Three essays in the microeconomics of development

Three Essays in the Microeconomics of Development

Thèse

Setou Mamadou DIARRA

Doctorat en économique Philosophiæ doctor (Ph.D.)

Québec, Canada

Three Essays in the Microeconomics of Development

Thèse

Setou Mamadou DIARRA

Sous la direction de:

Sylvain Dessy, directeur de recherche John Cockburn, codirecteur de recherche

Résumé

Dans cette thèse, j’explore les facteurs qui minent les chances de vie des enfants dans les pays en développement, avec un accent particulier sur les pays d’Afrique sub-saharienne. Cette thèse est composée de 3 essais. Les deux premiers (chapitres 1 et 2) se concentrent sur le mariage précoce des jeunes filles, tandis que le troisième et dernier essai (chapitre 3) met l’accent sur la pauvreté des enfants, spécifiquement à la question de la concordance/discordance entre mesures monétaires et multidimensionnels de ce phénomène.

Le mariage précoce est pratiqué dans toutes les régions du monde, mais c’est en Afrique subsaharienne que le phénomène est prédominant, 8 des 10 pays avec les prévalences de mariage précoce les plus élevés sont sur le continent. En 2010, 34% (environ 67 millions) de jeunes femmes âgées de 20 à 24 à l’échelle mondiale ont été marié avant leur dix-huitième anniversaire et environ 12% ont été marié avant l’âge de 15 ans. L’Organisation des Nations Unies pour la population (FNUAP) estime que si cette tendance continue, 142 millions de filles seront mariées avant 18 ans dans la prochaine décennie (UNFPA, 2012).

Dans les pays où cette pratique est prédominante, il reflète les normes basées sur le genre qui façonnent la vie des adolescentes, contraignant leur choix et capacités de vie en limitant leur accès à l’éducation, leur mobilité ainsi que leur autonomisation au sein du ménage en particulier sur les décisions sexualité et de fertilité. La lutte contre le mariage des enfants en Afrique subsaharienne et ailleurs peut avoir des retombées positives importantes pour la réalisation de l’Agenda 2030 des Nations Unies pour le développement durable.

La littérature existante sur le mariage précoce des filles met en évidence le rôle conjoint joué par les facteurs de l’offre — à savoir, pourquoi les parents marient leurs filles mineures — et les facteurs de la demande — à savoir, pourquoi les hommes entrent en relations conjugales avec des adolescentes — comme déterminants de la prévalence de cette pratique dans les pays en développement. Pour que cette évidence empirique soit convertible en action effi-cace, il est primordial d’avoir une évaluation quantitative de ces deux facteurs de demande et d’offre dans l’explication de ces taux de prévalence élevés. Le premier essai de ma thèse vise à combler cette lacune en mesurant l’importance quantitative de la valeur intrinsèque que les hommes attachent à avoir des épouses adolescentes dans le cadre du Niger. Le deux-ième essai fait suite au premier, en développant un modèle de demande de mariage précoce

avec une application empirique au Nigeria, pour comprendre pourquoi une grande partie des hommes dans les pays en développement se marient à des jeunes filles mineures.

Le troisième essai explore théoriquement et empiriquement les causes de la discordance ob-servée entre la pauvreté monétaire et multidimensionnelle des enfants. Comme les deux premiers essais, il est empiriquement fondé sur les expériences des pays d’Afrique subsa-harienne, avec une application à la Tanzanie. Cet essai relie théoriquement les dimensions du bien-être des enfants, tel que la nutrition et la scolarisation, aux caractéristiques socioé-conomiques des parents, tel que le revenu et l’éducation parentale. Le modèle prédit que l’éducation des parents influe sur le niveau de discordance entre la pauvreté monétaire et multidimensionnelle des enfants. Ce résultat théorique est testé empiriquement en utilisant les données de la Tanzanie. Les résultats montrent que l’éducation des parents agit néga-tivement sur la probabilité qu’un enfant non-pauvre monétairement souffre de privations de base, et agit positivement sur la probabilité qu’un enfant pauvre monétairement ne souf-fre pas de privations de base.

Dans l’ensemble, ces trois essais contribuent à faire progresser notre connaissance des fac-teurs qui contraignent les chances de vie des enfants en Afrique subsaharienne. En parti-culier, ma thèse suggère que les interventions politiques qui ne tiennent pas compte de la résistance locale à la mise en œuvre des programmes de prévention du mariage précoce des filles peuvent être confrontés à des rendements incertains (Essai 1 et 2). Il met également en évidence un autre canal par lequel l’éducation des parents peut jouer un rôle important dans l’amélioration des chances de vie des enfants dans les pays en développement (Essai 3).

Abstract

In this thesis, I investigate factors that undermine children’s life chances in developing coun-tries, with a particular focus on sub-Saharan African (SSA) countries . Three essays comprise this thesis. The first two (Chapters 1 and 2) focus on the life chances of adolescent girls in relation to the issue of child marriage, while the third essay (Chapter 3) focuses on child poverty, in relation to the issue of concordance/discordance between monetary and multi-dimensional measures of this phenomenon.

Child marriage is found in almost all regions of the world, but SSA gets the brunt of it, as it is home to 8 of the 10 countries worldwide reporting the highest prevalence rates of this phe-nomenon. In 2010, 34% (about 67 million) of young women aged 20-24 globally were married before their eighteenth birthday and about 12% were married by age 15. The United Nation Population Fund (UNFPA) estimates that if present trends continue, 142 million girls will be married before age 18 in the next decade (UNFPA, 2012). Child marriage has been shown to hamper developing countries girls’ life chances both directly and indirectly (UNFPA, 2012). Where it exists as a mass phenomenon, it reflects gendered norms that shape adolescent girls’ lives through constrained choices and capabilities relative to boys, including a higher care work burden for girls, restricted access to education, limited mobility; limited author-ity in the family for wives ( particularly over sexualauthor-ity and fertilauthor-ity decisions). Combating child marriage in SSA and elsewhere may thus yield significant positive spillovers for the achievement of the 2030 United Nation’s Agenda for Sustainable Development.

The existing child marriage literature highlights the joint role played by supply-side factors — i.e., why parents marry off their underage daughters— and demand-side factors— i.e., why men enter into marital relationships with underage girls— in driving the prevalence rates of child marriage in the developing world. To turn this empirical finding into effective policy action, however, a quantitative assessment of the relative strength of both demand-side and supply-demand-side factors in explaining these high prevalence rates is of paramount im-portance. The first essay of my thesis aims to fill this knowledge gap by measuring the quantitative importance of the intrinsic value Niger’s men attach to having child brides. The second essay follows up on the first, by developing a demand-side model of child mar-riage with empirical application to Nigeria, to explain why a large proportion of men in

developing countries marry underage girls.

The third essay explores both theoretically and empirically the causes of the observed mis-match between monetary and multidimensional child poverty. Like the first two essays, it is empirically grounded in the experiences of SSA countries, with a practical application to Tanzania. This essay theoretically links child outcomes, such as nutritional status and school-ing achievements to parental and household characteristics includschool-ing household income and parental education. The model used to formalize this link predicts that parental education influences the level of the mismatch between monetary and multidimensional child poverty. Empirical evidence drawn from Tanzania NPS data is consistent with this prediction. In par-ticular, results show that parental education is a negative predictor of the probability that a monetarily non-poor child suffers some basic deprivations, and a positive predictor of the likelihood that a monetarily poor child suffers no basic deprivations.

Overall, these three essays contribute to advancing our knowledge of factors that constraint children’s life chances in SSA. In particular, my thesis suggests that policy interventions that ignores the extent and causes of local resistance to the implementation of child marriage pre-vention programs may face uncertain results (Essay 1 and Essay 2). It also highlights another channel through which parental education can play an important role in the improvement of children’s life chances in developing countries (Essay 3).

Contents

1 Child Marriage in Niger: Measuring the Quantitative Importance of

Reduc-ing the Demand for Child Brides 4

1.1 Introduction . . . 5

1.2 A Model of Child Marriage . . . 8

1.3 Quantitative Analysis. . . 15

1.4 Conclusion . . . 24

2 Adolescent Brides and Grooms’ Education: Theory and Evidence 26 2.1 Introduction . . . 27

2.2 Data and Empirical Strategy . . . 33

2.3 Estimation Results . . . 37

2.4 A Model of Bride Choice . . . 41

2.5 Testing the Mechanism . . . 48

2.6 Conclusion . . . 50

3 Monetary and Multidimensional Child Poverty: Why they Differ 61 3.1 Introduction . . . 62

3.2 A Model of Parental Investment in Child’s Outcomes . . . 66

3.3 Empirical Analysis . . . 74

3.4 Conclusion . . . 87

Appendix A. . . 89

Conclusion 97

List of Tables

1.1 Summary statistics for Niger. . . 16

1.2 Independence test . . . 19

1.3 Penalized likelihoods for candidate copula models . . . 21

1.4 Estimates of Fréchet parameters for the margins . . . 22

1.5 Selected values for Parameters . . . 23

1.6 Calibration Results . . . 23

1.7 Counterfactual Simulation . . . 24

2.1 Summary Statistics . . . 52

2.2 Correlation between Professional Occupation and Wealth Index . . . 52

2.3 Determinants of Demand for Adolescent Brides . . . 53

2.4 IV Estimation of the Effect of Males’ Education on the Demand for Adolescent Brides . . . 54

2.5 IV First-Stage Regressions . . . 55

2.6 Robustness Check: Subset of Males Aged 30 or Higher at the Time of Marriage 56 2.7 Heterogeneous Effects of Males’ Education by Region . . . 57

2.8 Heterogeneous Effects of Males’ Education by Urban/Rural . . . 58

2.9 Interaction Effects of Father’s and Mother’s Education on Child’s Quantity and Quality . . . 59

2.10 Interaction Effects of Father’s Education and Mother’s Early Marriage on Child’s Quantity and Quality . . . 60

3.1 Sample Information . . . 75

3.2 Normative criteria for poverty measurement . . . 76

3.3 Child monetary and Deprivation Rates. . . 76

3.4 Patterns of mismatch . . . 78

3.5 Shorrocks-Shapley decomposition . . . 85

3.6 Determinants of child education . . . 89

3.7 Determinants of child nutrition . . . 90

3.8 Interaction effects between household income and parental education . . . . 91

3.9 Estimates of the Heckman model for deprived children in education in non-poor household . . . 92

3.10 Estimates of the Heckman model for deprived children in nutrition in non-poor house-hold . . . 93

3.11 Estimates of the Heckman model for non-deprived children in education in poor Household . . . 94

3.12 Estimates of the Heckman model for non-deprived children in nutrition in poor

house-hold . . . 95

3.13 Hausman and Sargan tests results . . . 96

List of Figures

1.1 Selection of Copula . . . 20

1.2 Probability density functions . . . 22

2.1 Male education and the prevalence of adolescent marriage . . . 28

2.2 Proportion of men married to adolescent girls by education in Nigeria . . . . 28

2.3 Proportion of men married to adolescent girls by education among men whose

age at marriage was 30 or higher in Nigeria . . . 29

2.4 Geographic distribution of average males’ schooling and prevalence rates of

adolescent brides in Nigeria . . . 34

2.5 Effect of male’s level of education on the probability of marrying an adolescent

girl . . . 39

2.6 Proportion of men married to underage girls by region and rural/urban in

Nigeria . . . 40

3.1 Consumption Gradients for Education and Nutrition Deprivations . . . 77

3.2 Multidimensional child poverty and parental education. . . 77

A ma mère Sokona Soucko, ma grand-mère Siraly Fofana et mon oncle Niory Keïta.

A la mémoire de ma tante Mariam Fofana, partie trop tôt.

Poverty is not just a lack of money; it is not having the capability to realize one’s full potential as a human being.

Remerciements

Une thèse est loin d’être un travail personnel. Je tiens à exprimer ma gratitude et mes remer-ciements à certaines personnes qui ont contribué de près ou de loin à la réalisation de cette thèse ainsi qu’à la réussite de mes études.

J’aimerais tout d’abord remercier mon directeur de thèse Prof. Sylvain Dessy pour sa très grande disponibilité, ses précieux conseils et son encadrement tout au long de cette épreuve de doctorat. En dehors, de l’encadrement académique, je le remercie pour son soutien quo-tidien et sa bienveillance paternelle à mon égard qui ont été pour moi un appui inestimable pour surmonter certains moments difficiles. Je remercie également Prof. John Cockburn qui a accepté de codiriger ma thèse. Je le remercie pour sa disponibilité et son encadrement qui m’ont été précieux pour l’aboutissement de cette thèse. Je le remercie également pour le soutien financier tout au long de ces années, qui m’a permis de participer à de nombreuses conférences académiques. A travers lui, je remercie également le PEP pour tout le soutien financier tout au long de cette thèse.

Je tiens à exprimer ma gratitude et mes remerciements à tous les professeurs du département d’économique pour la qualité de l’enseignement reçu. Un grand merci au professeur Bernard Fortin pour sa disponibilité et surtout ses judicieuses suggestions qui ont grandement con-tribué à améliorer mes travaux. Je le suis aussi reconnaissant d’avoir accepté d’examiner cette thèse. Mes sincères remerciements aux professeures Sabine Kröger et Marion Goussé pour les échanges que nous avons eus après chacune de mes présentations aux séminaires internes. Je remercie également le personnel du département d’économique, en particulier, Ginette Therrien, Josée Desgagnés et Jacinthe Morin pour leur professionnalisme.

Un grand merci à tous mes camarades de promotion et ami(e)s. Spécialement à Gilles Koumou, pour son soutien tout au long de ces années. Merci à Ali Yedan, Jean Armand Gnagne, Mbéa Bell, Aimé Simplice Nono et Isaora Diahali pour la bonne ambiance créée au département. Merci aux autres collègues du programme de doctorat en économique. Sans oublié Rokhaya Dieye qui a été un mentor pour moi.

Je remercie également, ma meilleure amie et petite sœur Anna, pour tout son soutien, ses encouragements et son attention envers ma personne. Je remercie également Demba Baldé

ainsi que Keba Camara et sa femme Mame Codou N’diaye pour leur soutien dans les mo-ments difficiles.

Ma profonde gratitude et mes remerciements les plus sincères à ma famille: Diarra, Keita et Coulibaly pour leur soutien inestimable dans ma vie. Spécialement à: ma mère Sokona Soucko, qui, malgré le fait qu’elle n’a pas eu la chance d’aller à l’école, a fait tout son possible pour qu’aucuns de ses enfants et particulièrement ses filles ne subissent le même sort. Je la remercie du fond du cœur.

Du fond du cœur, je remercie ma grande mère Siraly Fofana (Yayi), qui a toujours été une mère pour moi. Je la remercie pour son combat et tous ses sacrifices pour que je puisse continuer mes études. Merci d’être encore la dans ma vie.

Mon profond remerciement à mon oncle Niory Keita qui a toujours été un père pour moi. Pour tout le soutien tout au long de ma vie. Je le remercie pour toutes les bonnes valeurs qu’il m’a inculqué. Je rends hommage à sa femme, ma tante Mariam Fofana, qui nous a quitté trop tôt. Merci à vous de m’avoir élevé comme votre propre enfant. Je remercie également ma cousine Sira Keita, qui m’a toujours soutenu dans mes projets. Un grand merci à mon oncle Alou Diarra, pour sa présence et son soutien. Un grand merci à tous mes oncles, tantes, frères et sœurs des familles Diarra et Keita.

Pour finir, je remercie mon conjoint Mohamed Coulibaly, pour avoir embarqué avec moi dans ce projet dans ce pays de grand froid. Merci pour ta patience durant toutes ces années.

Avant-propos

Les chapitres de la présente thèse constituent des articles soumis ou à soumettre à des revues scientifiques avec comité de lecture pour publication.

Le premier chapitre de cette thèse est un article réalisé avec mon directeur de recherche, Syl-vain Dessy, et mon co-directeur, John Cockburn. Cet article, dont je suis l’auteure principale, fait l’objet de quelques révisions pour être soumis à une revue scientifique en développe-ment avec comité de lecture pour publication.

Le deuxième chapitre est un article réalisé avec mon directeur de recherche, Sylvain Dessy. Une version de cet article écrite en collaboration avec le Prof Roland Pongou de l’université d’Ottawa sera très prochainement soumise à une revue scientifique avec un comité de lecture pour publication. Je suis l’auteure principale de cet article.

Le dernier chapitre de cette thèse est un article réalisé avec mon directeur de recherche, Syl-vain Dessy, mon co-directeur, John Cockburn, et Paola Ballon, chercheure associée à Oxford Poverty and Human Development Initiative (OPHI). Cet article, dont je suis l’auteure prin-cipale, a été soumis dans le Journal of African Economies le 04 novembre 2016. Cet article est présentement sous le processus d’évaluation du comité de lecture de cette revue.

Introduction

Development is often defined as a process of economic and social transformation leading to better living standards for the entire population. It refers to a process whereby changes in economic structures interact with changes in social structures to enhance the creation of wealth, reduce poverty, increase life-expectancy at birth, and enhance individual social pro-motion irrespective of gender and social background. Yet cultural and social factors, such as traditional norms underpinning women’s age at first marriage, are still largely under-represented in the larger development debate, though there has been significant progress in recent decades.

For example, the newly established United Nations’ Sustainable Development Goals (SDGs) underscore the need to transform women’s social status as a precondition for long-term and sustainable economic prosperity. In countries that have enjoyed a high level of prosperity, women have been breaking down barriers to their empowerment and have been achieving parity with men in terms of participation in education, the labor market, as well as the social and political life of the countries in which they live. To this day in the developing world, however, child marriage – an age-old institution tantamount to sexual slavery (Vogelstein, 2013) – continues to stand in the way of women’s empowerment, depriving millions of girls of their basic human rights.

An example of proposed policies to bring about changes in the economic structures of poor countries is the targeting of African women for microcredit as a tool for fighting poverty. Yet, if an African woman has no control over her own fertility say, due to culture-induced asymmetry in household bargaining power, and ends up facing repeated interruptions in her microcredit-financed business operations due to numerous pregnancies and births, how effective will this policy be in mitigating poverty for herself and her children? Unless women are freed from cultural and social traps, it is unlikely that they will be able to take full ad-vantage of economic opportunities afforded them in a way that significantly reduce child mortality (SDG 3.2) or improve maternal health (SDG 3.1).

Child marriage is found in almost all regions of the world, but the phenomenon is ubiquitous in South Asia and sub-Saharan Africa. In 2010, 34% (about 67 million) of young women aged 20-24 globally were married by age 18 and about 12% were married by age 15. According

to the United Nation’s Population Fund (UNFPA), if present trends continue, 142 million girls will be married before age 18 in the next decade (UNFPA, 2012). Child marriage is a complex phenomenon, but is certainly linked to poverty and girls’ lack of educational opportunities. It affects the poorest girls with the least education. Girls with no education are up to six times more likely to marry than girls with a secondary education. Girls living in poorer households are almost twice as likely to marry before the age of 18, compared with girls in higher-income households (The World Bank, 2014).

Combating child marriage in Sub-Saharan Africa and elsewhere may thus yield significant positive spillovers for the achievement of the 2030 Agenda for Sustainable Development: it can promote gender equality and empower women and girls (SDG 5) by reducing the age gap between married women and their spouses; it can reduce both child mortality (SDG 3.2) and maternal mortality (SDG 3.1) by increasing the average age at first birth for women.

My thesis addresses specifically the issues of child marriage and child poverty in Sub-Saharan Africa. It consists of three essays. The first two address issues related to child marriage, with applications to Niger and Nigeria, while the third essay addresses the issue of non-concordance between monetary and multidimensional child poverty measurements, with an application to Tanzania.

The existing child marriage literature (e.g., Jensen and Thornton 2003; Vogelstein, 2013) high-lights the joint role played by supply-side factors — i.e., why parents marry off their under-age daughters— and demand-side factors— i.e., why men enter into marital relationships with underage girls— in driving the prevalence rates of child marriage in the developing world. To turn this empirical finding into effective policy action, however, a quantitative assessment of the relative strength of demand and supply-side factors in explaining these high prevalence rates is of paramount importance. The first essay aims to fill this knowledge gap by measuring the quantitative importance of the intrinsic value Niger’s men attach to having child brides. The second essay follows up on the first, by developing a demand-side model of child marriage with an empirical application to Nigeria, to explain why a large proportion of men in developing countries marry underage girls.

The first of the United Nations’ new Sustainable Development Goals (SDGs) simultaneously targets the eradication of extreme monetary poverty and a reduction by at least half of the proportion of individuals of all ages and genders living in poverty in all its dimensions. This objective is both timely and challenging as, around the globe, 836 million people still live in extreme monetary poverty, of which the majority are children (United Nations 2015). This figure, combined with the 2030 deadline set by the United Nations for the SDGs, calls for effective poverty-alleviation strategies to be put into place as soon as possible. To fulfil this task, however, requires that development experts possess a highly functional and adequate tool for identifying the poor and the severity of their plight. Monetary poverty measures are

thus attractive because they are functional and an adequate indicator of a lack of purchasing power, which in turn may cause an individual to face basic deprivations such as malnutrition or lack of education. Yet, the poverty measurement literature recently found that children who are monetarily non-poor often suffer from basic deprivations. The main contribution of the third essay is to propose an explanation for this observed mismatch between monetary and multidimensional child poverty.

The remainder of this dissertation is organized as follows. Section 1 presents the first chapter of my thesis on measuring the quantitative importance of reducing the demand for child brides in Niger. Section 2 presents the second chapter on adolescent brides and grooms’ education, theory and evidence from Nigeria. Section 3 presents the last chapter of this dissertation.

Chapter 1

Child Marriage in Niger: Measuring

the Quantitative Importance of

Reducing the Demand for Child

Brides

Abstract: Child marriage is known fromField and Ambrus(2008) to be associated with poor social and physical outcomes for child brides. It is known fromJensen and Thornton(2003) to be driven by both parents’ multifaceted poverty and the added value men attach to marrying an underage girl. We incorporate these elements into a model of parental decisions on the timing of their daughter’s marriage. We calibrate this model to Niger and use it, first to assess the added value men attach to having a child bride, and second, to compute the effect of eliminating this added value. We find that Niger men have a preference for child brides. Eliminating this bias, however, reduces the prevalence of child marriage by only 27.5%, leaving parents multifaceted poverty to account for the remaining 72.5%, which is quite large.

JEL: C12, C13, C14, J12, J13, O12.

1.1

Introduction

The Millennium Development Goals underscore the need to transform women’s social status as a precondition for long-term economic prosperity. In countries that have enjoyed a high level of prosperity, women have been breaking down barriers to their empowerment and have been achieving parity with men in terms of participation in education, the labor market, as well as the social and political life of the countries in which they live. Yet to this day in the developing world, child marriage — an age-old institution tantamount to sexual slavery

(Vogelstein(2013)) — continues to stand in the way of women’s empowerment, depriving

millions of underage girls of their basic human rights.

The existing child marriage literature (e.g., Jensen and Thornton(2003);Field and Ambrus

(2008);Vogelstein(2013)) highlights the joint role played by supply-side factors— i.e., why parents marry off their underage daughters— and demand-side factors— i.e., why men enter into marital relationships with underage girls— in predicting the probability that an under-age girl will be married off by her parents before she reaches adulthood. However, to date there is still no systematic quantitative evaluation of the predictive power of each of these factors to inform effective policy action. This research aims to fill this knowledge gap by quantitatively assessing the predictive power of the added value men attach to having child brides on the probability that an underage girl will fall victim to child marriage.

We first propose a theory of child marriage in which parents time the marriage of their un-derage daughter in reaction to both supply-side and demand-side factors. On the supply side, the starting point of our theory is that child marriage is a parental decision, with both parents (or legal guardians) holding the decision-making power over the timing of their daughters’ marriage. This assumption is supported by the 2012 DHS1data for Niger show-ing that parents or legal guardians are reported to decide on the timshow-ing of their daughters’ marriage in roughly 65% of cases.2

Further, consistent with the development literature on poverty (e.g.,Berenger and Verdier-Chouchane(2007a)), in each household, we relate the parents decision on the timing of their daughter’s marriage to their joint socioeconomic outcomes: (i) their average level of educa-tion, and (ii) their household’s standard of living, as measured by an appropriately scaled wealth index. Given that child marriage is harmful to the cognitive and emotional develop-ment of the children involved (Field and Ambrus(2008);UNFPA(2012);Vogelstein(2013)), and that parents are altruistic towards their offspring ((John Cockburn,2009)), it is arguably unlikely that these parents would marry off their underage daughter before she reaches adulthood, unless compelled by strenuous circumstances. On the one hand, a household

1_{Demographic and Health Survey.}

2_{Authors’ own calculation using Niger’s 2012 DHS data. One of the novelties of the 2012 survey is the}

inclusion of a question asking married women to reveal who made the decision regarding the timing of their marriage (the father, the mother, another member of the family, or themselves).

may be short of vital resources (e.g., livestock, poultry, food or cash crops) for a number of reasons including aggregate economic conditions or crises, or idiosyncratic economic shocks such as bad harvests or illnesses. In a household in which parents are affected by such ad-verse conditions, adjusting household size through child marriage may emerge as a viable economic survival strategy in terms of both releasing household resources for alternative uses, or adding to these resources through the brideprice received from the groom’s family, as in sub-Saharan Africa. On the other hand, parents may be hampered by a low level of education and poor standards of living in their effort to nurture their underage daughter. This, in turn, may lower the benefits of nurturing their daughter’s cognitive and emotional development until she reaches adulthood.

On the demand side of our model, the starting point is that child marriage does not exist unless potential grooms fail to see a girl’s age as a barrier to bridehood. According to a 2006 report by the International Planned Parenthood Federation (IPPF)3, societies where power struc-tures are male-dominated or patriarchal in all aspects of social and political life are those in which men are likely to attach an added value to marriage with an underage girl. In par-ticular, in a society where desired fertility is high, pubescent girls may be seen as having longer reproductive lives (Jensen and Thornton(2003)). Moreover, high desired fertility may incline men to seek to control their wives’ sexuality. From this perspective, child brides may be seen as more easily controllable by the groom and his family to achieve their desired fer-tility objectives (Jensen and Thornton(2003)). This means that there is tremendous pressure on parents to marry off their underage girls before they reach the legal age to preserve family honour and minimize the risk of improper sexual activity or conduct (IPPF 2006).

The main goal of our child marriage theory is to provide a basis for a statistical model of the prevalence of child marriage in a given population of underage girls. In particular, as parents are the decision makers with regard to the timing of their daughter’s marriage, our model relates the prevalence of child marriage to the fraction of households in which parents gain from marrying off their underage daughter. The relevance of this statistical model stems from the fact that the average level of education of parents in a given household and the standard of living of its members are each probabilistically distributed among households. Furthermore, these two socioeconomic outcomes are stochastically related, as parental edu-cation is a prime determinant of household living standards. We relate the probability that parents in a given household gain from marrying off their daughter early to the probability that an underage girl is married off before she becomes an adult. We express this probabil-ity as a function of the added value men attach to having child brides. We then estimate the parametric structure of this probability function using Niger’s DHS data. The choice of Niger as a case study is interesting because it is the country with the highest prevalence rate of child marriage in the world. A 2012 DHS carried out in Niger establishes that 76.3% of

married women aged 20−24 had married before the legal age of 18.

A key technical issue confronting the parametrization of the function representing the prob-ability that an underage girl is married off is how to estimate the unknown joint probprob-ability distribution function of parents’ education and standard of living. To guide our choice of a proper parametric model for this joint probability distribution function, we first perform an independence test for this pair of outcomes using a nonparametric method proposed by (Deheuvels,1979), and formalized byGenest and Favre(2007). Test results lead us to reject the null hypothesis of independence in favor of the alternative that, in Niger, the average level of years of schooling completed by parents and their standard of living are stochasti-cally dependent. A further visual test performed using a scatter plot of normalized ranks confirms the presence of a positive dependence between the two socioeconomic outcomes, with this positive dependence visibly stronger in the upper tail. This, in turn, motivates our strategy of adopting a copula-based approach for modeling the parametric structure of the joint probability distribution function of these pairs of socioeconomic outcomes.

As is well-known in the statistics literature on multivariate analysis (e.g.,Joe(1997);Genest and Favre(2007);Trivedi and Zimmer(2007)), using a copula-based approach poses a num-ber of important issues, including how to choose the best copula model, and how to estimate its parametric structure. To resolve the model selection issue, we combine visual tools and formal selection criteria. In particular, since the scatter plot of normalized ranks confirms the presence of a positive association featuring a dependence that is stronger in the upper tail, we eliminate from consideration all copula families that generate dependence that is weaker in the tails (e.g., the Frank copula family) or stronger only in the lower tail (e.g., the Clayton copula family). For the candidate copula families considered, including Gaussian, Gumbel, Plackett, and t-Student, we then apply the Akaike Information Criterion (AIC). This lead us to select the Gumbel copula as the best parametric fit for Niger.

One of the appealing features of parametrically-specified copulas is that estimation and in-ference are based on standard maximum likelihood methods. Yet applications of this method are not always straightforward and may require practical adjustments to maximize efficiency or to mitigate computational difficulties. Our estimation procedure relies on a maximum pseudolikelihood method due to Genest and Favre(2007). This semiparametric estimation method is similar toJoe(1997)’s Inference From Margins method, except for the fact that the estimation of the copula component of the log-likelihood function is carried out by replacing the unknown margins by their model-free empirical counterparts. We complete the param-eterization of our statistical model by matching selected moments computed using Niger’s DHS data. We then use the parameterized model to perform a counterfactual thought ex-periment. This experiment proceeds in two steps. First, we quantitatively assess the added value Niger men attach to having child brides. This is done by calibrating this added value so as to match the observed prevalence of child marriage among Niger’s married women

aged 20−24 in 2012.

To calibrate the added value Niger men attach to having child brides, we apply the law of large numbers to interpret the probability that an underage girl is married off before she reaches adulthood as the prevalence of child marriage. We find that Niger’s men do have a preference bias towards child brides, although it is not strong enough to entirely preclude marriage with women of legal age. As such, our analysis is consistent with the empirical the child marriage literature, which finds that this harmful practice is driven by both supply-side factors and demand-supply-side factors (Jensen and Thornton,2003). This finding motivates the second step of our counterfactual thought experiment, which addresses the following question: if Niger’s men were to be made indifferent between a child and an adult bride, how much would the observed prevalence of child marriage among married women aged 20−24 in 2012 be reduced? Note that when this preference bias is eliminated, men become indifferent between a child and an adult bride. The idea then is that as men are indifferent, demand is no longer a driver of child marriage, thus leaving parents’ multifaceted poverty as the sole driver of the probability that an underage girl is married off before adulthood. This counterfactual experiment thus allows us to isolate the predictive power of demand (men’s preference for child brides) from that of supply (parents’ multifaceted poverty) on the prevalence of child marriage. We find that making Niger’s men indifferent between child and adult brides reduces this prevalence by 27.5%. This finding suggests that parents’ multifaceted poverty, by itself, accounts for more than 72% of the country’s prevalence of child marriage among married women aged 20 - 24 in 2012.

There are several reports on child marriage (e.g.,UNICEF and UNFPA(2010),UNFPA(2012), World Health Organization 2012(a)and 2012(b),Vogelstein(2013)), as well as case studies that measure this phenomenon in terms of its effects on demographic trends, fertility, educa-tional attainment, and other considerations (e.g.,Jensen and Thornton(2003);Clark(2004);

Field and Ambrus (2008); Lloyd and Mensch(2008); Nguyen and Wodon(2012)). Wahhaj

(2015) provides the first systematic attempt at modeling the effect of demand-side factors, namely the added value men attach to marriage with underage girls, with an application to South Asia. We contribute to this literature by evaluating the quantitative importance of the added value developing countries men attach to marriage with underage girls.

The remainder of this article is structured as followed. Section 2 presents the model and its qualitative properties. Section 3 presents the quantitative analysis, and Section 4 concludes.

1.2

A Model of Child Marriage

In this section, we describe a simple model of parents’ timing of own-daughter’s marriage that incorporates both supply factors— parents’ incentives to marry off their underage daughters— and demand factors— the added value men attach to marriage with underage girls.

According to the 2012 DHS for Niger, the timing of women’s marriage is predominantly their parents’ decision. Consistent with this evidence, we assume that there is a measure N of underage girls, each associated with one household, with parents (the father and the mother, or adult legal guardians) as joint decision makers. Thus N is both the measure of underage girls and that of households in this environment. Each household’s decision on the timing of their daughter’s marriage is binary. In each household i, parents may either marry off their daughter at ti=0, when she is still underage, or delay her marriage until time

t_i =1, when she legally becomes adult, so as to nurture her social, emotional, and cognitive development in the meantime. Marriage-timing is important to all individuals, but, to keep the focus on the drivers of child marriage, we restrict our attention to the marriage-timing decisions involving the N underage girls. Out of these N underage girls, a measure m∈ [0, N] will be married off before their 18th birthday. We normalize N to unity, and interpret m as the prevalence of child marriage in this environment.

The child marriage decision, ti∈ {0, 1}, is linked to the parents’ socioeconomic outcomes, as

determined by their average number of years of schooling completed, Si, and their

house-hold standard of living measured by an appropriately scaled wealth index, Wi. Household’s

standard of living may be determined from ownership of poultry, livestock, a farm, the sup-ply of labor services, and other sources of livelihood. For each household i, the average level of education of parents is obtained by adding up the father’s and the mother’s years of schooling completed, and by dividing this sum by 2. Thus both Si and Wiare measured on

a continuous scale.

1.2.1 Household’s Payoff

From the viewpoint of a household with an underage girl, the timing of the daughter’s mar-riage has a utility payoff. Considerations of both household survival and daughter’s well-being underlie the structure of this payoff. Indeed, parents care about the level of economic stability of their household, denoted as h, as well as their daughter’s level of well-being, denoted as b.

In each household i, let the parents’ payoff function be additive separable in the household’s level of economic stability and the child’s level of well-being:

Ui:=hi+βbi, (1.1)

for all i, where β is a positive scalar that converts units of child’s well-being into equivalent units of household economic stability. Conceptually, we expect the terms biand hito capture

incentives, forces and constraints that put an underage girl at a risk of becoming a child bride. The structure of these payoff components reflects the idea that both the demand for, and the supply of, underage brides must simultaneously exist for there to be child marriage.

In other words, we structure biand hiso that their respective levels reflect both demand-side

and supply-side factors.

Marriage-Timing and Household Economic Stability

We link the level of household economic stability, hi, to the level of household per capita

expenditures on each of the ¯η household members, with ¯η >0. Without loss of generality, we assume equal household size, ¯η. If parents in household i decides to delay their daugh-ter’s marriage (i.e., ti =1) they will have to allocate a share of household wealth, Wi, to

ex-penditures aimed at nurturing her development (including food, clothing, health care, and education). Assuming that each member of the household receives an equal share of house-hold income, the level of househouse-hold economic stability associated with this marriage-timing strategy is

hi=ln

Wi

¯η , (1.2)

Expression 1.2 reflects the fact that, having a lot of mouths to feed (i.e., ¯η high) tends to reduce the level of per capita expenditures on each household member.

Next, suppose that parents in household i decide to marry off their underage daughter in-stead (i.e., ti =0). Then the child bride immediately leaves the family home. From the

parents’ viewpoint, the decision to marry off their underage daughter will release house-hold resources for alternative uses, and may also add to househouse-hold resources as well. This is particularly the case in the context of sub-Saharan African countries, where it is customary for the groom’s family to pay a brideprice to the bride’s family. We therefore denote the level of resources added to the family through brideprice by εωeg, where ε∈ (0, 1), and ωgdenotes the average level of wealth of potential grooms in this environment, implying that the bride-price does not vary across households.4 Thus, if parents in household i decides to marry off their underage daughter (i.e., ti=0), the household’s level of economic stability becomes:

hi=ln  Wi+εωeg ¯η−1  , (1.3)

all i, reflecting both the facts that there is one less mouth to feed ( ¯η−1) and more resources for the household (Wi+εωeg). This pecuniary gain from adhering to the traditional institution of child marriage is one of the determinants of parents’ incentive to marry off their underage daughter.

Since ti∈ {0, 1}, we can express the level of household economic stability more generally as

a function of parents’ decision, ti, making use of1.2and1.3:

H(ti) =ln  Wi+ (1−ti)εωeg ¯η− (1−ti)  , (1.4)

4_{In a survey of the literature on brideprice and dowries,Anderson(2007) finds evidence that the amount of}

all i. This completes the structuring of the link between the household’s level of economic stability, H(ti), and the parents’ decision on the timing of their daughter’s marriage, ti.

Marriage-Timing and Daughter’s Future Well-being

Next, we turn to the impact parents’ marriage-timing decision, ti, has on their daughter’s

well-being (both present and future) as perceived by themselves, and denoted as bi. Child

education is seen by international organizations as (e.g., UNICEF) protecting the rights of children and a viable alternative to child marriage. This raises the issue of why parents in countries’ reporting a high prevalence of child marriage do not choose the former. Our model incorporates this issue by linking a girl’s outcomes (education or marriage) to both parental socioeconomic outcomes (their average level of education, Si, and level of combined

wealth, Wi) and the value men attach to having underage brides, φ.

The choice of education and standard of living as key parental characteristics is motivated by a large literature that links these two socioeconomic outcomes to a child’s outcomes (e.g.,Mirza and Knighton(2002), andFoley et al. (2014)). On the one hand, household re-sources invested in nurturing the child (education and nutrition) contribute to her future prospects (better health and higher educational attainment) proportionately to the level in-vested, Wi/ ¯η. This implies that the more resources the household invests in the child, the

better her present and future prospects when adult. By contrast, a poor household may be hampered in its ability to enhance the child’s future prospects through participation in schooling. For example, a pubescent girl whose needs are not well provided for may be more tempted to adopt a risky sexual behavior that could lead to out-of-wedlock teenage pregnancy. Parents may thus fear that if they do not have sufficient resources to adequately invest in their daughter’s nurturing, she may be at risk of becoming victim to out-of-wedlock teenage pregnancy, and this may undermine her present and future prospects (as well as add to household expenditures). This feature of the relation between the amount of resources in-vested in the child and her well-being (both present and future) is consistent with empirical evidence showing that richer parents may have a comparative advantage at delaying the marriage of their underage daughters (UNFPA(2013);Jensen and Thornton(2003);UNFPA

(2012)).

Further, children’s education may be undervalued by parents when they themselves have low or no education (Foley et al.,2014). Better educated parents may thus put more value on child education because they are more able to create an environment wherein the child’s learning ability can be stimulated leading to success in school. In some African societies, this has justified child out-fostering, as a strategy for improving the child’s outcome (Serra

(2009)). What is more, educated parents are more able to access news from the mass media informing families about the health risks associated with girls’ early marriage, leading them to put more value on their daughter’s education. We take these facts into consideration

in modeling bi. In particular, our modeling of bi reflects the fact that undervaluation of

children’s education by uneducated parents may lower their resistance to child marriage, despite knowledge of its harmful effects.

To capture the role played by the demand for child brides, we let φ∈ [−1, 1] denote the exogenously given relative value men attach to having a child bride. φ = −1 means that men do not value child brides at all, and only value adult brides. Thus when φ= −1, men will never consider marrying underage girls. By contrast, φ=1 means that men only desire child brides, and will not consider having adult brides. As long as−1<φ<1, men value

both child and adult brides. When φ=0, men are indifferent between child and adult brides. Where φ∈ (0, 1), men will be said to have a preference bias for child brides, because they attach an added value (i.e., φ>0) to having a child bride, and so will only consider having an adult bride as a second-best option. The opposite is true where φ∈ (−1, 0).

Suppose first that parents in household i decide to time their daughter’s marriage at ti=1

(i.e., they delay her marriage so as to nurture her cognitive and emotional development in the meantime, say through participation in schooling). From the parents’ standpoint, and as argued above, the impact this decision will have on their daughter’s well-being depends on their socioeconomic outcomes,(Si, Wi), but also on the added value men attach to having

child brides. Indeed, to the extent that marriage is the institution that organizes reproduc-tion, and parents adhere to it as is the case worldwide, they may see no gain in delaying their underage daughter’s participation in the marriage market, if men only want underage brides (i.e., φ=1). To capture this fact, we assume that the benefits to parents of delaying their daughter’s marriage until she is legally adult (aged 18 or above) is decreasing in the value men attached to marriage with underage brides, φ. More formally therefore, if parents with combined socioeconomic outcomes (Si, Wi)in household i time their daughter’s

mar-riage at ti =1 (i.e., they delay their daughter’s marriage until adulthood), this choice will

lead to the following level of well-being for the daughter (as perceived by her parents):

bi=ln " (1−φ) (Si)γ  Wi ¯η 1−γ# , (1.5)

where γ ∈ (0, 1). The parameter γ measures the relative importance of average parental education in the process of nurturing the cognitive and emotional development of their un-derage daughter. Expression1.5implies that if φ=1, i.e., men only want underage brides, then bi= −∞, which makes the decision ti=1 infeasible under these circumstances.

Next, suppose that parents in household i time their daughter’s marriage at t=0 (i.e., they marry her off before her 18th birthday), the outcome of this strategy depends on the probabil-ity that the daughter escapes poor emotional and reproductive health due to early marriage. The child marriage literature (e.g.; Nawal (2006) and 2009) documents the harmful effects of child marriage on the girls involved. The probability that a child brides experience poor

physical and emotional health as a result of child marriage thus incorporates this stylized feature of child marriage.

More formally, let ρ∈ (0, 1)denote the exogenously given probability that a girl experiences poor emotional and/or reproductive health as a result of early marriage. Assume without loss of generality that parents know ρ.5 Then, from the viewpoint of the parents, the expected level of daughter’s well-being resulting from the decision to marry her off before she is adult (ti=0) is given by:

bi= (1−ρ)ln(1+φ)ωeg , (1.6) all i, where, just to recall,ωegdenotes the average level of wealth of potential grooms in this environment. Observe from 1.6that when φ= −1, i.e., men do not value underage brides, b_i = −∞, which makes the decision t_i=0 unfeasible from parents standpoint. Therefore, in order for ti=0 and ti=1 to both be feasible marriage-timing choices, φ must satisfy

−1<φ<1. (1.7)

In other words, the demand for child brides must exist in order for child marriage to occur. This feasibility condition will be assumed to hold throughout the remainder of this study.

To sum up, the link between household i’s marriage-timing decision, ti, and its consequences

on the daughter’s well-being is more generally characterized as follows, making use of1.5

and1.6: B(ti) =tiln " (1−φ) (Si)γ  Wi ¯η 1−γ# + (1−ti) (1−ρ)ln(1+φ)ωeg , (1.8) all i.

1.2.2 Optimization and the Level of Prevalence of Child Marriage

Parents in each household make an optimizing decision on the basis of their combined socioeconomic outcomes, (S_i, Wi), and the payoff associated with each of the

marriage-timing strategies. Let Pi(ti, φ, Si, Wi)denote the payoff to household i when parents play

the marriage-timing strategy ti. From1.1, substituting in1.4and1.8, yields:

Pi(ti, φ, Si, Wi) =H(ti) +βB(ti), i=1, ..., N. (1.9)

If, in household i, parents time their underage daughter’s marriage at ti ∈ {0, 1}, then by

optimality, it must be that:

ti=arg max ti∈{0,1}P

i_(t

i, φ, Si, Wi). (1.10)

5_{In reality, this need not be the case, as lack of education coupled with traditional customs and beliefs may}

hinder parental understanding of the harmful effects of child marriage. Relaxing this assumption will only reinforce our results.

In other words, in each household i, parents make their marriage-timing decision by bal-ancing between Pi(0, φ, Si, Wi)and Pi(1, φ, Si, Wi). A simple cutoff rule in terms of parental

socioeconomic outcomes, (Si, Wi), therefore determines a household’s optimal decision. In

particular, using 1.4 and 1.8, it follows that parents in household i choose to delay their daughter’s marriage (i.e., ti=1), if and only if, given φ, they have combined socioeconomic

outcomes,(Si, Wi), such that

I(Si, Wi) ≥ ¯η ¯η−1 "  (1+φ)ωeg 1−ρ (1−φ) #β ≡ϕ(φ). (1.11)

They prefer to marry her off instead (i.e., ti=0), if and only if

I(Si, Wi) <ϕ(φ), (1.12) where I(Si, Wi):= h (Si)γ(Wi/ ¯n)1−γ iβ Wi Wi+εωeg , (1.13)

for all i. Since, by construction, ϕ(−1) =0, and I(Si, Wi) >0 for all φ, it can be seen from 1.11and1.12that there is no child marriage in this environment unless φ> −1.

Note that, from 1.13, it can be shown that I(Si, Wi) < ϕ(φ)is equivalent to Si <χ(Wi, φ),

where χ(Wi, φ):=    Wi+εωeg
ϕ(φ) 1 β (Wi) 1 β   1 γ  ¯η Wi 1−_γγ (1.14)

denotes the threshold level of average parental educational attainment in household i below which there is a gain from marrying off the underage age girl. Since ϕ0 >0, by partial differentiation of1.14, it follows that

∂χ ∂φ

>0.

In other words, the threshold average level of education below which parents in household i gain from marrying off their underage daughter is higher, the higher the demand for child brides as measured by φ. Furthermore, the wealthier a household, the lower the threshold average level of education below which they gain from marrying off their underage daugh-ter:

∂χ ∂Wi

<0.

Let Ωm ⊂ [0, 1] denote the set of households who gain from marrying off their underage

daughter:

Given our normalization of the population size of underage girls in this environment, Ωm

is also the set of all child brides. If we pick an underage girl i randomly from the total population of underage girls,[0, 1], the probability that she is married off before she reaches the legal age, denoted as Pr(i∈Ω_m), is given as follows:

M(φ) =Pr(i∈Ωm):=Pr[S<χ(ω, φ)], (1.15)

where ω denotes the realization of the random variable W, and χ(ω, φ), that of the random

variable S. By the law of large numbers, and given our normalization of the size of the population of underage girls, this probability can be interpreted as the prevalence of child marriage in this environment, m∈ [0, 1]. This prevalence can thus be reformulated as follows:

m≡M(φ) = Z ∞ 0 Z _χ(_ω,φ) 0 h (s, u)ds  dω, (1.16)

where s and ω denote realizations of the random variables S and W respectively, and, h(s, ω), the joint probability density function of the random pair (S, W). Partial differentiation of

1.16with respect to φ leads to the following result:

Proposition 1. Under condition1.7, the prevalence of child marriage is higher, the higher the added value men attach to having a child bride: M0>0.

This result raises the following issue: how quantitatively important is the impact, on the prevalence of child marriage, of a reduction in φ? This issue is the subject of the counterfac-tual thought experiment we undertake in the next section.

1.3

Quantitative Analysis

In this section we aim to achieve two objectives. First, we aim to quantitatively assess the added value men in Niger attach to having child brides, φ, by calibrating our model so as to match Niger’s DHS data. This amounts to estimating the parameters of the probability function M(.) defined in 1.16. Second, given the calibrated value of φ, we aim to probe the predictive power of φ on the prevalence of child marriage. The data supporting this estimation process comes from Niger’s DHS.

1.3.1 Data

For our quantitative analysis, we need data on the prevalence of child marriage, m, and on parents’ socioeconomic outcomes,(S, W). The data for the prevalence rate of child marriage comes from the 2012 DHS for Niger. The DHS data contains information about women aged 15 and above, including their number of years of schooling completed, their age at first marriage, their husband’s age and number of years of schooling completed if married, their marital household standard of living, etc.. We use the 2012 DHS to extract the prevalence

of child marriage, m, among women aged 20−24 at the time the survey. The reported prevalence goes from a country low of 32.82% in Niamey, to a high of 88.60% in the sub-national region of Maradi, leading to a country average of 76.27%, the highest prevalence in the world.

A major problem with the DHS however is that it is not a longitudinal survey. This im-plies that we cannot directly trace back the socioeconomic outcomes of survey respondents’ parents. To get around this problem, we use a proxy for parents socioeconomic outcomes constructed as follows. First, key findings of the 2012 DHS show that the median age at first marriage in Niger is 15.7 for women. Arguably, among married women aged 20−24 in 2012, many of those who identified themselves in the survey as child brides were married off around the year 2006, when they were aged between 14−18. Second, the median age at first birth is 18.6 in 2006. Third, the average fertility rate in Niger is 7.6. These three facts put together make it highly plausible that women aged 25−49 in 2006 are those most likely to have daughters aged 20−24 in 2012. We therefore target the socioeconomic outcomes of married couples in which the wives were aged 25−49 in 2006 as a proxy of the socioeco-nomic outcomes of the population of parents whose married daughters were aged 20−24 in 2012.

For each married couple identified in the 2006 DHS and for which the wife was aged 25−49, we compute the average number of years of schooling completed by the husband and his wife (Si). We also compute an index of household standard of living (Wi), built from

respon-dents’ answers to the DHS questionnaire on living standards. We thus obtain a bivariate sample{(S1, W1), ...,(Sn, Wn)}, where n denotes the sample size. Table1.1below presents

summary statistics relative to this bivariate sample.

Summary Statistics for Niger

Variables n Median S Median W s ¯s ω ω¯

Values 4384 0 0.37373 0 21 0.1543 5.6989

Table 1.1: Summary statistics for Niger

The terms s and ω denote the lowest observations for average years of schooling completed, S, and household standard of living, W, respectively. Likewise the terms ¯s and ¯ω denote

highest observations and n, the sample size. As can be seen from Table 1.1, the mean of average years of schooling completed by married couples identified in the 2006 DHS as those in which the wife was aged 25−49 at the time of the survey is close to zero, suggesting a high rates of illiteracy among married couples in Niger.

1.3.2 A Copula-Based Approach for Parameterizing the Probability of Being A Child Bride

Just to recall we calibrate our model by estimating the parameters of the probability function m≡ M(φ) specified in 1.16. In this sub-section, we lay out the empirical approach used

to estimate these parameters. Our calibration proceeds in three steps. In a first step, we formulate and estimate a parametric model for the unknown pdf, h(s, ω), using a copula-based approach. In a second step, we use Niger’s DHS database to assign numerical values for the parameters of the cut-off function, χ(.), specified in 1.14 above. In the final step, we calibrate the added value men attach to having a child bride, φ, by using the parametric function, M(.), to match the observed prevalence of child marriage among Niger’s married women aged 20−24 in the 2012 DHS.

A Copula-Based Approach for Modeling the Joint pdf, h(s, ω)

As stated above, to calibrate φ, we must first estimate the parametric structure of the un-known joint pdf, h(s, ω). FollowingGenest and Favre(2007), we adopt a copula-based ap-proach for building and estimating a parametric model for h(s, ω). The two random vari-ables of interest are, for each household, the parents’ average number of years of schooling completed (S) and their combined household wealth (W), both of which are measured on a continuous scale. From Sklar’s 1959 theorem,6 the joint cdf, H(s, ω), of these two continuous outcomes has a unique copula representation, in terms of its margins, F(s)and G(ω), and

the copula function, C(.; θ), that binds these two margins together:

H(s, ω):=C(u, v; θ), (1.17)

where u :=F(s) ∈ [0, 1], v :=G(ω) ∈ [0, 1], and θ denotes the dependence parameter.

There are three estimation issues we must resolve to make effective use of this copula-based approach for estimating a parametric model for the joint pdf, h(s, ω). These issues stem from the fact that, as can be seen from1.17, the copula approach parametrizes the unknown cdf, H(s, ω), instead of its pdf, h(s, ω).

The first issue is how to recover the needed pdf, h(s, ω), from1.17. Since the joint bivari-ate cdf, H(s, ω), describes the behavior of two continuous random variables, this issue has a simple solution: the pdf h(s, ω) is simply determined as the cross-partial derivative

∂2C[u, v; θ]/∂s∂ω: h(s, ω) = f(s)g(s)c(u, v; θ) (1.18) where c(u, v; θ) =∂ 2_{C(u, v; θ)} ∂u∂v , 6_{SeeNelsen(1999).}

u :=F(s), and v :=G(ω). Notice then that while the parametric structure of the copula pdf,

c(u, v; θ), is known, those of the marginal pdfs, f(s)and g(s)are not.

This leads us to the second issue: how to estimate the unknown pdf h(s, ω)from the data, given that f(s)and g(s)are themselves unknown. We address this issue by specify a para-metric model for each margin, and by applying a maximum-likelihood-based estimation method. There are two competing estimation methods. One consists of specifying a full MLE function based on (1.18), where the parameters of each margin and the copula param-eter are estimated simultaneously. The second method consists of estimating h(s, ω)in two separate steps: in one step, the marginal pdfs f(s)and g(s)are estimated using standard univariate techniques, and in the other, the copula pdf, c(u, v; θ), is estimated. Because the former is computationally more demanding, we adopt the latter approach instead.

This choice, however, confronts us with the third and final estimation issue: how to estimate the copula pdf, c(u, v; θ), given that its parametric structure depends on the unknown mar-gins F(s) and G(ω). One solution to this problem is to apply Joe’s Inference From Margins

(IFM) method, which is a parametric two-step procedure whereby the estimation of c(u, v; θ) is performed through the maximization of a log-likelihood function based on c(u, v; θ), in which the unknown margins u :=F(s)and ν :=G(ω)are replaced by their suitable

para-metric families (Joe, 1997, chap 10). A drawback of this estimation method, however, is that it may lead to a loss of efficiency, if the margins’ respective parametric models turn out to be misspecified (Genest and Favre,2007)). For this reason, to resolve this third estimation issue, we use a rank-based semi-parametric estimation method due toGenest and Favre(2007) and also known as the maximum pseudolikelihood estimation method. This estimation method is similar to Joe’s IFM, except for the fact that the estimation of the copula function, c(u, v; θ), is carried out by replacing the unknown margins, u :=F(s)and ν :=G(ω), by their

model-free empirical counterparts determined as:

Fn(s) = 1 n+1 n

∑

∑

where rank(Si)and rank(Wi)denote the ranks of observations Siand Wirespectively, n, the

point in the support of the empirical distribution Fn(respectively Gn) is bounded away from

1, in which case the margin is always contained in the unit interval[0, 1], as required. In other words, we estimate θ with ˆθnobtained by maximizing the log-pseudolikelihood function

` (θ):= nj

∑

Recall that, to implement our estimation approach, we need to specify a copula model, C(., θ), the pdf of which is an essential component of the pseudo-likelihood function1.19. If the random variables S and W were independent, a suitable copula model would simply be the independent copula function determined as the product of the two margins, F(s)G(ω).

But if S and W are dependent, then we may have a model selection problem to resolve. Hence the importance of testing for the presence of dependence in the data between S and W.

Testing for Dependence

We perform an independence test for S and W using Niger’s 2006 DHS data. Our indepen-dence test is carried under the null hypothesis of indepenindepen-dence between S and W, and is based on the empirical copula process,pn[Cn(u, v) −uv], due toDeheuvels(1979), where

Cn(u, v):= 1 n nj

∑

denotes the empirical joint cumulative distribution function (also known as the empirical copula) for the random pair(S, W), with u :=Fn(s), v :=Gn(ω) ∈ [0, 1], and 1(·)is an

indi-cator function which takes values in[0, 1]2_{. The test uses a rank-based version of the}

Cramér-von Mises test statistic formalized byGenest and Favre(2007) and defined by

Bn= nj

∑

i=1

{Cn(ui, vi) −uivi}2, (1.21)

where ui:=Fn(Si)and vi :=Gn(Wi). Expression1.21is a measure of the distance between

the empirical joint cumulative distribution, Cn(u, v), and its independent counterpart, uv.

Table1.2below reports the test results under the null hypothesis of independence.

Independence test

Sub-national region Bn P-value

Niger 5.666541 4.9995e−05

Table 1.2: Independence test

Since the reported P-values is less than 0.05 in all 7 sub-national regions, we reject the null hypothesis of independence in favor of the alternative that the pairs (S_i, Wi)are dependent

Having thus established that the random variables S and W are associated, we must next formulate a copula model summarizing this dependence.

Selecting a Copula Model

We combine pragmatism and formal methods for selecting a suitable copula model for the two random variables. First, we present in Figure 1 below the scatter plots of normalized ranks for the pair of outcomes(S, W)for Niger, using the 2006 DHS.

Figure 1.1: Selection of Copula

Figure1.1suggests that average years of schooling completed by adults in a household (S) and household’s standard of living as measured by an appropriately scaled wealth index (W) are positively correlated in the data, with dependence particularly stronger in the right tail. This feature of dependence suggests that the two socioeconomic outcomes are more likely to simultaneously assume large values. Therefore we need to exclude from our set of candidate models copula families that generate a pattern of dependence that is weaker in the tails (such as the Frank copula family), or that is stronger only in the lower-tail (such as the Clayton copula family). Thus, the candidates are the Gaussian, Gumbel, Plackett, and t-Student copula families.

test using the Akaike Information Criterion (AIC). The AIC allows us to select the copula model that yields the highest penalized log-likelihood, 2` ˆθ
−2 dim ˆθ
, where dim ˆθ
denotes the dimension of the maximum pseudolikelihood estimator ˆθ (Joe 1997). Table 1.3 below reports the penalized log-likelihoods for the respective copula models.

Penalized likelihoods for candidate copula models Copulas Gaussian Gumbel Placket t-Student AIC 701.1855 1075.533 595.4499 681.0175

Table 1.3: Penalized likelihoods for candidate copula models

Results in Table1.3show that the Gumbel copula model, which generates a positive depen-dence that is systematically stronger in the right tail, is by far the best parametric model for the bivariate data at hand; because it yields the highest penalized log-likelihood (AIC= 10775.533). The maximum pseudo-likelihood estimator associated with the Gumbel copula is ˆθ=1.304. To interpret this dependence parameter, it is more convenient to compute its as-sociated Spearman rank correlation coefficient known as ρ or its asas-sociated Kendall τ. These moment-based correlation measures, computed using the copula package in R are ρ=0.396 and τ=0.273, respectively, implying that Niger’s DHS data features a modest positive cor-relation in parental level of education (S) and standard of living (W).

On the basis of the reported model selection results, we can then express the partially es-timated joint cdf of S and W as follows, using the parametric expression for the Gumbel copula: H(s, ω) =exp  −h(−log[F(s)])1.304+ (−log[G(ω)])1.304 i_1.3041  .

We therefore obtains cross-partially differentiating the above quantity. The next step there-fore is the estimation of the margins, F(s)and G(ω).

Modelling the Margins

As mentioned above, one of the main advantages of a copula-based approach to parametriz-ing a cdf is that it allows for the margins F and G to be estimated separately from the copula function C that binds them together (Genest and Favre(2007)). We follow a two-step proce-dure for parameterizing each of the two margins, F and G. First, we rely on visual tools to select a parametric model for each of the two margins, using the corresponding univariate sample. Figure 1.2below shows that, for each of the two variables S and W, the shape of the probability density function display a right tail (see solid black curve), corresponding to the shape of a Generalized Extreme Value (GEV) distribution function, such as the Gumbel, Fréchet, or Weibull distribution.

In a second step, using standard univariate estimation techniques, we find that the Fréchet distribution is the parametric best fit for both sets of univariate data (see dotted black curve