Emmanuel Duguet
email: emmanuel.duguet@u-pec.fr

Loic Du Parquet

Pascale Petit

Www Tepp Eu

Loïc Du Parquet

HIRING DISCRIMINATION AGAINST WOMEN: DISTINGUISHING TASTE BASED DISCRIMINATION FROM STATISTICAL DISCRIMINATION

Keywords: C51, C93, J16, J24, J71 Hiring discrimination, Field experiments, Gender, Asymptotic Least Squares, France

We propose a new method which allows for measuring separately taste based discrimination from statistical discriminations in the hiring process. We consider two types of statistical discriminations against women: first, when a recruiter doubts the productivity of the workers; second, when a recruiter anticipates a maternity leave. We show that the experimental data that we have collected can be represented by an over-identified model, which can be estimated optimally by the Asymptotic Least Squares. The method is applied to experimental data on three construction jobs: masonry, plumbing and electricity. We find that each job exhibits a different discrimination type. Furthermore, the most obvious forms of discrimination may not be the most harmful.

Introduction

Over the last decades, women have increased their qualification level and their activity rates (OECD, 2012). However, the strong inequalities between women and men in the labour market remain a major societal challenge [START_REF] Bertrand | New Perspectives on Gender[END_REF]. Inequality persists in terms of working time, working conditions, occupation and sector. This leads to income inequality.

Women employment suffers both from a vertical segregation, the glass ceiling, and from a horizontal segregation, gendered occupations. Therefore, despite of the development of new technologies, women and men continue to specialize in different occupations in the USA [START_REF] Hegewisch | Separate and not equal? Gender segregation in the labor market and the gender wage gap[END_REF] and in Europe [START_REF] Bettio | Gender Segregation in the Labour Market: Root Causes, Implications and Policy Responses in the EU. EU Expert Group on Gender and Employment[END_REF]. For instance, according to OECD (2012), more than 70% of the workers in education, health and social services are women. This is of consequence in France, since the half of the gender hourly wage gap, estimated at 18.4%, can be explained by occupation differences (Chamki, 2015).

Notwithstanding some progress in occupation balancing, only 17% of occupations in the French labour market included at least 40% of women or men [START_REF] Naves | Lutter contre les stéréotypes filles-garçons[END_REF]). These occupations represented 16% of French employment over 2009-2011. One of the sector were women are especially at a disadvantage is construction. In 2014, they represented 5% of this sector's total employment, even though the environment was favourable. Indeed, the Construction Federation had announced its will to triple women employment, counting on a change in mentalities, strong needs of qualified personnel and less physically demanding working conditions. At the same time, communication campaigns by public authorities are accompanying this decision by the Construction Federation. The goal of these private and public actions is to correct the over-representation of men in the construction sector. It originates both from demand and supply factors.

On the supply side, the disequilibrium could come from the under-representation of women in the construction training fields. Since few women choose the construction training channels, few candidate and get the jobs. And girls indeed do different choices than boys. According to the French Ministry of Education (2012), girls represented 1% of the pupils or apprentices in the building-construction-roofing trainings in 2010, and 9% in the building-constructionfinishing trainings. The same year, the proportion of girls in office secretary training reached 92%, and 91% in health and social occupations. On the demand side, a low proportion of women could come from hiring discrimination [START_REF] Heckman | Detecting Discrimination[END_REF]. Several discrimination mechanisms may be at work. First, taste discrimination from employers, the other workers or customers may reduce the access of women to some occupations [START_REF] Becker | The Economics of Discrimination[END_REF]. The second mechanism, statistical discrimination, is based on beliefs about the discriminated group (Arrow, 1972; [START_REF] Phelps | The statistical theory of racism and sexism[END_REF][START_REF] Spence | Job Market Signaling[END_REF]. At the hiring stage, an employer may not observe the productivity of the candidate perfectly well and, for this reason, forms an anticipation from both objective and subjective elements. At the hiring stage, women may be discriminated because of an increased risk of career interruption (maternity leaves) and, in the construction sector, because of the beliefs of the employer regarding the productivity of women in this field.

In this paper, we focus on labour demand. We examine whether there is a gender discrimination in three occupations of the construction sector. We consider three types of discriminations: taste discrimination, statistical discrimination on productivity beliefs and statistical discrimination on career interruptions. We have performed correspondence tests designed to address this issue [START_REF] Firth | Sex Discrimination in Job Opportunities for Women[END_REF][START_REF] Neumark | Sex discrimination in restaurant hiring: an audit study[END_REF][START_REF] Riach | Field experiments of discrimination in the market place[END_REF]. In order to distinguish the three discrimination types, we use the differences between them. Taste discrimination should apply to all the women. Statistical discrimination on productivity beliefs should apply to women with standard qualifications only. The most difficult case is that of statistical discrimination on career interruptions. We can obviously not cancel the ability of young women to have children by modifying a CV template. Still, we can select offers for which there is no extra cost associated with a maternity leave. In France, the only cost for the firm is the replacement cost since the replacement revenues are paid by the Sécurité Sociale. Therefore, there should be no gender discrimination on the shortest contracts, since the replacement issue is the same for women and men.

The first section presents the experiment which produces the main statistics. The second section is about the identification of the discrimination coefficients, because the different discrimination types are entangled. In the third section we present an original method for exploiting the results of correspondence tests. We conclude to the presence of different discrimination types in the last section.

The experiment

We have collected data about the construction sector in the Paris area between February and July 2015. We have replied to all the full-time jobs posts for electricians, plumbers and masons. This includes both short term and long term contracts.

Candidates. Four candidates were sent in reply to each offer: a woman and a man with the standard qualification, and a man and a woman with an excellence qualification. Table 1 indicates the identity of the candidates. All the candidates have French sounding first and last names,1 are either 23 or 24 years old, childless and own a driving licence and a car. 2 . They had a vocational training certificate (CAP) in the same profession, in 2008 or 2009 (depending on their age). They have three professional experiences in small companies, did not experience any unemployment period and are searching on the job. 3 . They live inside the city of Paris, in districts ("arrondissements") with comparable socio-economic characteristics. 4 Overall, we have given to our candidates the characteristics which are the most favourable in the French labour market according to the previous applied discrimination literature, except for the three characteristics that the wish to test (gender, qualification, maternity). We did not use any photograph to avoid appearance biases (see Rich, 2017), used standard and impersonal hobbies (sport, cinema, reading, music) and have included some differencing elements in the CV layout. We have randomized the differencing elements among the candidates.

The CAP (Cerfificat d'Aptitude Profesionelle, literally "professional capacity certificate") is a vocational training certificate which grants a qualified worker/employee degree. It exists for around 200 professions. 188,386 CAP have been granted in France in 2015. We focus on three professions: electricity, plumbing and masonry. This basic diploma is often demanded by the construction firms in their posts. We indicate it as the "required" level in our statistical model.

In order to implement our methodology, we need to distinguish short and long contracts. After examining the distribution of the contracts durations, it appears that our method is applicable if we keep, on the one hand, the contracts of 6 months or less and, on the other hand, Excellence: "best French apprentice" (MAF) or "Worldskills competition" (OM) regional laureates the contracts of 12 months or more (including the permanent contracts).5

Excellence qualifications (MAF and OM). The MAF ("un des Meilleurs Apprentis de France", literally "one of the best French apprentices") is a prize created in 1986 by the MOF National Society (MOF, "un des Meilleurs Ouvriers de France" means literally "one of the best French craftsmen"), in 104 professions. Its goal is to "promote among apprentices ... the taste of well done work, asserting their personality, their passion, spirit of initiative, progress in their applied competencies, obtaining the fair reward of their effort and to testify with pride about the efficiency of their training to manual professions". Depending on their profession, the candidates must either make a craft work during 5 months or pass a trial. The best apprentices obtain a medal. The contest takes place in three steps: first, at the département level. 6 The best apprentices get a bronze, silver or gold medal. The silver and gold medal at this level can compete at the regional level. 7 . A the regional level, the best apprentices can get a gold or silver medal. Finally, the regional gold medals can compete at the national level, were gold medals only are awarded. In 2015, there were 5196 participants (in all professions). There were 3472 laureates at the departement level, 1517 at the regional level. 817 apprentices went in final, and 316 were rewarded. The national level of the competition would send too strong a signal and cause detection because the laureates are invited to a ceremony by the President of the Senate. We indicate a gold medal at the regional level, which represent 13% of the total number of candidates.

The OM ("Olympiade des Métiers" or "Worldskills Competition") is organized by the Regional Councils in partnership with the professional and training organisms in 50 professions. It is a three-stage contest. First, at the French regional level; second, at the national level where a team is made for each profession; third, the national teams are sent at the Worldskills Competition, organized every two years. In 2015, the competition took place in Sao-Paulo. There were 1000 finalists from 59 countries. About 6000 French apprentices have participated to this competition. In order to avoid detection, we cannot use the national level selection, because the team is received by the President of the French Republic. We indicate a selection at the regional level, which represent 800 candidates out of 6000. The selection rate is therefore 13.3%, close to the MAF selection level. Overall, our excellence qualifications indicate candidates if the first decile of the competitors. This achievement could be used for international comparisons because it exists in many countries.

Experiment and protocol tests. Table 2 provides some sample statistics. We have data 133 posts for masonry, 141 for electricity and 288 for plumbing. This corresponds to the dispatch of 2248 CVs (4× 462 posts). The global callback rates are high, at least one of the four candidates gets a callback in 29.8% of the cases for electricity, 36.1% for plumbing and 24.8% for masonry. We need to perform two tests in order to validate our experimental protocol. First, we check that the rotation of CVs was efficient, by performing a chi-squared test of independence between the sending order of the candidates and their callback status. Second, in order to avoid detection, we cannot send two MAF or two OM candidates. We send two CAP, one MAF and one OM candidates. This raises the issue of differentiated effects of MAF and OM candidates, and we need to test this hypothesis.

The tests are reported in Table 2. We never reject the independence assumption between the sending order and the callback status at the conventional levels (p-value between 0.57 and 0.98). In order to test the homogeneity of the excellence characteristics, we have performed the following test. We first compute the callback rate difference between the MAF candidates and the CAP candidate on the same posts; this difference eliminates (additive) unobserved heterogeneity. We get an estimate of the MAF advantage over the standard qualification. Then, we perform the same operation for the OM candidate and get an estimate of the callback rate advantage of the OM candidate over the standard candidates on the same posts. Finally, we test the equality of these two differences, separately for each gender and profession. This is a difference-in-differences test. The results are presented in Table 2: we never reject the homogeneity effect at conventional levels of significance (p-values between 0.149 and 0.907). For this reason, we will regroup the OM and MAF characteristics under the "excellence" appellation in the statistical model.

The raw callback rates are reported in Table 3. They mix all the effects of the components model and, for this reason, are hard to interpret. Overall, men tend to be called more often than woman, so that some discrimination may be at work. In electricity, men enjoy an advantage on long term contracts, but not women. Something must restrain the hiring of women on long term contracts. For masonry, women are almost always ranked behind their male counterpart. For plumbing, men are not preferred to women for the strongest qualification, but this can happen for low qualifications. Something reduces the hiring of standard qualification women.

Identification and Estimation

We wish to distinguish taste discrimination from statistical discrimination. There are two types of statistical discrimination against young women: first, the employer may question their professional skill; second, the candidate could be pregnant in a near future. Our methodology allows for estimating these two types of statistical discrimination separately. 8The identification of these discrimination components relies on the differences between them. Taste discrimination, like sexism, should apply to all women. It is not the case of the two other discriminations. Statistical discrimination on skills may only apply to the women with the standard skills, not to the women with excellence qualifications. Here, we use two excellence markers, which indicate workers at the top of their profession. Therefore we can assume that statistical discrimination on skills apply to the standard qualification level only. There remains to isolate statistical discrimination on pregnancy. Here, it should apply to all the women, like taste discrimination, but there is one way to isolate its effects. We use information about the length of the labour contract. If the contract is very short, the probability that a maternity could affect the firm is negligible, since the firm has anticipated the end of the contract. We consider contracts whose duration is lower than 6 months, and compare them to contracts of 12 months and more. Therefore we do not suppress the maternity characteristic from the candidates, since it is impossible, but its consequences for the firm.

Notice that this method can be easily applied to all correspondence tests: adding an extra qualification to some candidates is straightforward, and the term of labour contracts is indicated in almost all job offers. In order to clarify the important identification issue, we use a component model. We also use this model in order to discuss the issues of unobserved heterogeneity and optimal estimation.

Identification

We model the probability of a positive answer. Since the data are experimental, we will consider a components model. There are eight probabilities since there are two types of labour contracts (less than 6 months, 12 months and more) and we send four candidates in reply to each of them. The four candidates correspond to the two genders times the two qualifications. Gender is denoted by w and m (woman, man) and the qualification by r and e (required, excellence) and the length of the labour contract by s and (short, long). The probabilities for the short term contracts are described by the following equations:

Pr(s, m, r ) = θ s + u s,i Pr(s, m, e) = θ s + θ e + u s,i Pr(s, w, r ) = θ s + δ T + δ Q + u s,i Pr(s, w, e) = θ s + θ e + δ T + u s,i
where u s,i is the job level heterogeneity. It may be specific to each job post and is likely to be correlated with all the other components of the model. We will eliminate this component by differencing from a benchmark case. Since the model includes a constant term, θ s , we can assume E(u s,i ) = 0 without loss of generality. The parameter θ s represents the job opportunities in the labour market for short term jobs, labour market tightness, since it represents the average probability of success for a man with the required qualification. By definition, this candidate should not suffer from discrimination and provides a natural benchmark. The second probability concerns the excellence candidates. The effect of excellence is denoted θ e , it is not a discriminatory component, and measures the potential increase in the recruitment probability caused by an excellence qualification. We expect θ e ≥ 0. Then come the probabilities for women. By definition, they include the gender based discrimination components, denoted δ. The first component, δ T , is the taste discrimination coefficient. Since discrimination reduces the hiring probability, we expect δ T ≤ 0 in the presence of a Beckerian discrimination. The statistical discrimination on the labour quality also contributes to the hiring probability, and we denote it δ Q . By definition, it only affects women with the standard qualification, not the other women. Finally, there is no effect related to pregnancy in this first block of equations because they deal with short term contracts. For the long term labour contract we must account for statistical discrimination related to the maternity leaves (denoted δ M ). We get:

Pr( , m, r ) = θ + u ,i Pr( , m, e) = θ + θ e + u ,i Pr( , w, r ) = θ + δ T + δ Q + δ M + u ,i Pr( , w, e) = θ + θ e + δ T + δ M + u ,i
where E(u ,i ) = 0 without loss of generality since there is a constant term θ . Here we should be careful that the unobserved heterogeneity term u ,i can have different distributions for long run and short run contracts, so that we cannot take a direct difference between the probabilities of the long and short run contracts. One simple reason is that we provide an application in the construction sector, where the duration of a contract may be related to the duration of a construction site. We must take the differences inside each category of labour contract before to go any further. These differences eliminate the fixed effect heterogeneity.

Since we send four candidates on each offer, we can use differencing from the benchmark case: a man with the required qualification. These probabilities measure the difference of treat- Women with the required qualifications can be discriminated both because they are woman (δ T ) or because the recruiter doubts their qualification (δ Q ). Women with an excellence qualification can be discriminated only because they are woman (δ T ). Using the terminology of asymptotic least squares (henceforth ALS), it is clearly possible to invert the previous system and write the parameters of interest (θ e , δ T , δ Q ) as functions of the auxiliary parameters (the three probability differences). We get:

θ e = D(s, m, e) δ T = D(s, w, e) -D(s, m, e) δ Q = D(s, w, r ) -(D(s, w, e) -D(s, m, e))
the excellence qualification effect is measured by comparing the two male candidates, since their probabilities are not affected by discrimination; taste discrimination is measured by comparing the two excellence candidates, since statistical discrimination is absent from both probabilities, and statistical discrimination on skills is obtained by a difference in differences, equal to Pr(s, w, r )-Pr(s, m, r )-(Pr(s, w, e)-Pr(s, m, e)) after simplification, which represents the variation of the difference of treatment caused by excellence. For the long term contracts, we take the differences from the benchmark case ( , m, r ): the first equation clearly indicates an overidentification case since it is a new way to estimate θ e . In order to get δ M , there are also two different ways to proceed. First, one can compare the probability differences for short and long run contracts, for the women with the required qualification. Second, we can use the equivalent quantity on the excellence qualification. This gives the following overidentification constraint: w,w,e) Overall, we have six probability differences, which represent the auxiliary parameters in the ALS terminology. From these probabilities, we estimate four structural parameters (θ e , δ T , δ Q , δ M ). The degree of overidentification equals 6 -4 = 2. It allows for an overidentification test and an optimal estimator.

δ M = D( , w, r ) -D(s, w, r ) δ M = D( ,

Estimation

The optimal estimation of the structural parameters is given by the Asymptotic Least Squares method 9 . The six probability differences can be rewriten:

         D(s, m, e) D(s, w, r ) D(s, w, e) D( , m, e) D( , w, r ) D( , w, e)          π =          1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 1 1 0 1          A      θ e δ T δ Q δ M      β or π = Aβ
This system simply represents the identification constraints. π is the auxiliary parameter and is easily estimated from the data, β is the interest parameter, and is not directly observable. In order to estimate β, we need to replace π with an estimate π. Let:

π = π + ω
where ω is the estimation error on the auxiliary parameter. Substituting into the identification constraints, we get an equation that can be used for estimation: π = Aβ + ω where π and A are observable, so that a minimum distance estimation is feasible. Let Ω = V(ω), its diagonal elements are the variances of the auxiliary parameters estimators, and the off diagonal term, the covariance between the estimators. They are correlated because the answers to all the candidates come from the same firms. The optimal estimator of β is the Feasible Generalized Least Squares (FGLS) estimator:

β = (A Ω-1 A) -1 A Ω-1 π
with estimated covariance matrix:

V( β) = (A Ω-1 A) -1
where Ω is a consistent estimate of Ω. The overidentification statistic, denoted S, is simply an estimate of the norm on the identification constraints, we get:

S = ω Ω-1 ω with ω = π -A β. Under the null hypothesis (H 0 : π = Aβ), it is χ 2 (2) distributed.
Application. The results are presented in Table 4. Our method proceeds with backward elimination, which has a different meaning in this context. When a coefficient equals zero, it often means that candidates can be regrouped. Therefore the number of observations available for estimation increases, and so does the precision of the estimate. We give a full account of the application for electricians. The first column of table 4 reports that the lowest Student statistics (0.19) is associated to θe . Therefore, we set θ e = 0 and we find that:

Pr(s, m, r ) = θ s + u s,i Pr(s, m, e) = θ s + u s,i Pr(s, w, r ) = θ s + δ T + δ Q + u s,i Pr(s, w, e) = θ s + δ T + u s,i Pr( , m, r ) = θ + u ,i Pr( , m, e) = θ + u ,i Pr( , w, r ) = θ + δ T + δ Q + δ M + u ,i Pr( , w, e) = θ + δ T + δ M + u ,i
In order to estimate θ s , we simply take the average of the corresponding probabilities, since the same number of candidates is sent on each offer. This is equivalent to take a new reference candidate. Instead of (m, r ), we take both (m, r ) and (m, e) for both contract lengths. We get:

1 2 (Pr(s, m, r ) + Pr(s, m, e)) = θ s + u s,i Pr(s, w, r ) = θ s + δ T + δ Q + u s,i Pr(s, w, e) = θ s + δ T + u s,i 1 2 (Pr( , m, r ) + Pr( , m, e)) = θ + u ,i Pr( , w, r ) = θ + δ T + δ Q + δ M + u ,i Pr( , w, e) = θ + δ T + δ M + u ,i
which is the estimation basis of column (2) in table 4. Since the Student statistic of δT is 0.62, wet set δ T = 0 in the previous system and get: Statistical discrimination on labour qualification is found for plumbers. Women are at a disadvantage by -3.8 pp (t-stat: 2.20). In this case, the recruiters may trust women less than man because they believe that women would work less well.

1 2 (Pr(s, m, r ) + Pr(s, m, e)) = θ s + u s,i Pr(s, w, r ) = θ s + δ Q + u s,i Pr(s, w, e) = θ s + u s,i 1 2 (Pr( , m, r ) + Pr( , m, e)) = θ + u ,i Pr( , w, r ) = θ + δ Q + δ M + u ,i Pr( , w, e) = θ + δ M + u ,i
Last but not least, we find a maternity leave discrimination for electricians. Women are at a strong disadvantage since their loss reaches -12.8 pp (t-stat: 2.67). In this case, the fear of career interruption by the recruiters may drive the results.

Conclusion

We find evidence of hiring discrimination against women in the construction sector. However, the discrimination types really are different from one profession to another, as well as their magnitude.

The Beckerian explanation seems to hold in masonry, where taste-based discrimination is at work. In this context all women should suffer from discrimination. Persuasive advertising campaigns could help in changing the attitudes in this field, as well as legal sanctions. The situation is different in the two other jobs that we have tested.

The occupation of electrician is characterized by a statistical discrimination on qualification. Here, the employer may doubt the competences of the female candidates. Informative advertising campaigns should give the employers the right information and contribute to reduce the discriminatory hiring gap. Increasing the internship length during the training of the apprentices may also contribute to reduce information asymmetry.

Eventually, we find that plumbing exhibits another type of discrimination. The anticipation of a maternity by the employer may hinder the chances of young women to get a job. Since the full cost of the maternity leave is incurred by the Sécurité Sociale, the issue may be about the birth-related career interruptions of women. This issue is difficult to tackle. One solution would be to increase the parental leave by men, so as to bring nearer the career interruptions of women and men.

  ment from the benchmark candidate (s, m, r ): D(s, m, e) = Pr(s, m, e) -Pr(s, m, r ) = θ e D(s, w, r ) = Pr(s, w, r ) -Pr(s, m, r ) = δ T + δ Q D(s, w, e) = Pr(s, w, e) -Pr(s, m, r ) = θ e + δ T

  D( , m, e) = Pr( , m, e) -Pr( , m, r ) = θ e D( , w, r ) = Pr( , w, r ) -Pr( , m, r ) = δ T + δ Q + δ M D( , w, e) = Pr( , w, e) -Pr( , m, r ) = θ e + δ T + δ M

Table 1 :

 1 Experiment candidates

	Candidates	Plumbing	Masonry	Electricity
	Woman, Standard	Aurélie DUVAL	Juliette LEROY	Anaïs DUBOIS
	Woman, Excellence Pauline LEMAIRE	Laura BONNET	Elodie FOURNIER
	Man, Standard	Thomas ROUX	Alexandre PETIT	Julien GUERRIN
	Man, Excellence	Jonathan MOREL Jérémy MOREAU Anthony DURAND

Standard: standard vocational training diploma (CAP, "Certificat d'Aptitude Professionnelle")

Table 2 :

 2 Sample StatisticsThe table reports the p values for all the tests.

	Profession	Electricians Plumbers Masons
	Short term	72	108	70
	Long term	69	180	63
	Total	141	288	133
	Observations	564	1152	532
	Call-back rate	0.298	0.361	0.248
	Qualifications callback equality test
	Women	0.896	0.215	0.472
	Men	0.278	0.149	0.907
	Independence test:
	Sending order	0.571	0.982	0.986

Table 3 :

 3 Call-back rates

	Proportions.
	Profession	Electrician Plumber Mason Reference *
	Short term contracts:
	woman, required	0.111	0.148	0.057	Pr(s, w, r )
	woman, excellence	0.139	0.231	0.100	Pr(s, w, e)
	man, required	0.167	0.120	0.143	Pr(s, m, r )
	man, excellence	0.153	0.167	0.171	Pr(s, m, e)
	Long term contracts:
	woman, required	0.116	0.161	0.111	Pr( , w, r )
	woman, excellence	0.145	0.206	0.063	Pr( , w, e)
	man, required	0.246	0.222	0.079	Pr( , m, r )
	man, excellence	0.261	0.200	0.159	Pr( , m, e)
	Global	0.298	0.361	0.248

* : reference used in the components model.

Table 4 :

 4 Discrimination components estimates

	Estimation by the Asymptotic Least Squares method. Asymptotic Student statistics between parentheses (critical
	values: 1.645 at 10%, 1.96 at 5%)
	Profession		Electrician			Plumber			Mason
	Model	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
	Levels
	θ s	0.167	0.160	0.153	0.142	0.120	0.144	0.144	0.173	0.143	0.143	0.157	0.157
		(3.78) (3.97) (4.14) (4.25) (3.76) (4.85) (4.85) (6.08) (3.30) (3.30) (4.32) (4.32)
	θ	0.246	0.254	0.254	0.254	0.222	0.211	0.211	0.209	0.079	0.079	0.119	0.119
		(4.62) (5.27) (5.27) (5.27) (7.11) (7.80) (7.80) (8.82) (2.28) (2.28) (3.55) (3.55)
	Differences
	θ e	-0.005				0.007				0.055	0.021
		(0.19)				(0.35)				(1.58) (1.08)
	δ T	-0.017 -0.021			0.068	0.071	0.033		-0.107 -0.080 -0.081 -0.058
		(0.49) (0.62)			(1.86) (2.06) (1.33)		(2.91) (2.78) (2.77) (2.69)
	δ Q	-0.036 -0.028 -0.036		-0.053 -0.059 -0.059 -0.038 0.044
		(1.07) (1.04) (1.36)		(1.81) (3.15) (3.14) (2.20) (1.17)
	δ M	-0.088 -0.088 -0.104 -0.128 -0.063 -0.067			0.059	0.058	0.051
		(1.52) (1.52) (2.03) (2.67) (1.48) (1.57)			(1.37) (1.35) (1.16)
	Overidentification
	p-value	0.876	0.982	0.809	0.443	0.163	0.315	0.175	0.509	0.068	0.080	0.116	0.130

Table 5 :

 5 Raw dataThe table give the cross-products of the call-back dummies. Each number gives the number of answers common to the two candidates indicated in line and column. The number of callbacks for each candidate is given by the diagonal of each matrix. These matrices allow for computing both π and Ω. req.: required, exc.: excellence.

					Electricians
			short (72)			long (69)
		woman	man	woman	man
		req. exc. req. exc. req. exc. req. exc.
	woman, required	8	5	6	4	8	6	6	7
	woman,excellence	5	10	7	7	6	10	6	6
	man,required	6	7	12	9	6	6	17	13
	man,excellence	4	7	9	11	7	6	13	18
					Plumbers
			short (108)			long (180)
		woman	man	woman	man
		req. exc. req. exc. req. exc. req. exc.
	woman, required	16	15	6	9	29	24	16	17
	woman,excellence	15	25	9	11	24	37	17	18
	man,required	6	9	13	9	16	17	40	25
	man,excellence	9	11	9	18	17	18	25	36
					Masons
			short (70)			long(63)
		woman	man	woman	man
		req. exc. req. exc. req. exc. req. exc.
	woman, required	4	4	4	3	7	3	3	4
	woman,excellence	4	7	5	5	3	4	1	3
	man,required	4	5	10	5	3	1	5	3
	man,excellence	3	5	5	12	4	3	3	10

A foreign origin can reduce the callback rates in the French labour market, see Duguet, du Parquet, L'Horty and Petit (2015).

Mobility can influence the callback rates, see Duguet, du Parquet, L'Horty and Petit (2017)

Past unemployment period can interfere with the callback rates, see Duguet, Le Gall, L'Horty and Petit(2017)

For evidence of address discrimination, see Duguet, Gray, L'Horty, du Parquet and Petit (2017).

Therefore, we have excluded the contracts of 7 to 11 months from all the computations

Metropolitan France is divided into 95 département.

Metropolitan France is divided into 22 regions

This is the first paper where we have developed this method. Two variants of this method, which do not address the issues of the discrimination types, have been used later in Duguet, Gray, L'Horty, du Parquet, Petit (2017) and Duguet, Le Gall, L'Horty and Petit (2017).

It was originally developed by[START_REF] Gouriéroux | Moindres carrés asymptotiques. Annales de l'Insee[END_REF] and[START_REF] Chamberlain | Multivariate regression models for panel data[END_REF][START_REF] Chamberlain | Panel data[END_REF]

* We thank Souleymane Mbaye for research assistance.

which leads to: 1 3 (Pr(s, m, r ) + Pr(s, m, e) + Pr(s, w, e)) = θ s + u s,i

Pr(s, w, r

(Pr( , m, r ) + Pr( , m, e)) = θ + u ,i Pr( , w, r

Pr( , w, e) = θ + δ M + u ,i and this leads to the estimations reported in column (3) of table [START_REF] Bettio | Gender Segregation in the Labour Market: Root Causes, Implications and Policy Responses in the EU. EU Expert Group on Gender and Employment[END_REF]. The Student statistics of δQ is 1.36 and wet set δ Q = 0 in the previous system. After some simplification we get: the first equation will be useful to estimate θ s only and, therefore, will not contribute to the estimations of the discriminatory component that remains. The two other equations will be used to perform a difference and identify δ M . The result is reported in the fourth column of table 4.

Results

The three professions tested have different market tightness depending on the contract duration. Electricians are preferred on long term contracts ( θ = 0.222 > 0.120 = θs ), as well as plumbers ( θ = 0.209 > 0.173 = θs ) and masons on short contracts ( θs = 0.157 > 0.119 = θ ). This may reflect the nature of these occupations. This is consistent with the fact that masons may be preferred for fixed term contracts because they are more often used during the construction phase, while electricians and plumbers may also be called for maintenance. The three professions do not seem to value the excellence qualifications. This is surprising at a first glance, but it can be understood if we account for the type of jobs the posts are about. These are rather basic jobs that any worker with the right training may be able to do. In this case, the absence of an excellence effect (θ e = 0) would simply reflect that the recruiters do not value excellence when they do not need it. Notice that, contrary to Neumark (2012), our method does not rely on a monotonicity condition between the call-back rate and the qualification level, so that this result has no consequence for our econometric analysis. This also explains why we did not apply this method when we had planned to do so.

All the other differences between the call-back rates of the candidates come from discrimination. However, we find that the discrimination type differs from one profession to another. This justify ex post the usefulness of our estimation method. The taste based discrimination appears in the mason profession. Women have a lower call-back rate than men by -5.8 pp (tstat: 2.69). This results may come from preconceptions in a predominantly male activity, which relied on physical force for a long time in the past.

A last result is about the magnitude of the discrimination coefficients. We find that the stronger effect is about maternity, far above the taste based discrimination. This suggests that the most obvious forms of discrimination may not be the most harmful.

TEPP Working


Thomas Barnay
email: barnay@u-pec.fr.

Éric Defebvre
email: eric.defebvre@univ-paris-est.fr.

Retired, at last? The short-term impact of retirement on health status in France

Keywords: I14, J26, C35, C36 Retirement, Physical health, Mental health, Mechanisms, Identifying variables

Reforms of the French pay-as-you-go pension system relies on increases in the contribution period, gradually postponing legal retirement ages. Several works analyse the effect of these reforms on employment rate or the financial equilibrium of pension schemes. The effect of retirement on health status has not received the same attention. In order to assess the role of retirement on physical and mental health status, we use data coming from the French Health and Professional Path survey (Sip, "Santé et itinéraire professionnel") and address the methodological issues (endogeneity biases such as reverse causality and unobserved characteristics) by setting up an instrumental variables method relying on discontinuities induced by legal ages of retirement. Unaccounting for endogeneity biases, we do not find any significant effect of retirement on health status as a whole. When instrumenting by legal ages of retirement, we find consistent and large short-term effects on activity limitations, anxiety disorders and depressive episodes. We also find that these effects are heterogeneous according to gender, education levels and past exposures to detrimental working conditions during the entire career. Finally, mechanisms such as social activities, sport and health-related risky behaviours may be able to explain such a positive effect on health status.

Introduction

Reforms of the French pay-as-you-go pension system relies on increases in the contribution period, gradually postponing legal retirement ages. Just like in the international literature, a set of French studies point out the effect of these reforms on employment rate or effective retirement age [START_REF] Bozio | Impact evaluation of the 1993 French pension reform on retirement age[END_REF]. The effect of transitioning into retirement has not received the same attention in the French economic literature (besides [START_REF] Blake | Collateral effects of a pension reform in France[END_REF].

Retirement in France mostly remains an absorbing state (combining work and a pension is very rare) and can thus be seen as an irreversible shock. The sharp transition into retirement can often affect perceived health status, but the nature of the causal relationship between retirement and health can also be bidirectional due to reverse causality.

Before retirement, health status already appears as one of the most important non-monetary drivers in the trade-off between work and leisure in older workers [START_REF] Barnay | Health, work and working conditions: a review of the European economic literature[END_REF][START_REF] Lindeboom | Health and Work of Older Workers[END_REF]. Two opposite effects of retirement on health status may arise. Retirement can free individuals from a job strain situation. But retirement, considered as non-employment, may also be the cause of a feeling of social utility loss, leading to a decline in cognitive functions and a loss in self-esteem [START_REF] Rohwedder | Mental Retirement[END_REF]. Finally, it appears difficult to isolate the health-related effects of retirement from those of the natural deterioration rate related to ageing, and many unobservable individual characteristics are also able to explain not only retirement behaviours, but also health status indicators (subjective life expectancy, risk aversion behaviours or labour supply disutility).

In this paper, we study the role of being retired on several physical and mental health status indicators. In order to take care of the inherent endogeneity biases, we set up an identifying variable approach relying on discontinuities in the probability to retire generated by legal incentives at certain ages as sources of exogeneity. Thanks to the Health and Professional Path survey (Santé et Itinéraire Professionnel -Sip) dataset, we are able to control for a set of covariates, including exposures to detrimental working conditions throughout the whole career. We also acknowledge the likely heterogeneity of the effect and the possible mechanisms explaining retirement effects on health status. To our knowledge, no study evaluates the effect of retirement on the physical and mental health conditions, after taking into account endogeneity biases as well as exposures to working conditions and the nature of the entire professional career.

The paper is organized as follows. Section 1 is dedicated to an empirical literature review on the relationships between retirement and health status. Section 2 and Section 3 then describes the database, Section 4 the empirical strategy. Section 5 then presents the results and Section 6 concludes.

Background and literature

The French economic literature is still relatively scarce in terms of studies on the relationships linking non-employment in general (and retirement in particular) and health status, compared to the number of international studies on this area of research [START_REF] Barnay | Health, work and working conditions: a review of the European economic literature[END_REF]. In general, job loss is associated with a deterioration of well-being. Persistent unemployment and recurrent forms of non-employment have a deleterious effect on health, for example on overweight and alcohol consumption [START_REF] Deb | The effect of job loss on overweight and drinking[END_REF]. Unemployment and inactivity, happening early in the professional life, can promote the onset of depressive symptoms thereafter [START_REF] Mossakowski | The Influence of Past Unemployment Duration on Symptoms of Depression Among Young Women and Men in the United States[END_REF]. Furthermore, job loss increases mortality [START_REF] Sullivan | Job Displacement and Mortality: An Analysis Using Administrative Data *[END_REF]. Finally, many studies agree on a negative effect of unemployment on health [START_REF] Böckerman | Unemployment and self-assessed health: evidence from panel data[END_REF][START_REF] Browning | Effect of job loss due to plant closure on mortality and hospitalization[END_REF]Eliason and Storrie, 2009b;Eliason and Storrie, 2009a;[START_REF] Kalwij | Health and labour force participation of older people in Europe: what do objective health indicators add to the analysis?[END_REF]. When it comes to retirement, two competing hypotheses can be advanced to disentangle its effects on health status.

"Retirement blues" 3 and "Unhealthy Retirement" 4

Retirement may generate a loss of social role [START_REF] Kim | Retirement transitions, gender, and psychological well-being: a lifecourse, ecological model[END_REF], a reduction of social capital and therefore a deterioration in health, strengthened by the indirect mean of a loss in terms of living standards. Since the seminal paper by [START_REF] Adam | Retirement and CognitiveReserve: a Stochastic Frontier Approach Applied to Survey Data[END_REF], a specific literature is dedicated to cognitive abilities. The so-called unengaged lifestyle hypothesis thus refers to the assumption that work environment is more cognitively stimulating than leisure environment. This adverse effect complies with the theoretical framework proposed by [START_REF] Grossman | On the Concept of Health Capital and the Demand for Health[END_REF] to the extent that retirees reduce their investment in cognitive abilities. In this respect, [START_REF] Rohwedder | Mental Retirement[END_REF] show that early retirement has a significant adverse impact on the cognitive abilities. Other studies also reach similar conclusions [START_REF] Behncke | Does retirement trigger ill health?[END_REF][START_REF] Bonsang | Does retirement affect cognitive functioning[END_REF][START_REF] Dave | The effects of retirement on physical and mental health outcomes[END_REF][START_REF] Mazzonna | Aging, Cognitive Abilities and Retirement in Europe[END_REF]. For instance, using English Longitudinal Study of Ageing (ELSA), [START_REF] Behncke | Does retirement trigger ill health?[END_REF] finds that retirement increases the occurrence of chronic health conditions.

A set of recent studies confirms the detrimental effect of retirement on health. Using SHARE data, [START_REF] Celidoni | Retirement and cognitive decline. A longitudinal analysis using SHARE data[END_REF] evaluate the causal impact of retirement on recall memory tests by using eligibility ages for early and legal retirement in several European countries as instruments. They stress out that retirement has a long-term negative effect on cognition for individuals who retire at the statutory eligibility age. Taking advantage of the panel dimension of SHARE by performing a two-stage least squares first difference, [START_REF] Mazzonna | Unhealthy Retirement?[END_REF] show that retirement is positive for both mental and physical health (depression and mobility limitation) and cognitive abilities (memory and fluency). By using SHARE and relying on a fixed-effect instrumental variable approach, Heller-Sahlgren (2017) investigate the short and long term effects of retirement on mental health (Euro-D scale) in ten European countries. They find a negative long-term effect.

A well-deserved retirement

Retirement can also free individuals from job strain situations and may improve their health condition in the short run. This virtuous circle will be sustainable provided that individuals have the capacity to invest in their health (income effect). Many international empirical studies show that retirement is beneficial to health status [START_REF] Blake | Collateral effects of a pension reform in France[END_REF][START_REF] Charles | Is Retirement Depressing?: Labor Force Inactivity and Psychological Well-Being in Later Life[END_REF][START_REF] Coe | Retirement effects on health in Europe[END_REF][START_REF] Grip | Shattered Dreams: The Effects of Changing the Pension System Late in the Game*: MENTAL HEALTH EFFECTS OF A PENSION REFORM[END_REF][START_REF] Insler | The Health Consequences of Retirement[END_REF][START_REF] Neuman | Quit Your Job and Get Healthier? The Effect of Retirement on Health[END_REF]. [START_REF] Coe | Retirement effects on health in Europe[END_REF] conclude that retirement decreases the likelihood of reporting poor perceived health (35%) after controlling for reverse causality. However, this effect cannot be found with both depression indicators. In the U.K., [START_REF] Bound | Estimating the Health Effects of Retirement[END_REF] found a positive but transitory health effect of retirement, only in men. Based on German data, [START_REF] Eibich | Understanding the effect of retirement on health: Mechanisms and heterogeneity[END_REF] finds that retirement improves general and mental health status by performing a Regression Discontinuity Design in order to explore financial incentives in the German pension scheme.

Using three different datasets5 , Shai (2018) uses a pension reform happening in 2004 (delaying the retirement age by two years) as source of exogeneity in order to study the influence of retirement on health. He underlines that being in employment at older ages is related to poor general health or, in other words, that retirement is beneficial.

Heterogeneous effects

This ambiguous effect of retirement might therefore find an explanation in its timing, inducing heterogeneous effects. Thus, as [START_REF] Mazzonna | Unhealthy Retirement?[END_REF], we can assume that these two competing hypotheses are not antagonistic. The positive effect of retirement on health is often related to early retirement or past employment in physically demanding occupations (individuals employed in low-skill jobs are overrepresented in early retirees).

Unlike for workers retiring late, people who retire as soon as possible benefit from positive effects on their cognitive abilities [START_REF] Celidoni | Retirement and cognitive decline. A longitudinal analysis using SHARE data[END_REF]. As a consequence, the negative effect of retirement may not be instantaneous [START_REF] Bonsang | Does retirement affect cognitive functioning[END_REF][START_REF] Mazzonna | Ageing, cognitive abilities and retirement[END_REF][START_REF] Heller-Sahlgren | Retirement blues[END_REF], inducing that the adverse effect may appear in the long run.

Data

The Santé et Itinéraire Professionnel survey (Sip) used in this study provides access to particularly detailed individual descriptions. Besides the usual socioeconomic variables (age, sex, activity sector, professional category, educational level, marital status), specific items are provided about physical and mental health. The survey was designed jointly by the French Ministries in charge of Healthcare and Labour and includes two waves (2006 and 2010), conducted on the same sample of people aged 20-74 years living in private households in metropolitan France. Two questionnaires are available: the first one is administered by an interviewer and accurately informs the individual and job characteristics and the current health status of the respondents. It also contains a biographical lifegrid to reconstruct individual careers and life events: childhood, education, health, career changes, working conditions and significant life events. The second one is a self-administered questionnaire targeting risky health behaviours (weight, cigarette and alcohol consumption). It notably informs the current or past tobacco and alcohol consumption (frequency, duration, etc.). A total of 13,648 people were interviewed in 2006, and 11,016 of them again in 2010. We make use of the biographic dimension of the 2006 survey by reconstructing workers' careers yearly.

We are therefore able to know, for each individual, his/her employment status and working conditions every year from their childhood to the date of the survey (2006). As far as work strains are concerned, the survey provides information about ten indicators of exposure: night work, repetitive work, physical load and exposure to toxic materials, full skill usage, work under pressure, tensions with the public, reward, conciliation between work and family life and relationships with colleagues. The intensity of exposure to these work strains is also known.

In our sample, we only retain interviewees present in both the 2006 and 2010 waves, i.e. 11,016 individuals. In order to avoid too heterogeneous samples, we select individuals aged 50-69 in 2010 for whom we benefit from all the information needed in terms of pension and health status characteristics. Thus, we work on a sample of 4,610 individuals, 2,071 of whom being retired.

Descriptive statistics

In our sample, retirees systematically self-report a worse general health condition and a better mental health status than non-retirees (Table 1). Obviously these raw statistics do not account for other characteristics, notably the 8-year difference in age between the two populations.

Yet, 38% of the retired population declare poor levels of self-assessed health against 36% in the non-retired population, 50% a chronic disease (against 40%) and 26% being limited in daily activities (vs. 24%). Yet, the retired population suffers from less anxiety disorders (5%) and depressive episodes (6%) than the control group (resp. 8% and 9%). Exposure to harsh physical and psychosocial working conditions is much higher among retirees than among non-retirees as it is likely that the last years of professional life are marked by greater exposures. Finally, retirees are more prone to having social activities such as associations, unions, religious or artistic activities (48% vs. 38%), have more physical activities (45% vs. 40%), are less often smokers (16% vs. 27%, most likely at least partly indicating a selection effect, the most heavy smokers having a shorter life expectancy) but are more often overweight (60% vs. 52%) than the rest of the population. As expected in the French context (see Appendix 1), three retirement ages seem to emerge as the most common in the sample: age 55, 65 but mostly age 60, which corresponds to the legal threshold for full-rate pension (Figure I). Thus, when the proportion of pensioners only represents about 45% of the sample's total at age 59, it amounts to more than 80% only a year later.

Empirical strategy

Two major sources of endogeneity may be raised. The first is the existing two-way relationship between retirement and health status. In particular, being retired depends on individuals' initial health condition, leading to a health-related selection bias. The second is the unobserved factors influencing not only health status but also retirement. To the extent that individuals have different characteristics, notably in terms of subjective life expectancy, risk aversion preferences or disutility at work, then the estimates are at risk of being biased.

Identifying variables approach

To address these methodological difficulties, we set up an identifying variable method, the objective being to determine the causal effect of being retired on health status. The identification strategy relies on the use of legal norms following which individuals undergo a change (retirement) or not, norms therefore regarded as sources of exogeneity [START_REF] Coe | Retirement effects on health in Europe[END_REF][START_REF] Mazzonna | Ageing, cognitive abilities and retirement[END_REF][START_REF] Mazzonna | Unhealthy Retirement?[END_REF]. The general idea of this method lies in the exploitation of discontinuities in the allocation of a treatment (retirement) related to laws granting incentives to retire at a certain age. To the extent that a full-rate legal retirement age in France exists (60 years-old for this study, before the implementation of the 2010 reform), we use this indicator as the identifying variable for the retirement process. However, it is noteworthy that age, and more importantly reaching a certain age, is not the only element predicting the retirement status.

Advantages

The two main advantages in our case of such a method are that it allows handling endogeneity biases coming from omitted variables as well as reverse causality. Using a minimum age as a source of exogeneneity, this identifying variable approach is close to a Regression Discontinuity Design (RDD) framework on panel data, the major difference between identifying variables and RDD being that the latter allows establishing different trends before and after reaching the threshold, which is not possible with a conventional instrumental variables method [START_REF] Eibich | Understanding the effect of retirement on health: Mechanisms and heterogeneity[END_REF]. Nevertheless, identifying variables allow for a greater flexibility in estimations: it does not exclusively focus on very short-term effects nor heavily selected (ie. small) samples. Also, RDD methods rely on the hypothesis that the discontinuity observed in the outcome solely comes from a discontinuity in the treatment (and not in other observed or unobserved covariates). This hypothesis, often difficult to verify thoroughly, is not necessary in our framework.

Hypotheses

The use of identifying variable methods such as ours is based on two assumptions widely discussed in the literature. The first, called the relevance assumption induces that the identifying variable is correlated with the endogenous variable. In our case, the identifying variable being a legal age of retirement at full rate (ie. inducing heavy financial incentives to retire), it appears intrinsically relevant to explain the decision to retire (see Figure I). The second, called the validity assumption, assumes that the identifying variable is not correlated with the error term. In other words, reaching a certain age shall not induce discontinuities on health status. While it is obvious that age as a whole plays a significant role on health, it appears more doubtful that reaching a specific given age (for instance reaching age 60) induces a significant decline in health in comparison to health status beforehand (for example at age 59) [START_REF] Eibich | Understanding the effect of retirement on health: Mechanisms and heterogeneity[END_REF]. To the extent that the legal age of retirement is decided at the level of the state and is not conditioned by health status requirements, this hypothesis, although not directly testable, does not appear as particularly worrying especially considering age is controlled for in the regressions.

Estimation

The classical issue faced in such studies is that individuals are either observed as retired (treated) or not (control), and not simultaneously in both states. Let and denote respectively the health outcomes for the treated ( = 1) and control ( = 0) groups. As such, is not observed when = 0 and vice-versa and evaluating the effect of retirement on health ( -) is not trivial. More specifically, because we rely on legal age thresholds to identify the relationship between health and retirement, we estimate the average treatment effect at this threshold (denoted ):

-| = ), as described in [START_REF] Coe | Retirement effects on health in Europe[END_REF] and [START_REF] Hahn | Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design[END_REF].

We explain health status in 2010 (vector , , for health indicator and individual ) by selfdeclared retirement status ( ), controlling the model for a vector of other explanatory variables (! ′ ). Formally, our identification strategy is based on the fact that, even if achieving or exceeding a certain age does not fully determine the retirement status, it causes a discontinuity in the probability of being retired at that certain age. The dummy variable " #$% & '#$% ) takes value 1 when individual is at least years-old. Consequently, we estimate simultaneously a system of two equations ( 1):

( , * = * + , + -! ′ + . * = * ′ + / " #$% & '#$% ) + -′ ! ′ + . ′ (1) , = 0 1 2 , * > 0 0 2 , * ≤ 0 = 5 1 2 * > 0 0 2 * ≤ 0
Empirically, to estimate this simultaneous two-equation system, we set up a bivariate probit model, estimated by maximum likelihood. The use of such models is justified by the fact that both explained and explanatory variables are binary indicators [START_REF] Lollivier | Économétrie Avancée Des Variables Qualitatives[END_REF]. This method is equivalent to conventional two-stage methods in a linear case.

( , * = * + , + -! ′ + . * = * ′ + / 67 89 ′ + -′ ! ′ + . ′ (2) , = 0 1 2 , * > 0 0 2 , * ≤ 0 = 5 1 2 * > 0 0 2 * ≤ 0
We simultaneously explain the probability of being retired and health status. We introduce the vector 67 89 ′ representing the identifying variables allowing the model's identification (2).

These variables take the form of dummies, taking value 1 if individual is at least yearsold and 0 otherwise. Bivariate probit models also assume the correlation between residuals .

and . ′ , ie. : = !;<<=. , . ′ >! ′ ) ≠ 0. In addition, residuals of this model are expected to follow a bi-normal distribution: @ . . ′ A → C @D 0 0 E , F 1 : : 1 GA.

Variables

We use three health indicators: self-assessed health status (very good and good vs. fair, bad and very bad), chronic illnesses (binary) and limitations in daily activities (binary). We also use two mental health indicators: Generalised Anxiety Disorders (GAD) or Major Depressive Episodes (MDE) (see Appendix 2).

Regarding our variable of interest, we use a question specifying the current occupation status at the time of the 2010 survey, and build a dummy variable equal to 1 if the individual has reported being retired or pre-retired at this date and 0 otherwise.

We control all our results by sex, age, age squared, educational level, having had at least one child and activity sector (public, private or self-employed, when applicable). Relying on the retrospective part of the data, we include indicators for having spent the majority of the career in long-term jobs of more than 5 years and finally an indicator for career fragmentation. We are also able to reconstruct, year by year, the professional path (including working conditions)

of individuals since the end of their initial studies to the end of their career. Exposure to physical and psychosocial working conditions during the whole career (the fact of having been exposed 20 years to single strains or 10 years to multiple simultaneous strains of the same type) are thus accounted for. We assume that individuals having faced such strains at work should be even more relieved by retirement, hence inducing heterogeneity in the effect of retirement on health status. Finally, we control for the duration individuals spent into retirement in the health status equations.

The potential mechanisms explaining the role of retirement on health status will be assessed by daily social activities (associations, volunteering, unions, political, religious or artistic activities), physical activity and health-related risky behaviours (tobacco, alcohol and BMI).

Results

Main results

Naive univariate models indicate, whatever the health indicator considered, no effect of retirement on health status whatsoever (Table 2). Based on the bivariate methods, the results are radically changed. Retirement indeed has a fairly strong negative effect on activity limitations (-9 percentage points -TT), anxiety disorders (-11TT) and depressive episodes (-10TT). Retirement yet seems to have no particular effect on perceived health status and chronic diseases. The effects of other control variables seem quite stable and are therefore confirmed in comparison to univariate models.

The bivariate probit's auxiliary models explaining the probability to be retired by being aged 60 or more are available in Appendix 2. As expected, the identifying variable appears to be strongly correlated with retirement (reaching age 60 induces a 16TT increase on the probability to be retired).

Heterogeneity

This mean impact of retirement on health status is heterogeneous, notably according to sex (the determinants of men's and women's health status and career outcomes differ and health condition suffers from declarative social heterogeneity - [START_REF] Barnay | Health, work and working conditions: a review of the European economic literature[END_REF][START_REF] Devaux | Hétérogénéité sociale de déclaration de l'état de santé et mesure des inégalités de santé[END_REF][START_REF] Shmueli | Socio-economic and demographic variation in health and in its measures: the issue of reporting heterogeneity[END_REF], education levels (because of the protective role of education in terms of career and health outcomes) and more importantly according to past exposures to detrimental working conditions (the beneficial effects of retirement on health status can be seen as a relief effect from strenuous jobs). We can therefore test these assumptions (Table 3) 7 .

7 All the following models also make use of the fact of being aged 60 or older as identifying variable. In the male population, retirement reduces the probability to declare activity limitations, generalized anxiety disorders and major depressive episodes (with respectively -12TT, -11TT and -13TT). Among women, retirement only seems favourable for GAD and MDE.

In the less educated population, retirement seems beneficial in terms of daily activity limitations, GAD and MDE. In the more educated sample, the role of retirement is sizeable on chronic diseases and even more important for mental health. Individuals having faced a physically strenuous career clearly experience the most positive effects of retiring on their health condition, as each indicator but self-assessed health status is impacted. When it comes to individuals with lower levels of physical exposures, only mental health is improved. The most psychosocially exposed individuals also experience massive improvements in all aspects of their health status. In the less exposed individuals, only GAD and MDE are affected. The massive impacts in the psychosocial subgroup specifically on self-assessed health and mental health indicators can be explained by the relief from a very stressful work-life. The impact on chronic diseases most likely depicts the role of retirement on long-term mental health deterioration.

Mechanisms

We investigate several possible reasons (mechanisms) as of why retirement appears to have such a positive impact on retirees' health. Retirement has a positive role on the probability of having daily social activities as well as on the probability to have physical activities, which is in line with the literature [START_REF] Eibich | Understanding the effect of retirement on health: Mechanisms and heterogeneity[END_REF] (Table 4). Even though it is not possible to say for sure this causally explains why retirees have a better health condition, daily social activities and sport are bound to be correlated with better health status and well-being [START_REF] Ho | Better Health With More Friends: The Role of Social Capital in Producing Health: BETTER HEALTH WITH MORE FRIENDS[END_REF][START_REF] Ku | Leisure-Time Physical Activity, Sedentary Behaviors and Subjective Well-Being in Older Adults: An Eight-Year Longitudinal Research[END_REF][START_REF] Sarma | The Effect of Leisure-Time Physical Activity on Obesity, Diabetes, High BP and Heart Disease Among Canadians: Evidence from 2000/2001 to 2005/2006: THE EFFECT OF LTPA ON OBESITY, DIABETES, HIGH[END_REF]. Retiring is also found to decrease the probability of smoking which is also in line with a general health status improvement and makes sense, because of the relief retirement generates from the stress of the work-life. Yet, most likely because of the increase in spare time and despite the fact that retirees do sport more often, they are also more numerous to have a risky alcohol consumption and to be overweight. These results are congruent with the literature too, which notably shows that quitting smoking involves higher BMI levels [START_REF] Courtemanche | The Effect of Smoking on Obesity: Evidence from a Randomized Trial[END_REF], just like the fact of retiring [START_REF] Godard | Gaining weight through retirement? Results from the SHARE survey[END_REF].

Robustness checks

First, we test other retirement thresholds, as three different thresholds are potentially relevant in the French case: years 55, 60 and 65 (see Figure I and Appendix 1). We estimate models including these three thresholds in the retirement estimations. The main results are unchanged, and the auxiliary models show a strong effect for the 60 and 65 thresholds, this potentially rendering them useful as identifying variables (Appendix 4). We then put our results to the test of linear probability models (LPM), estimated by the generalized method of moments (GMM) with heteroscedasticity-robust standard errors, in order to take advantage of the possibility of using our two relevant identifying variables (60 and 65 years-old thresholds) by initiating different tests. This type of modelling also allows for several tests, as well as for a better handling of unobserved heterogeneity [START_REF] Angrist | Mostly Harmless Econometrics: An Empiricist's Companion[END_REF]. It also allows relaxing the hypothesis of the residuals following a bi-normal distribution (which is the case of bivariate probits). The results (available upon request) are resilient to LPM modelling. It is the same for the results of auxiliary retirement models, which are also stable. Sargan-Hansen tests show that the instruments are correctly excluded and Kleibergen-Paap test statistics are consistently well above the arbitrary critical value of 10. Finally, we test whether the results hold up when not controlling for several endogenous covariates related to the professional career and without including civil servants (because this population is rather particular, notably in terms of retirement frameworks). The results (available upon request) appear as robust to this new specification, indicating that the effect of retirement was not driven by endogenous relationships with such variables or the particularity of part of the sample.

Discussion

Our findings underline a positive short-term effect of retirement on mental health. In the French case, they tend to reject the "Retirement blues" assumption in favour of the "Well deserved retirement" assumption, after controlling for endogeneity biases and retirement duration. Three main specificities of our dataset may be discussed in order to explain these results.

The first specificity is embodied by the fact that France has a relatively advantageous position in terms of retirement schemes compared to similar countries, while it is not as much the case (2017) and [START_REF] Mazzonna | Unhealthy Retirement?[END_REF] show that, for people retiring as soon as possible or working in more physically demanding occupations, retirement has a positive effect on cognitive abilities. French retirees thus happen to be overrepresented in both of these groups, explaining the mental retirement effect.

The second specificity is that French retirees tend to be richer than their European counterparts, and thus are more able to invest in their health status after retirement. The net replacement rate is 68%, which places France among the most generous countries with Italy and Sweden. In contrast, the Anglo-Saxon countries relying on funded schemes have lower replacement rates, and the share of individual savings in retirement is much higher than in countries where pension systems are of the pay-as-you-go scheme. As a consequence, the poverty rate among the elderly is the lowest among most countries (3.8% in France, compared to 12.6% on average for the OECD). Thus, thanks to the French welfare state, retirees' health status and well-being seem therefore more protected.

The last specificity is that the time spent in retirement in our sample is rather low. As stressed out by [START_REF] Mazzonna | Unhealthy Retirement?[END_REF], years spent into retirement play an important role: the more time spent in retirement, the worse the effect on health status. Because the average number of years spent in retirement in our study is of only 5 years, this could explain that our retirees have been relieved from their strenuous work lives, but did not spend enough time as retired to experience a potentially detrimental effect, on cognitive abilities notably.

Several limitations can be noted. As we do not rely on panel data per se, we do not have the possibility to account systematically for individual unobserved heterogeneity. Even though this should not matter because of our instrumental variables framework, panel data would have enabled RDD methods allowing the implementation of differentiated trends left and right of the thresholds, at the cost of temporal distance and sample sizes. Another main limit lies in the fact that we cannot determine precisely if the mean effect of retirement on health status differs according to the distance with the retirement shock. We do not know, because of our data, if this effect is majorly led by short-, mid-or long-run consequences, neither can we determine if the impact on health status happens right after retirement or in a lagged fashion.

There are also several missing variables, such as the professional status before retirement and standards of living as well as elements related to retirement reforms. It is also to be noted that comparisons between stratified samples are difficult because the results hold on different samples. These stratifications are also potentially endogeneous and thus should be taken with caution.

Conclusion

This study measures the causal effect of retirement on health status by mobilizing an econometric strategy allowing taking into account the endogenous nature of the retirementhealth relationship and retrospective panel data on individual careers. We find that retirement has an average positive effect on activity limitations, GAD and MDE after controlling for reverse causality and unobserved heterogeneity. No significant effect can be found on selfassessed health and chronic diseases. It is also the case in the male population when in women, retirement benefits appear only on GAD and MDE and no effect is to be measured on physical health status. These results are particularly strong in the less educated and in the most exposed individuals to physical and psychosocial working conditions during their career.

We also find that this positive effect on health status might be explained by a greater ability for retirees to have more social and physical daily activities and smaller tobacco consumption.

Yet, retirees are also found to be significantly more at risk for alcohol consumption and overweight. To our knowledge, this is the first study to give insights on the average effect of retirement on the whole population in France. It also deals with the mechanisms which could explain health effects as well as describing heterogeneous impacts according to sex, education levels and past exposures to two types of working conditions during the entire career, while addressing the endogeneity biases inherent to this type of study.

Delaying retirement ages may therefore induce health-related risks, retirement appearing as one important tool to relieve workers from their potentially poor working conditions. In that sense, postponing legal retirement ages may not be successful in balancing pension systems, simply because of the consequences in terms of health status at old ages of these reforms, and also because exposed workers may not be able to reach these higher thresholds at work.

Extensions of the contribution period or the reversibility of the status of retiree (increasingly desired in Europe in recent years - [START_REF] Barnay | Health, work and working conditions: a review of the European economic literature[END_REF]) should be accompanied by preventive measures for work strains, or at least by differentiated retirement schemes depending on the nature and intensity of the entire work life of pensioners. Finally, retirement generally seems to promote more healthy behaviours due to the increase of available free time but also suggests an increase in alcohol consumption and overweight. Thus, information campaigns and specific incentives towards retirees could be introduced.

should make sense to test the possibility of age 55 inducing a first threshold in the probability to retire.

For individuals who have started working late or have known breaks in their careers, an unconditional legal retirement age exists. These individuals may indeed retire after age 65. In this case whatever their number of validated quarters, they are not going to be impacted by penalties in their replacement rates. These incentives at age 65 might dissuade these workers to retire before age 65 when their number of quarters is not high enough and on the contrary prompt them to retire once being 65. Therefore, this may grant us with a nice threshold to study.

GAD are identified using a similar filter questions system.

Three questions are asked:

-Over the past six months, have you felt like you were too much concerned about this and that, have you felt overly concerned, worried, anxious about life's everyday problems, at work/at school, at home or about your relatives? Yes/No

In case of positive answer:

- For a person to suffer from generalized anxiety disorder, he/she must respond positively to the three filter questions, then three out of six symptoms described later. This protocol is consistent with that used by the DSM-IV.

Figure I :

 I Figure I: Proportion of retirees in the sample according to age

  Do you have such concerns almost every day? Yes/No In case of positive answer: -Is it difficult to control these concerns or do they prevent you to focus on what you have to do? Yes/No If the interviewee responds positively to the three filter questions, another question is asked in order to know the specific symptoms: "Over the last six months, when you felt particularly concerned, worried, anxious, you often happened: -To feel restless, tense, the edgy nerves? -To have tense muscles? -To feel tired, weak or exhausted easily? -To have trouble concentrating or vacuum passages? -To be particularly irritable? -To have sleep problems (difficulty falling asleep, waking in the middle of the night, waking early or sleeping too much)?

Table 1 : General descriptive statistics

 1

	Variable	Mean	Std. error	Min.	Max.	N	Mean Retirees	Mean retirees non-	Diff.
	Retirement
	Retired	.42	.49	0	1	2071	-	-	-
	Retirement duration	4.90	4.04	0	34	2071	-	-	-
	Aged 55 or more	.74	.44	0	1	3629	.98	.55	-.44***
	Aged 60 or more	.45	.50	0	1	2235	.90	.13	-.77***
	Aged 65 or more	.18	.38	0	1	876	.40	.01	-.39***
	Health status
	Poor perceived health	.37	.48	0	1	1802	.38	.36	-.02*
	Chronic diseases	.45	.50	0	1	2200	.50	.40	-.10***
	Activity limitations	.25	.43	0	1	1219	.26	.24	-.02*
	Anxiety disorder	.07	.25	0	1	321	.05	.08	.02***
	Depressive episode	.08	.27	0	1	380	.06	.09	.03***
	Demographics
	Men	.46	.50	0	1	2254	.51	.42	-.08***
	Age	58.79	.40	50	69	4932	63.47	55.40	-8.06***
	No education	.09	.28	0	1	421	.08	.09	.01
	Primary/secondary	.56	.50	0	1	2782	.62	.52	-.09***
	Equivalent to French BAC	.14	.34	0	1	679	.12	.15	.04***
	Superior	.19	.40	0	1	957	.17	.21	.04***
	One or more children	.91	.29	0	1	4466	.91	.90	-.01
	Employment
	Public sector	.18	.39	0	1	898	.12	.23	.11***
	Private sector	.36	.48	0	1	1772	.20	.47	.26***
	Self-employed	.07	.26	0	1	348	.04	.10	.06***
	Career in long-term jobs	.79	.41	0	1	3881	.84	.75	-.10***
	Stable career	.59	.49	0	1	2887	.53	.62	.10***
	Poor physical working cond.	.22	.41	0	1	1010	.29	.17	-.12***
	Poor psychosocial working cond.	.16	.37	0	1	731	.20	.13	-.07***
	Mechanisms
	Daily social activities	.42	.49	0	1	2088	.48	.38	-.10***
	Sport	.42	.49	0	1	2063	.45	.40	-.05***
	Tobacco consumption	.22	.42	0	1	1034	.16	.27	.11***
	Risky alcohol consumption	.24	.42	0	1	1085	.25	.23	-.02
	Overweight	.56	.50	0	1	2540	.60	.52	-.09***

Note: ***: significant at 1%, **: significant at 5%, *: significant at 10%. Reading: Retirees are 38% to report poor perceived health and 36% of non-retirees are in good perceived health. This difference of -2 percentage points is significant at the 10% level. Field:

Santé et Itinéraire Professionnel survey, individuals aged 50-69 in 2010.

Table 2 : Retirement and health status

 2

	Variable	Poor SAH Probit Biprobit Probit Biprobit Probit Chronic diseases Activity limitations Biprobit Probit Biprobit Probit Biprobit GAD MDE
	Retired	.00 .02	-.07 .05	.03 .02	-.02 .05	.00 .02	-.09** .04	-.02* .01	-.11*** .03	-.02 .01	-.10*** .03
	Demographics
	Men	.00	.00	-.00	-.00	.02	.02	-.04*** -.04*** -.03*** -.03***
	(ref.: women)	.01	.01	.02	.02	.01	.01	.01	.01	.01	.01
	Age	.06** .03	.06** .03	.03 .03	.02 .03	.07*** .03	.07*** .03	.03 .02	.03* .02	.03** .02	.04*** .02
	Age²	-.01** .00	-.01* .00	-.00 .00	-.00 .00	-.01** .00	-.01** .00	-.01* .00	-.00 .00	-.01** .00	-.01* .01
	Children	-.03	-.03	-.03	-.03	.01	.01	.03*	.03*	.03*	.03*
	(ref.: none)	.02	.02	.03	.03	.02	.02	.01	.02	.02	.02
	Education
	< French bac.	-.11*** -.11***	-.03	-.03	-.04*	-.04*	-.02	-.02	-.04*** -.04***
	(ref.: no dipl.)	.02	.02	.03	.03	.02	.02	.01	.01	.01	.01
	= French bac.	-.14*** -.14***	-.03	-.03	-.04	-.04	-.01	-.00	-.04**	-.03**
	(ref.: no dipl.)	.02	.03	.03	.03	.03	.03	.01	.02	.01	.02
	> French bac.	-.26*** -.26*** -.08***	-.08**	-.09***	-.09***	-.03**	-.04**	-.07*** -.07***
	(ref.: no dipl.)	.03	.03	.03	.03	.03	.03	.01	.02	.02	.02
	Employment
	Public sector	-.02	-.02	-.01	-.01	-.05**	-.05**	.01	.01	.01	.01
	(ref.: private)	.02	.02	.02	.02	.02	.02	.01	.01	.01	.01
	Self-employed	-.07**	-.08***	-.04	-.05	-.05*	-.06**	-.02	-.04**	-.04*	-.05**
	(ref.: private)	.03	.03	.03	.03	.03	.03	.02	.02	.02	.02
	Long-term jobs	-.12*** -.11*** -.08*** -.08***	-.10***	-.09***	-.02**	-.01	-.04*** -.03***
	(ref.: short term)	.02	.02	.02	.02	.02	.02	.01	.01	.01	.01
	Stable career	-.02	-.02	-.01	-.01	-.02*	-.02*	.00	.01	-.01*	-.01
	(ref.: unstable)	.01	.01	.02	.02	.01	.01	.01	.01	.01	.01
	Physical strains	.11*** .02	.12*** .02	.07*** .02	.07*** .02	.09*** .02	.10*** .02	.02*** .01	.03*** .01	.02* .01	.02** .01
	Psycho. strains	.07*** .02	.07*** .02	.06*** .02	.06*** .02	.04** .02	.04** .02	.03*** .01	.04*** .01	.04*** .01	.04*** .01
	Time in retirem.	.00 .00	-.00 .00	.00 .00	.00 .00	.00 .00	.00 .00	.00 .00	.00 .00	.00 .00	.01 .01
	Rho		.14 .09		.10 .08		.21** .08		.47*** .10		.41*** .12
	Hausman test 6		2.33	1.71	6.75***	10.13***	10.13***
	N					4,610
	Reading: Marginal effects. Standard errors in italics. ***: significant at 1%, **: significant at 5%, *: significant at 10%.
	Field: Santé et Itinéraire Professionnel survey. Individuals aged 50-69 in 2010.
					H I&JKLM&N OH PKLM&N )² R I&JKLM&N S OR PKLM&N

6

The Hausman test has been calculated as follow: S , followed by a Chi² test.

Table 3 : Heterogeneity analysis Variable Poor SAH Chronic diseases Activity limitations GAD MDE Probit Biprobit Probit Biprobit Probit Biprobit Probit Biprobit Probit Biprobit

 3

	Retired (male)	-.07*	-.09	.00	-.04	-.05*	-.12*	-.03	-.11***	-.03	-.13***
	N = 2,140	.03	.07	.04	.07	.03	.06	.02	.04	.02	.04
	Rho		.05 .13		.09 .11		.17 .12		.60*** .15		.61*** .17
	Retired (female)	.04	-.08	.04	-.03	-.04	-.06	-.02	-.09**	-.00	-.09**
	N = 2,470	.03	.07	.03	.07	.03	.06	.02	.04	.02	.04
	Rho		.22** .12		.13 .11		.20* .12		.34** .14		.30* .15
	Retired (low education)	-.00	-.07	.03	.02	-.02	-.13**	-.03	-.08***	-.02	-.08**
	N = 3,045	.03	.06	.03	.06	.03	.05	.01	.03	.02	.03
	Rho		.12 .10		.03 .09		.25** .10		.32** .14		.31** .13
	Retired (high education)	-.00	-.04	.01	-.15*	.04	.03	-.01	-.13***	-.02	-.22***
	N = 1,565	.04	.09	.04	.09	.03	.08	.02	.05	.02	.05
	Rho		.10 .17		.28* .15		.02 .17		.57*** .15		.77*** .14
	Retired (high phys. exp.)	-.07	-.08	-.10*	-.14*	-.10*	-.16*	-.08** -.17**	-.04	-.11**
	N = 1,010	.05	.05	.06	.08	.05	.10	.03	.08	.03	.06
	Rho		-.20 .16		.06 .17		.13 .17		.41* .25		.31* .17
	Retired (low phys. exp.)	.02	-.08	.05	.02	.03	-.07	.00	-.10***	-.00	-.09**
	N = 3,600	.02	.06	.03	.06	.02	.05	.01	.04	.01	.04
	Rho		.26** .10		.08 .09		.23** .10		.43*** .12		.39** .15
	Retired (high psych. exp.)	-.12** -.22** -.15*** -.35***	-.11**	-.19*	-.04	-.35***	-.02	-.23**
	N = 731	.05	.12	.05	.13	.05	.12	.03	.12	.04	.09
	Rho		.16 .21		.38* .21		.16 .23		.93*** .20		.70** .23
	Retired (low psych. exp.)	.03	-.08	.07***	.03	.03	-.10*	-.01	-.08***	-.01	-.09***
	N = 3,879	.02	.05	.02	.06	.02	.05	.01	.03	.01	.03
	Rho		.20** .09		.07 .09		.26*** .09		.39*** .12		.36** .14
	Note: Controlled, when applicable, for sex, age, age-squared, presence of children, education, activity sector (public,
	private), career stability, physical and psychosocial working conditions and time spent in retirement.

Reading: Marginal effects. Standard errors in italics. ***: significant at 1%, **: significant at 5%, *: significant at 10%. Field: Santé et Itinéraire Professionnel survey. Individuals aged 50-69 in 2010.

Table 4 : Mechanisms

 4

	Variable	Social activities Probit Biprobit Probit Biprobit Probit Sport Tobacco Biprobit Probit Biprobit Probit Biprobit Alcohol Overweight
	Retired	.09*** .02	.10** .04	.06** .02	.10* .05	-.05** .02	-.11*** .04	.04* .02	.08** .04	.03 .02	.12** .05
	Demographics
	Men	-.01	-.01	.00	.01	.08***	.09***	.26***	.26***	.19***	.19***
	(ref.: women)	.02	.02	.02	.02	.01	.01	.01	.01	.01	.01
	Age	-.00 .03	-.01 .03	-.04 .03	-.04 .03	.01 .03	.00 .03	.05** .03	.05** .03	.05* .03	.06* .03
	Age²	.00 .00	.00 .00	.00 .00	.00 .00	-.00 .00	-.00 .00	-.01** .00	-.01** .00	-.00 .00	-.01* .00
	Children	-.00	-.00	.01	.01	-.01	-.01	.00	.00	.01	.01
	(ref.: none)	.02	.02	.02	.02	.02	.02	.02	.02	.03	.03
	Education
	< French bac.	.11***	.11***	.11***	.12***	-.03	-.03	.04	.04	-.01	-.01
	(ref.: no dipl.)	.03	.03	.03	.03	.02	.02	.02	.02	.03	.03
	= French bac.	.21***	.21***	.20***	.20***	-.02	-.02	.04	.03	-.07**	-.07**
	(ref.: no dipl.)	.03	.03	.03	.03	.03	.03	.03	.03	.03	.03
	> French bac.	.34***	.34***	.31***	.31***	-.06**	-.06**	.04	.03	-.15*** -.15***
	(ref.: no dipl.)	.03	.03	.03	.03	.03	.03	.03	.03	.03	.03
	Employment
	Public sector	.05**	.05**	.03	.02	.00	.00	-.01	-.01	-.04*	-.04*
	(ref.: private)	.02	.02	.02	.02	.02	.02	.02	.02	.02	.02
	Self-employed	.02	.01	-.08*** -.09***	-.01	-.01	.02	.03	-.02	-.01
	(ref.: private)	.03	.03	.03	.03	.03	.03	.02	.02	.03	.03
	Long-term jobs	-.01	-.00	.06***	.07***	-.05***	-.05**	-.03*	-.04**	-.02	-.03
	(ref.: short term)	.02	.02	.02	.02	.02	.02	.02	.02	.02	.02
	Stable career	.01	.01	.02*	.03*	-.02	-.01	.01	.01	.01	.01
	(ref.: unstable)	.01	.03	.01	.02	.01	.01	.01	.01	.02	.02
	Physical strains	-.05*** -.05*** .02 .02	-.04** .02	-.04** .02	.03** .02	.04** .02	-.00 .02	-.00 .02	.07*** .02	.07*** .02
	Psycho. strains	.04** .02	.04** .02	.01 .02	.01 .02	.02 .02	.02 .02	.00 .02	.00 .02	-.02 .02	-.02 .02
	Time in retirem.	.00 .00	.00 .00	.00 .00	.00 .00	.00 .00	.00 .00	.00 .00	.00 .00	.00 .00	.00 .00
	Rho		.05 .08		.10 .08		.07 .10		-.09 .09		-.13 .08
	Hausman test	.00		.43		1.33		1.33	2.33
	N					4,610
	Note: Controlled for sex, age, age-squared, presence of children, education, activity sector (public, private), career stability,
	physical and psychosocial working conditions and time spent in retirement.
	Reading: Marginal effects. Standard errors in italics. ***: significant at 1%, **: significant at 5%, *: significant at 10%.
	Field: Santé et Itinéraire Professionnel survey. Individuals aged 50-69 in 2010.

  in terms of exposures to detrimental working conditions. The retirement age is comparatively lower (age 62 while the standard is age 65 in most other countries today). This position is convergent with better results in terms of life expectancy at age 65. French workers also tend to leave the labour market early (at age 60, the first year of full-rate pension for the studied generations in this paper -see FigureI). Yet, they appear to face poor physical and environmental working conditions in comparison to the European average, according to the data of the European Working Conditions Survey (EWCS). The EU28 average physical environment index reaches approximately 84 out of 100 (relatively stable throughout the 2005-2015 period) indicating rather low exposures to a variety of physical and environmental strains. In France, this score only amounts to 79 out of 100 (decreasing during the same time span), indicating significantly higher levels of exposure and ranking the country in the 23 rd

position (out of 28 countries)

(Eurofound, 2017)

. Based on SHARE data,

Celidoni et al.

Title of Heller-Sahlgren (2017)

Title of[START_REF] Mazzonna | Unhealthy Retirement?[END_REF]

The Israeli Health Surveys, the Israeli Household Expenditure Surveys, and the SHARE survey.

Acknowledgements

This research (meeting, workshop …), benefited from the support of the Chair «Demographic Transitions, Economic Transitions», under the aegis of the Risk Foundation. The authors would like to thank Pierre Blanchard (Upec Érudite), Eve Caroli (LEDa-LEGOS, Paris-Dauphine University), Emmanuel Duguet (Upec Érudite), Sandrine Juin (Ined, Upec Érudite), François Legendre (Upec Érudite), Maarten Lindeboom (VU University Amsterdam), Judit Vall Castelló (Pompeu Fabra University) and Yann Videau (Upec Érudite) for their useful advice. They also thank Alessandra Guariglia (University of Birmingham), Yannick L'Horty and Rémi Le Gall (Upec Érudite), Pierre-Jean Messe (GAINS, Le Mans University), Annaig-Charlotte Pédrant (IREGE, Savoie Mont Blanc University), Nicolas Sirven (Liraes, Paris-Descartes University) as well as the participants of the Public Policy Evaluation conference

(EPP) and of the Liraes Doctoral Seminars for their useful discussions and comments on the paper.

Appendix 1: the French pay-as-you-go system

Before 2003, most individuals benefitted from the main retirement scheme at age 60. In the case they worked enough time (in terms of quarters at work), they received their full-rate pension. This also means that workers retiring before age 60 suffered from reduced rates for their pension calculations. In 2003, a reform of the pension system was initiated by the Fillon government and indicated that, starting from year 2009, workers would have to validate more quarters in order to still benefit from a full-rate pension. In 2010, a new reform took place, increasing the main retirement age from 60 to 62 starting from year 2011. In our case, age 60 appears as an interesting cut-off point (especially considering our sample is rather old and thus was not really impacted by these reforms). Retiring before age 60 exposes the sample to substantial financial disincentives (for each year which was not validated, a 10% decrease in the replacement rate was operated). This is therefore likely that individuals will not retire earlier if they do not benefit from other retirement schemes.

Numerous pre-retirement schemes also existed. The opening age for pre-retirement schemes is age 55. During the 90's, economic pre-retirement frameworks were implemented in France, with the objective to ease the entry on the labour market for younger workers. Notably, the job search exemption (Dispense de recherche d'emploi) for older workers when unemployed as well as the assistance for finding a first job (Aide à la recherche d'un premier emploi -ARPE) for younger workers all went in this particular direction. Yet, because of the specific objectives of the OECD to reach higher employment rates (notably in older workers), these pre-retirement schemes mostly stopped (job search exemption for instance, implemented in 2006, was abrogated in 2008). Today, other pre-retirement frameworks are in place. They are mostly based on workers having faced specific detrimental working conditions during their lives and objective work drudgery in general. The special allocation of the national employment fund (Allocation spéciale du fonds national de l'emploi -ASFNE) handles older workers being fired for economic reasons by granting them money until they reach the fullrate retirement age. The cessation of salaried workers' activity framework (Cessation d'activité des travailleurs salariés -CATS) for workers aged 55 or more having troubles with new technologies or having been exposed to work drudgery also gives opportunities for early retirement. Finally, more specific frameworks (focusing on specific working conditions) like the early retirement allowance for asbestos workers (Allocation de cessation anticipée d'activité des travailleurs de l'amiante -ACAATA) handles this type of situations. All in all and even if these very diverse early-retirement frameworks do not operate the same way, it Appendix 2: Major Depressive Episodes (MDE) and Generalized Anxiety Disorder (GAD)

The MDE are identified in two stages. First, two questions making use of filters are asked:

-