Jean-Christophe Mercier
email: jean-christophe.mercier@sfr.fr

J.-C Mercier

A Maroni

I Melki

U Meinzer

J Gaschignard

C Beyler

A Santos

AMCP_291 / DOSSIER / MISE AU POINT COVID-19 et enfants Children and COVID-19

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

Jean-Christophe Mercier V2 -10 juin 2020 2

• une meilleure réponse immune des enfants fréquemment exposés à divers virus respiratoires ; • une distribution ou une maturation différente des récepteurs aux différents coronavirus qui utilisent tous le récepteur Angiotensin-Converting Enzyme-2 (ACE2) pour pénétrer dans les cellules épithéliales respiratoires [START_REF] Lee | Are children less susceptible to COVID-19?[END_REF].

Le rôle des enfants et des adolescents dans la transmission de SARS-CoV-2 dépend de leur susceptibilité au virus, de la charge virale, des comportements et des contacts sociaux. Cette question fondamentale dans la transmission virale et du rôle potentiel des enfants comme chaîne de transmission a été récemment évaluée par une analyse systématique des études épidémiologiques de traçage de cas et des études de tests systématiques dans des populations [START_REF] Viner | Susceptibility to SARS-CoV-2 infection amongst children and adolescents compared with adults: a systematic review and metaanalysis[END_REF]. Parmi les 6.327 études publiées sur COVID-19 au 16 mai 2020, 18 études répondaient aux critères d'inclusion : 9 études de traçage de cas à partir d'un cas index, 8 études de tests systématiques dans une population et une revue générale systématique. La probabilité d'être infecté à partir d'un cas contact était de 0,44 [IC95% 0,29 ; 0,69] pour un enfant par rapport à un adulte, avec pourtant une grande hétérogénéité (63 %) entre les études. Une étude systématique des clusters familiaux de COVID-19 montrait que seulement 3/31 (10 %) partaient d'un cas index pédiatrique et que la transmission intra-scolaire était en fait assez minime. De larges études systématiques de populations mettaient en évidence une prévalence faible de cas pédiatriques en Islande, en Hollande, en Espagne et en France [START_REF] Cohen | Prevalence of SARS-Cov2 carriage in asymptomatic and mildlysymptomatic children (COVILLE)[END_REF], tandis que d'autres études à Stockholm, en Angleterre et dans des municipalités en Suisse et en Allemagne ne montraient aucune différence de prévalence entre enfants et adultes.

Aspects épidémiologiques des coronavirus ? La pandémie SARS-CoV-2 par rapport à d'autres épidémies à coronavirus ?

Les coronavirus communautaires sont isolés dans 4 à 6 % des infections respiratoires aiguës de l'enfant et chez 8% des enfants ambulatoires asymptomatiques [START_REF] Zimmermann | Coronavirus infections in children including COVID-19. An overview of the epidemiology, clinical features, diagnosis, treatment and prevention options in children[END_REF]. [START_REF] Dong | Epidemiology of COVID-19 among children in China[END_REF]. Plus de 90 % des cas étaient asymptomatiques (4 %) ou présentaient une symptomatologie mineure (51 %) à type d'infection des voies aériennes supérieures (rhinopharyngite, toux non fébrile, etc.) ou de sévérité moyenne (39 %) à type d'infection des voies aériennes inférieures (fièvre élevée, toux sèche ou productive, sans lésions radiologiques marquées de pneumonie). Un seul enfant était décédé. Parmi les hypothèses pouvant expliquer cette atypie, une moindre affinité et densité des récepteurs ACE2 était principalement incriminée.

Cette moindre sévérité de l'infection COVID-19 chez les enfants était confirmée par des données épidémiologiques en provenance des USA. Ainsi, parmi les 149.000 cas confirmés de COVID-19 entre le 12 février et le 2 avril 2020, 2.572 (1,7 %) étaient des enfants âgés de moins de 18 ans. 72 % des enfants contre 93 % des adultes âgés de 18 à 64 ans présentaient des symptômes à type de fièvre, de toux ou de polypnée et seulement 5,7 % d'entre eux contre 20 % des adultes étaient hospitalisés [START_REF]Coronavirus Disease 2019 in children -United States[END_REF]. Entre le 14 mars et le 3 avril 2020, 48 enfants étaient hospitalisés dans 14 seulement des 46 unités de réanimation pédiatrique participant à un réseau coopératif nord-américain : 40 enfants (83 %) présentaient des comorbidités significatives (majoritairement des malformations congénitales) ; 35 (73 %) avaient une insuffisance respiratoire aiguë et 18 (38 %) nécessitaient une ventilation mécanique. 11 (23 %) patients avaient une défaillance multiviscérale et 1 seul enfant nécessitait une assistance respiratoire extracorporelle (ECMO) [START_REF] Shekerdemian | for the International COVID-19 PICU Collaborative. Characteristics and outcomes of children with coronavirus disease 2019 (COVID-19) infection admitted to US and Canadian Pediatric Intensive Care Units[END_REF]. Au 3 avril 2020, 2 (14 %) enfants étaient décédés et 15 (31 %) étaient toujours hospitalisés dont 3 ventilés et 1 sous ECMO. La durée médiane (extrêmes) de séjour en réanimation et d'hospitalisation était respectivement de 5 (3-9) et de 7 (4-13) jours.

États de choc associé à une myocardite aiguë et/ou un syndrome de Kawasaki dans un contexte « d'orage cytokinique »

Mi-avril 2020, le South Thames Retrieval Service, London (SAMU pédiatrique couvrant environ 2 millions d'enfants au sud de Londres) transportait sur une période de 10 jours 8 enfants présentant un état de choc « hyperinflammatoire », ayant les caractéristiques d'un syndrome de Kawasaki ou d'un « toxic-shock syndrome », alors que le nombre habituel est au maximum d'1 à 2 cas par semaine [START_REF] Riphagen | Hyperinflammatory shock in children during COVID-19 pandemic[END_REF]. Six de ces enfants étaient d'origine afrocaribéenne et 7 d'entre eux étaient en surpoids ou obèses. La présentation clinique initiale était très semblable avec une fièvre supérieure à 39-40°C prolongée, un rash cutané, une conjonctivite bilatérale, des douleurs des extrémités et des troubles digestifs. Tous progressaient vers un état de choc vasoplégique nécessitant un remplissage vasculaire et des vasopresseurs (noradrénaline et milrinone). La plupart de ces enfants n'avaient pas de défaillance respiratoire prédominante, bien que 7 d'entre eux étaient ventilés du fait de leur état de choc. En outre, il était observé de discrets épanchements pleuraux, péricardiques et péritonéaux suggérant un processus inflammatoire. Aucun enfant n'était testé positif par PCR pour COVID-19 sur une aspiration naso-pharyngée ou un lavage broncho-alvéolaire. Les marqueurs inflammatoires (CRP, PCT, ferritine, D-dimères et triglycérides) étaient très élevés. L'ECG était sans particularité, mais les échocardiographies successives mettaient en évidence des artères coronaires hyperéchogènes à leur origine avec progression vers un anévrysme coronaire géant chez un patient, une semaine après sa sortie de l'hôpital.

Jean-Christophe Mercier V2 -10 juin 2020 4 L'atteinte myocardique primitive de ces patients était authentifiée par une élévation des enzymes cardiaques. Tous les enfants recevaient 2 g/kg d'immunoglobulines intraveineuses et 50 mg/kg d'acide acétylsalicylique. Tous les enfants sortaient de réanimation pédiatrique après 4 à 6 jours, sauf un qui développait un état de choc cardiogénique réfractaire avec des troubles du rythme et qui décédait sous ECMO d'une hémorragie cérébrale. Une sérologie COVID-19 positive était mise en évidence chez 2 des enfants, dont celui qui décédait sous ECMO.

Une nouvelle série anglaise de 58 enfants (âge médian 9 ans [EIQ 5,7-14], 33 (57 %) étaient des filles et 40 (60 %) étaient d'origine africaine ou asiatique) présentant un « Pediatric Inflammatory Multisystem Syndrome Temporally Associated with SARS-CoV-2 » (PIMS-TS) observée dans 8 hôpitaux anglais entre le 23 mars et le 16 mai 2020 était rapportée un peu plus tard [START_REF] Whittaker | for the PIMS-TS Study Group and EUCLIDS and PERFORM Consortia. Clinical characteristics of 58 children with a Pediatric Inflammatory Multisystem Syndrome Temporally Associated with SARS-CoV-2[END_REF]. Une PCR SARS-CoV-2 était positive chez 15/58 ( En Italie, la région de Bergame a été la plus touchée par l'épidémie COVID-19. L'affection chez l'adulte comporte typiquement deux périodes successives d'environ 1 semaine chacune, la première caractérisée par une pneumonie virale (fièvre élevée, frissons, toux sèche, myalgies) suivie d'une deuxième phase caractérisée par un syndrome de détresse respiratoire aiguë (SDRA) possiblement du fait d'une endothélite thrombogène [START_REF] Ackermann | Pulmonary vascular endothelialitis, thrombosis, and angiogenesis in Covid-19[END_REF] et un syndrome de défaillance multiviscérale (SDMV) dans un contexte d'orage cytokinique avec une mortalité proche de 50 % malgré l'assistance ventilatoire, circulatoire et rénale [START_REF] Moore | Cytokine release syndrome in severe COVID-19[END_REF]. Ainsi, tous les dossiers d'enfants avec un diagnostic de syndrome de Kawasaki pris en charge à l'Hôpital Jean XXIII de Bergame sur une période de 5 ans ont été revus, avant (groupe 1, n=19) et après l'épidémie (groupe 2, n=10 dont 8 avaient une sérologie IgM et/ou IgG positive pour COVID-19) [START_REF] Verdoni | An outbreak of severe Kawasaki-like disease at the Italian epicenter of the SARS-CoV-2 epidemic: an observational cohort study[END_REF]. Les deux groupes différaient par l'incidence (0,3 vs. 10 par mois), l'âge moyen (3,0 vs. 7,5 ans), l'atteinte myocardique (2/19 vs. 5/10), les scores « Kawasaki Disease Shock Syndrome » (KDSS 0/19 vs. 5/10) et « Macrophage Activation Syndrome » (MAS 0/19 vs. 5/10) et la nécessité de compléter l'administration intraveineuse d'immunoglobulines par une corticothérapie systémique (3/19 vs. 8/10) (pour tous les items p<0,01). Ainsi, il était observé en un mois de pandémie une augmentation par 30 du nombre de cas de syndrome de Kawasaki, survenant chez des enfants plus âgés et associés à des marqueurs hyper-inflammatoires et à une atteinte cardiaque plus sévère [START_REF] Viner | Kawasaki-like disease: emerging complication during the COVID-19 pandemic. Comment[END_REF].

En France, 35 enfants avec un choc cardiogénique, une dysfonction ventriculaire gauche et un syndrome inflammatoire sévère étaient rétrospectivement identifiés en 2 mois dans 14 unités de réanimation pédiatrique (dont celui de Genève) [START_REF] Belhadjer | Acute heart failure in multisystem inflammatory syndrome in children (MIS-C) in the context of global SARS-CoV-2 pandemic[END_REF]. Leur âge médian à l'admission était de 10 ans (extrêmes 2-16). Des comorbidités (asthme, obésité) étaient présentes dans 28 % des cas. Les symptômes initiaux étaient fréquemment digestifs. La fraction d'éjection ventriculaire était inférieure à 30 % chez un tiers d'entre eux et un support inotrope nécessaire chez 80 % d'entre eux, tandis que 28 % nécessitaient une ECMO. Les Jean-Christophe Mercier V2 -10 juin 2020 5 marqueurs inflammatoires suggéraient fortement un « orage cytokinique » (IL-6 médian 135 pg/mL) et une activation macrophagique (D-dimères médians 5.284 ng/mL). 31/35 (88 %) enfants étaient testés COVID-19 par PCR nasopharyngée ou par sérologie. Tous les patients ont reçu des immunoglobulines intraveineuses et une corticothérapie était adjointe dans un tiers des cas. La fonction ventriculaire gauche se normalisait chez 25/35 (71 %) de ceux qui sortaient de réanimation. Aucun patient n'est décédé et tous les patients supportés par ECMO ont pu être sevrés. Il était ainsi conclu que les enfants pouvaient présenter une dysfonction ventriculaire gauche aiguë associée à un syndrome hyper inflammatoire sévère dans les suites d'une infection à COVID-19. Un traitement par immunoglobulines intraveineuses était associé à une récupération rapide de la fonction ventriculaire.

Entre le 27 avril et le 11 mai 2020, soit en l'espace de 11 jours, 17 enfants avec un syndrome de Kawasaki étaient admis à l'hôpital des Enfants malades à Paris, alors que la moyenne n'était que d'1 cas toutes les deux semaines au cours des deux années antérieures [START_REF] Toubiana | Outbreak of Kawasaki disease in children during COVID-19 pandemic: a prospective observational study in Paris, France. medRixv[END_REF]. Leur âge médian était de 7,5 (extrêmes Ces observations peuvent être complétées par une série de 42 enfants testés COVID-19 par PCR pris en charge à l'Hôpital Robert Debré à Paris. 29 (69 %) étaient hospitalisés dont 8 (19 %) en réanimation pédiatrique. 5 (17 %) enfants présentaient un syndrome de Kawasaki et 5 (17 %) autres enfants un tableau de myocardite avec défaillance cardiaque aiguë [START_REF] Ouldali | Emergence of Kawasaki disease related to SARS-CoV-2 infection in children: a time series analysis[END_REF]. Un enfant est décédé mais il était traité par chimiothérapie pour une leucémie lymphoïde aiguë. L'analyse rétrospective de tous les cas de syndrome de Kawasaki confirmés et hospitalisés à l'Hôpital Robert Debré entre 2005 et 2020 apportait une donnée nouvelle. Si le nombre moyen d'hospitalisation mensuelle estimée par un modèle de Poisson au cours de ces 15 années était de 1,2 par mois, deux pics étaient constatés, le premier de 6 enfants (+ 497 % [IC 95% +72 ; +1082], p=0,0011) avec syndrome de Kawasaki entre le 15 et le 30 avril 2020 lié à SARS-CoV-2 et le deuxième (+ 365 % [IC 95% +31 ; +719], p=0,0053) au cours des semaines 48/49 de l'année 2009, soit environ 1-3 semaines après le pic de l'épidémie de grippe A H1N1 2009pdm. Toutefois, la maladie de Kawasaki associée au SARS-Cov2 diffère de la maladie de Kawasaki classique, car elle se produit à un âge plus avancé et se présente avec une fréquence plus élevée de myocardite et/ou de péricardite graves [START_REF] Ouldali | Emergence of Kawasaki disease related to SARS-CoV-2 infection in children: a time series analysis[END_REF]. Les caractéristiques pronostiques semblent être un âge supérieur à 5 ans et un taux de ferritine élevé sont des facteurs de gravité (>1400 μg/L). [START_REF]Guidance -Paediatric multisystem inflammatory syndrome temporally associated with COVID-19[END_REF] Ce nouveau syndrome PIMS-TS partage-t-il les mêmes étiologie et physiopathologie que le syndrome de Kawasaki [START_REF] Mccrindle | SARS-CoV-2-related Inflammatory Multisystem Syndrome in children: different or share etiology and pathophysiology as Kawasaki disease?[END_REF] ? L'étiologie de ce dernier syndrome est resté mystérieuse pendant 50 ans après sa description. Une prédisposition génétique est partiellement expliquée par des gènes de susceptibilité associés au système immunitaire [START_REF] Onouchi | ITPKC functional polymorphism associated with Kawasaki disease susceptibility and formation of coronary artery aneurysms[END_REF]. Cependant, les grandes variations d'incidence entre les pays, une certaine saisonnalité spécifique entre régions, la survenue de clusters de cas ou par petites épidémies suggèrent une origine infectieuse. Des études anatomopathologiques ont mis en évidence des inclusions intracytoplasmiques au niveau de l'épithélium bronchique qui évoquent la possibilité d'un Jean-Christophe Mercier V2 -10 juin 2020 6 nouveau virus [START_REF] Rowley | A protein epitope targeted by the antibody response to Kawasaki disease[END_REF]. Une hyperactivation du système immunitaire innée constitue une autre possibilité, en particulier dans certaines populations d'origine africaine ou asiatique, comme il a été observé dans ces différentes séries de cas. Une telle convergence de cas est troublante et elle incite à approfondir la susceptibilité génétique et immunologique de ces syndromes de physiopathologie probablement proche.

Un nouveau concept ? Le Paediatric Inflammatory Multisystem Syndrome (PIMS) temporally associated with emerging viral diseases

Conclusion

S'il est manifeste que les enfants sont moins susceptibles que les adultes au SARS-CoV-2 (COVID-19) et qu'ils développent des formes cliniques moins sévères, un petit nombre, peutêtre du fait de comorbidités associées (malformations congénitales, obésité, hypertension artérielle) ou d'une dysrégulation cytokinique inflammatoire, peut présenter une dysfonction ventriculaire gauche et/ou un syndrome de Kawasaki régressant rapidement après un traitement par immunoglobulines intraveineuses et/ou une corticothérapie associée.

Cette évolution particulière à l'enfant pose évidemment beaucoup de questions physiopathologiques quant aux liens entre fonction myocardique, atteinte endothéliale et immunologie [START_REF] Willyard | Coronavirus blood clot mystery intensifies. Research begins to pick apart the mechanisms behind a deadly COVID-19 complication[END_REF]. L'évaluation de facteurs immunologiques et génétiques de l'hôte sont nécessaires pour de mieux comprendre ces formes sévères.

En pratique

Moindre gravité chez les enfants, en dehors du risque de choc par myocardite aiguë et/ou de syndrome de Kawasaki dans un contexte d'orage cytokinique. Emergence d'un nouveau concept, le PIMS : Paediatric Inflammatory Multisystem Syndrome associé à l'infection virale.

Déclaration de liens d'intérêts

Les auteurs déclarent ne pas avoir de liens d'intérêts.

Une moindre sévérité de l'infection COVID-19 chez les enfants

	pic de l'épidémie (14 avril 2020), 350 nouveaux patients y étaient enregistrés chaque heure et un total d'environ 60.000 patients ambulatoires ont été ainsi télésurveillés.
	Entre le 16 janvier et le 8 février 2020, 2.143 patients pédiatriques âgés de moins de 18 ans (âge médian 7 ans, EIQ 2-13) avec une infection COVID-19 (731 [34,1 %] cas confirmés par PCR et 1412 [65,9 %] cas suspects) étaient déclarés au « Chinese Center for Disease Control and Prevention »
	juin 2020, il était recensé dans le monde environ 7,3 millions de cas et 412.000 décès (mortalité 5,6 %) [7], en Europe 1,450 million de cas et 170.000 décès (mortalité 11,7 %) [8], en France 155.000 cas et 29,296 décès (mortalité 18,9 %) dont 18.912 à l'hôpital et 10.384 en EPHAD et en Île de France 25.895 cas guéris et 7.274 décès à l'hôpital (mortalité 18,7 %) avec 5.288 patients toujours hospitalisés et 444 en réanimation [9]. Les chiffres discordants de mortalité proviennent principalement des incertitudes quant au dénominateur, c'est-à-dire du nombre de patients COVID-19 prouvés par PCR ou simplement suspectés cliniquement. Dans cette même région d'Île de France, la majorité des patients COVID-19 positifs ou suspects avec une forme clinique moins sévère étaient isolés à domicile et surveillés quotidiennement par une plateforme constituée de centaines d'étudiants en médecine encadrés par une centaine de médecins retraités volontaires via une application mobile appelée COVIDOM® [10]. Au
	Jean-Christophe Mercier	3	V2 -10 juin 2020

En 2002, a émergé dans la province du Guangdong au sud de la Chine un nouveau bêta-coronavirus qui a rapidement disséminé de Hong Kong dans de nombreux autres pays. Parce que ce nouveau coronavirus était responsable d'un Syndrome de Détresse Respiratoire Aiguë (SDRA) et d'une mortalité élevée proche de 50 %, il a été appelé « Severe Acute Respiratory Syndrome » ou SARS-CoV. Une contamination interhumaine était bien établie et SARS-CoV était responsable d'environ 8.000 infections respiratoires dans 29 pays et de 774 décès. En 2012, un nouveau bêta-coronavirus émergeait en Arabie Saoudite, appelé « Middle East Respiratory Syndrome » ou MERS-CoV. Transmis par contact direct entre personnes, il était responsable d'une mortalité élevée entre 20 et 40 %, avec 2.494 infections respiratoires et 858 décès recensés dans le monde. La pandémie à SARS-CoV-2 (COVID-19) est d'une toute autre échelle. Le 10

  26 %) patients et une sérologie IgG positive chez 40/46 (87 %). Tous les enfants se présentaient avec de la fièvre et des signes digestifs non spécifiques comme des vomissements (26/58 [45 %]), des douleurs abdominales (31/58 [53 %]) et de la diarrhée (30/58 [52 %]). Un rash était présent dans 30/58 (52 %) et une injection conjonctivale dans 26/58 (45 %) des cas. La biologie était compatible avec une réaction inflammatoire marquée (CRP 229 mg/L [EIQ 156-338] ; ferritine 610 µg/L [EIQ 359-1290]. 29 d'entre eux développaient un état de choc (avec une élévation des biomarqueurs cardiaques) et nécessitaient un traitement inotrope et un remplissage vasculaire et 23/29 ventilés mécaniquement : 13 satisfaisaient les critères AHA d'un syndrome de Kawasaki [16] et 23 présentaient fièvre et inflammation sans signes de choc ni de syndrome de Kawasaki. 8 (14 %) développaient une dilatation ou un anévrysme de l'artère coronaire. La comparaison des enfants avec PIMS-TS et syndrome de Kawasaki ou syndrome de Kawasaki avec choc montrait des différences cliniques, notamment de l'âge médian 9 ans [EIQ 5,7-14] vs. 2,7 [1,4-4,7] et 3,8 [0,2-18] et biologiques, notamment des marqueurs de l'inflammation comme la CRP médiane 229 mg/L [EIQ 156-338] vs. 67 [40-150] et 193 [EIQ 83-237].

  3,7-16,6) ans. 59 % des patients étaient originaires d'Afrique sub-saharienne ou des îles caraïbes. 11 patients présentaient un état de choc qui nécessitait un remplissage vasculaire et un traitement vasoactif et 12 avaient des signes de myocardite aiguë. Tous les enfants présentaient initialement des symptômes digestifs et des marqueurs inflammatoires élevés. 14 patients avaient des signes d'infection récente à COVID-19 (7/17 PCR positive et 14/16 des anticorps IgG spécifiques). Tous les patients recevaient des immunoglobulines (2 g/kg) par voie intraveineuse et 5/17 une corticothérapie. Le pronostic était favorable chez tous les enfants avec cependant la détection d'une dilatation coronaire modérée chez 5/17 (29 %) d'entre eux.


Aurélie Corne
email: aurelie.corne@univ-perp.fr

Nicolas Peypoch
email: peypoch@univ-perp.fr

On the determinants of tourism performance

Keywords: Performance modeling, tourism efficiency, tourism attraction, complexity Performance modeling, tourism efficiency, tourism attraction, complexity

The purpose of this paper is to propose an innovative direction in order to analyze the determinants of tourism performance. The literature on this topic reveals diverging results about the impacts of the determinants of tourism performance. This paper advocates for the identification of the multiple and complex effects of the determinants in order to overcome the characterization of single net effects derived from an average behavior. A two-stage efficiency analysis is implemented, mixing Data Envelopment Analysis and fuzzy-set Qualitative Comparative Analysis. An illustration about the tourism efficiency in French regions is proposed and emphasizes the multiple impacts of the determinants.

Introduction

Performance modeling in tourism research received a great attention from scholars this last decade [START_REF] Assaf | A review of research into performance modeling in tourism research-Launching the Annals of Tourism Research curated collection on performance modeling in tourism research[END_REF]. Several techniques are available in the literature in order to model tourism performance. Among others, Data Envelopment Analysis (DEA) and its derivatives is very popular. As identified by Assaf and Tsionas (2019, p.274), a key point in tourism performance analysis is the question about the determinants of efficiency. In a first stage, efficiency scores are calculated by using non-parametric approaches based on linear programming in the DEA framework. In a second stage, the efficiency scores are regressed by using determinants which are termed contextual or environmental variables in the literature. The goal is to explain their possible impacts on the efficiency level of the units analyzed and these two-stage approaches have been used extensively by tourism researchers [START_REF] Assaf | Frontier analysis: A state-of-the-art review and metaanalysis[END_REF].

Different methods are available in the literature in order to explain the performance scores in the second stage analysis. Tobit regression was mainly used, but the technique changed with the important contribution by [START_REF] Simar | Estimation and inference in two-stage, semi-parametric models of production processes[END_REF]. They provided a robust econometric technique based on bootstrapping. However, a debate about the method appeared with the work of [START_REF] Mcdonald | Using least squares and tobit in second stage DEA efficiency analyses[END_REF] who recommended regressions estimated by ordinary least squares for second stage analysis of efficiency. [START_REF] Simar | Two-stage DEA: caveat emptor[END_REF] answered and proposed a demonstration of the robustness of their method. They underlined that their contribution in 2007 is the more appropriate but under very specific conditions. Finally, they argued in conclusion: "we do not recommend the use of second-stage regressions involving DEA efficiency scores" (Simar and Wilson, 2011, p.216). However, the analysis of the determinants of performance is still of paramount importance in tourism research and Assaf and Josiassen (2016, p.624) recommend to pay more attention on this topic. Given both the necessity and the uncertainty about the choice of the method for second stage analysis in the literature, this paper proposes an alternative way and advocates to use fsQCA (fuzzy-set Qualitative Comparative Analysis) for second stage analysis of tourism performance.

From a theoretical point of view, the reductionist approach, simplifying the analysis to the principal components of the phenomenon studied, has some limits in order to model the tourism sector [START_REF] Baggio | Symptoms of complexity in a tourism system[END_REF]. Tourism is a complex phenomenon [START_REF] Goeldner | Tourism Principles, Practices, Philosophies[END_REF] that can be viewed as a complex system [START_REF] Farrell | Reconceptualizing tourism[END_REF]. The relationships between the components of the tourism sector can be nonlinear [START_REF] Urry | The complexity Turn[END_REF]. This is particular relevant in the analysis of tourism destinations in which multiple stakeholders are present (Baggio et al., 2010a,b). Some studies have attempted to address the complexity of the tourism destinations by applying qualitative or quantitative methods (Baggio et al., 2010a). However, in our knowledge, none have tried to use qualitative comparative analysis (QCA) whereas this last offers the possibility of a middle path between qualitative and quantitative methods [START_REF] Ragin | Redesigning social inquiry: Fuzzy sets and beyond[END_REF]. The fuzzy version of QCA, termed fsQCA, is a technique permitting to capture the complexity and was introduced by the sociologist [START_REF] Ragin | Redesigning social inquiry: Fuzzy sets and beyond[END_REF]. It is based on the theory of complexity [START_REF] Gigerenzer | How to make cognitive illusions disappear: Beyond "heuristics and biases[END_REF][START_REF] Urry | The complexity Turn[END_REF] and provides a real value to apprehend the complexity of the tourism sector. Contrary to regression analysis that identifies net effects, the advantage of this method is the characterization of multiple effects of the exogenous variables on the dependent variable. Accounting for complexity in the explanation of tourism performance seems particularly relevant since the tourism phenomenon is "complex" [START_REF] Goeldner | Tourism Principles, Practices, Philosophies[END_REF]. Then this paper investigates the use of fsQCA in order to explain the DEA efficiency scores in tourism research.

In order to illustrate the use of fsQCA in efficiency second stage analysis, the case of tourism destinations is considered. Modeling tourism destination efficiency received a lot of attention in the literature [START_REF] Tsionas | Short-run and long-run performance of international tourism: Evidence from Bayesian dynamic models[END_REF]. The interest of this two-stage approach is illustrated with the French regions [START_REF] Botti | Tourism Destination Competitiveness: The French Regions Case[END_REF][START_REF] Barros | Performance of French destinations: Tourism attraction perspectives[END_REF] and by using the tourism attraction theory [START_REF] Lew | A framework of tourist attraction research[END_REF][START_REF] Leiper | Tourist attraction systems[END_REF] in order to select the determinants. For a comparative purpose, the [START_REF] Simar | Estimation and inference in two-stage, semi-parametric models of production processes[END_REF] method is also implemented.

The paper unfolds as follows. Section 2 presents a literature review in order to identify the research gap. Section 3 briefly introduces the background of DEA and fsQCA. Section 4 proposes an empirical illustration. Section 5 concludes and underlines a methodological question for future research.

The determinants of tourism efficiency: current gap

In tourism performance modeling, the two-stage approach with the DEA method is widely used [START_REF] Assaf | Frontier analysis: A state-of-the-art review and metaanalysis[END_REF]. On the one hand, scholars use the DEA method and its derivatives to measure the tourism performance at a micro or macro level (hotels, restaurants, airports, destinations, etc.) and to obtain a benchmarking analysis. On the other hand, they employ methodologies based on regressions such as Tobit or bootstrapping techniques with a truncated distribution in order to identify the determinants of tourism performance.

The purpose of this subsection is not to provide another literature review on the determinants of tourism efficiency in the extensive existing literature (Assaf andJosiassen, 2012, 2016;[START_REF] Sellers-Rubio | Analyzing hotel efficiency from a regional perspective: The role of environmental determinants[END_REF]. In order to identify the current gap this paper intends to reduce, we focus on the net effects identified in the empirical literature devoted to the determinants of tourism efficiency. More precisely, we point out some examples of opposite or contradictory findings in empirical contributions in order to highlight the determinants in which there is no consensus in the literature.

The literature devoted to hotel efficiency shows several examples of diverging results. For instance, destination quality can have different impacts on efficiency [START_REF] Sellers-Rubio | Analyzing hotel efficiency from a regional perspective: The role of environmental determinants[END_REF] and the link between hotel size and performance shows no real consensus [START_REF] Oukil | Performance evaluation of the hotel industry in an emerging tourism destination: The case of Oman[END_REF]. At a destination level, the variable beach affects positively the tourism regions in France [START_REF] Barros | Performance of French destinations: Tourism attraction perspectives[END_REF] whereas it plays a negative role in the tourism performance in Oman [START_REF] Oukil | Performance evaluation of the hotel industry in an emerging tourism destination: The case of Oman[END_REF]. For the variable related to monuments, [START_REF] Barros | Performance of French destinations: Tourism attraction perspectives[END_REF] show a positive impact on French tourism performance while [START_REF] Cuccia | The effects of UNESCO World Heritage List inscription on tourism destinations performance in Italian regions[END_REF], by using the World Heritage List, find a negative impact for the tourism efficiency in Italy. In two applications to the Spanish regions that differ according to the time-periods studied and in which all the variables used are the same, [START_REF] Benito | Determinants of Spanish regions' tourism performance: a two-stage, double-bootstrap data envelopment analysis[END_REF] and Solana-Ibanez et al. (2016) find different findings concerning the impact of ski and golf attractions. Another example of diverging results includes the variable hotel ownership with a positive impact in the study by [START_REF] Barros | Technical efficiency of African hotels[END_REF] and [START_REF] Shang | A stochastic DEA study of hotel efficiency[END_REF] while [START_REF] Oukil | Performance evaluation of the hotel industry in an emerging tourism destination: The case of Oman[END_REF] identify a negative impact. The same applies for the size effect in the hotel sector which can be a positive [START_REF] Assaf | Modelling the performance of Australian hotels: a DEA double bootstrap approach[END_REF] or a negative [START_REF] Oukil | Performance evaluation of the hotel industry in an emerging tourism destination: The case of Oman[END_REF] impact. Table 1 summarizes these different impacts in some empirical contributions of the literature. This survey permits to identify a gap in the literature. Indeed, the determinants of tourism performance can have different effects according to the case and the scale studied, showing an interesting feature of the complexity of the tourism sector.

This paper contributes to reduce this gap and innovates by considering the complexity in the determinants of tourism performance. In words, the use of fsQCA in second stage DEA models permits to consider multiple effects instead of net effects.

Methodologies

This section presents and develops a two-stage procedure based on a combination between two existing methodologies: DEA and fsQCA. The objective is to model the tourism performance by using DEA and to identify its determinants in a second stage with the fsQCA approach.

DEA method

The DEA method proposes an analysis of performance through the notion of efficiency. It is a non-parametric approach based on linear programming. DEA was introduced by the works of [START_REF] Charnes | Measuring the efficiency of decision making units[END_REF] and [START_REF] Banker | Some models for estimating technical and scale inefficiencies in data envelopment analysis[END_REF], which differ regarding the assumption on returns to scale of the production technology, respectively constant and variable. DEA is a well-known and useful method for managerial and strategic purposes. Its two main advantages are related to the possibility to deal with multi-input/output production technologies and to not assume a functional form for this latter.

DEA measures the relative efficiency of a given sample of decision making units that transform inputs into outputs. The production technology of the decision making units transforms the inputs x = (x , ⋯ , x ) ∈ R into the outputs y = (y , ⋯ , y ) ∈ R . In other words, the production technology T can be rewritten as T = (x, y) ∈ R : x can produce y and is defined by:

T = (x, y): x ≥ θ x , y ≤ θ y , θ ≥ 0, i = 1, ⋯ , k.
The linear program for computing the efficiency score of the DEA model [START_REF] Charnes | Measuring the efficiency of decision making units[END_REF] of each decision making unit is given by:

Max δ s.t. x ≥ ∑ θ x δy ≤ ∑ θ y θ ≥ 0, i = 1, ⋯ , k.
This program is run k times, k corresponding to the number of units analyzed in the sample. This model is output oriented, a common practice in tourism destination management because the objective is to maximize the results [START_REF] Dong | Do contextual factors matter? Evidence from Chinese hotel productivity with heterogeneity[END_REF]. The DEA model by [START_REF] Banker | Some models for estimating technical and scale inefficiencies in data envelopment analysis[END_REF] can be obtained by adding the constraint ∑ θ = 1 in the previous linear program in order to account for variable returns to scale. [START_REF] Assaf | Frontier analysis: A state-of-the-art review and metaanalysis[END_REF] and [START_REF] Assaf | A review of research into performance modeling in tourism research-Launching the Annals of Tourism Research curated collection on performance modeling in tourism research[END_REF] propose recent surveys of empirical contributions using DEA in tourism research.

fsQCA approach

fsQCA is a set-theoretic method that comes from political and social sciences. It is a set of approaches based on connections between several relationships developed by [START_REF] Ragin | The Comparative Method: Moving Beyond Qualitative and Quantitative Strategies[END_REF][START_REF] Ragin | Redesigning social inquiry: Fuzzy sets and beyond[END_REF]. Ragin exposes this approach in detail by showing that set-theoretic connections are asymmetrical whereas correlational connections are symmetric. This method is based on the complexity theory and can be applied to small, medium and large samples [START_REF] Ragin | Redesigning social inquiry: Fuzzy sets and beyond[END_REF]. Recently, [START_REF] Woodside | Embrace• perform• model: Complexity theory, contrarian case analysis, and multiple realities[END_REF][START_REF] Woodside | Visualizing⋅ matching⋅ generalizing: Case identification hypotheses and case-level data analysis[END_REF] explained the interest and advantages for scholars to use fsQCA in management sciences. According to [START_REF] Woodside | Embrace• perform• model: Complexity theory, contrarian case analysis, and multiple realities[END_REF], the complexity theory involves the following six tenets: i) a single condition can be necessary but it is rarely sufficient to explain a result. ii) a small number of configurations (or combinations of conditions) are sufficient; it is the recipe principle. This latter is composed of two or more conditions in order to explain the result with a high consistency score. iii) a simple antecedent condition can contribute positively or negatively to the result, depending of its association with other conditions. iv) the equifinality principle: several paths or configurations lead to performance. v) the causal asymmetry principle: paths leading to a high performance are not the opposite mirror to the paths leading to a low performance. vi) a given configuration is not relevant for all cases. Woodside (2015, p.253) provides also an interesting explanation about the comparison between fsQCA and regression analysis. The endogenous variable in the regression is the outcome condition (or result) in fsQCA while the exogenous variables are the antecedent conditions. Regression-based approaches analyze the net effects of the variables and focus on the explanatory power of the model (measured by R 2 ) while fsQCA identifies configurations, i.e. combinations of conditions, which lead to the result with the most consistent accuracy possible (measured by the consistency index).

The determination of the configurations in order to model and explain the complexity of the phenomenon studied requires different stages. The first stage is the calibration of the variables. It is a crucial step and, according to [START_REF] Ragin | Redesigning social inquiry: Fuzzy sets and beyond[END_REF], it must be based on the most complete knowledge from the researcher. Three main points or thresholds are considered (full nonmembership, crossover and full membership) with calibrated values equal respectively to a fuzzy score between 0 and 1 (respectively 0.05, 0.5 and 0.95). The second step is the necessity analysis. By using Boolean algebra, fsQCA estimates indexes of consistency and coverage to analyze the necessity. According to Ragin (2008, p.44-45), the notions of consistency and coverage can be explained as follows. Consistency measures a kind of degree of significance insofar as it underlines if the researcher has to pay attention or not to a configuration regarding the theory. Coverage indicates a kind of degree of importance of a configuration.

For the necessity analysis, the consistency index is based on the following formula [START_REF] Ragin | Redesigning social inquiry: Fuzzy sets and beyond[END_REF]:

Consistency(X ≥ Y ) = ∑[min(X , Y )] ∑(Y )
The calculation of the coverage index is defined by:

Coverage(X ≥ Y ) = ∑[min(X , Y )] ∑(X )
where Xi is the calibrated antecedent condition and Yi is the calibrated outcome condition for the unit i.

A condition is necessary if its consistency index is greater than or equal to 0.9 [START_REF] Ragin | Set relations in social research: Evaluating their consistency and coverage[END_REF]2008). The next step is the construction of the truth table. This configuration table provides all the logical configurations between causality conditions in order to obtain the result with a level of empirical evidence associated with each configuration. It is composed of 2 k lines where k represents the number of conditions (variables). The number of lines retained depends of the consistency cutoff and the frequency threshold selected. Finally, the identification of sufficient configurations is done by using Boolean minimization and the Quine-McCluskey algorithm. The corresponding consistency and coverage indexes for sufficiency analysis are defined by [START_REF] Ragin | Redesigning social inquiry: Fuzzy sets and beyond[END_REF]:

Consistency(X ≤ Y ) = ∑[min(X , Y )] ∑(X ) Coverage(X ≤ Y ) = ∑[min(X , Y )] ∑(Y )
where Xi is the calibrated antecedent condition and Yi is the calibrated outcome condition for the unit i.

Application to the French regions

Tourism in France is characterized by a paradox which shows the relative inefficiency of the French destination at the international level when tourist arrivals and tourism receipts are compared [START_REF] Barros | Performance of French destinations: Tourism attraction perspectives[END_REF]. This weakness of the French tourism sector motivated scholars to analyze and benchmark the best practices at the regional level on the French territory. Hence, modeling the tourism performance of the French regions received some attention in the literature [START_REF] Botti | Tourism Destination Competitiveness: The French Regions Case[END_REF][START_REF] Barros | Performance of French destinations: Tourism attraction perspectives[END_REF][START_REF] Corne | Benchmarking and tourism efficiency in France[END_REF]. In this line, this paper revisits the determinants of the tourism performance of French regions by using fsQCA in the second stage of the DEA framework.

The 13 French administrative regions are considered for this study. The territorial reform changed the number of French regions from 22 to 13 since 2016. This is of particular importance for efficiency analysis as the literature clearly shows that, in order to be discriminatory in terms of efficiency, some rules are required between the number of units in the sample and the number of inputs and outputs [START_REF] Sarkis | Preparing your data for DEA[END_REF]. In general, but without real consensus, the number of units is expected to be greater or equal to three times the sum of inputs and outputs [START_REF] Cooper | Introduction to Data Envelopment Analysis and its Uses: With DEA-solver Software and References[END_REF] or larger than two times the product of the number of inputs and outputs [START_REF] Dyson | Pitfalls and protocols in DEA[END_REF]. Then, a production technology with two inputs and two outputs is considered. The variables are selected by following the literature and according to the data availability. The two inputs are accommodation capacity in the hospitality sector (number of rooms) and number of employees in the tourism sector (Sellers-Rubio and Casado-Díaz, 2018). These two inputs characterize capital and labor and are commonly used in tourism performance studies [START_REF] Assaf | Frontier analysis: A state-of-the-art review and metaanalysis[END_REF]. The two outputs are the number of tourist arrivals and the tourist tax. These two outputs permit to capture the attractiveness and the economic repercussions of the tourism flows. The number of tourist arrivals is commonly used in frontier research in tourism [START_REF] Assaf | Frontier analysis: A state-of-the-art review and metaanalysis[END_REF]. The tourist tax is more innovative in terms of output and it is a good proxy at the regional level when tourism revenue is unavailable (like in the French official statistics). Finally, all the inputs and outputs are expressed in value, without proportion data in order to avoid bias in the DEA estimation [START_REF] Olesen | Efficiency measures and computational approaches for data envelopment analysis models with ratio inputs and outputs[END_REF].

Data for the inputs and outputs are sourced from the "Mémento du tourisme 2018" for the year 2017 and are available at: https://www.entreprises.gouv.fr/etudes-et-statistiques/ Regarding the variables for the second stage analysis, a focus is made on tourism attraction theory. Since the works of [START_REF] Lew | A framework of tourist attraction research[END_REF] and [START_REF] Gunn | Vacationscape: Designing tourist regions[END_REF], it has been commonplace to consider tourism attraction as a key element of the tourism supply side. [START_REF] Leiper | Tourist attraction systems[END_REF] extended the characterization of the tourism attraction and several classifications appeared in the literature [START_REF] Gunn | Tourism planning: Basics, concepts[END_REF][START_REF] Beckendorff | Attraction megatrends[END_REF][START_REF] Botti | Time and tourism attraction[END_REF]. [START_REF] Swarbrooke | The development and management of visitor attractions[END_REF] showed the importance of the tourism attractions in the development of the destination and they have also a core place in the conceptual framework of destination competitiveness of [START_REF] Ritchie | The competitive destination: A sustainable tourism perspective[END_REF] for the destination management organizations. In the empirical literature, the study of the impacts of tourism attractions on regional performance by using two-stage models is now well established [START_REF] Barros | Performance of French destinations: Tourism attraction perspectives[END_REF][START_REF] Benito | Determinants of Spanish regions' tourism performance: a two-stage, double-bootstrap data envelopment analysis[END_REF]. The case of the determinants of the French regional tourism performance is implemented by following the literature devoted to the impacts of tourism attractions on regional performance [START_REF] Barros | Performance of French destinations: Tourism attraction perspectives[END_REF][START_REF] Benito | Determinants of Spanish regions' tourism performance: a two-stage, double-bootstrap data envelopment analysis[END_REF][START_REF] Huang | Dynamic efficiency assessment of the Chinese hotel industry[END_REF]. In order to analyze the determinants of the French tourism performance, we follow these contributions and four variables are then considered: number of monuments, number of museums (labelled 'musées de France'), presence of beaches in the region, presence of ski resorts in the region. The number of museums is provided by the French Ministry of Culture ( 2018) and all the other data are sourced from the Mémento du Tourisme (2018) for the year 2017.

From a theoretical point of view, the expected impact of a tourism attraction is positive. This is confirmed for these four determinants by a large part of the empirical literature and more precisely with a previous study by [START_REF] Barros | Performance of French destinations: Tourism attraction perspectives[END_REF] for the French tourism regions. However, the complexity of the tourism sector can reveal some contradictory findings (Table 1).

With the territorial reform, the French regions are more homogeneous in terms of size. Then the DEA model with constant returns to scale [START_REF] Charnes | Measuring the efficiency of decision making units[END_REF] is used and this choice is confirmed by a test on returns to scale implemented by following the procedure proposed by [START_REF] Bogetoft | Benchmarking with DEA, SFA and R[END_REF] and by using the package 'benchmarking' in the R software (R Core Team, 2019).

The findings of the output-oriented DEA model with constant returns to scale are presented in Table 3. 0748 -Note: i) In output orientation, the DEA score is greater or equal to 1. The efficiency level is derived from 1/score and indicates the percentage level of efficiency. ii) For inefficient units, shortfalls in output production are obtained by score -1. For instance, the Occitanie region is inefficient with a relative efficiency level of 88.59% and it should improve simultaneously the two outputs by 12.88%.

In 2017, the average efficiency level of French regions is 91.82%. Four regions are technically efficient. In terms of relative efficiency, these findings are in line with previous research, especially concerning the region Ile-de-France that is technically efficient and constitutes the main benchmark [START_REF] Botti | Tourism Destination Competitiveness: The French Regions Case[END_REF][START_REF] Barros | Performance of French destinations: Tourism attraction perspectives[END_REF]. Provence-Alpes-Côte d'Azur and Corse are two other regions technically efficient which are very reputed for their beaches. The efficiency scores of other cases like the region Bourgogne-Franche-Comté can be explained by the merger of regions with the territorial reform. The lowest region is Auvergne-Rhône-Alpes with a relative efficiency level of 76.66% characterized by a shortfall of 30.45% in the outputs production, confirming that this region is too big in size [START_REF] Corne | Tourism performance and management of the French territory: the impact of the NOTRe territorial reform[END_REF].

For the second stage with fsQCA, all the calculations are made by using the fs/QCA 2.5 software [START_REF] Ragin | fs/QCA [Computer Programme[END_REF]. The calibration of the variables is the first step. Concerning the efficiency score and the explanatory variables monuments and museums, the thresholds are selected by using a cluster analysis [START_REF] Cronqvist | Presentation of TOSMANA. Adding Multi-Value Variables and Visual Aids to QCA[END_REF] and the researcher knowledge [START_REF] Ragin | Redesigning social inquiry: Fuzzy sets and beyond[END_REF]. The calculations are done with the Tosmana software [START_REF] Cronqvist | Tosmana [Version 1[END_REF]. The variables beach and ski are dummy variables coded 1 for presence and 0 for absence. For the efficiency score, as the model is output-oriented, the calibration is made on the inverse of the score. Table 4 presents the calibration of the variables. Table 5 shows the results of the necessity analysis. The tests are performed on the efficiency score variable after calibration (score-c) and its negation (~score-c). Clearly, none condition is necessary for the presence or absence of efficiency because all the consistency indexes are less than 0.9 [START_REF] Ragin | Redesigning social inquiry: Fuzzy sets and beyond[END_REF]. In other words, the presence or absence of one of these four explanatory variables is not necessary to explain the performance of French regions. The truth table translates the causal combinations and indicates the number of cases in each of them. Theoretically, 16 (2 4 ) combinations are possible but, in this study, only 10 combinations have at least one case. A frequency threshold (number of cases) is fixed and only the configurations with a minimum cutoff value for consistency are fuzzy subsets of the outcome. As recommended by Ragin (2008, p.136), for macro level data, a minimum cutoff value for consistency of 0.85 is selected. Regarding the frequency threshold, as the sample of this study is small, a value of 1 case is selected. Four combinations are then retained. It means that at least one case is present in each of these four causal combinations which have a consistency of at least 0.85. They are designated as fuzzy subsets of the calibrated performance variable.

The sufficient configurations are finally obtained by using the Quine-McCluskey algorithm and the intermediate solution recommended by [START_REF] Ragin | Redesigning social inquiry: Fuzzy sets and beyond[END_REF] is presented in Table 6. Three complex configurations are sufficient to explain the French tourism performance with a high level of consistency. Combination (1) ~monuments-c*beach-c*ski-c indicates that 98.5% of the empirical evidence is consistent with the fact that this configuration is sufficient to generate the performance of French regions. This solution covers 27% of the cases.

From a managerial point of view, the presence of beach and ski associated with the absence of monuments is a path leading to performance. This configuration suggests that the performance of the region can be explained by the presence in the territory of attractions linked to ski and beach activities. Such regions are very popular and attract a large number of tourists. Figure 1 illustrates this configuration. The regions Corse and Provence-Alpes-Côte d'Azur are typical cases (Schneider and Rohlfing, 2013, p.595). This figure shows also that regions such as Bourgogne Franche-Comté and Ile-de-France reach a high level of relative efficiency without this configuration. By considering this path, these cases are deviant for coverage and thus they can be explained by another configuration. The third combination (3) monuments-c*museums-c*~beach-c*~ski-c indicates that 93% of the empirical evidence is consistent with the fact that this configuration is sufficient for the French regions in order to be efficient. This solution covers 40% of the cases.

It is interesting to note here that the absence of beach and ski associated with the presence of museums and monuments permits to explain the tourism performance. This configuration suggests a form of cultural tourism without the mass tourism effect that can be observed in French regions where beach and ski are present. This is typically the case for Bourgogne Franche-Comté and Ile-de-France regions.

These two configurations (1) and (3) show that different kind of attractions such as beach, ski and monuments can play different roles in order to explain the tourism performance depending on their association with other variables. Another interesting insight is that beach and ski resorts explain a high level of performance when they are associated in configuration (1). In other words, the presence of one of these attractions alone is not sufficient. This permits to understand the case of the region Auvergne Rhône-Alpes which has the biggest ski resorts of the French territory, but without coastline and that is the most inefficient unit.

The configuration (2) is more complex to interpret but it characterizes very few cases with a low coverage and then it can be omitted. Indeed, the coverage of an acceptable and informative solution is between 0.25 and 0.65 (Woodside, 2013, p.468) and this is not the case for this configuration.

The findings of this study also confirm the tenets of the complexity theory for the case of tourism destinations. A single tourism attraction is not sufficient to obtain a high efficiency level. A high efficiency level is explained by a complex combination with at least two or more Provence-Alpes-Côte d'Azur Corse Bourgogne Franche-Comté Ile-de-France tourism attractions and this is the case of the three configurations obtained in Table 6. A single tourism attraction can have both a positive and negative impact depending on its association with other kind of attractions. A high efficiency level can be reached by three different configurations. The configurations explaining a low efficiency level are not opposite to the configurations obtained for a high efficiency level; the fsQCA procedure has been implemented separately on the negation of the calibrated score (low level of performance) and all the complex configurations are different from the configurations obtained in Table 6, confirming the causal asymmetry principle. A given complex configuration explaining a high efficiency level is not relevant for all cases; indeed, the coverage index is less than 1 for each complex combination.

To ensure the robustness of our analysis, we do not limit the findings to fit validity and predictive validity is also performed [START_REF] Woodside | The good practices manifesto: Overcoming bad practices pervasive in current research in business[END_REF]. Predictive validity can be done when different time-periods are available or by splitting the sample into two subsamples, a modeling and a holdout subsample [START_REF] Pappas | Hotel decision-making during multiple crises: A chaordic perspective[END_REF][START_REF] Pappas | The complexity of consumer experience formulation in the sharing economy[END_REF]. By using the same data sources, we consider the year 2016 in order to test the predictive validity of the configurations we obtained in Table 6 for 2017. First, DEA efficiency scores are estimated and the same four regions are again technically efficient. Second, the fsQCA procedure is done and the three configurations identified in Table 6 obtain a high consistency index. More precisely, configurations (1) and (3) obtain respectively 0.981 and 0.901 for the consistency index and 0.235 and 0.315 for the coverage index, suggesting that these models have a good predictive validity.

For a comparative purpose, Table 7 shows the findings of the bootstrapped truncated regression proposed by [START_REF] Simar | Estimation and inference in two-stage, semi-parametric models of production processes[END_REF]. Calculations are implemented with the R software by using the rDEA package [START_REF] Simm | rDEA: Robust Data Envelopment Analysis (DEA) for R. R package version 1[END_REF]. The number of replications is 2000 and, as the dependent variable is greater or equal to 1, a coefficient with a positive sign is associated with an improvement of inefficiency. The only finding in line with the study by [START_REF] Barros | Performance of French destinations: Tourism attraction perspectives[END_REF] is about the variable museums which positively impacts tourism efficiency. For the variables monuments, ski and beach, the results are opposite. Although the sample (before and after the reform, respectively 22 and 13 units), the production technology and the years studied are not the same, this result is another example of contradictory empirical studies in the literature. Furthermore, the limitation of such approaches, based on net effects, is that managerial recommendations are restrictive. For instance, what are the propositions for decision-makers of regions with few museums? Clearly, accounting for complexity with the identification of multiple effects enlarge the explanation of the phenomenon and the possible recommendations. The French case, as an illustrative example, shows that regions cannot be summarized by an average behavior. Indeed, the French regions have different kind of resources and attractions and they can achieve a high level of efficiency in different ways.

Conclusion and future research

This paper advocates to consider complex relationships in the analysis of the determinants of tourism efficiency. An illustration of the complexity of the tourism sector is provided by considering the French destinations at the regional level. In a first stage, the relative efficiency of French tourism regions is computed by using DEA. In a second stage, several determinants of the tourism performance are selected by considering the tourism attraction theory. These determinants are analyzed with fsQCA in order to highlight and to identify complex combinations. The findings of this paper are twofold. First, the findings confirm the complexity of the tourism destinations. A single tourism attraction is not sufficient and complex combinations of attractions should be considered in order to obtain a high level of performance. Hence, methods such as fsQCA should be used to deal with this complexity. Second, the results of this study overcome the limits of net effects analysis based on an average behavior. By using an asymmetric analysis and the tourism attraction theory, the recommendations for the decision-makers are based on complex combinations of conditions.

A determinant can play a positive or negative role depending on its association with another determinant. This is the case for French destinations with tourism attractions such as beach, ski and museums. These complex solutions permit a better understanding of the tourism performance at the regional level.

The present paper has some limits. On the one hand, the territorial reform reduced the number of French regions and therefore the choice of the inputs and outputs is limited in order to implement efficiency comparisons based on DEA. The construction of the production technology is also subject to a constraint of data availability but alternative selections are possible before to analyze the impact of the determinants in the second stage. For instance, by including regional tourism receipts, a key economic indicator which is unavailable in France.

On the other hand, some variables in the second stage can be measured by different ways.

Beaches and ski resorts are examples that can be identified by binary variables [START_REF] Benito | Determinants of Spanish regions' tourism performance: a two-stage, double-bootstrap data envelopment analysis[END_REF] or by kilometers and numbers [START_REF] Barros | Performance of French destinations: Tourism attraction perspectives[END_REF]. This is of particular interest when they are treated in the QCA analysis as crisp or fuzzy variables [START_REF] Ragin | Redesigning social inquiry: Fuzzy sets and beyond[END_REF].

This paper provides some perspectives for future research. First, concerning the performance variable (the efficiency score) in the second stage by using fsQCA analysis, the calibration choice opens some methodological questions. Indeed, the efficiency score from the DEA method is between 0 and 1 when it is expressed in efficiency level with percentages. Then the question is how to calibrate it or not? Calibration is a crucial step in the use of fsQCA [START_REF] Ragin | Redesigning social inquiry: Fuzzy sets and beyond[END_REF] and it can be done by following researcher/expert opinions and by using statistical tools. In the context of destination management organizations, decision-makers could be useful in order to determine what is a membership or a nonmembership in terms of relative efficiency. This paper provides a direction for future research about the calibration of the efficiency score. Second, comparative analyses could be done with specific econometric techniques. Depending of the number of variables used in second stage, sufficient configurations could be compared with interaction terms in multiple regression analysis. Third, the analysis of the determinants with fsQCA could be done by distinguishing proximate and remote factors, depending on whether or not they are controllable by the decision-makers, with a two-step QCA [START_REF] Schneider | Reducing complexity in Qualitative Comparative Analysis (QCA): Remote and proximate factors and the consolidation of democracy[END_REF]. Fourth, this paper has adopted a case study based on tourism attraction theory for the analysis of the determinants of tourism performance but other research questions can be considered to model the complexity of the tourism sector. At the macro level, the determinants identified in the conceptual models of tourism destination competitiveness can be mobilized to analyze destination performance. At the micro level, governance, environmental actions and quality are some examples of determinants to study the impact on the performance of tourism firms. Furthermore, this two-stage approach goes beyond tourism research and could be useful for other areas and economic sectors in which the performance analysis is of interest.

Figure 1 .

 1 Figure 1. X-Y Plot for sufficient configuration (1)

Table 1 .

 1 Impacts of the determinants of tourism efficiency

	Authors			Second stage	Units	Impacts
						Positive	Negative
	Barros and Dieke	Truncated	Angolan hotels	Ownership
	(2008)			regression		Market share
						International
						strategy
	Shang et al. (2010) Tobit regression	Taiwanese	Location
					hotels	Age
						Ecommerce
						Ownership
	Assaf and Agbola	Truncated	Australian hotels Age
	(2011)			regression		Location
						Star rating (quality)
						Size
	Barros et al (2011) Truncated	French regions	Monuments
				regression		Beach
						Theme park
						Ski
						Natural park
						Museums
	Huang	et	al.	Tobit regression	Chinese	International	Trade
	(2012)				provinces	attractiveness	openness
						Education	Time
						Earnings
	Benito	et	al.	Truncated	Spanish regions Beach
	(2014)			regression		Museums
						Ski
						Natural areas
						Cultural heritage
						MICE
						Golf
						Gastronomy
						Shopping
	Oukil et al. (2016) Truncated	Oman hotels	Star rating (quality)	Nature
				regression		Culture	(beach, etc.)
						Activities	Ownership
							Size
	Cuccia et al (2016) Truncated	Italian	Sea	Theft
				regression	destinations	Culture	Time trend
						Environment	WHL
							Unesco

Table 2

 2 presents the descriptive statistics of the inputs and outputs used.

Table 2 .

 2 Descriptive statistics

		Max	Min	Mean	Standard dev.
			Inputs and outputs
	Employees	420498	8442	100688	105194
	Capacity	156405	12517	49328	39280
	Arrivals	33812	1477	9068	8184
	Tourist Tax
	(million €)	100.3	1.05	17.8	27.3
				Determinants
	Monuments	1871	140	1122	451
	Museums	143	10	95	42
	Beach	1	0	0.62	0.51
	Ski	1	0	0.38	0.51

Table 3 .

 3 Tourism performance of French regions in 2017

			Output shortfall
	Region	Efficiency level	(in %)
	Auvergne-Rhône-Alpes	0.7666	30.45
	Bourgogne-Franche-Comté 1	-
	Bretagne	0.8484	17.87
	Centre-Val de Loire	0.9711	02.98
	Corse	1	-
	Grand Est	0.9335	07.12
	Hauts-de-France	0.9252	08.08
	Ile-de-France	1	-
	Normandie	0.8915	12.17
	Nouvelle Aquitaine	0.8654	15.55
	Occitanie	0.8859	12.88
	Pays de la Loire	0.8484	17.87
	Provence-Alpes-Côte d'Azur 1	-
	Mean	0.9182	-
	SD	0.

Table 4 .

 4 Calibration of variables

			Thresholds
		0.95	0.5	0.05
	Efficiency
	score	0.98	0.9	0.82
	Beach	1	0.5	0
	Ski	1	0.5	0
	Monuments	1438.25	1005.5	572.75
	Museums	118.5	76	25

Table 5 .

 5 Necessity analysis

			score-c		~ score-c
		Consistency Coverage Consistency Coverage
	monuments-c	0.6199	0.5995	0.7933	0.5399
	~ monuments-c 0.5242	0.7828	0.4115	0.4325
	museums-c	0.772	0.6655	0.7412	0.4497
	~ museums-c	0.3617	0.6651	0.4488	0.5807
	ski-c	0.3578	0.6423	0.3743	0.4729
	~ ski-c	0.7064	0.616	0.7169	0.44
	beach-c	0.536	0.521	0.7914	0.5414
	~ beach-c	0.5282	0.7825	0.2998	0.3126

Note: "-c" means calibrated variable; "~" is the negation of the variable.

Table 6 .

 6 Sufficiency analysis

	frequency cutoff: 1
	consistency cutoff: 0.9307
		raw	Unique
		coverage	Coverage	consistency
	(1) ~monuments-c*beach-c*ski-c	0.2674	0.2005	0.9855
	(2) ~monuments-c*~museums-c*~beach-c*~ski-c	0.1468	0.0537	1
	(3) monuments-c*museums-c*~beach-c*~ski-c	0.3996	0.2726	0.9307
	solution coverage: 0.6304
	solution consistency: 0.9582

Table 7 .

 7 Bootstrapped truncated regression results

	Constant	1.0818***
	Monuments	0.0002**
	Ski	0.1765***
	Beach	0.036
	Museums	-0.0017**
	Note: ** and *** mean respectively statistically significant at 5% and 1%.