Three Essays in the Microeconomics of
Development
Thèse présentée
à la Faculté des études supérieures et postdoctorales de l’Université Laval dans le cadre du programme de doctorat en Économique
pour l’obtention du grade de Philosophiæ Doctor (Ph.D.)
Faculté des Sciences Sociales UNIVERSITÉ LAVAL
QUÉBEC
2012
c
Cette thèse aborde essentiellement deux problématiques à travers trois essais tous indépendants l’un de l’autre. La première problématique, qui est couverte par les deux premiers essais, se rapporte à des pratiques pouvant impacter d’une façon ou d’une autre le devenir des enfants. La deuxième problématique quant à elle, a trait à la persistance des activités de quasi-subsistance dans les pays en développement.
Deux raisons ont motivé notre intérêt pour ces deux problématiques : en pre-mier lieu, la réussite de tout projet de développement doit compter sur des acteurs présents et futurs stables et épanouis à tous les niveaux. À ce titre, les enfants qui constituent les acteurs d’avenir de toute collectivité, sont au cœur de tout processus de développement. Mieux encore, la réussite future de tout plan de développement présent est tributaire de l’environnement et de l’encadrement dont ils bénéficient aujourd’hui. Dès lors, il ne serait pas exagéré de penser qu’une enfance mal négo-ciée a de fortes chances de conduire à une société de demain vulnérable. En second lieu, les prédispositions des peuples à se projeter vers le sentier de développement ne peuvent être possibles que si la satisfaction de besoins élémentaires n’est plus une préoccupation pour la collectivité. Autrement dit, la lutte pour la survie ne garantit pas les conditions nécessaires à l’éclosion du génie et de la créativité, tous des facteurs indispensables pour le processus de développement.
Le premier essai traite de l’institution informelle du child fostering, encore ap-pelée la pratique des enfants confiés, qui se définit comme la délégation volontaire et temporaire des rôles parentaux à d’autres personnes que les parents biologiques, au sein du réseau familial élargi. Ces arrangements sont courants dans les pays en développement où l’on estime à 25% la proportion d’enfants concernés. Cet essai analyse donc l’impact de ces arrangements informels sur le bien être des enfants confiés, dans un environnement où l’altruisme parental est limité aux seuls enfants
biologiques.
Le deuxième essai porte sur le phénomène de trafic d’enfants qui a atteint de proportions inquiétantes depuis quelques années. Il est question dans cet essai, d’explorer les principes fondamentaux d’une bonne coordination internationale des plans d’actions nationaux visant à lutter contre le trafic d’enfants dans le monde. Autrement dit, nous investiguons dans cet essai les approches optimales pour les nations de coordonner leurs politiques en vue de combattre de façon efficace ce fléau.
Le troisième essai qui porte sur la problématique de persistance des activités de quasi-subsistance dans les pays en développement apporte une nouvelle approche à l’explication de ce phénomène et propose une piste de solution pour sortir les pays en développement de la spirale des activités de quasi-subsistance pour les replacer sur le sentier des activités de marché.
This thesis addresses two main issues through three essays that are independent from each other. The first issue, which is covered by the first two essays, refers to such practice that may impact one way or another the welfare of children. The second issue which is covered by the third essay relates to the persistence of quasi-subsistence activities in developing countries.
Two reasons motivated our interest in these two issues: first, the success of any development project must rely on the actors both present and future which are emotionally and psychologically stable. As such, children who are the actors of the future of any community, are at the heart of any development process. Better yet, the success of any development plan in the future is inevitably dependent on the en-vironment and supervision they receive today. Thus, there would be no exaggeration to argue that a poorly negotiated childhood is likely to lead to a society vulnerable in the future . Secondly, the predispositions of people to project themselves into the path of development may not be possible if the satisfaction of basic needs is no longer a concern for the community. In other words, the struggle for survival does not guarantee the necessary conditions for the emergence of genius and creativity, all necessary factors for the development process.
The first essay discusses the informal institution of child Fostering which is de-fined as the voluntary and temporary delegation of parental roles to others than biological parents, within the extended family network. Such arrangements are common in developing countries where the proportion of children involved is esti-mated arround 25%. This essay therefore analyzes the impact of these informal arrangements on the welfare of foster children, in an environment where parental altruism is restricted to biological children.
The second essay analyses the phenomenon of child trafficking which has reached alarming proportions in recent years. It explores the fundamental principles of a successful international coordination of national action plans aimed at curbing global child trafficking. Specifically, in this essay we investigate optimal approaches for nations to coordinate their policies to effectively fight this practice.
The third essay which deals with the problem of persistence of quasi-subsistence activities in developing countries provides a new approach to the explanation of this phenomenon and proposes a possible solution to propel developing countries out of the spiral of quasi-subsistence activities in order to place them on the path of market economy.
Cette thèse doit son accomplissement à certaines personnes dont je voudrais re-mercier ici sans avoir la prétention de les citer de façon exhaustive.
Tout d’abord, je tiens à remercier mon directeur de thèse, Professeur Dessy pour toute sa disponibilité et son encadrement tout au long de ce travail. Tel un enfant à qui on apprend à faire ses premiers pas, il a su m’initier aux rouages Ô combien délicats de la recherche en sciences économiques. Ses conseils et surtout sa patience ont été pour moi un appui inestimable à certains moments de la rédaction de cette thèse, particulièrement lors des moments difficiles. Son soutien constant et son appui considérable ont permis l’aboutissement de cette thèse et je lui suis grandement reconnaissant.
Je remercie aussi tous les professeurs du département d’économique pour la qual-ité des enseignements reçus. Un grand merci au professeur Patrick Gonzalez pour son appui de toute sorte lorsque cela lui a été possible, de même que pour tous les échanges instructifs que nous avons eus. Mes sincères remerciements aux professeurs Arnaud Dellis et Sabine Kröger pour les échanges que nous avons eus à un moment donné de la rédaction de cette thèse.
Ma gratitude va également à l’endroit de la professeure Lucie Samson, pour m’avoir permis de nourrir ma passion pour l’enseignement et pour m’avoir soutenu dans mes différentes recherches d’emploi.
Je voudrais également remercier le Centre interuniversitaire sur le risque, les politiques économiques et l’Emploi (CIRPÉE) pour tout le soutien financier ap-porté pendant la réalisation de cette thèse, ainsi que pour l’espace d’échange qu’il a su mettre à notre disposition via les conférences annuelles organisées afin de nous
permettre de présenter les résultats de nos travaux, et d’en recevoir des critiques constructives.
Je remercie aussi tout le personnel administratif du département d’économique pour leur disponibilité et les bons rapports que nous avons entretenus.
Comment puis-je vous oublier mes enfants Teddy Emmanuel, Coretta Gisèle, Gabrielle Joséphine et toi le petit Ken-Godwill, ainsi que ma conjointe Suzanne Solange, vous qui avez toujours été présents lors des moments difficiles, et qui m’avez toujours encouragé et apporté votre soutien moral et affectif tout au long de la réali-sation de ce travail. À vous mes enfants, votre indulgence, votre patience et surtout votre joie si contagieuse ont fini par devenir pour moi la raison du dépassement de soi, la source intarissable d’où je puise mes derniers efforts. Que ce travail soit pour vous une lumière qui vous aide à vous frayer votre propre chemin. À toi ma conjointe, je ne saurai mesurer le poids de tous tes sacrifices consentis au cours de ces cinq dernières années. Pour tout cela, je vous suis infiniment reconnaissant.
Mes remerciements vont également à l’endroit de ma famille demeurée au Camer-oun qui, en dépit des milliers de kilomètres qui nous séparent, n’a jamais cessé de m’encourager dans ce projet et de m’apporter tout leur soutien moral et affectif à travers les communications téléphoniques constantes et coûteuses. Je remercie égale-ment mon cousin Maurice Wobeng et toute sa famille, pour cette bonne fraternité que nous entretenons depuis mon arrivée au Canada, ainsi que pour son soutien de toute sorte.
Un grand merci à mes amis Christian Wappi, pascal Kammoe, Jean-René Tagne, Rodrigue Yossa, Fulbert Tchana, ainsi qu’à toute leur famille. De nombreux débats que nous avons eus quand bien mêmes ils n’étaient pas directement reliés aux sujets abordés dans cette thèse, ont contribué à enrichir ma compréhension des problèmes qui sont abordés ici.
Enfin, je remercie mes collègues étudiants du département d’économique de l’université Laval, avec qui j’ai eu des échanges constructifs tout au long de la ré-daction de cette thèse. Une attention particulière à Agnès Zabsonré, pour tous ses conseils prodigués.
con-tribué à rendre ce travail effectif, et dont le nom a été omis, trouvent ici l’expression de ma profonde gratitude.
travail.
À ma mère, Maman Mégni Yémélé Jososephine, elle qui sacrifia tous ses projets et ambitions personnels pour consacrer sa vie entière à notre éducation.
Une société sans problèmes est une société morte.
Résumé 2 Abstract 4 Avant-propos 6 Contents 11 List of Figures 14 List of Tables 15 Introduction Générale 16
1 Do Informal Child Fostering Arrangements Make Foster Children
Better Off ? 21
1.1 Introduction . . . 21
1.2 Basics . . . 27
1.2.1 Preferences and Budget Constraint . . . 27
1.2.2 Production of Nutrition . . . 29
1.3 Household Outcomes in Autarky . . . 30
1.3.1 The Child Labor Motive for In-Fostering . . . 30
1.3.2 A Human Capital Motive for Out-Fostering . . . 31
1.3.3 Parent’s Autarky Welfare . . . 32
1.4 A Bargaining Game of Child Fostering . . . 33
1.4.1 Who Gains from In-Fostering? . . . 34
1.4.2 Who Gains from Out-Fostering? . . . 36
1.4.3 Optimal Child Fostering Arrangement . . . 38
1.5 A Numerical Simulation . . . 40
1.5.2 Child Nutrition . . . 42
1.5.3 Child Human Capital . . . 43
1.5.4 Household Net Gain from Participating in Child Fostering . . 45
1.6 Conclusion . . . 46
1.7 Appendix . . . 48
1.7.1 Proof of Lemma1.1 . . . 48
1.7.2 Proof of Proposition1.3 . . . 48
1.7.3 Proof of Lemma1.2 . . . 49
1.7.4 Results of the Numerical Simulation . . . 49
1.7.4.1 Child Labor . . . 50
1.7.4.2 Child Nutrition . . . 51
1.7.4.3 Child’s Human Capital . . . 52
1.7.4.4 Parent’s Net Gain from the Fostering Arrangement . 53 Bibliography 54 2 The Global Fight against Child Trafficking: How Can It Be Won? 57 2.1 Introduction . . . 57
2.2 The Setup . . . 61
2.2.1 Household’s problem . . . 62
2.2.2 Optimal Household Decision on Child Protection . . . 63
2.2.3 Child’s Vulnerability to Trafficking . . . 65
2.2.4 Child Trafficking: Upstream Operations . . . 66
2.2.5 Child Trafficking: Downstream Operations . . . 68
2.2.6 National Action Plan against Child Trafficking . . . 70
2.3 Market Equilibrium . . . 71
2.3.1 Incidence of Child Vulnerability to Trafficking . . . 71
2.3.2 Incidence of Child Trafficking . . . 75
2.3.3 Equilibrium Price . . . 77
2.3.4 The Global Incidence of Child Trafficking . . . 80
2.4 International Cooperation . . . 81
2.4.1 Properties of the Cooperative Equilibrium under Strategic Substitutability: ς > 0 . . . 81
2.4.1.1 Cooperation between Poorer Countries . . . 81
2.4.1.2 Cooperation between Richer Countries . . . 84
2.4.1.3 Cooperation between Richer and Poorer Countries . 85 2.4.2 Properties of the Cooperative Equilibrium under Strategic Complementarities: ς < 0 . . . 87
2.4.2.1 Cooperation between Poorer Countries . . . 88
2.4.2.2 Cooperation between Richer Countries . . . 89
2.4.2.3 Cooperation with Asymmetric Countries . . . 90
2.5 Conclusion . . . 92
Bibliography 94 3 Exit Path from Quasi-Subsistence Livelihoods 96 3.1 Introduction . . . 96
3.2 A Model of Occupational Choice . . . 98
3.2.1 The Government . . . 99
3.2.2 The Manufacturing Sector . . . 100
3.2.3 Households . . . 103
3.3 Equilibrium Analysis . . . 106
3.3.1 Equilibrium Size of the Market Sector . . . 106
3.3.2 Social Welfare . . . 107
3.3.3 A Numerical Simulation . . . 108
3.4 Conclusion . . . 112
Bibliography 113
1.1 Child’s labor supply . . . 50
1.2 Child’s nutrition status . . . 51
1.3 Child’s human capital . . . 52
1.4 Parent’s Net Gain from the Fostering Arrangement . . . 53
2.1 Cooperation between poorer countries: Substitutability . . . 83
2.2 Cooperation between richer countries: Substitutability . . . 85
2.3 Cooperation between rich and poor countries: Substitutability . . . . 86
2.4 Cooperation between poorer countries: Complementarity . . . 88
2.5 Cooperation between richer countries: Complementarity . . . 89
2.6 Cooperation between between rich and poor countries: Complemen-tarity . . . 90
3.1 Social welfare ¯V (σ, θ) as a function of θ . . . 109
3.2 The Degree of market penetration by counterfeit µ as a function of θ 110 3.3 Equilibrium size of market sector ¯L as a function of θ . . . 111
2.1 Substitutability (ς = 1): ¯kA= ¯kB = 1 . . . . 82 2.2 Substitutability (ς = 1): ¯kA= ¯kB = 5 . . . . 84 2.3 Substitutability (ς = 1): k¯A = 5; ¯kB= 1 . . . . 86 2.4 Complementarity (ς = −1/2): ¯kA= ¯kB = 1 . . . 88 2.5 Complementarity (ς = −1/2): ¯kA= ¯kB = 5 . . . 89 2.6 Complementarity (ς = −1/2): ¯kA= 5; ¯kB = 1 . . . 90 3.1 Parameter Values . . . 108 3.2 Simulation Results . . . 109
Les problématiques touchant les enfants sont au coeur des préoccupations des dé-cideurs publics. Cet intérêt porté aux questions touchant directement l’avenir des enfants ne date pas d’aujourd’hui et trouve son explication, entre autres, dans le fait que les enfants sont l’avenir de demain et à ce titre, l’encadrement et l’environnement dont ils bénéficient aujourd’hui déterminent de façon irréfutable ce qu’ils seront de-main. C’est fort de cet intérêt que cette thèse, qui est composée de trois essais tous indépendants, a consacré deux d’entre eux à des questions touchant directement les enfants: Le premier de ces essais porte sur la pratique des enfants confiés en-core dénommée le Child fostering. Le deuxième essai quant à lui porte sur le trafic d’enfants et investigue les mécanismes de coopération internationale qui pourront permettre d’endiguer ce phénomène. En dehors des problématiques touchant les enfants, cette thèse aborde également la question de la prépondérance des activités de subsistance qui est caractéristique dans les économies du sud.
La pratique des enfants confiés consiste en un transfert volontaire et non définitif des responsabilités parentales sur un enfant à d’autres personnes que les parents bi-ologiques. Ce placement d’enfants par leurs parents dans une autre famille constitue une pratique ancienne, rencontrée dans de nombreuses sociétés à travers le monde. Pratique assez courante dans les pays en développement, où on estime qu’environ 25% 1 d’enfants vivent à l’extérieur de leur foyer biologique, elle y est considérée
comme d’autant plus normale que le rôle de parents dans ces régions n’est pas la seule responsabilité des parents biologiques. Elle prend en général trois principales formes selon les circonstances du placement de l’enfant : le placement auprès de proches (kinship fostering), qui est la forme la plus répandue, le placement auprès des membres extérieurs à la familles (non-kin fostering) et enfin le placement en cas de crise (crisis fostering), qui intervient lorsque des parents rencontrent subitement une crise, qu’elle soit familiale, financière ou autre et qu’ils ne peuvent donc plus faire face et subvenir temporairement aux besoins de la famille.
1
D’après Frederick J. Zimmerman dans Cinderella goes to school: the effect of child fostering on school enrollment in South Africa. 2003
Le débat au sujet des effets possibles générés par cette institution informelle sur le bien-être des enfants ainsi confiés souffre d’une absence de consensus parmi les chercheurs qui se sont penchés sur cette question. En effet, tandis que pour certains cette pratique affecte négativement le capital humain des enfants concernés d’après des recherches qui ont été menées dans certains pays, d’autres par contre estiment que, l’institution informelle du child fostering améliore plutôt le bien être des enfants ainsi confiés, ou tout au moins, que dans certains pays où des études ont été réalisées sur le sujet, il n’y a pas d’évidence qui pousse à affirmer que les enfants confiés sont désavantagés par rapport aux enfants vivant avec leurs parents biologiques, en ce qui concerne la scolarisation par exemple. L’absence de consensus met ainsi en lumière l’existence d’une certaine dissymétrie entre les pays en ce qui concerne les effets générés par la pratique des enfants confiés. On peut alors se demander le pourquoi de ces différences entre pays au niveau des effets possibles de la pratique des enfants confiés? Si la loi d’Hamilton2
s’applique à tous les pays où l’on relève une incidence élevée de la pratique des enfants confiés, alors qu’est ce qui peut justifier les différences d’effets entre ces pays? Par ailleurs, au regard de la loi d’Hamilton, qu’est-ce qui motive un parent à confier son enfant chez un proche?
Le chapitre 2 de notre thèse est entièrement consacré à ces questions. Nous y proposons une modélisation théorique des décisions de participation des ménages aux arrangements informels du confiage d’enfant et ce dans un contexte où la loi d’Hamilton s’applique. La décision de confier ou non un enfant est ainsi concep-tualisée comme l’issu d’un jeu coopératif entre le ménage qui envoie l’enfant et le ménage qui le reçoit. Les variables au centre de la négociation sont: le temps alloué aux activités domestiques dans le ménage d’accueil par l’enfant confié et son niveau de nutrition. Le mérite de ce travail consiste à explorer l’ensemble des facteurs ou circonstances pour lesquelles l’arrangement informel du child fostering impacte néga-tivement le bien-être de l’enfant confié. L’autre contribution de ce travail consiste aussi à expliquer l’existence des effets dissymétriques observés entre pays.
Le chapitre 3 de cette thèse est consacré à l’essai 2, qui traite du trafic d’enfants. Cette pratique a dépassé le cadre des frontières nationales pour englober désormais un trafic transfrontalier un peu partout à travers le monde, bien qu’on dénote une forte incidence en Afrique, en Amérique Latine et en Asie du Sud (UNICEF-IRC 2009). L’exploitation des victimes varie de la participation dans des travaux dan-gereux, l’exploitation sexuelle, la servitude domestique, la mendicité, à des activités criminelles (UNICEF-IRC 2008). Et comme c’est le cas de la plupart des activités
2
D’après la loi d’Hamilton, "les comportements altruistes des parents vont d’abord et avant tout vers les enfants biologiques, et décroît au fur et à mesure que le lien de parenté s’affaiblit"
criminelles, des données concrètes sur cette pratique ne sont pas disponibles, mais des estimations existent. Par exemple en 2002, l’organisation internationale du tra-vail estimait qu’environ 1,2 millions d’enfants ont été victimes du trafic d’enfants à travers le monde entier pour des fins de travail ou d’exploitation sexuelle (UNICEF-IRC 2008). Dans son rapport Trafficking in Persons couvrant les années 2004 à 2006, le département d’état américain estimait qu’entre six cent mille (600 000) à huit cent mille (800 000) personnes, y compris les enfants, étaient victimes du trafic humain chaque année à travers le monde. Ces estimations montrent que cette pratique est devenue une entreprise mondiale, ce qui soulève des préoccupations majeures des gouvernements nationaux et de la communauté internationale au sens large.
Les préoccupations internationales au sujet du trafic d’enfants transparaissent à travers le protocole de Palerme, qui est un protocole des Nations Unies relatif au trafic d’êtres humains. Ce protocole est venu compléter la convention des Na-tions Unies contre la criminalité transnationale organisée, dans le but : de prévenir et de lutter contre le trafic d’êtres humains avec une attention particulière portée aux femmes et aux enfants, de protéger et de porter assistance aux personnes vic-times de cette pratique, et de promouvoir la coopération entre États. Cependant, la ratification ce protocole par l’ensemble de la communauté internationale n’est pas encore effective. Par ailleurs, la complexité de l’entreprise du trafic d’enfants con-stitue aujourd’hui un réel obstacle aux investigations des chercheurs sur les actions à entreprendre par les États pour coopérer à l’éradication de cette pratique.
Théoriquement, le trafic d’enfants peut être interprété comme une activité com-merciale illicite dont les opérations se déroulent sur deux fronts : il y’a d’un côté les opérations en amont qui impliquent des actes d’enlèvement ou de recrutement d’enfants vulnérables dans un État ou une région donnée ainsi que leur transport illégal aux points d’échange au sein de l’État ou de la région concernée et même au-delà des frontières. Ces opérations sont assimilées à l’offre. D’un autre côté, il y’a les opérations en aval qui incluent des pratiques de production impliquant l’exploitation sans scrupules du travail des enfants, ces pratiques génèrent une demande pour les enfants victimes de trafic, dont le travail est alors exploité aux fins de production pour maximiser les profits.
Au niveau de chaque pays, un plan national de lutte contre le trafic d’enfants peut donc impliquer la mobilisation des efforts sur les deux fronts : L’amont et l’aval, par exemple en répandant un filet de sécurité sur les enfants potentiellement vulnérables (lutte en amont), ou en menant des inspections régulières et de façon inopinée sur les lieux de production afin de décourager les potentiels exploitants de cette main d’œuvre (lutte en aval). Dès lors, on est en droit de se poser la question
suivante : y’a-t-il gain à la spécialisation entre les États qui sont impliqués dans la lutte mondiale contre le trafic d’enfants? Si oui, quel est le modèle ou la structure de cette spécialisation?
Il est donc question dans ce chapitre d’explorer les principes fondamentaux d’une bonne coordination internationale des plans d’actions nationaux visant à lutter con-tre le trafic d’enfants dans le monde.
Le quatrième chapitre de notre thèse, quant à lui, est consacré au troisième essai. Il propose une piste de solution pour sortir les pays en développement de la spirale des activités de quasi-subsistance pour les replacer sur le sentier de l’économie de marché.
En effet, la prédominance des activités de subsistance entrave de façon consid-érable l’économie des pays en développement, notamment l’Afrique sub-saharienne, l’Asie du Sud, et certaines parties d’Amérique centrale et d’Amérique du sud, où la pauvreté et les niveaux de famine sont parmi les plus élevés au monde. De nombreux chercheurs intéressés par les questions de développement ont préconisé la promotion d’une économie de marché comme voie ultime afin de propulser les économies de ces pays hors du sentier des activités de subsistance (Hayami et Ruttan, 1985), avançant comme argument le fait que la développement du marché de travail qui en découlerait devrait promouvoir l’industrialisation et le développement économique. Cependant la spécialisation complète de la main d’œuvre aux activités de marché requiert la mise en place d’institutions et de politiques qui promeuvent la commercialisation des services de travail afin de garantir des surplus sur une base soutenue.
Du point de vue de la théorie économique, la conception de ces institutions doit s’attaquer aux causes sous-jacentes à la participation populaire aux activités de subsistance afin de formuler des pistes de réponses aux interrogations suivantes : pourquoi la prédominance des activités de quasi-subsistance à travers les pays en développement? Quelle est la nature des institutions coercitives et des politiques susceptibles de libérer les populations de ces pays du piège de l’économie de subsis-tance?
Ces questions ont reçu une attention considérable dans la littérature sur le développement. Certains auteurs ont blâmé le gonflement des coûts de transport par les offices de commercialisation para-étatiques comme cause de la persistance d’une agriculture de subsistance dans les pays en développement, et préconisent le libre marché comme institution à mesure de promouvoir la commercialisation des services du travail. D’autres auteurs pointent du doigt l’absence de couver-ture d’assurance dans les zones rurales. Pour d’autres auteurs encore, c’est plutôt l’absence ou l’insuffisance d’infrastructures routières reliant les zones rurales où se
déroulent généralement ces activités, et les zones urbaines qui doivent être blâmées. Il est donc question dans ce chapitre de partir de cette littérature existante pour bâtir une approche qui met plutôt l’accent sur la contrefaçon et le piratage comme cause de la persistance des activités de subsistance dans les pays en développement. Pour ce faire, nous soutenons qu’une taxe forfaitaire soigneusement choisie et une politique rigoureuse de lutte contre le phénomène de la contrefaçon, peuvent être combinées pour propulser les économies des pays en développement hors du piège des activités de quasi-subsistance. L’intuition sous-jacente est que lorsque les produits manufacturés substitués à la production domestique sont victimes de contrefaçons et que ces contrefaçons sont non seulement des imitations bon marché mais sans valeur et dangéreux pour la santé, alors les individus qui choisissent de façon optimale leur occupation, peuvent se replier vers des activités de subsistance à faible productivité leur offrant des biens faits maisons mais sûrs pour leur santé.
Le premier et le cinquième chapitre de cette thèse, quant à eux, sont consacrés respectivement à l’introduction générale et à la conclusion générale.
Do Informal Child Fostering
Arrangements Make Foster Children
Better Off?
1.1
Introduction
Informal child fostering arrangements pervade Africa, though their occurrence is not restricted to this continent.1 Informal child fostering refers to a reversible transfer
of a child’s residence from own-parents to non-parents, often within rural-urban extended family networks (Eloundou-Enyegue and Stokes 2002). The central issue underlying the debate on the persisting tolerance of this phenomenon stems from the claim that when it involves school-age children, there is an incompatibility between receiving parents’ demand for child labor and sending parents’ desire to improve their children’s human capital prospects, resulting in foster children being made worse off (Ainsworth 1990 and 1996). This chapter revisits this issue by developing a model of child fostering in which sending parents and receiving parents bargain over the foster child’s level of involvement in household chores and his or her level of nutrition. The key analytical question is whether informal child fostering arrangements represent a Pareto-improvement for all actors involved relative to the counterfactual situation of what would have happened had the children not been fostered out.
Research on the effects of fostering arrangements on the welfare of the children involved was pioneered by Ainsworth (1990 and 1996) who finds evidence in Côte
1
See Eloundou-Enyegue and Stokes 2002, Zimmerman 2003, Akresh 2009, and Serra 2009 for detailed reviews of the evidence on the prevalence of this traditional institution in sub-Saharan Africa.
d’Ivoire that these arrangements adversely affect the welfare of foster children. This conclusion was subsequently rejected by Zimmerman (2003), who provides empirical evidence that foster children in South Africa are not at a disadvantage compared to biological children, in terms of school enrolment rates. Indeed, Zimmerman finds that the risk of not attending school is estimated to be about 14–22 percent lower for foster children than it would have been, had they stayed with their natural parents. But critics may argue that similar school enrolment rates for biological and foster children are not by themselves hard evidence of foster children’s success at accumulating human capital. How these children perform in national tests at the end of primary and secondary education, for example, may in fact matter more than school attendance. Moreover, in most African countries, where poor quality schools are ubiquitous, parents often have to seek after-school private tutoring for their children in order the boost their performance in national tests and prevent grade repetition (Buchmann 2002). Since after-school private tutoring is costly and tends to trade off children involvement in household chores, it is not clear, for instance, whether access to this crucial educational resource in African countries is equally shared between the biological children and their foster siblings.
So far, the scholarly debate on the effects of informal child fostering arrangements involving school-age children has taken place predominantly in the empirical strand of the literature, which raises the important question of why the effects uncovered by these empirical studies might be true. For instance, consider the empirical evidence that informal child fostering arrangements have an adverse effect on the well-being of foster children (e.g., Ainsworth 1990 and 1996; Fafchamps and Wahba 2006). As these arrangements involve the transfer of children’s residence from own-parents to non-parents, presumably, this adverse effect reflects the operation of Hamilton rule, according to which parental altruism is limited to own-children. Such adverse effect in turn would suggest that non-parent residence is undesirable for children, thereby creating a case for government to regulate this traditional institution.
However, in a seminal theoretical paper, Serra (2009) question the validity of this case, arguing that the operation of Hamilton rule need not prevent informal child fostering arrangements from yielding a Pareto-improvement for all actors involved (i.e. the sending parents, the receiving parents, and the foster children). Serra’s argument is anchored on the hypothesis that fostering out school-age children to better-off households is an opportunity to harness positive fostering externalities linked to the socioeconomic status of the receiving households (i.e. good locations, superior social connections, better nutrition and health). This positive fostering ex-ternality, she argues, is the mechanism that mitigates the incompatibility between
the receiving parents’ immediate demand for child labor and the sending parents’ future benefits of having well-educated children. Indeed, her model predicts that informal child fostering arrangements yield a Pareto-improvement for all actors in-volved if and only if (i) there are positive fostering externalities, (ii) sending parents treat all their children symmetrically (no discrimination), and (iii) they have perfect information about the socioeconomic status of the receiving households (no uncer-tainty). In other words, if informal fostering arrangements leave the foster child worse, it must be for reasons unrelated to the arrangement itself namely, sending parents’ discriminatory practices (e.g., boys against girls), or the sending parent’s imperfect knowledge of the socioeconomic status of the receiving household.
In this chapter, we build a child fostering model imbedding all three conditions put forward in Serra (2009) as crucial for resolving the apparent incompatibility between receiving parents’ demand for child labor and sending parents’ desire for improvements in their children’s human capital prospects. Firstly, as in Serra (2009), parents in our environment have perfect information about the socioeconomic status of potential receiving households, as measured by their human capital levels, and Hamilton rule applies. Secondly, in each household a single child is born, implying that our model abstracts away from within-offspring discriminatory issues raised in Serra (2009). In addition, school enrolment is compulsory. Thirdly, in our model, nutrition is an input into a child’s human capital along with child’s time allocated to after-school learning activities, including receiving private tutoring, doing homework assignments, or reading books and magazines to improve his or her math and writing skills.2
Despite similarities between Serra’s model and ours, there are important demar-cations in our model. In Serra (2009), for each foster child, only his or her level of nutrition is allowed to adjust to the socioeconomic distance between the sending and the receiving households. In other words, the greater this distance, the greater the level of nutrition the foster child receives (and by analogy to Serra, the greater the fostering externality). However, the intensity of a foster child’s involvement in household chores, by contrast, is invariant to this distance. In other words, a child fostered in by a receiving parent who earns $20000 more than the sending parent
2
There is evidence that academic excellence in school begins at home, where parents create a good learning environment for their children, giving them adequate time to organize for national tests, review daily lessons, and make a sustained effort to improve their writing and math skills (Pohlsen, 1984). For example, in a case study of school performance in the Thiruvananthapuram District of the Indian State of Kerala, Nair, Mini and Padmamohan (2003) found that not allocating enough studying time to reviewing daily lessons was an important factor in poor school performance among adolescents.
has the same level of involvement in household chores as a child fostered by a parent who earns $50000 more than the sending parent. In our model, both the intensity of the foster child’s involvement in household chores and the quantity of nutrition this child receives adjust to the socioeconomic distance between the sending and the receiving households. Furthermore, the adjustment process of these two outcomes is construed as a bargaining process between the sending and the receiving parents. This departure, as we show in this chapter, provides new insights on the issue of the incompatibility between the receiving parent’s demand for child labor and the sending parent’s desire for child educational progress. In Serra (2009), because the intensity of a foster child’s involvement in household chores does not adjust to a change in the socioeconomic distance between the sending and the receiving par-ents, the mechanism likely to turn the receiving parent’s demand for child labor and the sending parent’s desire for child educational progress into two incompati-ble motives is somehow disaincompati-bled. Our bargaining process restores the operation of this mechanism, by causing both the intensity of the foster child’s involvement in household chores and the nutrition this child receives in compensation to be increas-ing functions of the socioeconomic distance between the sendincreas-ing and the receivincreas-ing parents.
We highlight necessary and sufficient conditions for the foster child’s human cap-ital to decrease compared to a counterfactual situation of what would have happened had the child not been fostered out: either (i) the socioeconomic distance between the sending and the receiving parents is not sufficiently high, or (ii) nutrition, while essential for a child human capital process, is relatively less productive in that pro-cess than child’s time allocated to after-school learning activities. The first of these two conditions is likely to obtain in most African countries where repeated episodes of economic downturns (with their backlog of governments’ spending cuts, hiring freezes, layoffs, and forced retirements) appear to have eroded the socioeconomic distance between urban and rural households, thereby making it harder for urban households to support foster children. The second condition (i.e. child’s nutrition is relatively less productive than child’s time allocated to after-school learning ac-tivities) is also likely to obtain in most African countries where low public resources continue to impede the government’s capacity to arrest the erosion of education quality in the face of increased enrolment. Arguably, in such circumstances, being well-nourished and attending school may not be enough to prevent grade repetition or low levels of human capital. Instead, to prevent this negative outcome parents, for example, may have to seek their children’s participation in after-school private tutoring as a means to boost their school performance. In such an environment,
children’s after-school learning activities are likely to be at least as important as their nutrition level in determining the acquired level of human capital. Therefore, in both cases discussed above, the optimal child fostering arrangement fails to re-solve the incompatibility between the receiving parent’s demand for child labor and the sending parent’s desire for child educational progress.
Overall, compared to Serra (2009), our relative contribution is to expand the set of factors that lead to foster children being made worse off by informal child fostering arrangements. Whereas Serra (2009) sees parental discrimination towards own-children and uncertainty about the socioeconomic status of receiving parents as the only culprits, our analysis suggests that (i) sub-Saharan Africa’s high vulnerability to economic downturns that erode socioeconomic distances between rural and urban households, and (ii) governments’ low capacity or lack of political will to boost the quality of in-school education children receive must be added to this list. Both these factors cause informal child fostering arrangements to become merely an inter-household mechanism for redistributing child-rearing costs at the expense of the children involved.
We assume that nutrition is an input into a child’s human capital. This as-sumption is supported by advances in the fields of clinical nutrition and by stud-ies conducted by international organizations focusing on the well-being of children (UNICEF 1999). For example, in a recent UNICEF-sponsored study, Pruthi (2012) warns that children deprived of critical nutritional elements face such adverse effects as reduced learning capability and poor school performance, which ultimately will impact the way they can live and perform as adults. Furthermore, empirical research in the field of clinical nutrition suggests that poor nutrition among school-age chil-dren has a negative impact on their education (Simeon and McGregor, 1989; Simeon, 1998; Pollitt, Cueto, and Jacoby, 1998). Arguably, while quality schools, textbooks, and well-motivated and qualified teachers are essential for an education system to function well, these cannot result in improved education outcomes if the children involved are unable to learn due to malnutrition. Hunger can reduce a child’s ability to perform school tasks but can readily be reversed by feeding. Simeon (1998), for example, found that children aged 11 to 13 years in Jamaica improved their scores on arithmetic tests after one semester of receiving breakfast at school because they attended more regularly and studied more effectively. Pollitt, Cueto, and Jacoby (1998) have found that missing breakfast impairs school performance for children suffering from malnutrition. Furthermore, according to a report by Partnership for Child Development (1998), more than half the school-age children in low-income countries are believed to suffer from iron deficiency anemia, while Bobonis, Miguel,
and Puri-Sharma (2006) find this phenomenon to be at least partly responsible for low participation and high rates of absenteeism among school-age children in India. We also assume that the optimal child fostering arrangement is the outcome of a bargaining process involving the sending and the receiving parents over how much labor time the foster child is to allocate to household chores, and how much nutri-tion he or she is to receive in compensanutri-tion. In this bargaining process, the threat point for each party represents household welfare in the absence of child fostering. Modeling the optimal child fostering arrangement as the outcome of a bargaining game can be justified as follows. Asymmetric motives for child fostering generate a potential conflict between the sending and the receiving households, stemming from the trade-off between the immediate benefits of child labor to the former and the future human capital benefits to the latter. It is therefore reasonable to expect the optimal child fostering arrangement to be one that resolves this conflict. Second, even though the receiving household may only care about the well-being of its nu-clear members, and may be the one to effectively decide on the foster child’s time allocation, it may do so while being mindful of the threat of child withdrawal by the sending-household. Indeed, there is some evidence derived from the sociology literature that some informal bargaining takes place between the sending and the receiving households (Eloundou-Enyegue and Shapiro, 2005). Furthermore, in a case study of Cameroon, Eloundou-Enyegue and Stokes (2002) point out that child fos-tering takes place within rural-urban networks of social and family relationships so as to harness solidarity. As solidarity is a two-way (rather than, a one-way) street, the bargaining between the two types of households can naturally be viewed as a process of harnessing mutual help as the foundation of self-enforcing solidarity.
The rest of this chapter is structured as follows. Section1.2presents a description of the environment. Section1.3 characterizes household welfare and child welfare in autarky, corresponding to the enforcement of own-parent residence for all children. This provides a benchmark case against which welfare performances of informal child fostering arrangements can be compared. Section1.4describes a bargaining game of child fostering between a sending household and a receiving household. The outcome of this bargaining game is then numerically simulated in section1.5 to uncover the welfare properties of the optimal child fostering arrangement. Section 1.6 provides concluding remarks, while section 1.7 provides proofs of results presented in the main text.
1.2
Basics
Let there be two households, indexed 1 and 2, respectively. Interactions between the two households involve the fostering of children. Initially, a household is composed of a parent, and her unique child. 3 Parents have one period left to live, while their child
has two left. A typical parent is endowed with one unit of labor time and a quantity θi of a composite market good, and may have to purchase an additional quantity
x from the market in order to meet the nutritional needs of his or her household members. A parent allocates a fraction, lm
i , of his or her time to doing household
chores, and the remainder, 1−lm
i , to delivering human capital, hmi ∈
h, ¯h, to firms, where 0 < h < ¯h < +∞. For simplicity, assume that households only differ on the basis of the level of human capital of the parent (i.e., θi = θ, all i and hm1 6= hm2 ).
There are three main activities in this environment, namely, household produc-tion of nutriproduc-tion, producproduc-tion of a composite market good by perfectly competitive firms, and child education. Children may engage in the first and third activities, and parents in the first and second. Production of nutrition requires the use of the composite market good and household labor as inputs. The composite market good is the numeraire.
1.2.1
Preferences and Budget Constraint
Parental preferences are defined over the parent’s own consumption of nutrition (cm
i ) and the future human capital level of his or her biological child (hbi). These
preferences are represented by an additively separable utility function:
Ui = ln cmi + γbln hbi (1.1)
i = 1, 2, where γb ∈ (0, 1) is the utility weight the parent in household i places on
his own child’s well-being as measured by the child’s accumulated human capital, hb
i. The above parametric specification of parental utility function is standard in the
literature on parental investment in child outcomes (Becker, Murphy and Tamura 1990; Glomm 1997; Kremer and Chen 1999; de la Croix and Doepke 2004).
Denote by s ∈ {b, f} a child’s household status. In any household, a child is either the biological child (s = b) or the foster child (s = f). Assume all children attend school in this environment, say, due to a compulsory education law. Each child is endowed with one unit of after-school time. There are two competing claims on a
3
The assumption of a single-headed household is made purely for simplicity of exposure, so as to keep the focus on inter- (as opposed to intra-) household bargaining issues.
child’s after-school time. We denote as ls
i the proportion of a child’s time allocated
to household chores needed to produce nutrition, and by 1 − ls
i, the proportion
allocated to after-school learning activities.
A child’s time allocated to after-school learning activities, 1 − ls
i, and a child’s
nutrition level, cs
i, are the only private inputs into his or her human capital.
4
There-fore a child with schooling attributes (1 − ls
i, csi) will attain a level of human capital
hsi = D × (1 − l s i) (1−δ) × (csi) δ , (1.2)
where D > 0 is an education efficiency parameter, and δ ∈ (0, 1) is a measure of the relative productivity of the child’s nutrition.
Let ai ∈ {−1, 0, 1} denote the child fostering decision of household i.
Conven-tionally, ai = −1 is the decision to foster out the child, ai = 1, the decision to foster
in a child, and ai = 0 means no fostering. When no fostering occurs, households are
said to be in autarky. The number of children residing in household i thus is 1 + ai.
For example, in a receiving-household (ai = 1), the number of resident children is
2, while the corresponding number is 0 in a sending-household, and 1 in autarky. Household i’s disposable income is (1 − lm
i )hmi , which is spent entirely on the
composite market good x. Therefore, the total quantity of the composite market good available to household i is θi+ (1 − lim)hmi , i = 1, 2.
4
By stressing a child’s nutrition and time allocated to after-school learning activities as joint determinants of his or her future human capital level, we do not at all pretend that no other factors are likely to impact this human capital level. Peer effects, for example, may also be factors, as in Calvo-Armengol, Patacchini, and Zenou (2009) and to a certain extent Bobonis and Finan (2009), and may even drive out-fostering strategies, as in Serra (2009). However, as peer effects are basically externalities, which may have their source in the neighborhood or the city the child is living in (Bobonis and Finan, 2009), or in the network of school-enrolled friends the child has access to (Calvo-Armengol, Patacchini, and Zenou 2009), low economic status need not be a characteristic of the sending household, nor high socio-economic status a characteristic of the receiving household. For example if there are no schools in rural areas or those that exist are poor quality schools (e.g., due to a high incidence of teachers’ absenteeism), both rich and poor rural dwellers should gain from fostering out their children through social and family networks in urban areas so as to harness these peer effects. However, this would not be consistent with the "Cinderella" story prevalent in the empirical literature, whereby out-fostering parents are those who cannot afford to adequately invest in their children (e.g., Zimmerman, 2003; Akresh, 2009). Critics might also argue that we left out time allocated to school attendence. This is not so. We only assume that school attendance is mandatory, as is now the case in many african countries. Our assumption of mandatory education thus is simply a reflection of the observed coexistence throughout Africa between mandatory education laws and informal child fostering arrangements.
1.2.2
Production of Nutrition
The technology for producing nutrition is Cobb-Douglas in the composite market good (x) and in household labor (L). Therefore, the total quantity of nutrition produced in household i is given by:
zi = [θ + (1 − lmi ) hmi ] σ
(Li)1−σ (1.3)
for all i, where σ denotes the relative share of the market good in the production of nutrition.
Let us assume for the sake of simplicity that resident children, when they ex-ist, receive a constant relative share α ∈ (0, 1) of the nutrition produced, with the remainder, (1 − α), accrued to the parent. When there are no children in the household, the parent takes all. In other words, in the presence of child fostering, the biological child and the foster child will share a quantity αzi of total nutrition
produced.
Given the fostering decision, ai ∈ {−1, 0, 1}, taken by household i, the labor
requirement for the production of nutrition satisfies the following constraint: Li = Li(ai), where Li(ai) = lmi + (1 + ai) [1 + ai(1 − ai)] 1 + a2 i lib+ ai(1 + ai) 2 l f i (1.4)
is household i’s total supply of labor, given the household’s fostering decision ai, all
i. In other words, if household i chooses to remain in autarky (i.e., ai = 0), total
labor allocated to household chores is Li(0) = lm
i + lbi. In a sending-household (i.e.,
ai = −1), total labor allocated to household chores reduces to Li(−1) = lmi ; the
comparative figure for a receiving household is Li(1) = lm
i + lbi + l
f
i. Therefore, if
household i follows a fostering strategy ai ∈ {−1, 0, 1}, its consumption profile will
look as follows: Cim(ai) = 1 − (1 + ai) (2 − ai) 2 α [θi+ (1 − lmi ) h m i ] σ (Li(ai))1−σ, (1.5) Cib(ai) = α 1 − ai µ(1 + ai) − (1 − ai) 2 [θi+ (1 − lmi )h m i ] σ [Li(ai)]1−σ(1.6), Cif(ai) = αai(1 + ai) 2 µ(1 + ai) − (1 − ai) 2 [θi+ (1 − lim)h m i ] σ [Li(ai)]1−σ(1.7).
To investigate the social outcomes of informal child fostering arrangements, we contrast household outcomes under the child fostering arrangements with their cor-responding autarky levels— taken as the counterfactual case of what would have happened in the absence of informal fostering arrangements. We therefore start by characterizing the child’s and parent’s outcomes under autarky.
1.3
Household Outcomes in Autarky
In this section, we characterize the child’s and parent’s outcomes under autarky. We want to formalize the motives driving child fostering arrangements. In particular, we ask what forces may cause the emergence of asymmetric motives for child fostering as documented by the empirical literature (e.g., Akresh, 2009).
1.3.1
The Child Labor Motive for In-Fostering
In this sub-section, we compute household i’s utility payoff in autarky. Define a real valued function Vi : [0, 1]2× H → R , by:
∀(lm
i , lbi, hmi ) ∈ [0, 1]2 × H, Ui = Vi(lim, lbi, hmi ),
where Vi(lm
i , lbi, hmi ) denotes household i’s utility payoff from choosing autarky (i.e.,
ai = 0), when household total labor input in household chores is Li(0) = lmi + lib.
For the remainder of this study, let us set θ at unity. From (1.1), substituting in (1.2), (1.4), (1.5), and (1.6), and re-arranging terms yields:
Vi(lm i , lbi, hmi ) = (1 + γbδ) σ ln [1 + (1 − lm i ) hmi ] + (1 − σ) ln lmi + lib +B0+ γb(1 − δ) ln 1 − lbi , (1.8) where B0 = ln(1 − α) + γb[ln D + δ ln α] . (1.9)
Clearly, the level of this utility payoff depends on household i’s choice of the vector (lm
i , lib). In autarky, each household chooses (lmi , lib) so as to maximize (1.8). In
other words, letting (ˆlm
i , ˆlib) denote household i’s optimal allocation of labor input
in household chores, we have that (ˆlmi , ˆl b i) = arg max hlm i , lbii Vi(lmi , l b i, h m i ). (1.10)
Using (1.8), it can be shown that the optimal household time-allocation is given by: ˆlb i = 1 − γb(1 − 2δ) − γb(1 − δ) (hmi ) −1 1 + γb , (1.11) 1 − ˆlb i = γb(1 − δ) 1 + γb 2 + (hm i ) −1 , (1.12) ˆlm i = [(1 − σ)(1 + γb) + σγb(1 − δ)] 1 + (hm i ) −1 − σ (1 + γbδ) 1 + γb . (1.13) The following proposition can thus be derived from this optimal allocation:
Proposition 1.1. The intensity of a parent’s involvement in household chores is lower, the higher his or her human capital level (i.e., ∂ˆlm
i /∂hmi < 0). By contrast,
the intensity of the child’s involvement in household chores rises with his or her parent’s human capital level (i.e., ∂ˆlb
i/∂hmi > 0).
Proposition 1.1 is a reflection of the assumption of perfect substitutability be-tween the parent’s labor input and the child’s labor input in household chores. This assumption is reasonable when talking about school-age children and given the fact that most household chores require raw labor, including dish-washing, mopping the floor, doing laundry, etc.. When the parent has a high opportunity cost of time in household chores (say, as measured by her human capital level), this puts a higher demand on the child to help out more, thereby reducing the time he or she spends in after-school learning activities. Concerns for the child’s well-being may thus provide such a parent with the incentive to foster in a child for labor purposes, in order to boost his or her biological child’s educational attainment. In other words, in the absence of a well-functioning market for domestic labor services, a parent’s high opportunity cost of labor input in household chores generates a child labor motive for fostering in a child.
1.3.2
A Human Capital Motive for Out-Fostering
Just to recall, a child’s human capital is jointly determined by his or her level of nutrition and his or her after-school time allocated to learning activities. In this sub-section, we relate these two features of a child’s human capital formation to parental out-fostering strategies.
First, from (1.6), substituting in (1.11) and (1.13), and re-arranging terms yields the child’s nutrition level as follows:
ˆ cb i = ασ σ(1 − σ)(1−σ) 1 + γbδ 1 + γb 2 + (hm i ) −1 (hm i ) σ , (1.14)
for all i. Likewise, from (1.2), substituting in (1.12) and (1.14), and re-arranging terms yields the child’s human capital level as follows:
ˆhb i = φ 2 + (hm i ) −1 (hm i ) σδ , (1.15)
for all i, where
φ(δ) ≡ [ασ σ(1 − σ)1−σ(1 + γ bδ)] δ [γb(1 − δ)](1−δ)D 1 + γb .
The main observation from Eq. (1.15) is that the opportunity cost of parent i’s labor time in household chores has two opposite effects on his or her child’s human capital. One is a negative effect due to the substitutability between a parental labor and the child’s labor in household chores. The other is a positive effect stemming from the contribution of nutrition to the child’s human capital.
To the extent that the composite market good is sufficiently contributive to household nutrition, households where the parent supplies more market-labor will provide better nutrition for their members. The opportunity to take advantage of the human capital effects of adequate nutrition may therefore provide a low-opportunity cost parent with the incentive to foster out his or her child to a high-opportunity cost parent.
We have just argued above that in an environment with no market or an im-perfect market for domestic labor services, inter-household differences in parental socioeconomic status (as these affect their relative opportunity cost of time in house-hold chores) combine with the productivity of nutrition (as an input in a child’s hu-man capital) to generate potential asymmetric motives for child fostering. However, households will not act upon these motives unless the resulting outcomes are no less than their corresponding autarky levels— corresponding to own-parent residence for all children. Therefore, we compute each parent’s welfare in autarky.
1.3.3
Parent’s Autarky Welfare
Define a real-valued function ¯V :h, ¯h → R, ∀hm
i ∈ h, ¯h by: ¯ V (hm i ) ≡ max hlm i ,lbii Vi(lm i , lbi, hmi ). We interpret ¯V (hm
i ) as a measure of a parent’s autarky welfare, when the parent
faces a level of opportunity cost hm
substituting in (1.11) and (1.13), and re-arranging terms yields parent i’s autarky welfare level as follows:
¯ V (hm i ) = ¯B0+ (1 + γb) ln 2 + (hm i ) −1 + σ (1 + γbδ) ln(hmi ) (1.16)
for all i, where ¯ B0 = B0+ (1 + γbδ) lnhσσ(1 − σ)(1−σ)i + ln 1 + γbδ 1 + γb +γb(1 − δ) ln γb(1 − δ) 1 + γb (1.17) and B0 is as defined in (1.9).
As was the case for the child’s human capital, the parent’s socioeconomic status as determined by his or her human capital, hm
i , has an ambiguous effect on his or
her welfare. We use this autarky welfare as a basis for exploring a parent’s gains from agreeing an informal child fostering arrangement with another parent.
1.4
A Bargaining Game of Child Fostering
Child fostering involves the determination of the fraction of time lf ∈ [0, 1] the foster
child will contribute to household chores and the relative share µ ∈ (0, 1) of resident children nutrition accrued to the foster child. Since by assumption parents only care about the human capital level of their own child, there may be a conflict between the immediate benefits of child labor to the receiving household and the future benefits of the child’s human capital to the sending household. There is also a conflict between the immediate benefits of nutrition accrued to the biological child and the immediate benefits of nutrition accrued to the foster child, since fostering in a child adds another mouth to feed in the household, thus generating more competition for household resources. Because of these conflicts of interest, it is convenient to approach a traditional child fostering arrangement as a cooperative game between the sending and the receiving parents. Indeed, owing to the operation of Hamilton rule, if the receiving parent were to uncooperatively determine lf and µ, this would set the level
of lf at unity and the level of µ at the minimum survival level, implying that the
foster child would have no time for after-school learning activities. Furthermore, he or she would have a poor nutrition status. Were this situation to materialize, no altruistic parent would voluntarily send his child out for fostering. Therefore, in order for there to be child fostering in this environment, the sending parent and the receiving parent must bargain over lf and µ.
In deciding whether or not to cooperate, parents will balance the payoff from cooperation against the autarky payoff. To study the implications of informal child fostering arrangements for the foster child’s welfare, we first characterize the coop-erative game that determines the foster child’s time allocated to home-production and his or her level of nutrition in the receiving household. Since this game is played between a parent who wants to foster his or her child out and another who wants to foster the child in, it is important to outline the characteristics of the parent that gains from fostering out as well as those of the parent that gains from fostering in.
1.4.1
Who Gains from In-Fostering?
Suppose that any of the two parents i would consider fostering in a child. For the receiving parent i, the non-cooperative choice of the pair (lm
i , lbi) yields the following
payoff: VI hm i , l f, µ= max hlm i ,lbii Vi lm i , l b i, h m i , l f, µ (1.18) where V (lmi , l b i, h m i , l f , µ) = (1 + γbδ) h σ ln [1 + hmi (1 − l m i )] + (1 − σ) ln lim+ l b i + l f i i +B1+ γbδ ln (1 − µ) + γb(1 − δ) ln(1 − lib), (1.19) B1 = ln(1 − α) + γb(ln D + δ ln α) . (1.20) Denote as (˜lm
i , ˜lib) the interior solution to the maximization problem in (1.18):
˜lm i , ˜l b i = arg max hlm i ,lbii Vi lmi , l b i, h m i , l f , µ (1.21)
all i. We prove the following Lemma in Appendix1.7.1.
Lemma 1.1. Given lf, household i’s labor allocation in household chores is given
as follows: ˜lb i = ˆl b i − γb(1 − δ) 1 + γb lf, (1.22) ˜lm i = ˆlmi − σ (1 + γbδ) 1 + γb lf, (1.23) where (ˆlb
i, ˆlim) denotes the vector of time allocation in autarky, for all i.
Lemma 1.1 states that child fostering partially relieves the receiving parent and his or her biological child from participation in household chores. Indeed, as long as lf > 0, we have that
˜lb
for all i.
From (1.19), substituting in (1.22) and (1.23), re-arranging terms yields VI hm i , l f, µ= ¯B 1+ γbδ ln (1 − µ) + σ (1 + γbδ) ln hmi + (1 + γb) ln 2 + lf + (hmi ) −1 (1.24)
for all i, where ¯ B1 = B1+ (1 + γbδ) ln σσ(1 − σ)(1−σ)(1 + γ bδ) 1 + γb +γb(1 − δ) ln γb(1 − δ) 1 + γb , (1.25) and B1 is as defined in (1.20). Given (hm
i , lf, µ), it is important to ask which parent i gains from fostering in a
child. We propose the following definition of gains from in-fostering:
Definition 1.1. Parent i gains from in-fostering if and only if, given (hm
i , lf, µ),
the level of parental welfare from in-fostering is no less than its autarky level: VI hmi , l
f
, µ− ¯V (hmi ) ≥ 0 (1.26)
all i.
As an implication of Definition 1.1, the parent who stands to lose from in-fostering is one with a level of socioeconomic status, hm
i , such that given lf, µ
, VI hmi , l
f
, µ− ¯V (hmi ) < 0.
Define the net gain from in-fostering as the difference: ϑI(hmi , l
f
, µ) ≡ VI hmi , l f
, µ− ¯V (hmi ),
for all i. Then, using (1.16) and (1.24) along with (1.17) and (1.25), and re-arranging terms, yields this net gain as follows:
ϑI hm i , lf, µ = γbδ ln (1 − µ) + (1 + γb) ln " 1 + 2 + lfhm i 1 + 2hm i # , (1.27)
for all i. The following proposition summarizes the characteristics of a parent who gains from in-fostering:
Proposition 1.2. The net gain to a receiving parent from fostering in child labor is increasing in (i) his or her socioeconomic status (i.e., ∂ϑI/∂hm
i > 0) and in (ii)
the foster child’s time spent in household chores (i.e., ∂ϑI/∂lf > 0). However, (iii)
this net gain decreases with the share of nutrition accrued to the foster child (i.e., ∂ϑI/∂µ < 0). Furthermore, (iv) the receiving parent’s socioeconomic status and the
foster child’s time allocated to household chores (lf) are strategic complements in
the net gain from fostering in (i.e., ∂2ϑI/∂hm
i ∂lf > 0).
Proposition 1.2-(iv) implies that the receiving parent’s demand for child’s labor (lf) rises with his or her socioeconomic status. In other words, during the bargaining
process, a receiving parent with a high socioeconomic status will always want the foster child to be highly involved in household chores, as a condition for being fostered in.
1.4.2
Who Gains from Out-Fostering?
Suppose that parent i decides to foster out his or her child. In this case, the parent will be left alone to supply labor in household chores (i.e., lb
i = 0 and lim > 0), in
addition to delivering his or her human capital to firms. Furthermore, the nutrition produced will accrued solely to the parent (i.e., α = 0). The only variable parent i can choose non-cooperatively in this situation is his or her time allocation between household chores and market labor. Therefore, we can define parent i’s welfare from out-fostering as follows VO hm i , hmj , lf, µ = max hlm i i Vi(x) (1.28) where x = lm i , lf, hmi , hmj , µ and Vi(x) = γ b(1 − δ) ln(1 − lf) + σ ln [1 + hmi (1 − l m i )] + (1 − σ) ln (l m i ) +γbδ h σ lnh1 + hmj (1 − ˜l m j ) i + (1 − σ) ln˜lmj + ˜l b j + l fi +B−1+ γbδ ln µ, (1.29) B−1 = γb(ln D + δ ln α) (1.30) and ˜lm j , ˜l b j = arg max hlm j,lbji V lmj , l b j, h m j , l f , µ
all j, as characterized in Lemma 1.1 above. Letting ¯lm i = arg maxhlm i iV i(x), it can be shown that ¯lm i = (1 − σ) 1 + (hm i ) −1 (1.31)
all i. Therefore, from (1.29), substituting in (1.22), (1.23), and (1.31), and re-arranging terms yields:
VO hmi , h m j , l f , µ = B¯−1+ γbδ ln µ + σ ln hmi + ln 1 + (hmi ) −1 + σγbδ ln hmj +γb(1 − δ) ln(1 − lf) + γbδ ln h 2 + lf + hm j −1i (1.32) all i, where ¯ B−1 = B−1+ (1 + γbδ) ln σσ(1 − σ)1−σ+ γ bδ ln 1 + γbδ 1 + γb , (1.33) and B−1 is as defined in (1.30).
We propose the following definition of the gain from out-fostering a child. Definition 1.2. A parent i gains from out-fostering his or her child if and only if the welfare level from following this strategy is no less than its autarky level:
VO hm i , h m j , l f, µ− ¯V (hm i ) ≥ 0, (1.34) all i.
Let us define parent i’s net gain from out-fostering as follows: ϑO hmi , h m j , l f , µ ≡ VO hmi , h m j , l f , µ− ¯V (hmi ).
Then, using (1.16) and (1.32) as well as (1.30) and (1.33), respectively, we obtain this net gain as follows:
ϑO hmi , h m j , l f , µ = γbδ ln µ + γb(1 − δ) ln(1 − lf) + γb(1 − σδ) ln hmi − (1 + γb) ln (1 + 2hmi ) + γbδ ln 1 + 2 + lfhm j −δγb(1 − σ) ln hmj + ln (1 + hmi ) + ¯B (1.35) where ¯ B = − ln(1 − α) − γb(1 − δ) ln γb(1 − δ) 1 + γb + ln 1 + γbδ 1 + γb , and hm i ∈
Proposition 1.3. For γb(1 − σδ) sufficiently small, (i) the net gain to a parent
from out-fostering his or her child is decreasing in his or her socioeconomic status (i.e., ∂ϑO/∂hm
i < 0). However, (ii) this net gain is increasing in the socioeconomic
status of the receiving parent (i.e., ∂ϑO/∂hm
j > 0), if and only if
hmj >
1 − σ
σ (2 + lf). (1.36)
Furthermore, (iii) this net gain also rises with the foster child’s nutrition level (i.e., ∂ϑO/∂µ > 0). Finally, (iv) it is decreasing in the time the foster child spends in
household chores (∂ϑO/∂lf < 0) if
δ ≤ 2 + l
f
3 . (1.37)
Condition (1.36) of Proposition 1.3 states that the receiving parent must be sufficiently well-off. Condition (1.37) implies that the productivity of child nutrition as an input into a child’s future human capital is not too high. Both conditions can be easily met for an appropriate choice of parameters. When condition (1.37) is satisfied, out-fostering a child creates a conflict between the immediate benefits of child labor to a receiving parent and the future human capital benefits desired by the sending parent. It is therefore clear that an altruistic parent will exhaust his or her bargaining power to ensure that this conflict is resolved in his or her best interest. Hence the relevance of the Nash-bargaining game as a mechanism for characterizing the optimal child fostering arrangement from the parents’ viewpoint.
1.4.3
Optimal Child Fostering Arrangement
In this sub-section, we characterize the process by which an agreement is reached between two parents over the transfer of residence of a child from own-parent to non-parent. The optimal child fostering arrangement is construed as a bargain between the sending and the receiving parents over the pair lf, µ, specifying the fraction
of after-school time the foster child is to spend doing household chores, lf, and the
share, µ, of nutrition this child is to receive.
For convenience, we denote the sending parent as Parent i = 1 and the receiving parent as Parent i = 2. It will also be convenient to express the optimal informal child fostering arrangement (when it does exists) as a function of the socioeconomic distance between the sending and the receiving parents. This socioeconomic distance is proxied by the ratio β = hm
2 /hm1 . The higher β, the higher the gap in earning
power between the two parents. Again for convenience, we set hm
