Edouard Leaune
email: edouard.leaune@ch-le-vinatier.fr

Raphael Allali

Jean-Yves Rotgé

Louis Simon

Maxime Vieux

Philippe Fossati

Raphael Gaillard

David Gourion

Marc Masson

Emilie Olié

Philipe Fossati

Raphaël Gaillard

Emile Olié

Guillaume Vaiva

Prevalence and impact of patient suicide in psychiatrists: Results from a national French web-based survey

Keywords: Patient suicide, psychiatrists, postvention, adverse events, second victims, PTSD, suicide survivors études suicide de patient, psychiatre, postvention, événements indésirables, secondes victimes, symptômes de stress post-traumatique, survivants de suicide

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

RESUME

Contexte : L'exposition aux suicides de patients est une expérience fréquente et difficile pour les professionnels de la santé mentale, marquée par un potentiel impact traumatique, émotionnel et professionnel qui peut placer les professionnels exposés en grande vulnérabilité. Pour autant, aucune étude n'a jusqu'alors évalué la prévalence et l'impact du suicide d'un patient chez les psychiatres français. Méthode : Une enquête nationale a été réalisée entre septembre et décembre 2019 afin d'évaluer chez les psychiatres français a) la prévalence de l'exposition aux suicides de patients, b) les impact traumatiques, émotionnels et professionnels de l'exposition au suicide d'un patient, et c) le soutien reçu dans l'après-coup du suicide d'un patient. Les participants ont été contactés par mail pour répondre à un questionnaire en ligne de 62 items, incluant une mesure de l'impact traumatique via l'Impact of Event Scale. L'impact émotionnel et professionnel, ainsi que le soutien perçu, étaient évalués à l'aide d'échelles dédiées non validées. Résultats : Un total de 764 psychiatres a entièrement rempli le questionnaire. 87,3% d'entre eux avaient été exposés au suicide d'un patient au cours de leur carrière et 13,7% rapportaient des symptômes de stress post-traumatique dans les suites de l'exposition. La culpabilité, la tristesse et le sentiment de choc étaient les émotions les plus fréquemment rapportées. Sur le plan professionnel, 15,1% des psychiatres exposés au suicide d'un patient ont envisagé de changer de carrière. Les suicides de patients les plus impactants sur le plan émotionnel étaient ceux survenant pendant l'internat ou pendant les dix premières années d'exercice. 37,1% des participants n'avaient reçu aucun soutien après l'exposition au suicide du patient et 50,4% rapportaient qu'aucune réunion n'avaient été mise en place dans les suites de l'évènement. Le sentiment de responsabilité vis-à-vis du suicide étaient le prédicteur le plus important pour l'impact négatif du suicide d'un patient. Conclusion : Nos résultats démontrent l'importante prévalence de l'exposition aux suicides de patients chez les psychiatres français, associée à un impact important sur le plan émotionnel, traumatique et professionnel. Nos résultats soulignent l'importance d'implémenter des programmes de formation au cours des

INTRODUCTION

According to numerous studies based on psychological autopsies [START_REF] Cavanagh | Psychological autopsy studies of suicide: a systematic review[END_REF], 91% (95% CI 81-98%) of people who die by suicide suffered from mental disorders. Mental health professionals, especially psychiatrists, are thus highly prone to encounter patient suicide (PS) during their career [START_REF] Séguin | Professionals' reactions following a patient's suicide: review and future investigation[END_REF][START_REF] Dransart | Impact of client suicide on health and mental health professionals[END_REF]. Previous surveys for example reported prevalence of exposure to PS ranging from 51% to 91.5% in psychiatrists worldwide [START_REF] Séguin | Professionals' reactions following a patient's suicide: review and future investigation[END_REF][START_REF] Dransart | Impact of client suicide on health and mental health professionals[END_REF][START_REF] Rothes | Patient suicide: the experience of Flemish psychiatrists[END_REF][START_REF] Gibbons | Effects of patient suicide on psychiatrists: survey of experiences and support required[END_REF][START_REF] Greenberg | Patient suicide[END_REF]. PS is known to be a particularly challenging and distressing occupational hazard for mental health professionals [START_REF] Séguin | Professionals' reactions following a patient's suicide: review and future investigation[END_REF][START_REF] Rothes | Patient suicide: the experience of Flemish psychiatrists[END_REF][START_REF] Gibbons | Effects of patient suicide on psychiatrists: survey of experiences and support required[END_REF][START_REF] Greenberg | Patient suicide[END_REF], so that the terms "suicide survivors" [START_REF] Cerel | The continuum of "survivorship": definitional issues in the aftermath of suicide[END_REF] or "second victims" [START_REF] Farberow | The mental health professional as suicide survivor[END_REF] are used to designate the professionals affected by a PS. Previous studies indeed identified high-level of psychological and professional distress in psychiatrists in the aftermath of PS, including high prevalence of traumatic and emotional reactions and impaired feelings of self-confidence and competence [START_REF] Séguin | Professionals' reactions following a patient's suicide: review and future investigation[END_REF][START_REF] Dransart | Impact of client suicide on health and mental health professionals[END_REF][START_REF] Rothes | Patient suicide: the experience of Flemish psychiatrists[END_REF][START_REF] Gibbons | Effects of patient suicide on psychiatrists: survey of experiences and support required[END_REF][START_REF] Greenberg | Patient suicide[END_REF].

However, while the suicide rates in France is higher than in many other high-income countries [START_REF] Bremberg | Suicide rates in European OECD nations converged during the period 1990-2010[END_REF], no study previously explored the prevalence and impact of PS in a sample of French psychiatrists. A recent study [START_REF] Leaune | Impact of exposure to severe suicidal behaviours in patients during psychiatric training: An online French survey[END_REF] assessed the impact of PS on French psychiatric trainees, reporting that 43.2% of them were exposed to PS during their residency, without evaluating the impact on senior psychiatrists. Of those exposed, 7.2% exhibited clinically relevant symptoms of post-traumatic stress disorder and 11.2% high level of emotional impact. A total of 44.8% reported a negative professional impact and 25.6% received no support in the aftermath. The aim of the current study was thus to assess a) the prevalence of the exposure to PS, b) the emotional, traumatic and professional impacts PS, and c) the perceived support in the aftermath of PS in French psychiatrists.

METHOD Survey

The survey followed the CHERRIES statement for online surveys [START_REF] Eysenbach | Improving the quality of web surveys: The checklist for reporting results of internet E-surveys (CHERRIES)[END_REF]. Based on two literature reviews [START_REF] Séguin | Professionals' reactions following a patient's suicide: review and future investigation[END_REF][START_REF] Leaune | Encountering patient suicide during psychiatric training: an integrative, systematic review[END_REF], a 62-item comprehensive questionnaire was constructed by a pluri-professional team. The online questionnaire used in this study was comprehensively described elsewhere [START_REF] Leaune | Impact of exposure to severe suicidal behaviours in patients during psychiatric training: An online French survey[END_REF]. This survey was offered to French psychiatrists, without exclusion criteria, between September and December 2019. The online questionnaire was available on the website of the Encéphale online (https://www.encephale.com/Actualites/2019/Enquete-l-impact-du-suicidedes-patients-sur-les-psychiatres) and the weblink was sent through a national email listing and social networks to French psychiatrists. The survey completion time ranged from 5 to 15 minutes.

Exposure

We assessed the prevalence of exposure to PS through a declarative answer of respondents to the following question "have you been exposed to patient suicide during your career?". The number of exposures was assessed. Participants were asked to detail the conditions of the most distressing exposure, including the moment of the exposure in the career (during residency, first ten years of practice between ten and twenty years of practice, after more than twenty years of practice) the characteristics of the patient (age, gender, diagnosis, inpatient or outpatient), the conditions of the PS (localization of the event, duration of clinical follow-up, exposure to the corpse, use of resuscitation techniques), the characteristics of the physician-patient relationship (therapeutic alliance, time of care period, place of care), and the context of the exposure (exposure during clinical follow-up or afterwards, ambulatory or inpatient care, exposure to the corpse, police inquiry). The quality of the therapeutic alliance and the feeling of responsibility for the death were assessed through analog visual scales.

Variables, impacts and support

Sociodemographic characteristics (age, gender, location, duration of practice as psychiatrist) were recorded. For those who were exposed to PS, the traumatic impact was measured through the French version of the Impact of Event Scale-Revised (IES-R) [START_REF] Horowitz | Impact of Event Scale: a measure of subjective stress[END_REF][START_REF] Weiss | The impact of event scale -revised[END_REF][START_REF] Brunet | Validation of a French version of the impact of event scale-revised[END_REF]. The IES-R is a 22item self-report questionnaire assessing intrusion, avoidance and hyperarousal symptoms. Each item is rated on a 5-point scale from 0 (not at all) to 4 (extremely). According to previous literature, a threshold of 24/88 to indicate a significant traumatic reaction [START_REF] Asukai | Reliability and validity of the Japanese-language version of the impact of event scale-revised (IES-R-J): four studies of different traumatic events[END_REF] and a threshold of 34 for PTSD [START_REF] Bienvenu | Posttraumatic stress disorder in survivors of acute lung injury: evaluating the Impact of Event Scale-Revised[END_REF] were retained. An emotional score was obtained through a non-validated scale considering six main emotions previously reported in the literature (anger, denial, guilt, sadness, shame and shock) [START_REF] Wurst | Patient suicide: A survey of therapists' reactions[END_REF][START_REF] Yousaf | Impact of patient suicide on psychiatric trainees[END_REF]. Each emotion was scored on a 6-point Likert-scale from 0

(not at all) to 5 (extremely), for a total score ranging from 0 to 30. The professional impact was assessed through four non-validated questions on the modifications of practice and the will to change career path. Regarding the self-reported modifications in professional practice, a fear and avoidance of suicidal patients, an increased tendency to hospitalize patients, a fear of granting passes for patients and a prolonged duration of hospitalization were considered negative professional impacts. A better assessment of suicidal ideation in patients, an increased tendency to ask advice to colleagues, a better trackability of information in patients' files and an interest in suicide prevention were considered positive professional impacts. The population of the most impacted psychiatrists was analyzed by identifying those who reported in the same time an IES-R>24, an ES>18 and a negative professional impact. Those who reported suicidal ideation and the intent to change their career path were also considered as being severely impacted. A descriptive analysis of their sociodemographic and professional characteristics was performed.

The perceived support was evaluated through a non-validated 5-item questionnaire assessing the types of support (informal from peers, colleagues or relatives, formal from superiors or the institution) and the quality of the support.

Statistical analysis

Data manipulation and analyses were performed using JASP software. Qualitative variables were summarized using numbers and percentages, and quantitative variables were calculated using means and standard deviations. Comparisons were made with a χ 2 test or Fisher's test for qualitative variables, depending on the applicable conditions. Quantitative variables were analyzed with the appropriate test, depending on the application conditions. To assess the role of independent variables in moderating the association between the exposure to PS and the three dimensions of impact, we measured the Pearson's r correlation coefficients using the following dependent variables: (a) traumatic reaction (score at IES-R); (b) emotional impact (score at emotional score); and (c) negative professional impact (NPI) (e.g., the presence of at least one item indicating negative professional impact). Then, we conducted a multivariate linear regression for non-dichotomous dependent variables (e.g.. IES-R and emotional scores) and a multivariate logistic regression for negative professional impact to examine the role of independent variables. The independent variables were selected based on the univariate analysis results. Variables with p< 0.5 in the univariate analysis were included in the multivariate analyses. A threshold alpha of 0.05 was considered statistically significant; all tests were twosided.

Ethical approval

The study received ethical approval from The Ethics Committee of The Hospices Civils de Lyon (n° 20/37).

RESULTS

Participants

A total of 795 psychiatrists participated in the survey, of which 764 fully completed the questionnaire. The mean age of respondents was 44.5 (SD= 12.4). Most were women, practicing in public settings. The sample included psychiatrists from all French regions. The characteristics of participants are given in Table 1.

PLEASE INSERT TABLE 1 ABOUT HERE

Exposure

Of the participants, 87.3% reported an exposure to PS during their career (Table 1). The majority reported exposure to several PS and indicated that their first exposure to PS occurred during their residency or the ten first years of their career (Table 1). The feeling of responsibility for the death was significantly higher in early career psychiatrists (p= 0.042).

Most of the psychiatrists were not exposed to the corpse (87.9%) and were involved in informing the family (60.0%). A minority went to the funerals (5.4%). Almost one in five was involved in an administrative or police inquiry (17.7%).

Most of the patients were male, aged 36 to 65 years, and were mainly suffering from mood or personality disorders. The most frequent methods of suicide were hanging and jumping. PS mostly occurred at home or in the hospital (Table 2).

PLEASE INSERT TABLE 2 ABOUT HERE

Traumatic impact

The participants reported that the most distressing PS occurred during their ten first years of practice (Table 3). The mean IES-R score was 19.2 (SD = 15.9). A total of 23.6% reported an IES-R>24, and 13.7% an IES-R>34.

PLEASE INSERT TABLE 3 ABOUT HERE

Emotional impact

The mean total emotional score was 11.25 (SD = 6.14). Sadness (mean score = 2.87; SD= 1.80), guilt (mean score = 2.86; SD= 1.86), and shock (mean score = 2.06, SD= 1.64) were the most frequent emotions reported. Most of psychiatrists did not engage in a personal psychotherapy (97.0%) and did not consummate anxiolytics (96.6%) after PS, while 2.8% reported suicidal ideation. Those who reported suicidal ideation showed the highest IES-R and emotional scores (p<0.001).

Professional impact

A total of 81.9% of the respondents reported modifications in their practice. The professional impact was mostly reported as positive, including an increased interest for suicide prevention (39.7%), a better assessment of suicidal risk in patient (37.7%) and a better trackability of suicidal risk in patients' files (30.4%). The negative professional impact included an increased tendency to hospitalize patients (19.3%), the fear of granting passes (16.6%) and the fear and avoidance of suicidal patients (13.3%). 15.1% of exposed psychiatrists considered changing their career path.

Most impacted psychiatrists

A total of 33 psychiatrists were identified as the most impacted. They were predominantly women (63.6%), working in public hospitals (75.8%) and exposed to PS during residency or early career (84.8%). Almost one in five (18.2%) of them reported suicidal ideation in the aftermath of PS. A great majority had a last contact with the patient on the day of PS (84.8%), 66.7% contacted the family and 32.3% reported no support in the aftermath of the PS.

All the participants who reported suicidal ideation (n= 19) also considered to change their career path. The association between the intent to changer career path after PS and suicidal ideation was significant (p= 0.001).

Moderating factors

The association between independent variables and each dimension of impact are given in Table 4 for the univariate analysis. Table 5 shows the results of the linear regression for emotional and traumatic impact. No significant association was found between the diagnosis and the impact of PS on psychiatrists.

PLEASE INSERT TABLE 4 AND 5 ABOUT HERE

In the multivariate analysis, the feeling of responsibility for the death was significantly associated with the three dimensions of negative impact (B= 0.037; SE= 0.009; p<0.001 for professional impact). The last contact with the patient on the day of suicide was associated with higher IES-R score. The first exposure during early career (e.g., residency or ten first years of practice) and younger age were associated with higher emotional score. Regarding professional impact, the exposure during late career was significantly associated with negative impact (B= -0.901; SE= 0.421; p= 0.032).

Those who felt unprepared to encounter PS were at higher risk for negative impact in the univariate but not in the multivariate analysis.

Perceived support

A total of 37.1% of respondents felt unsupported and 50.4% reported that no team-meeting had been organized in the aftermath. Support from colleagues was the most common (67.3%), especially from other psychiatrists (41.2%). Perceived support was reported as being of good quality by most respondents (6.0/10). Unsupported psychiatrists were not more prone to report higher scores for negative impact (Table 4).

Unexposed psychiatrists

A minority of psychiatrists (11.3%) was not exposed to PS. The unexposed psychiatrists were younger than those who were exposed (mean age= 36.4; SD= 10.7) and were mostly women (73.2%) in their five first years of practice (68.0%). Most of them (63.2%) reported that they felt unprepared to encounter PS.

DISCUSSION

Summary of results

To the best of our knowledge, we performed the largest survey to date on the impact of PS on psychiatrists [START_REF] Séguin | Professionals' reactions following a patient's suicide: review and future investigation[END_REF][START_REF] Dransart | Impact of client suicide on health and mental health professionals[END_REF][START_REF] Rothes | Patient suicide: the experience of Flemish psychiatrists[END_REF][START_REF] Gibbons | Effects of patient suicide on psychiatrists: survey of experiences and support required[END_REF][START_REF] Greenberg | Patient suicide[END_REF][START_REF] Alexander | Suicide by patients: questionnaire study of its effect on consultant psychiatrists[END_REF][START_REF] Kelleher | A study of consultant psychiatrists' response to patients' suicide[END_REF][START_REF] Erlich | Why we need to enhance suicide postvention: evaluating a survey of psychiatrists' behaviors after the suicide of a patient[END_REF]. Our results show that the exposure to PS is highly prevalent among French psychiatrists. A substantial part of the exposed psychiatrists exhibits high level of emotional, traumatic and/or professional impact in the aftermath. The feeling of responsibility for the death was significantly and strongly associated with the three dimensions of negative impact. A substantial part of the participants reported that they received no support and that no team meeting was performed after PS. Interestingly, we reported that encountering PS may become a beneficial and learning experience for psychiatrists, notably through positive modifications of professional practices.

Interpretation of results

The prevalence of exposure to PS measured in our study is slightly higher than those reported in previous studies on the topic [START_REF] Séguin | Professionals' reactions following a patient's suicide: review and future investigation[END_REF][START_REF] Dransart | Impact of client suicide on health and mental health professionals[END_REF][START_REF] Gibbons | Effects of patient suicide on psychiatrists: survey of experiences and support required[END_REF][START_REF] Greenberg | Patient suicide[END_REF][START_REF] Alexander | Suicide by patients: questionnaire study of its effect on consultant psychiatrists[END_REF][START_REF] Kelleher | A study of consultant psychiatrists' response to patients' suicide[END_REF][START_REF] Erlich | Why we need to enhance suicide postvention: evaluating a survey of psychiatrists' behaviors after the suicide of a patient[END_REF]. For example, Alexander et al. [START_REF] Alexander | Suicide by patients: questionnaire study of its effect on consultant psychiatrists[END_REF] found a prevalence rate of 68% in a sample of 247 Scottish psychiatrists, while Kelleher and Campbell [START_REF] Kelleher | A study of consultant psychiatrists' response to patients' suicide[END_REF] reported that 80% of their Irish sample of 74 psychiatrists encountered PS. In an US sample of 90 psychiatrists, Erlich et al. [START_REF] Erlich | Why we need to enhance suicide postvention: evaluating a survey of psychiatrists' behaviors after the suicide of a patient[END_REF] reported a 63% prevalence rate of exposure to PS. The higher prevalence measured in our survey may be explained by the higher suicide rates in France compared to other countries [START_REF] Bremberg | Suicide rates in European OECD nations converged during the period 1990-2010[END_REF]. Consistent with this hypothesis, a study on Belgian psychiatrists [START_REF] Rothes | Patient suicide: the experience of Flemish psychiatrists[END_REF] found a higher prevalence of PS (91.5%), while the suicide rate is higher in Belgium than in France [START_REF] Bremberg | Suicide rates in European OECD nations converged during the period 1990-2010[END_REF]. A selection bias of psychiatrists who encountered PS may also partly explain the result on the prevalence of PS in our sample. However, the prevalence of 42.3% of psychiatrists in our sample reporting an exposure to PS during their training period is consistent with previous studies [START_REF] Leaune | Impact of exposure to severe suicidal behaviours in patients during psychiatric training: An online French survey[END_REF][START_REF] Leaune | Encountering patient suicide during psychiatric training: an integrative, systematic review[END_REF] and does not argue for a selection bias. Compared to the total number of French psychiatrists, our sample of participants comprised more female (60% versus 52%), public practitioners (63% versus 59%) and younger psychiatrists (mean age = 44.5 versus 52.0). This may have significantly impeded the representativeness of our sample and of our results. For example, most of the respondents in our survey work in public inpatient facilities, where suicide rated are known to be remarkably high [START_REF] Walsh | Meta-analysis of suicide rates among psychiatric inpatients[END_REF] so that the prevalence of the exposure to PS may have been overestimated.

Consistent with previous studies [START_REF] Séguin | Professionals' reactions following a patient's suicide: review and future investigation[END_REF][START_REF] Dransart | Impact of client suicide on health and mental health professionals[END_REF][START_REF] Rothes | Patient suicide: the experience of Flemish psychiatrists[END_REF][START_REF] Gibbons | Effects of patient suicide on psychiatrists: survey of experiences and support required[END_REF][START_REF] Greenberg | Patient suicide[END_REF][START_REF] Alexander | Suicide by patients: questionnaire study of its effect on consultant psychiatrists[END_REF][START_REF] Kelleher | A study of consultant psychiatrists' response to patients' suicide[END_REF][START_REF] Erlich | Why we need to enhance suicide postvention: evaluating a survey of psychiatrists' behaviors after the suicide of a patient[END_REF], we found a high emotional, traumatic and professional impact of PS on psychiatrists, especially the youngest ones. The high level of posttraumatic reactions and willingness to change career path observed in our sample after PS are notably worrying phenomena. Moreover, we found that the great majority of the participants had been exposed to PS in early career, especially during residency, and that this early exposure was emotionally particularly distressing. This result is consistent with previous studies which found that PS occurring during psychiatric training may be more distressing [START_REF] Leaune | Encountering patient suicide during psychiatric training: an integrative, systematic review[END_REF], and indicate the need to provide effective and adequate support to early career psychiatrists exposed to PS.

Youngest psychiatrists may indeed be confronted to additional stressors (personal and professional evolution, lack of experience, partial knowledge on the available support) which may induce a greater vulnerability toward the impact of medical adverse events such as PS [START_REF] Leaune | Encountering patient suicide during psychiatric training: an integrative, systematic review[END_REF].

We also found that the feelings of responsibility for the death were more prevalent in younger psychiatrists and were strongly associated with negative impact after PS. This result is consistent with a systematic review on the effects of medical adverse events on healthcare professional, in which feelings of responsibility were found to be highly correlated with the "second victim" phenomenon [START_REF] Seys | Health care professionals as second victims after adverse events: a systematic review[END_REF]. Feelings of responsibility are also prevalent in the grieving process of people bereaved by suicide and may foster complicated grief and impede helpseeking and post-traumatic growth [START_REF] Dransart | Reclaiming and reshaping life: patterns of reconstruction after the quicide of a loved one[END_REF].

The lack of preparedness to manage PS was associated with negative impacts in the univariate but not in the multivariate analysis in our study. In the study of Castelli-Dransart et al. [START_REF] Dransart | Stress reactions after a patient suicide and their relations to the profile of mental health professionals[END_REF], mental health professionals who felt prepared to encounter PS reported lower IES scores regardless of the support received in the aftermath. At the same time, a majority of the unexposed psychiatrists of our sample reported that they felt unprepared to encounter and manage PS. These results advocate for the need to implement educational programs at the entry of psychiatric residency to enhance the preparedness of residents and early career psychiatrists to face and manage PS, and to enhance their willingness to self-help and help an affected colleague. A small number of previous studies [START_REF] Prabhakar | Helping psychiatry residents cope with patient suicide[END_REF][START_REF] Lerner | Coping with a patient's suicide: A curriculum for psychiatry residency training programs[END_REF][START_REF] Jefee-Bahloul | Teaching psychiatry residents about suicide loss: Impact of an educational program[END_REF] showed the effectiveness of educational programs to increase the feelings of preparedness to manage PS and the willingness to help and support colleagues affected by a PS. Information about PS, its prevalence and impacts should be taught when starting psychiatric training. Practical guidance on how to manage PS and how to support a colleague affected by PS would also be helpful. However, the existing literature on the effectiveness of such prevention programs did not evaluate their long-term impact when participants are effectively exposed to PS as residents or senior psychiatrists. Further studies are thus needed to better elucidate the long-term effectiveness of prevention programs dedicated to the exposure to PS. Interestingly, younger psychiatrists reported less negative professional impact than more seasoned ones in the aftermath, indicating that encountering PS can serve as a beneficial and learning experience during early career.

When looking at the support provided in the aftermath, it is notable that informal support from peers and colleagues was the most common form of help received by the participants to cope with PS. Consistent with previous studies [START_REF] Séguin | Professionals' reactions following a patient's suicide: review and future investigation[END_REF][START_REF] Dransart | Impact of client suicide on health and mental health professionals[END_REF][START_REF] Leaune | Impact of exposure to severe suicidal behaviours in patients during psychiatric training: An online French survey[END_REF][START_REF] Leaune | Encountering patient suicide during psychiatric training: an integrative, systematic review[END_REF][START_REF] Ruskin | Impact of patient suicide on psychiatrists and psychiatric trainees[END_REF], we found a lack of institutional support in the aftermath of PS. However, we found no significant association between the lack of perceived support and higher levels of negative impact in the univariate analysis. This result questions the best means to effectively help exposed psychiatrists in coping with PS. According to previous studies [START_REF] Figueroa | Exploring the impact of suicide on clinicians: a multidisciplinary retreat model[END_REF][START_REF] Leaune | The SUPPORT-S protocol study: a postvention program for professionals after patient or user suicide[END_REF], implementing protocolized guidelines, programs and teams aiming at providing support in the aftermath of PS for mental health professionals, including psychiatrists, may be beneficial. However, evidence-based postvention strategies having demonstrated their effectiveness in reducing the psychological and psychological impact after PS are lacking [START_REF] Leaune | The SUPPORT-S protocol study: a postvention program for professionals after patient or user suicide[END_REF]. Nonetheless, our results entail considerations for the support needed to prevent negative mental health outcomes in psychiatrists after PS. First, guidelines encouraging and guiding peer-support in the aftermath of PS are needed. We propose in the Figure 1 eleven recommendations to effectively help and support a colleague affected by a PS.

PLEASE INSERT FIGURE 1 ABOUT HERE

Second, postvention programs should be implemented and evaluated for psychiatrists and, more broadly, mental health professionals and teams exposed to PS. These programs should focus on and encourage the early emotional first aid provided by colleagues and superiors to the most affected professionals. The impact of team-based interventions in exposed settings need to be properly evaluated in further studies [START_REF] Leaune | The SUPPORT-S protocol study: a postvention program for professionals after patient or user suicide[END_REF]. Interestingly, when considering the three domains of impact, we found the existence of a particularly vulnerable group showing high levels of emotional distress associated with a substantial traumatic and professional impact. Moreover, this highly affected group is also more prone to exhibit suicidal ideation in the aftermath of PS.

This result highlights the need to promote early detection of the most affected professionals after PS in those programs, to provide them an effective and adaptive intervention. Buffering the feelings of responsibility for the suicide in exposed professionals must be on the key target of such postvention programs to prevent post-traumatic and negative emotional reactions.

Mortality and Morbidity Conferences have also been reported to be helpful in the aftermath of PS for psychiatric trainees, as they offer an effective mean to buffer the feelings of individual responsibility for the death by allowing an in-depth understanding of the processes which led to the suicide [START_REF] Leaune | Encountering patient suicide during psychiatric training: an integrative, systematic review[END_REF]. However, to date, no study evaluated their impact on psychiatrists after PS.

Limitations

Our study has several limitations. First, the sample of participants may not be representative of all French psychiatrists. Indeed, the total number of psychiatrists is estimated to be about 15,388 [33] in France, so that only about 5% of the French psychiatrists, mostly from the public sector, participated in our survey. Notably, a selection bias of exposed psychiatrists has to be considered regarding the generalizability of our conclusions. Moreover, psychiatrists who effectively changed their career path due to the exposure to PS did not participate in our survey.

No study previously examined this specific population and further studies are needed to better evaluate this population. However, the sample of participants was large and previous studies on the impact of PS on psychiatrists included smaller samples of participants [START_REF] Rothes | Patient suicide: the experience of Flemish psychiatrists[END_REF][START_REF] Gibbons | Effects of patient suicide on psychiatrists: survey of experiences and support required[END_REF][START_REF] Greenberg | Patient suicide[END_REF][START_REF] Alexander | Suicide by patients: questionnaire study of its effect on consultant psychiatrists[END_REF][START_REF] Kelleher | A study of consultant psychiatrists' response to patients' suicide[END_REF][START_REF] Erlich | Why we need to enhance suicide postvention: evaluating a survey of psychiatrists' behaviors after the suicide of a patient[END_REF].

Second, the cross-sectional design of the study limits the ability to make any causal inference.

Notably, the memory bias related to the retrospective design of our survey has to be considered, as a substantial part of the respondents reported their reactions to a PS that occurred several years ago. However, the large sample of respondents to our survey allowed us to collect comprehensive and relevant data on the impact of PS on psychiatrists. Third, the use of nonvalidated questionnaires to assess emotional impact and perceived support limits the relevance of our results. However, this choice was made to improve the acceptability of the survey, as validated scales on emotional state or professional support are time consuming to complete.

1 . 7 .Figure 1 .

 171 Figure 1. Recommendations from the authors on how to provide peer-support to a colleague affected by a patient suicide

Table 1 . Characteristics of participants Variables % n

 1

	Variables	Percentage	n
	Age (mean)	44.5	764
	Gender
	Female	60.3	461
	Male	39.7	303
	Duration of practice at completion
	Less than 5 years	29.3	224
	Between 5 and 10 years	20.1	154
	Between 10 and 20 years	20.4	156
	More than 20 years	30.1	230
	Location of practice at completion
	Public hospital	63.1	482
	Liberal office	22.5	172
	Private hospital	8.1	62
	Association	1.8	14
	Mixed	1.6	12
	Other	2.9	22
	Exposure to PS
	Yes	87.3	667
	No	12.3	97
	Number of exposure
	Two or more	68.2	455
	One	31.8	212
	Time of first exposure
	Residency	42.3	282
	During the 10 first years of practice	39.1	261
	Between 10 and 20 years of practice	6.9	46
	After more than 20 years of practice	1.5	10
	NA	10.2	68
	PS= patient suicide

* the percentage may overreach 100

Table 2 . Characteristics of patients who died by suicide

 2

	Variables	IES-R (mean)	SD	Total emotional score (mean)	SD	Negative professional impact (%)
	Gender
	Male	17.85	15.62	9.96	6.03	77.5
	Female	20.05	16.04	12.07	6.07	85.1
	Time of exposure
	Residency	18.53	15.98	11.96	6.17	85.6
	< 10 years of practice	20.74	16.88	11.86	6.16	83.7
	10 to 20 years of practice	16.42	13.95	9.05	5.67	52.2
	>20 years of practice	18.09	13.35	10.37	5.90	66.7
	Exposure to the corpse or
	resuscitation techniques
	Yes	19.25	16.21	10.01	5.88	84.1
	No	19.12	14.51	11.48	6.19	81.2
	Last contact with the patient on
	the day of PS
	Yes	25.64	15.59	12.25	5.83	95.7
	No	17.95	15.72	11.08	6.16	79.3
	Preparedness to encounter PS
	Yes	16.48	13.98	10.01	5.65	76.1
	No	21.26	16.62	12.16	6.19	86.0
	Support in the aftermath
	Yes	19.65	15.50	11.58	5.84	84.0
	No	19.18	16.67	10.86	6.44	77.7
	Administrative or police inquiry
	Yes	22.20	16.48	11.19	6.19	90.7
	No	18.46	15.74	11.28	6.13	79.5
	Contact with the family after the
	suicide
	Yes	17.30	15.79	11.27	6.07	81.3
	No	19.70	15.57	11.04	6.23	81.7
	Suicidal ideation
	Yes	44.26	16.78	18.72	5.85	92.3
	No	18.25	15.10	10.99	5.97	81.8
	*p<0.05 **p<0.01; ***p<0.001

PS= patient suicide; IES-R= Impact of Event Scale -Revised

Table 3 . Traumatic, emotional and professional impacts reported by the participants in the aftermath of patient suicide

 3

				Negative
	Variable	IES-R score	Emotional score	professional
				impact
	Gender (women)	-0.068	-0.169	0.098
	Age	-0.094*	-0.215***	-0.271***
	Exposure during early career	-0.084	-0.174***	-0.303***
	Exposure to the corpse or resuscitation techniques	-0.003	-0.084	0.026
	Last contact with the patient on the day of PS	0.179***	0.073	0.156**
	Alone for follow-up	-0.050	-0.023	-0.062
	Lack of preparedness	-0.151**	-0.175***	-0.126*
	Lack of support in the aftermath	0.014	0.057	0.080
	Administrative or police inquiry	0.092*	0.006	0.114
	Contact with the family after the suicide	0.017	0.07	-0.005
	Feelings of responsibility for the death	0.351***	0.432***	0.353***
	*p<0.05 **p<0.01; ***p<0.001
	PS= patient suicide; IES-R= Impact of Event Scale -Revised

Table 4 . Univariate analysis for factors associated with emotional, traumatic and professional impacts after patient suicide (Pearson'r correlation coefficient)

 4

	Variable	IES-R score	Emotional score
		R 2 = 0.149	R 2 = 0.205
		β	β
	Feelings of responsibility	0.349***	0.418***
	Last contact
	on the day of	0.138**	-
	PS
	Age	-	-0.170**
	Exposure
	during early	-	0.094*
	career
	*p<0.05; **p< 0.01; ***p<0.001
	IES-R= Impact of Event Scale -Revised

Table 5 . Multivariate linear regression for predictive variables for traumatic and emotional impact after patient suicide

 5

Remerciements

Les auteurs tiennent à remercier le Comité Scientifique de l'Encéphale et Europa Group pour avoir permis la réalisation de l'enquête.

CONCLUSION

Based on the largest web-based survey to date on psychiatrists, we demonstrated that the exposure to PS is highly prevalent in French psychiatrists and leads to significant emotional, traumatic and professional impacts. The deleterious role of the feelings of responsibility for the death indicates the need to develop prevention and postvention programs dedicated to buffering the negative effects of PS and foster post-traumatic growth in psychiatrists. If correctly addressed, the aftermath of PS can indeed shape a beneficial professional experience.

Conflits d'intérêt


Philippe Delacote

Gwenolé Le Velly

Gabriela Simonet

Gwenole Le Velly

Gabriela Simonet'

Revisiting the location bias and additionality of REDD+ projects: the role of project proponents status and certification

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

REDD+ is an international umbrella encompassing a wide variety of initiatives aimed at compensating developing countries for their participation in the global effort to mitigate climate change through the reduction of deforestation and forest degradation, as well as through the conservation and enhancement of their forest carbon stocks. Although REDD+ was initially proposed as a national mechanism, pilot activities were encouraged during COP 13 in Bali [START_REF] Pistorius | From red to redd+: the evolution of a forest-based mitigation approach for developing countries[END_REF]. As of September 2018, over 400 REDD+ projects were being implemented across the tropics (Simonet, Agrawal, Bénédet, Cromberg, de Perthuis, Haggard, Jansen, Karsenty, Liang, Newton et al., 2018a). Some of these projects are financed through the sale of carbon credits, which are assumed to remunerate project proponents based on project effectiveness.

Effectiveness of REDD+ projects is generally assessed through the concept of additionality, which can be defined as the avoided deforestation attributable to the project [START_REF] Engel | Designing payments for environmental services in theory and practice: An overview of the issues[END_REF][START_REF] Wunder | Revisiting the concept of payments for environmental services[END_REF]. Additionality is estimated here based on a comparison between the actual deforestation in the area under conservation and a baseline level of deforestation that corresponds to a counter-factual situation without project implementation which is determined using an accepted business-as-usual scenario. If the baseline scenario is accurately estimated, it is possible to compute the additionality of the projects which is the area kept under forest cover, that otherwise (without the project) would have been deforested.

The literature underlines that the effectiveness of conservation instruments, including REDD+ projects, is strongly heterogeneous [START_REF] Baylis | Mainstreaming impact evaluation in nature conservation[END_REF][START_REF] Börner | Mixing carrots and sticks to conserve forests in the brazilian amazon: a spatial probabilistic modeling approach[END_REF]. On the one hand, a strong body of empirical literature assesses that avoided deforestation projects and other policies are affected by location bias1 [START_REF] Joppa | High and far: Biases in the location of protected areas[END_REF][START_REF] Pfaff | Protected areasâĂŹ impacts on brazilian amazon deforestation: Examining conservation âĂŞ development interactions to inform planning[END_REF][START_REF] Pfaff | Protecting forests, biodiversity, and the climate: predicting policy impact to improve policy choice[END_REF][START_REF] Sims | Do protected areas reduce forest fragmentation? a microlandscapes approach[END_REF]: they tend to be implemented in remote areas characterized by low development pressures, where forests are not threatened. Such biases generally result in low additionality, as the baseline deforestation is low. On the other hand, in areas where development pressures are too high and monitoring is imperfect, conservation projects may also fail to be additional because of economic pressures. This suggests a complex relationship between opportunity costs and additionality where low additionality can be associated with locations characterized by opportunity costs that are either too low or too high

In the context of REDD+ projects, the choice of location is made by the project proponent. This choice is then likely to be influenced both by its type and its own objectives. First, the vast majority of REDD+ projects is implemented by the private sector, either by not-for-profit organizations such as Non-Governmental Organisations (NGOs) that see REDD+ projects as a new source of financing for forest conservation projects; or by for-profit carbon companies that seek to start capital-generating projects focused on carbon2 .

Second, projects may differ in terms of objectives: some of them only focus on forest conservation while others also pursue development objectives. The choice of certification can reflect this diversity. Data provided by Simonet et al. (2018a) indicates that 40 percent of REDD+ projects certified or in the process of certification are using the Verified Carbon Standard (VCS), which is the most commonly used voluntary market standards [START_REF] Hamrick | Raising Ambition: State of the Voluntary Carbon Markets[END_REF]. The VCS validates carbon monitoring methodologies proposed by project proponents and strictly focuses on environmental effectiveness. To address buyers' concerns regarding the potential negative impacts of REDD+ projects on biodiversity or the local population, project proponents often combine VCS certification with a certification awarded by the Climate, Community and Biodiversity (CCB) Alliance standard, which focuses on the non-carbon benefits of the project. Therefore, the choice of single carbon (VCS) or double (VCS + CCB) certification can be understood as an indicator of the project proponent's objectives.

In this article, we contribute to the literature in two areas: we first question which factors determine the location choices of REDD+ projects, and second, how those choices influence the project's additionality. For that manner, we distinguish what we call "potential additionality", which can be approximated by a high deforestation baseline or reference level; and "effective additionality", which is the difference between this reference level and actual deforestation. Using an original database, we empirically study the characteristics of six REDD+ projects located in Brazil, and estimate their additionality in the short-run using impact evaluation methodologies as recommended in the literature on forest conservation policy instruments [START_REF] Miteva | Evaluation of biodiversity policy instruments: what works and what doesn't?[END_REF][START_REF] Baylis | Mainstreaming impact evaluation in nature conservation[END_REF]. The six projects studied are heterogeneous in terms of the type of project proponent and the choice of certification schemes. We consider two types of actors: NGOs and private-for-profit organizations, along with the two types of certification standards mentioned above. Our results suggest that the choice of project location and the project additionality are likely to be influenced by both the type of project proponent and the choice of certification scheme. Moreover, we show that proponents who choose to target areas that are structurally threatened by deforestation may fail to achieve additionality, while those who focus less on endangered forests may implement more additional projects.

Section 2 discusses the link between location choices, opportunity costs and additionality in light of existing evidence. Section 3 introduces the methods used in our empirical analysis and Section 4 presents the results. Section 5 concludes and proposes recommendations for the implementation of future REDD+ projects.

Location bias and additionality

Fifteen years ago, [START_REF] Ferraro | Money for nothing? A call for empirical evaluation of biodiversity conservation investments[END_REF] published an article pointing out the lack of rigorous impact evaluation of conservation instruments. Since 2006, a vast body of literature has emerged to fill this evidence gap which includes articles focusing on protected areas [START_REF] Pfaff | Park location affects forest protection: Land characteristics cause differences in park impacts across costa rica[END_REF][START_REF] Sims | Do protected areas reduce forest fragmentation? a microlandscapes approach[END_REF], payments for environmental services (PES) [START_REF] Arriagada | Do payments for environmental services affect forest cover? A farm-level evaluation from Costa Rica[END_REF][START_REF] Shapiro | Forest conservation and slippage: Evidence from Mexico's national payments for ecosystem services program[END_REF][START_REF] Jayachandran | Liquidity constraints and deforestation: The limitations of payments for ecosystem services[END_REF][START_REF] Chervier | Heterogeneous impact of a collective payment for environmental services scheme on reducing deforestation in cambodia[END_REF], certification [START_REF] Blackman | Evaluating forest conservation policies in developing countries using remote sensing data: An introduction and practical guide[END_REF][START_REF] Tritsch | Do forest-management plans and fsc certification help avoid deforestation in the congo basin?[END_REF] or REDD+ projects (Simonet, Subervie, Ezzine-de Blas, Cromberg and Duchelle, 2018b) among others. As the literature grows, other authors take stock of existing evidence, highlight current patterns in conservation policy and attempt to understand the theoretical mechanisms leading to additionality. In the early reviews, [START_REF] Miteva | Evaluation of biodiversity policy instruments: what works and what doesn't?[END_REF] and [START_REF] Samii | Effects of payment for environmental services (pes) on deforestation and poverty in low and middle income countries: a systematic review[END_REF] highlighted the inefficiencies of many PES to reduce deforestation.

One of the main factors affecting additionality is not directly related to the design of the instruments but rather to the location of the projects. As later emphasized by [START_REF] Börner | Emerging evidence on the effectiveness of tropical forest conservation[END_REF] and [START_REF] Börner | The effectiveness of forest conservation policies and programs[END_REF], this inefficiency can be explained by location bias. Conservation policies tend to be located in remote areas [START_REF] Joppa | High and far: Biases in the location of protected areas[END_REF] characterized by very low, if not null, opportunity costs. These areas are unlikely to be deforested which explains the low additionality of the programs. However, focusing on areas characterized by high opportunity costs may also lead to low additionality if the development pressures are too high and the monitoring is imperfect [START_REF] Keles | Conservation-development trade-offs in the Brazilian Amazon : the case of protected areas downgrading, downsizing and degazettement[END_REF]. In such cases, the efficiency of the funds dedicated to conservation is low because they fail to compensate for the high opportunity costs. In other words, one could make the distinction between potential and effective additionality: potential additionality is greater in areas where opportunity costs are high, but effective additionality may be lower because protection of the forests located in these areas is more difficult to achieve. Some authors have already highlighted the link between the national REDD+ strategy, the type of REDD+ projects implemented in a country, and the country's position on the forest transition curve [START_REF] Angelsen | Designing and implementing effective redd+ policies: A forest transition approach[END_REF][START_REF] Simonet | Climate Economics in Progress 2013. chapter Forest Transition and REDD+ in developing countries: challenges for climate change mitigation[END_REF]. Others have shown that the location of REDD+ projects can be explained by the presence of protected areas [START_REF] Lin | Site selection for forest carbon projects[END_REF], as well as by the baseline CO2 emissions, the forest carbon stock, the number of threatened species, the quality of governance and the region, with a bias toward Latin America [START_REF] Cerbu | Locating redd: A global survey and analysis of redd readiness and demonstration activities[END_REF].

However, [START_REF] Pirard | Effectiveness of forest conservation interventions: an evidence gap map[END_REF] recently noted that REDD+ projects have received less attention than other conservation instruments in the impact evaluation literature. Under the umbrella of REDD+ projects, a vast heterogeneity of projects can be found, notably in terms of project type, location, proponents and funding sources [START_REF] Simonet | Redd+ projects in 2014: An overview based on a new database and typology[END_REF]. Given this heterogeneity among projects, it seems crucial when questioning the additionality of REDD+ projects to wonder, not only whether REDD+ projects generate additionality, but also which types of projects do.

Our intuition is that the objectives of project proponents are crucial to understanding the links between location and additionality. As explained by [START_REF] Delacote | Unveiling information on opportunity costs in redd: Who obtains the surplus when policy objectives differ?[END_REF], the objectives of the project proponent strongly influence both the way REDD+ projects are implemented and their additionality. For this reason, we explore, using 6 different projects, how the type of project proponents influences the choice of location which in turns impacts the project's additionality.

First, we use certification as an indicator of the proponent's objectives. Indeed, we assume that projects that only certify carbon credits have avoided deforestation as their main objective. In contrast, projects certifying both carbon credits and livelihood credits are expected to give more importance to local development. We can expect that projects with double certification put less effort into forest conservation than projects with only carbon certification, implying smaller additionality. Second, we also consider NGOs vs for-profit organizations. Indeed, it is likely that these two types of organizations implement REDD+ projects in a different manner, and with different objectives, which would tend to influence both their location and additionality. For instance, as we'll demonstrate below, private-for-profit firms are likely to rely more financially on voluntary carbon markets.

Data and methods

Sample of REDD Projects in Brazil

Brazil is a key player in the field of deforestation, with deforestation generating 44 percent of the total greenhouse gases emissions (GHG) of the country (in 2012, according to data from the World Resource Institute) and because of the significant shift observed in its deforestation since 2004. Indeed, the annual deforestation rate in Brazil fell by 70 percent between 2005 and 2013 due to the implementation of command-and-control measures, the expansion of protected areas, and interventions in the soy and beef supply chains, such as the Soy Moratorium established in 2006 [START_REF] Nepstad | Slowing amazon deforestation through public policy and interventions in beef and soy supply chains[END_REF]. In 2009, Brazil received about one billion of USD to implement REDD+ projects, mainly from Norway, through the Amazon Fund. This fund made Brazil the main recipient of REDD+ funding [START_REF] Silva-Chavez | REDD+ Finance Flows 2009-2014: Trends and Lessons Learned in REDDX Countries[END_REF]. However, recent evidence suggests that, because of radical changes in the Brazilian Forest Code, deforestation has drastically increased in recent years [START_REF] Junior | The brazilian amazon deforestation rate in 2020 is the greatest of the decade[END_REF]. Simonet et al. (2018a) have built an international database of REDD+ projects around the world. This database is available online3 and contains 454 projects located in 56 countries. As of August 2018, the database included information about 59 projects in Brazil, 30 of which are ongoing projects of avoided deforestation (REDD+). However, the vast majority of these projects were not certified. Given the scope of this article and the fact that we approximate objectives through certification choices, we focus on projects that have relied, or will soon rely, on funding from the voluntary carbon markets. Therefore, we choose to focus on projects that have already obtained the VCS and/or CCB certifications.

Moreover, we choose to focus on conservation projects rather than reforestation projects for two reasons. First, it is easier to monitor deforestation than reforestation with the use of satellite images. Second, reforestation projects [START_REF] Simonet | Redd+ projects in 2014: An overview based on a new database and typology[END_REF]. Eventually, we exclude projects that partially overlap with protected areas in order not to bias the estimates of additionality. A recent article by Simonet et al. (2018b) studies the impact of a REDD+ project in Brazil using similar techniques. Note that this project is not included in our sample but we improve on the author's work by studying six projects and providing explanations for the underlying mechanisms that lead to heterogeneous results. Table 1 presents our sample composed of 6 REDD+ projects that cover around 1.5 million hectares of forest. Average project size is 216,000 hectares and varies between 71,000 and 940,000 hectares. We hypothesize that the projects that are promoted by private-for-profit organizations tend to rely financially more on the voluntary market and that the potential income from the projects is a stronger objective for these actors than for NGOs. Qualitative evidence collected during the construction of the ID-RECCO database (Simonet et al., 2018a) showed us that NGOs rely only partially on the carbon market. As a matter of fact, most NGOs already existed and relied on other sources of funding before they began selling carbon credits, while many private-for-profit organizations emerged for the sole purpose of selling carbon credits. Our hypothesis is supported by the fact that, according to the database, selling carbon credits appears as an objective of the project in around 50% of the REDD+ projects implemented by private-for-profit organizations, compared to only 36% of those implemented by NGOs. This insight also helps us to link our projects to the proponent's alleged objectives, as shown in Table 1.

The six projects are representative of a sub-sample of Brazilian REDD+ projects that are focused on reducing emissions from deforestation (or REDD+) opposed to projects focused on afforestation/reforestation (or AR) certified by at least one standard of the voluntary carbon market, and not located in a protected area under the governance of federal, regional or indigenous entities according to the database by UNEP-WCMC (2018). For comparison purposes, out of the 57 REDD+ projects identified in Brazil in 2018, 36 were oriented toward REDD versus 21 oriented toward AR; 38 were certified or in the process of certification, the others did not seek to sell carbon credits but rather relied on other funding sources (notably, in Brazil, the Amazon Fund) and only 12 were located in protected areas. Moreover, 14 had a component of direct conditional cash payments (PES-like) and two of these projects are in our sample. 4 Our sample thus shows a small over-representation of projects that include a PES component compared to the whole sample of Brazilian REDD+ projects.

We assume that the objectives of the project proponents are reflected through their choice of certification. Looking at REDD+ projects in Brazil using the ID-RECCO database, development mostly appears as a primary or secondary objective for the projects with double certification while it is a third objective for most projects that only obtained VCS certification. Our sample of projects is composed of three groups, detailed in Table 1. All the projects have obtained VCS certification but only four of them have obtained CCB certification. The two projects that did not obtain CCB certification are implemented by private-for-profit proponents. Two projects are implemented by NGOs and both obtained both CCB and VCS certifications. We assume that the projects with both certifications aim more at providing social benefits and livelihood improvements given that they obtained a premium for development outcomes due to the CCB certification. In contrast, projects only relying on the VCS certification are assumed to focus more on the environmental objective.

Data

Project proponents seeking VCS certification must submit a Project Design Document (PDD) that describes the methodology used to estimate the emissions reductions or carbon sequestration to be generated by the project. We georeferenced each project using these PDDs. The PDDs include a map of the projects in PDF format that can be projected using GIS software but there are no geographic coordinates. In order to correctly locate each project, we use shape files that map waters, urban areas, protected areas and roads provided on-line by the Instituto Brasileiro de Geografia e Estatistica (IBGE), ESRI's Digital Chart of the World, and the shape file of protected areas provided by the International Union for Conservation of Nature (UNEP-WCMC, 2018). We overlap each image extracted from the PDD with some of these geographic features to locate the six projects. Once they are located, we draw the polygons that correspond to each of the six REDD+ projects. The polygons measure, on average, 103% of the project areas declared by the project proponents in the PDDs. This ratio is heterogeneous but for all six projects, the difference between the computed and declared areas is lower than 15%. For this reason, we are confident that we have successfully georeferenced the six REDD+ projects.

In order to build a database, we use a similar procedure as Le Velly, Sauquet and Cortina-Villar (2017), combining conservation policies, gridding and forest cover. We use a gridding of 5 km x 5 km so that each cell measures 2,500 hectares. Given the size of REDD+ projects in Brazil, it seems relevant to consider that the decisions made by project proponents involve large forested areas. Therefore, we choose to build grids of 5km x 5km as it both seems relevant as a unit of decision for the project proponent and allows us to capture heterogeneity within the project boundaries.

We intersect this grid with all of the REDD+ project boundaries. Therefore, each forested cell is either entirely within or outside a REDD+ project. Regarding forest cover and deforestation, we use data provided by PRODES 5 . PRODES is a national program that provides geographic data about deforestation and forest cover in the Legal Amazon between 2000 and 2014, based on LandSat images of 20 to 30 meter resolution. The georeferenced projects all started during this period of analysis which allows us to compute deforestation before and after implementation of the project. This procedure allows us to compute yearly deforestation rates within each cell. We drop cells of less than 1000 hectares as they mainly result from polygons overlapping and may bias our results.

Analyzing the choice of location

In the first stage of our analysis, we study the choice of a location by project proponents according to the certification and the type of proponents. Note that in this analysis, we do not study if the areas under REDD+ are different from non REDD+ areas but rather if, within a sample of REDD+ areas, there are differences correlated with the type of proponent. In Section 3.1, we define three groups of projects. In order to study the difference in the location choice for each type of REDD+ project, we restrict our sample to the cells included in one of the six projects. We obtain a sample of 566 observations.

In order to study the heterogeneity between the different types of projects, we run two analyses. First, we provide descriptive statistics of our sample of grid cells 𝑖 in order to study the distribution of a vector 𝑋 𝑖 of six variables including geographic characteristics that are structural determinants of deforestation [START_REF] Kaimowitz | Economic models of tropical deforestation: a review[END_REF][START_REF] Pfaff | What drives deforestation in the brazilian amazon?: evidence from satellite and socioeconomic data[END_REF][START_REF] Robalino | Ecopayments and deforestation in Costa Rica: A nationwide analysis of psa's initial years[END_REF] such as distances to the closest waters, main roads 6 and localities in hundreds of kilometers, as well as slope in percent rise. We also include two measures of deforestation before the implementation of the REDD+ projects. The first is the average yearly deforestation rate between 2006 and the first year of implementation of the project within the cell 𝑖. The second variable measures the average yearly deforestation rate for this same period before the implementation of the project in the direct neighboring cells. Details on the sources of the data can be found in Appendix 5.

For all measures of deforestation, we compute the average yearly ex-ante deforestation rates in grid cells 𝑖 according to the following equation where 𝑡 is the first year of implementation of the project:

𝐷𝑒𝑓 𝑜𝑟𝑒𝑠𝑡𝑎𝑡𝑖𝑜𝑛 𝑖 = 1 -(𝐶𝑜𝑣𝑒𝑟 𝑖,𝑡-1 ∕𝐶𝑜𝑣𝑒𝑟 𝑖,2006 ) 1 𝑡-1-2006
(1) 5 http://www.dpi.inpe.br/prodesdigital/prodes.php 6 Note that the data we use do not include secondary roads and tracks into the forests.

For each variable in 𝑋 𝑖 , we provide the median, the minimum and maximum values and the first and last decile. These statistics allow us to analyze the heterogeneity of the grid cells for each type of projects. As a matter of fact, for distances or deforestation measures, the median values may be of lesser interest than the first and last decile, as these measures can allow us to assess if those areas are likely to be deforested.

Second, we run a multinomial logit in order to estimate how each of the variables included in 𝑋 𝑖 influences the probability that the grid cell 𝑖 is located within the boundary of a project of a given type as presented in Table 1. Based on the results of our estimation, we derive the marginal effect of each variable at the mean values of other variables.

Estimating additionality

In the second stage of the analysis, we estimate the additionality of each of the six projects separately. Remember that there are two projects per proponent type. The additionality is here defined as the avoided deforestation that can be directly attributed to the project. It cannot be estimated only by comparing enrolled and non-enrolled areas. As a matter of fact, there are factors, called confounding variables, that influence both deforestation and the enrollment in a REDD+ project, making simple comparisons biased. To estimate the additionality, we rely on impact evaluation methodologies, and more specifically matching methods, in order to estimate the Average Treatment Effect on the Treated (ATT). In line with the literature, we define the areas enrolled in the REDD+ projects as treated areas and build a counterfactual using a control group of non-enrolled areas.

In order to build a relevant counterfactual, we use difference-in-difference (DID) matching [START_REF] Chabé-Ferret | How much green for the buck? estimating additional and windfall effects of french agro-environmental schemes by did-matching[END_REF][START_REF] Chabé-Ferret | Analysis of the bias of matching and difference-in-difference under alternative earnings and selection processes[END_REF]. Contrary to simple matching, DID-matching introduces a control on timeunvarying unobservable confounding factors. The objective of this procedure is to select a group of observations that are as similar as possible to the treated areas and only differ regarding the treatment. For each REDD+ project we consider as treated the cells that are located within the polygon of the project area and build a control group of observations that are outside the boundary of a REDD+ project.

We use covariate matching based on the Mahalanobis distance using Abadie and Imbens (2011)'s correction. In order to check the robustness of our results, we display for each project the results of the matching procedure using the three and five nearest neighbors. We use the weights generated by the matching procedure in order to compute the impact of the program on the difference in average yearly deforestation rates before and after the project's implementation. Thus, we examine if deforestation rates decreased or increased more in areas within the boundary of the REDD+ projects using the matched control group as a counterfactual situation. For deforestation rates before the project, we consider the difference between 2006 and the first year of of the project in order to average deforestation rates over three years at least. Our outcome variable is defined as:

𝐷𝐼𝐷 𝑖 = (1 -(𝐶𝑜𝑣𝑒𝑟 𝑖,2015 ∕𝐶𝑜𝑣𝑒𝑟 𝑖,𝑡 ) 1 2015-𝑡 ) -(1 -(𝐶𝑜𝑣𝑒𝑟 𝑖,𝑡-1 ∕𝐶𝑜𝑣𝑒𝑟 𝑖,2006 ) 1 𝑡-1-2006 ) (2)
We define our control group as all the cells located within a distance of 15 to 100km around each project. In order to obtain a valid estimation of the impact, the Stable Unit of Treatment Value Assumption (SUTVA) must hold. This hypothesis requires that the outcome of an observation, here deforestation, is only influenced by its own status in terms of the treatment. In our case, it means that the project must not impact deforestation in the control group. For this reason, we consider that the direct buffer of 15km around the projects (approximately the three cells closest to the project) is likely to be influenced by the project through leakage for instance (Alix-Garcia et al., 2012) so we exclude this buffer from our control group. This is similar to [START_REF] Arriagada | Do payments for environmental services affect forest cover? A farm-level evaluation from Costa Rica[END_REF]'s analysis of Costa Rica's PES in which the areas that were contiguous from the PES farms were excluded from the control group. If we did not exclude the neighboring cells, the SUTVA hypothesis would not hold and the estimation might be biased. However, in order to identify the impact of the projects, the choice of the control and treated groups must also take into account unobservable confounding factors that affect both deforestation and the location of the REDD+ projects. By restricting our control group to the cells that are located no farther than 100km from the REDD+ project, we hope to balance unobservable covariates such as agro-ecological conditions. We also exclude protected areas and/or other REDD+ projects from the control group since they can influence deforestation.

We introduce seven variables into the matching procedure: the six variables from 𝑋 𝑖 described above and the area forested in 2006 in hundreds of hectares. This procedure allows us to build a relevant control group for each of the six REDD+ projects.

One of the key assumptions of DID-matching is the conditional parallel trend. This assumption states that, once controlled for observable confounding factors through the matching procedure, there are no significant differences between the two groups in terms of deforestation rates before the implementation of the program. In order to test for the validity of our matching procedure, we run placebo tests for each estimation using as an outcome variable the difference in average yearly deforestation rates between 2006 and the beginning of the project compared with average yearly deforestation rates between 2003 and 2005. Here again, we choose 2003 in order to average deforestation rates over three years. Our outcome variable for placebo tests is defined as:

𝐷𝐼𝐷 𝑖 = (1 -(𝐶𝑜𝑣𝑒𝑟 𝑖,𝑡 ∕𝐶𝑜𝑣𝑒𝑟 𝑖,2006 ) 1 𝑡-2006 ) -(1 -(𝐶𝑜𝑣𝑒𝑟 𝑖,2005 ∕𝐶𝑜𝑣𝑒𝑟 𝑖,2003 ) 1 3 ) (3)
Therefore, we estimate the impact of the REDD+ projects on the increase of deforestation rates in the few years before their implementation compared to the period between 2003 and 2005. If the conditional parallel trend assumption holds, there should be no statistically significant differences between the treated and control groups after weighting.

Results

Choice of location

Tables 6 to 11 in the Appendix present the descriptive statistics as explained in Section 3.3. Figure 1 also plots the kernel density estimates for each six variables. Kernel densities estimate using a non-parametric method the probability density function of each variable. For all three samples and for each variable, it represents the probability (left-axis) that this variable is equal to a given value (right-axis). However, the distribution of deforestation rates is highly skewed toward zero making difficult the interpretation of panel (d) and (e) in Figure 1.

[INSERT FIGURE 1 ABOUT HERE]

According to these statistics, NGOs and private-for-profit organizations with both VCS and CCB certification seem to focus on more threatened forests than do private-for-profit organizations with single VCS certification. As a matter of fact, looking at Tables 9 and10, the most threatened forests targeted by the private-for-profit organizations projects with single VCS certification have experienced lower levels of deforestation in the past than the others.

Moreover, according to Table 6 and 7 and panel (a) and (b) in Figure 1, these projects are located further away from roads and urban areas than the projects led by private-for-profit organizations with both certifications. We assumed that the proponents with only one certification would focus more on the environmental objective, carbon, than the other proponents who pursue multiple objectives. Therefore, our results show that the proponents with a lesser social objective and a greater environmental objective tend to be located in areas where deforestation pressures related to development opportunities are lower.

These indications can be interpreted in the light of the location bias frequently identified in the literature. Both private-for-profit organizations with both certifications and NGOs tend to implement projects closer to roads and where deforestation rates are higher. These areas characterized by higher opportunity costs and possibly higher potential additionality. Yet, because of high opportunity costs, effective additionality may be more difficult to achieve because of high economic pressure. In contrast, private-for-profit with only VCS certifications tend to choose locations farther from roads where deforestation rates are lower, which can be interpreted as location bias. Projects take place in areas with lower development pressure and opportunity costs. Our results regarding additionality of the six projects give us some insights regarding how the choice of location can influence the impact of a project.

Results of the multinomial logit are displayed in Table 2. In our estimation, the cells located in a project led by an NGO were used as a baseline category. For each variable, Table 2 displays the marginal effect of a variation equals to one on the probability that a cell is part of one sub-sample or another. For each variable, the sum of the marginal effects is equal to zero because, if following a variation in variable 𝑋 an observation is more likely to be part of sub-samples 1 or 2, it automatically decreases the probability that it is part of sub-sample 3.

Here, we do not find statistically significant results regarding the location choice made by the project proponents with single VCS certification. This is probably due to the fact that there are fewer grid cells for those projects. However, comparing Column (1) and (3) confirms that the location choices are made differently depending on the type of project proponent. NGOs tend to enroll areas in REDD+ projects where neighboring deforestation is higher. However, these areas are more remote from the roads and waters than the areas enrolled by private-for-profit organizations with double certification.

[INSERT TABLE 2 ABOUT HERE]

Nevertheless, these results should be interpreted cautiously. Despite the high number of cells, our sample is only composed of two projects per proponent type. Therefore, the external validity of our results regarding the location choice according to the proponent type remain questionable and definitive conclusions on this matter cannot be drawn. However, the evidence we provide here by comparing six project proponents with very different incentives and heterogeneous objectives still represents a notable addition to the existing literature.

Additionality

Tables 3 and4 display the results regarding the additionality of the projects estimated using the methodology presented in Section 3.4. Remember that there are two projects per proponent type. Each table displays the number of treated observations for each project and the results before and after matching for the impact estimation and placebo tests. As a comparison, using yearly deforestation data from FAO Stat, average yearly deforestation rates in Brazil were around 0.7% between 2003 and 2006, 0.6% between 2007 and 2011 and 0.3% between 2012 and 2015. We do not find much evidence of additionality for our set of projects. Our results tend to show that only projects implemented by private-for-profit proponents with single VCS certification decrease deforestation. These results remain stable and statistically significant using the three and five nearest neighbors matching for one project and the five nearest neighbors matching for the other. According to our placebo tests, the conditional parallel trend assumption is not always verified but when it is not, the difference between the treated and matched samples remains very small. However, as will be explained below, the results regarding Columns ( 7) and ( 8) should be interpreted with caution as the estimates are likely to be biased.

In contrast to our results regarding the additionality of projects implemented by private for-profit proponents with single VCS certification, we do not find any impact for the other projects. Projects with double certification do not appear to reduce deforestation. Our results in Table 4 suggest that the projects implemented by an NGO could even increase deforestation but this impact is very small and only significant in one estimation. These results can be explained by the fact that projects with double certification, because they have livelihood objectives, tend to choose locations in areas with potential livelihood improvement, which makes additionality harder to achieve. Note that the fact that some projects include a PES-like component (see Table 1) does not seem to influence their impact according to our results.

[INSERT TABLES 3 and 4 ABOUT HERE]

In order to test whether the matching procedure succeeded in balancing confounding factors between the treated and control groups, we use balancing tests for each estimation. Results for each matching procedure (Table 12 to 23) are available in the Appendix. Despite some remaining imbalances, the bias has been largely reduced for most estimations, which does not reject the validity of our results, with the notable exception of the second project implemented by a private-for-profit organization with single VCS certification (Columns 7 and 8 in Tables 3 and4). In particular, one should be cautious about the biases regarding ex-ante deforestation rates highlighted in Tables 15 and21; these are consistent with the bias identified in the placebo estimates. Therefore, the results regarding this project must be interpreted with a great deal of caution.

Moreover, as a robustness test, we increase the size of the buffer around each project that is excluded from the control group. The results, which are available upon request, do not allow us to reject our findings but, in most cases, we are not able to validate the conditional parallel trend assumption with a larger buffer. This is probably due to the fact that, with a lower number of control observations, the procedure fails to find appropriate matches.

Eventually, since all treated observations are part of the same project, our estimates of standard errors could be biased by a correlation in the unobserved component of the outcome variable [START_REF] Abadie | When should you adjust standard errors for clustering?[END_REF]. In order to check for the robustness of our results to this potential bias, we use a pre-matching procedure and cluster standard-errors at the project level in our estimations of additionality. First, for each type of proponent, we run a matching procedure for both projects that are implemented by this type of proponent in order to select a control group for each project. As previously, we use covariate matching based on the Mahalanobis distance using Abadie and Imbens (2011)'s correction with three and five nearest neighbour matching. Second, we merge the samples of treated and matched observations for both projects implemented by the same type of proponent and estimate the impact of the REDD+ projects using Ordinary Least Squares. Our outcome variable is the variation in average yearly deforestation rates as defined in Equation 2 and standard errors are clustered at the project level in these estimates. Results are displayed in Table 24 and 25 in the Appendix. The robustness test does not reject the additionality of the projects implemented by private-for-profit organizations with single VCS certification. Moreover, the results in Table 24 does not reject that the impact of the other two types of projects is very close to zero but this result is not statistically significant in Table 25.

Discussion

Our results show that the type of proponents influence the location choice of a project. NGOs tend to select locations farther away from roads and water. Similarly, private-for-profit firms with single carbon certification tend to target areas that are less threatened by deforestation. Two kinds of explanations can be made on this result. First, if baseline scenarios are not correctly set, selecting areas with low deforestation may be related to the creation of "hot air" carbon credits [START_REF] Seyller | The'virtual economy'of redd+ projects: does private certification of redd+ projects ensure their environmental integrity[END_REF] that are not supported by actual additionality. A second explanation, as described in [START_REF] Delacote | Distinguishing potential and effective additionality to revisit the location bias of redd+ projects[END_REF], is that project proponents select areas where forests are less threatened, but may nevertheless achieve additionality, because the implementation of the project is less complicated to implement than in high opportunity costs areas.

In contrast, private-for-profit organizations with double certification select areas nearer roads and waters. According to the location bias concept, one would expect projects led by NGOs and private-for-profit firms with single certification to have lower additionality, and projects led by private-for-profit organizations with double certification to have higher additionality. Yet, our results on additionality differ from that prediction.

Indeed, according to our additionality analysis, none of the projects with double certification (either led by NGOs or private firms) did achieve any avoided deforestation. This result provides evidence that the location bias concept should be considered more carefully in future work: locating a project in areas with higher development pressure does not mean that the project will be more effective in terms of avoided deforestation. In other words, effective additionality does not necessarily correspond to potential additionality.

The only projects for which we find additionality only obtained an environmental certification. Moreover, projects with double certification failed to avoid deforestation, whatever their location choice. This result suggests that environment/development trade-offs are strong, and that projects with double certification are likely to put their emphasis on the development objective, which can be detrimental to avoided deforestation.

Note that our results do not allow to conclude that only private-for-profit organizations can effectively tackle deforestation. For instance, the project studied by Simonet et al. (2018b) was implemented by an NGO and led to a decrease in deforestation rates of about 50%. In this paper, we only focus on six case studies which is a sample statistically too small to draw general conclusions regarding the relative effectiveness of the different types of proponents. Moreover, and perhaps more important, our results do not tell us if, in the long-run, pursuing both objectives can lead to better trade-offs between development and conservation. However, our results do highlight the complex relationship between opportunity costs, efficiency of conservation funds and additionality.

Finally, our results using DID-matching can not reject that the impact of the REDD+ projects is rather small if not null. With the notable exception of Simonet et al. (2018b) that we've already mentioned, this result is in line with other findings using quasi-experimental methods published in the literature. Using a sample of 23 sub-national REDD+ projects in Latin America, Africa or South-East Asia, [START_REF] Bos | Comparing methods for assessing the effectiveness of subnational redd+ initiatives[END_REF] find small impacts of these projects. More recently, West, Börner, Sills and Kontoleon (2020) also finds in the Brazilian Amazon, that once controlled for relevant confounding factors using synthetic control, most of the twelve projects studied display a very low level of additionality which questions the credibility of the crediting baseline. More recently, Chabé-Ferret and Voia ( 2021) provide an updated meta-analysis of the effectiveness of forest conservation programs. They test for the existence of publication bias and build cost/benefit estimates. They provide evidence of the existence of publication bias: studies that do not find evidence of additionality may experience difficulty in getting published, which artificially increase the estimated impacts. The authors find a relatively low additionality of forest conservation programs, in line with [START_REF] Samii | Effects of payment for environmental services (pes) on deforestation and poverty in low and middle income countries: a systematic review[END_REF]. Finally, they estimate the cost-benefit ratio of forest conservation programs to be below one at current carbon prices.

Conclusion

In this article, we empirically study how the type and objectives of project proponents influence the location choice and additionality of the REDD+ projects. Doing so, we revisit the concept of location bias. According to our results, project proponents that rely more on carbon funding tend to target areas with lower opportunity costs. They also tend to be more additional in the short-run, which we explain by the fact that lower opportunity costs are more easily compensated making the projects more efficient. On the contrary, proponents with multiple objectives target areas with higher development pressures and opportunity costs but this focus on areas with higher opportunity costs may come at the expense of additionality.

Our work therefore provides evidence that location biases, often identified in the literature, are not independent of the REDD+ project manager type. Furthermore, the existence of location bias toward areas with lower opportunity costs does not necessarily imply a lack of additionality. By contrast, choosing a location with high opportunity costs may lead to low (if any) levels of additionality.

Our analysis provides innovative empirical evidence regarding the mechanisms that lead to additionality and contributes to filling the evidence gap regarding REDD+ projects [START_REF] Pirard | Effectiveness of forest conservation interventions: an evidence gap map[END_REF]. We show how the incentives behind the REDD+ mechanism can lead to target areas with lower development potential. Following recent calls by [START_REF] Baylis | Mainstreaming impact evaluation in nature conservation[END_REF], among others, we do not question whether REDD+ projects are effective instruments for forest conservation but, instead, how and under what conditions they deliver the expected results. Moreover, given the publication bias identified by [START_REF] Chabé-Ferret | Are forest conservation programs a cost-effective way to fight climate change?[END_REF], by studying six projects and reporting non-significant results for four of them, we also participate in increasing the available information regarding the potential effectiveness of conservation instruments. We believe that this focus on the mechanisms is a crucial issue that needs to be tackled by academics in order to improve our understanding of conservation policies.

Figure 1 :

 1 Figure 1: Characteristics of the locations according to the types of proponents

First

  Author et al.: Preprint submitted to Elsevier

Table 2

 2 Impact of location characteristics on the type of REDD+ proponents (marginal effects)

	Proponent type	Private-for-profit Private-for-profit	NGO
	Certification	VCS + CCB	VCS	VCS + CCB
	Distance to waters	-0.1526***	0.0001	0.1525***
		(0.0541)	(0.0006)	(0.0541)
	Distance to roads	-0.1583***	-0.0021	0.1603***
		(0.0590)	(0.0030)	(0.0591)
	Distance to closest urban area	-0.0305	0.0083	0.0222
		(0.0340)	(0.0119)	(0.0353)
	Slope	-0.0396**	0.0002	0.0394***
		(0.0166)	(0.0004)	(0.0166)
	Ex-ante deforestation in	-6.6696***	-0.1081	6.7777***
	neighbouring cells	(2.4001)	(0.1861)	(2.4061)
	Ex-ante deforestation	-0.5079	-0.1193	0.6272
		(1.7533)	(0.1165)	(1.7570)
	Number of observations		566
	Pseudo-𝑅 2		0.4758
	Standard errors in parentheses
	*** p<0.01, ** p<0.05, * p<0.1

Table 24

 24 Additionality of the projects: OLS after pre-matching using three nearest neighbour matching

	(1)	(2)	(3)

Some authors use the term location bias as a synonym for the term selection bias used in econometrics to explain why it is difficult to find a relevant counter-factual situation for conservation instruments. Here, we understand the location bias as a bias in the location choice that leads to enroll non-threatened forests in the program, which may reduce their effectiveness.First Author et al.: Preprint submitted to Elsevier

Public sector and research institutes represent less than 20 percent of the proponents[START_REF] Simonet | Redd+ projects in 2014: An overview based on a new database and typology[END_REF].

http://www.reddprojectsdatabase.org/ First Author et al.: Preprint submitted to Elsevier

Note that the other projects may also include wages for local populations for patrolling or the adoption of alternative activities but no direct payments for conservation.