τ i t i t i a a a
is the difference in travel time along a and m .

] E[ ] E[ ] E[ 1 a m m τ + η = η - ,
(2.3) whereas, by the bi-linearity of covariance,

) , cov( 2 ] V[ ] V[ ] V[ 1 1 a m a m m τ η + τ + η = η - - .
(2.4) Formula (2.2) and its consequences (2.3-4) state the propagation of vehicle headways from station to station.

On the conservation of headway rank

Of course, the conservation of schedule order is assumed along the line, under a First In -First Out discipline. Let us focus on the rank of each run in the "local" distribution of headway, characterized by the fractile ) ( H

m m m η = α
. In this study, the postulate of conservation of headway rank is made:

) ( ) ( ) ( , , i i i n m i n m α = α = α ≠ ∀ ∀ . (2.5)
This states that if a vehicle run is associated to a relatively low (resp. large) headway at a given station, it is associated to relatively low (resp. large) headways at all the stations of the line. However, local magnitudes may differ, only the rank remains stable.

The postulate is realistic enough in various instances:

-when the operations are regular along the line, the headway at the initial station is maintained from station to station.

-If most of traffic disruptions occur on a given section a , then the main source of variation pertains to a τ and the rank in its distribution may be assumed to apply on the rest of the line as well.

The most noteworthy consequence is the functional dependency between the headways along the line:

) ( H ) ( H 1 1 1 - - - η = α = α = η = α m m m m m m , hence (2.6) ) ( H H 1 1 1 - - - η = η m m m m o . (2.7) Thus 1 - η - η = τ m m a also is a function of 1 - η m .
Assuming further that the dependency is linear, i.e.

µ + λη = τ -1 m a for some parameters 0 ≥ λ and µ , then it would hold that ] [ ]. [ ) , cov( 1 1 a m a m τ σ η σ = τ η - - .
(2.8)

This relationship notably holds for random variables 1 -η m and a τ that are distributed along a similar pattern, i.e. when

] [ ] E[ ] [ ] E[ 1 1 1 - - - η σ η - η ≈ τ σ τ - τ m m m a a a .
This holds notably for perfectly correlated normal variables: in this case a valuable complementary property is that m η is normal, too, yielding normal variables for headway and section time variation along the line.

Paper submitted to EWGT XV, 2012, Paris 5/14

Vehicle journey time with respect to schedule order

Let us turn to the journey time of each vehicle run with respect to its order in the schedule of operations, denoted by i . Let r denote a reference station and r m ≥ a subsequent station in the selected direction of traffic, ) (i t rm be the journey time of vehicle run i between the instants of departure from r and m , )

(i h m and ) (i h r respectively. It holds that ) ( ) ( ) ( i h i h i t r m rm - = , so ) ( ) ( ) 1 ( ) ( i i i t i t r m rm rm η - η + - = and
( )

∑ = η - η + = i j r m rm rm j j t i t 1 ) ( ) ( ) 0 ( ) ( , (2.9)
Wherein vehicle run #0 is an ideal vehicle run of nominal performance which immediately precedes the reference period. By the linearity of expectation, it then follows that

]) E[ ] (E[ ) 0 ( )] ( E[ r m rm rm i T i T η - η + = .
(2.10)

Given the fact that the α(i) are assumed i.i.d., the runs are mutually independent, which implies that:

] V[ . )] ( V[ r m rm i i T η - η = , (2.11)
Under the conservation of headway rank and the assumption of normality,

∑ ∈ τ + η = η ] , [ m r a a r m satisfies that ∑ ∈ τ σ + η σ = η σ ] , [ ] [ ] [ ] [ m r a a r m , which entails that ] [ ] [ ] [ ] [ ] , [ r m m r a a r m η - η σ = τ σ = η σ - η σ ∑ ∈ .
(2.12)

Combining (2.12) and (2.11), we get that

] [ )] ( [ r m rm i i T η - η σ = σ . (2.13)
Of course the assumption of conservation of headway rank and the run independence are likely to interfere in practice. However, eqns (2.10) and (2.13) give some insight into the progressive deterioration of the vehicle journey time with respect to the order of the run in the schedule of operations, when submitted to irregularity and random disruptions.

Vehicle loading

So far, two sources of variability have been made explicit: headway rank, denoted as α , and the order in the schedule, denoted as i . In this section, two other sources are introduced, namely the level of passenger transport demand, denoted as β , and the train capacity, denoted as κ . Sources α and β jointly influence the vehicle load in passengers. Sources α , β and κ jointly influence the ratio of load to capacity by vehicle run.

This section establishes some analytical properties of the passenger load and load ratio along a transit line, by taking into account the demand (passenger flow) between stations of entry and exit.

Assumptions about passenger demand

A reference period of given duration is considered for line operations. In fact it refers in some average way to a population of periods, for instance the morning peak hour throughout a series of working days. To depict the variability of periods, let us associate to each period its level β of passenger demand, with CDF B in the population of periods.

Paper submitted to EWGT XV, 2012, Paris 6/14

Within a given period, passenger flow is modeled as a stationary random process, with macroscopic properties as follows: between any pair s r < of stations along the line, the passenger flow arriving at r and destined to s

during time interval ] , [ h h ′ amounts to ) ( h h q rs - ′ β
. Thus the set of ] : [ s r q rs < describes the spatial structure of passenger demand per unit of time.

Across the population of periods, we could define β so as to satisfy that 1 ] E[ = β ; however we shall keep ] E[β in the formulae for the sake of traceability.

Vehicle loading conditional on β

Assuming that passenger demand is not restrained by vehicle capacity, at each station r of entry a given vehicle run will attract incoming passengers in proportion to its local headway, r η . On section a , the vehicle load denoted by a y consists in those passengers having entered at station a r ≤ (with obvious notation for ≤ and ≥ for position along the line):

∑ ≥ ≤ β η β = a s a r r rs a q y , ,
.

(3.1)

Then, on average:

∑ ≥ ≤ β η β = a s a r r rs a q y , , ] E[ ] E[ . (3.2)
Keeping to the postulate of conservation of headway rank, the vehicle run is characterized by its fractile α so that ) ( H )

1 ( α = η - r r . Then ∑ ≥ ≤ - β α β = α a s a r r rs a q y , ) 1 ( , ) ( H ) ( . ( 3

Vehicle loading, overall distribution

Let us now aggregate the analysis with respect to β . Denoting

∑ ≥ ≤ η = ξ a s a r
r rs a q , the random variable of reference link flow and by a X its CDF, it holds generally that:

∫ β β = ≤ βξ = ) dB( ) / ( X } { Pr ) ( Y z z z a a a .
(3.6)

In reality, demand level β may influence vehicle operations -for instance because the number of boarding and alighting passengers may determine the dwelling time. However, for simplicity, independence is assumed in this model, yielding that:

∑ ≥ ≤ η β = a s a r r rs a q y , ] E[ . ] E[ ] E[ . (3.7) ] V[ . ] E[ ] E[ . ] V[ ] V[ 2 2 a a a y ξ β + ξ β = due to ( 2 ), hence 2 ]² E[ ²] ² E[ ] var[ XY Y X XY - = ]² E[ ]² E[ ²] E[ ²] E[ Y X Y X - = = ] V[ ]² E[ ] V[ ²] E[ X Y Y X + Paper submitted to EWGT XV, 2012, Paris 7/14 ( ) ( ) 2 , 2 2 , ] [ . ] E[ ] E[ . ] V[ ] V[ ∑ ∑ ≥ ≤ ≥ ≤ η σ β + η β = a s a r

Vehicle loading ratio

Vehicle capacity, denoted as κ , pertains to the number of seats plus a reference number of positions for passenger standing with sufficient comfort (e.g. 4 persons per square meter). Heterogeneous vehicles may be used to operate the transit line, leading to the variability of capacity hence of the ratio of passenger load to capacity.

Let us denote that ratio as

κ βξ = κ = / / a a a y z . (3.9)
While it is quite natural to assume the independence of β and κ , it would be a wise policy of line operations to assign vehicle types according to the planned headways, by associated larger capacity to larger headways so as to balance the load ratio across the runs. Under such a balancing policy, the load ratio could be analyzed in the same way as vehicle load by replacing ) (α η r with α κ α η / ) ( r . On the contrary, a negligent policy may be modeled based on the assumption of independence between κ and α as well as β . Then the load ratio would have mean and variance as follows:

∑ ≥ ≤ - η κ β = a s a r r rs a q z , 1 ] E[ . ] E[ . ] E[ ] E[ . (3.10) 2 -1 -2 ] ]E[ V[ ] ]V[ E[ ] V[ a a a y y z κ + κ = .
(3.11)

Passenger exposition to physical time

Let us come to the perspective of the user at the level of the individual trip, as opposed to the operator's one at the level of the vehicle run.

User's exposure

Let us recall some basic properties of renewal theory (e.g. Kleinrock, 1975, pp. 169

) ( H ). ( B ) ( H ). ( B ) , ( f u u o o u η β = η β η β ∝ η β r r & & & & (4.4) In which ] /E[ ) ( B ) ( B o o u β β β = β & & and ] /E[ ) ( H ) ( H o o u r r r η η η = η & & . As η β = . u r n , its CDF is ∫ ∫ β β = β = ≤ βη = β ) ( dB ) / ( H ) ( dB ) ( N } { Pr ) ( N u u u u , u x x x x r r r
.

(4.5)

The independence property enables us to establish the mean and variance of group size as follows: From the equation above stems the unconditional variable u ,e a y . Its CDF is given by:

] E[ ] ) E[( ] E[ ] ) E[( ] E[ ] E[ ] E[ o 2 o o 2 o u u u r r r r n η η β β = η β = . (4.6)       -       +       - = η β + η β = β β β β η η η η η η β β 2 o 2 2 o o 3 o o 2 o 2 o 2 2 o o 3 o o 3 o ] E[ ] ) E[( ] E[ ] ) E[( 2 ] E[ ] ) E[( ] E[ ] ) E[( ] E[ ] ) E[( ] E[ ] ) E[( 2 u u u 2 u u ]) ](E[ V[ ] V[ ] E[ ] V[
∫ β η η β ≤ = ≤ = β η d d ) , ( f } { Pr } { Pr ) ( Y u u , ,
) / ( X H ) / ( X / ) ( X / ) ( H o ) 1 o( o ) 1 o( , ) 1 o( u , , , β ≤ η ⇔ β ≤ α ⇔ β ≤ α ⇔ β ≤ α ⇔ ≤ - η η - ≥ ≤ η - β η ∑ z z z z q z y a e
∫ ∫ β β = β β ≤ = - β ) ( B d ) / ( X H H d ) ( f } { Pr ) ( Y u o ) 1 o( u u u , ,
= + + + + + = β β β .
The ratio to the average vehicle load in the operator's perspective amounts to

s dispersion relative large too not for ) 1 )( 1 ( ] ) 1 ln( ) 1 ln( exp[ ) 1 ( ] exp[ ] exp[ ] E[ ] ) E[( ] E[ ] E[ 2 2 2 2 o 2 o 2 o 2 o u ,

Run time

In section 2.3 some statistical properties of run time have been established for vehicles: schedule order i determines the mean and variance of run time ) (i T rs . Any user that arrives at station r at a given instant h will board a vehicle of order i which is random due to irregularity, so he will get a random run time.

]] /E[ ) int[( 1 0 r h h i η - + ≈ on the reference period ] , [ 1 0 h h . Let ) ( 1 h i I = and I / 1 be the elemental probability of } ,.. 1 { I i ∈ . The average run time is ] E[ ] E[ E setting by E ) 0 ( ]) E[ ] (E[ ) 0 ( )] ( E[ ] E[ 2 1 1 1 1 1 u r s I rm I i I r s rm I i rs I rs t i t i t t η η η η - = ∆ ∆ + = - + = = + = = ∑ ∑ (4.14)
By the law of total variance, the variance of the run time is made of an interclass part plus an intra-class part in the following way:

( )

2 12 1 2 2 1 2 1 2 24 1 2 1 2 1 1 2 2 1 2 1 1 2 1 1 2 u 1 u ) ( E ) ( E ] [ setting by ) ( ) ( E )] ( [ ]) E[ )] ( (E[ ] V[ 2 σ σ η η σ σ σ σ ∆ + ∆ = ∆ + ∆ = - = ∆ ∆ + - ∆ = + - = - + + - = = + = = ∑ ∑ ∑ ∑ I I I I r s I i I I i I I I i rs I I i rs rs I rs i i i t t i t t (4.15)

Wait time

The user wait time on the station platform, e w , amounts to the residual span (or lifetime) of the on-going headway interval. From survival theory, its PDF is

] E[ ) ( H 1 ) ( W o o e e e x x η - = & . ( 4.16)
This leads to the following relationships between the moments of the two variables:

) 1 /( ] ) E[( ] E[ ) 1 ( ] ) E[( ] E[ u o 1 o + η = η + η = + k k w k e e k e

Travel time

The travel time of a user between stations r and s is composed by the wait time at r , r w , plus the run time between the two stations, u There may be some correlation between the two components. However independence may be assumed as a crude approximation, yielding:

] V[ ] V[ ] Ṽ[ u u rs

Platform crowding

A related issue pertains to the number of passengers waiting on platform at a given station r .

At any instant, this number is proportional to the level of the incoming flow, ∑ > β r s rs q .

, times the time elapsed since the departure of the last vehicle. From survival theory (e.g. Kleinrock, op cit), the latter is the random variable is independent of β , yielding

) ( ] E[ ] E[ ] E[ u 2 1 ∑ > β η = r s rs r r q S (4.25) [ ] 2 u u 2 2 ] E[ ]. V[ ] V[ ] E[ ) ( ] V[ r r r s rs r q S η β + η β = ∑ > .
(4.26)

The perspective of either the operator or the user must be specified by setting the adequate distribution of β .

On passenger generalized time

To a trip-maker, the "generalized time" of travel is a comprehensive disutility to capture both the physical travel time and the quality of service during the trip. Each physical state (e.g. sitting in-vehicle) or transition (e.g. vehicle egress) within the trip sequence, is associated with a specific penalty factor: from 1 for sitting in-vehicle to 2 for standing in-vehicle under dense crowding or more for waiting in crowd with no traffic information. The physical time spent in a given state is multiplied by its penalty factor to yield the generalized time of that state. This is aggregated along the trip sequence to yield the generalized time of the trip. It is used in discrete choice models of network route or transportation mode. It is also the basis to evaluate the benefits and costs of a transport plan to the community.

The formation of generalized time

The notion of generalized time involves penalty factors that vary across the individual tripmakers. Small persons resent standing in a crowd more than tall ones do. In general, old persons move and walk more slowly than younger ones. People are more or less sensitive to fatigue. Let ε denote the particular sensitivity of a given individual.

Wait time r w and link time a t are transformed into generalized times, denoted as ε ω r and ε θ a , respectively. The generalized travel time amounts to

∑ ∈ ε ε ε θ + ω = λ [ , ] ,
s r a a r rs .

(5.1)

To model the dependency of ω and θ on the crowding density, assume that y along successive links are correlated, too. Furthermore, platform variables and link loads are correlated due to headway rank. As all the correlations are positive, the generalized travel time conditionally to ε is subject to large relative dispersion.

) ( r r r r S w ε ε ψ = ω , ( 5

In-vehicle discomfort

Let us focus on in-vehicle time and the influence of crowding density on its specific penalty factor. A well-known model is the so-called BPR function (e.g. [START_REF] Spiess | Optimal strategies: a new assignment model for transit networks[END_REF]: to the physical link time. In the operator's perspective (resp. the user's one), the average additional cost is evaluated as (5.8) . Then = ρ 1.13 and the ratio varies from 1.13 to 3.5 as b is changed from 1 to 4. The discrepancy between the two evaluations would be much larger for larger values of exponent b . This demonstrates the need for accurate estimations of penalty functions and a consistent, user-oriented evaluation of vehicle crowding in the cost-benefit assessment of transport plans.

] ) / E[( ] E[ ] ) / ( E[ SC o/u o/u o/u o/u o/u

Numerical instance

Conclusion

A model of traffic along a transit line has been provided at both levels of traffic unit, the vehicle versus the passenger. The perspectives of the operator and the user have been identified. Based on a powerful postulate, the conservation of headway rank, it has been shown that service irregularity and demand variations, as well as other factors such as vehicle order in schedule, vehicle size and passenger sensitivity to quality of service, affect the passenger conditions of travel significantly. Crowding density above a ratio of say 80% exerts major influence on generalized travel time. The operator perspective is plagued with bias that must be corrected to represent passenger conditions objectively.

The model captures a set of variability sources. Analytical formulae have been established to assess their respective effects. The main postulate is the conservation of headway rank. Gaussian or log-normal approximations have been made to yield convenient approximations; in the authors' opinion their effect is innocuous.

The established properties will be useful in models of traffic assignment to a transit network, as they pertain to travel conditions hence to the leg quality of service, which determines the passenger travel choice of a network route.

  in the previous section the sum of totally dependent random variables sharing a Gaussian pattern satisfies that

  load by link as experienced by the userDepending on his entry station e , the user travelling along link e a ≥ experiences there a vehicle passenger load as follows, wherein u ,e r η depends on the entry station: postulate in the operator's perspective is maintained in the user's perspective. Then, conditionally to η:

  a b takes positive values such as 1 or 4, whereas factor a c takes positive values between 0 and 3 typically. Formulae (5.4) and (5.3) state that crowding discomfort inflicts a specific additional cost of

Fig

  apparent ratio, the experienced crowding density is equal to the disutility factor at 1 one: it differs from the apparent ratio in a significant yet not major amount.Irregularity also affects the base travel time, ] E[ a t . Between stations r and s , from (4frequency delivered at station r during a reference period of length H , instance, along the line A of the regional railways in the Paris area, at the morning peak hour westwards, thePaper submitted to EWGT XV, 2012, Paris 13resulting additional time is about 3' per trip. The train capacity is about 2,000 passengers and the apparent occupancy ratio of 83% upstream. The additional cost per trip, from nominal quality of service of '

Figure 1 .

 1 Figure 1. Generalized time versus Occupancy ratio, according to variability parameter.

  To gain further insight into the structure of influences, let us add to the assumption of Gaussian headways the approximation of the resulting flow, a ξ , by a log-normal variable

												y	a										r	a	s	a	q	rs	r	q	rs	r	.	(3.8)
	with same mean and standard deviation,	E[ a ξ	]	and	[ a ξ σ	]	. Denote by a m and a s ,
	respectively, the mean and standard deviation of	a ln . From the classical properties of log-ξ
	normal distributions, these are related to the moments of a ξ by:
	E[	ξ	a	]	=	exp(	a m +	2 1 a 2 s	)
	σ	2	[	ξ	a	]	=	(exp(	s	2 a	)	-	) 1	.	E[	ξ	a	]	2
	Assuming lastly that	β	≈	LN(	β m	,	β s	)	, then the link load	βξ	a	≈	LN(	m β	+	m	a	,	2 β s	+	s	2 a	)	.

  sq).

	By integration, the factor of proportionality amounts to	1	/E[	] η . The moments of u r o r η stem
	from those of o r η at the next order:
	E[( η	u r	)	k	]	=	E[( η	o r	)	k	1 +	]	/E[	η	o r	]	.	(4.2)
	Consider now the size of the passenger group that includes the individual user, to board in a
	vehicle run at station r , u r n . Its probability density stems from the density	) f u η , ( β	of pair
	) ( η , β , which is related to the PDF	) f o η , ( β	in the following way:
	f	u	, β (	) η	∝	β	η	f	o	, β (	) η	,	(4.3)
	where f o is the PDF of passenger group sizes from the perspective of the operator. Assuming
	independence between β and η, then			f	o	, β (	) η	=	B &	o	( β	).	H &	o r	(	) η	: thus independence is
	maintained in the user's perspective, since
	Denote by o H r the CDF of headway duration r η and by o H r & its PDF, with superscript o to
	mark the operator's perspective. A user willing to board at r arrives on platform at a random instant, which will belong to a headway interval of duration η with a probability proportional
	to η: in the user's perspective, marked by superscript u ,
			H &	u r	(	) η	∝	η	H &	o r	(	) η	.	(4.1)
	Paper submitted to EWGT XV, 2012, Paris																8/14

  ) provide a basis to analyze the influence of passenger flow on travel disutility. Taking wait time and link time as random variables, then so are ε ω r , ε θ a and

	Formulae (5.1-3ε λ , rs
	conditionally to ε . From the previous section, r w and r S are correlated. Link loads u a
															.2)
	θ	a	ε	=	t	u a	ϕ	a	ε	( u a y	,	κ	)	.	(5.3)
	Paper submitted to EWGT XV, 2012, Paris												12/14