WELFARE COMPARISONS WHEN POPULATIONS DIFFER IN SIZE

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1 WENDGLOUMDE AGNES ZABSONRE WELFARE COMPARISONS WHEN POPULATIONS DIFFER IN SIZE Thèse présentée à la Faculté des études supérieures de l Université Laval dans le cadre du programme de doctorat en Économique pour l obtention du grade de Philosophiae Doctor (Ph.D.) FACULTÉ DES SCIENCES SOCIALES UNIVERSITÉ LAVAL QUÉBEC 20 c Wendgloumdé Agnès Zabsonré, 20

2 Résumé L objectif principal de cette thèse est de faire des comparaisons sociales impliquant des populations de taille différente. Ceci est pertinent pour deux raisons. En premier lieu, l évaluation des politiques publiques implique souvent des comparaisons de situations où le nombre d individus diffère d une situation à une autre. En second lieu, les fondements théoriques de l évaluation sociale dans le cadre des populations de taille variable fournissent peu d indications sur la façon dont les changements dans la taille et dans la distribution des populations peuvent être socialement évalués. Après avoir fait une revue de la littérature sur les problèmes de populations et particulièrement sur les questions liées à la taille et au bien-être des populations, et après avoir examiné comment évaluer socialement des populations de taille différente, nous utilisons l utilitarisme généralisé de niveau critique comme fonction d évaluation sociale. Cette fonction a des fondements éthiques satisfaisants et est appropriée pour l évaluation sociale des populations de taille variable. Mais elle requiert l usage d une valeur du niveau critique, un paramètre clé dans cette approche. Nous proposons un cadre de dominance basé sur l utilitarisme généralisé de niveau critique. Nous montrons comment cette dominance est reliée à la dominance stochastique en pauvreté. Ceci est présenté dans le premier essai. Dans le deuxième essai, nous développons un cadre théorique, normatif et statistique pour estimer des bornes inférieures et supérieures robustes des niveaux critiques sur lesquelles les distributions des populations peuvent être ordonnées. Nous illustrons les résultats théoriques en utilisant des données réelles du Canada tirées d enquêtes auprès des ménages.

3 Résumé iii Nous étendons les applications à une échelle nationale, régionale et mondiale. Les résultats indiquent de manière convaincante que la valeur de l humanité peut être considérée comme ayant globalement augmenté entre 990 et 2005, mais pas pour beaucoup de régions du monde. Ceci fait l objet du troisième essai.

4 Abstract The main objective of this thesis is to make welfare comparisons involving different population sizes. This is relevant for two reasons. First, the evaluation of public policies often implies comparisons of situations where the number of individuals differs from one situation to another. Second, the theoretical foundations of social evaluation provide little measurement guidance on how changes in population size and population distribution can be socially evaluated. After a literature review on population problems and particularly questions related to population sizes and social well-being, and after discussing how variable populations are socially evaluated, we use critical-level generalized utilitarianism as a social evaluation function. This function exhibits ethically desirable foundations and is shown to be more convenient for comparing well-being between variable populations. But it requires a value of the critical level, a key parameter in this approach. We propose a dominance framework based on critical-level generalized utilitarianism. We show how this dominance is related to stochastic poverty dominance. This is presented in the first essay. In the second essay, we develop a theoretical, normative and statistical framework to estimate some robust lower and upper bounds of critical levels within which population distributions can be ordered. We illustrate our theoretical results by using real data from Canada s household surveys. We extend the applications to national, regional and world scales. The results indicate that the value of humanity can be persuasively shown to have increased globally between 990 and 2005, but not so for many of the world s regions. This is done in the third essay.

5 Avant-propos Je dois l accomplissement de ce travail au professeur Jean-Yves Duclos et à plusieurs personnes que je voudrais remercier sans avoir la prétention de réussir à être exhaustive. Tout d abord, je remercie sincèrement mon directeur de thèse le professeur Jean- Yves Duclos pour sa disponibilité et tout ce qu il m a patiemment et généreusement enseigné. Je ne saurais oublier son soutien sans faille et l appui considérable qu il m a accordés dans la rédaction de cette thèse, notamment pendant les moments difficiles. Sans son précieux soutien, cette thèse ne serait pas arrivée à ce stade. Je suis également reconnaissante envers le professeur Jean-Yves Duclos pour m avoir préparée et soutenue pour la recherche de l emploi. Je remercie également mon co-directeur le professeur John Cockburn pour sa précieuse contribution à la réalisation de la thèse. Les discussions que j ai eues avec lui m ont apporté une aide précieuse dans mes travaux de recherche. Ses conseils et ses suggestions m ont été d une grande utilité pour la rédaction de ma thèse. Je tiens à remercier la professeure Mme Lucie Samson, la directrice du département, le professeur Sylvain Dessy, le directeur de programme de doctorat, le professeur Patrick Gonzalez et le professeur Kevin Moran pour leurs conseils. Je remercie le professeur Guy Lacroix, le directeur du Centre Interuniversitaire sur le Risque, les Politiques Économiques et l Emploi (CIRPÉE), pour l appui dans l obtention de mon stage à la Banque Mondiale. Je remercie tous les professeurs du département pour la qualité de l enseignement que j ai reçu. Je remercie Abdelkrim Araar et Sami Bibi pour m avoir soutenue dans l écriture des codes en Stata. Mes remerciements vont également à Mme Sonia

6 Avant-propos vi Moreau, Mme Gaétane Marcoux et à tout le personnel administratif avec qui j ai échangé durant ces années. Pendant ma visite à la direction de la recherche en développement (DECRG) de la Banque Mondiale, j ai eu le privilège de connaître et de sympathiser avec des personnes très accueillantes que je tiens à remercier: Peter Lanjouw, Branko Milanovic, Dominique Van De Walle, Quy-Toan Do et Roy Van Der Weide. Je voudrais aussi remercier les différents organismes qui m ont apporté un support financier tout le long de ma formation: le réseau de recherche sur les Politiques Économiques et la Pauvreté (PEP), le Centre Interuniversitaire sur le Risque, les Politiques Économiques et l Emploi (CIRPÉE) et le Fonds Québécois de Recherche sur la Société et la Culture (FQRSC). Un Merci tout particulier : À mon frère Henri pour son soutien inconditionnel dont il a fait preuve pour moi durant mes études doctorales. À ma mère Blandine Zoungrana, mon père Mathias Zabsonré, mes frères Clément, feu Éric, Frédéric, Jean De Dieu et Patrice, mes sœurs Claire, Clarisse, Denise et Jeannine, pour leurs conseils et aussi leur patience durant ces années passées loin d eux. À mon amie Nadège pour son soutien quotidien, moral et inconditionnel et les discussions fructueuses que j ai eues avec elle. À mes amis, Firmin Doko, Prosper, Raphaël, Clarence, Fulbert, Rachid, Etienne et Alice pour leurs encouragements qui m ont été bénéfiques. À la chorale des étudiants catholiques de l Université Laval, au père Jean Abud et à Papa Jean Bouda pour leur soutien spirituel. Et enfin à tous les collègues étudiants du département et particulièrement à Legrand, Firmin Vlavonou, Bouba, Yélé, Komi, Habib et Aboudrahyme pour les rapports entretenus et les discussions enrichissantes pour la réalisation de cette thèse.

7 A Dieu le Père, Dieu le Fils et Dieu l Esprit Saint et à la Vierge Marie pour toutes les grâces reçues. A ma mère Blandine, à mon père Mathias, à mes frères Clément, feu Éric, Frédéric, Henri, Jean De Dieu et Patrice et à mes sœurs Claire, Clarisse, Denise et Jeannine.

8 Contents Résumé Abstract Avant-propos Contents List of Figures List of Tables ii iv v viii xi xiii Introduction 2 Population problems and social evaluations 4 2. Is a bigger society a better one? More people leads to greater human ingenuity and higher per capita income More people, less welfare When more people and more poverty go together More people is likely to bring more social happiness Social evaluations with variable population sizes Critical-level utilitarianism Optimal population Welfare comparisons with different population sizes: a theoretical analysis Introduction CLGU: an alternative social evaluation

9 Contents ix 3.2. Definition of CLGU Definition of dominance orderings CLGU and FGT dominance equivalence Poverty dominance CLGU dominance Critical level and dominance relations Generalization to a larger set of welfare indices Conclusion Appendix Proof of Proposition Proof of Proposition Proof of Corollary Proof of footnote Testing for social orderings when populations differ in size Introduction Definitions of dominance relations Statistical inference Testing dominance Estimating robust ranges of critical levels A few simulations Illustration using Canadian data Conclusion Appendix Graphical illustrations of higher orders of dominance Proof of Theorems 2 and Asymptotic equivalence of statistics Has global welfare improved between 990 and 2005? A criticallevel utilitarian approach Introduction Related literature Definitions and dominance criteria Robust ranges of critical levels Illustration using PovcalNet data

10 Contents x 5.5. Data description Some estimated values of the critical level Comparison between CLGU and per capita approaches Conclusion Appendix Critical level bounds for developing countries Developing countries not included in PovcalNet data High-income countries included in the analysis Comparison of PovcalNet and real data Conclusion 34 References 47

11 List of Figures 3. Smaller dominates larger when z + < α Larger dominates smaller Poverty incidence curves adjusted for differences in population sizes Poverty incidence curves with α = α adjusted for differences in population sizes Poverty incidence curves with α = α adjusted for differences in population sizes Population poverty incidence curves and dominance of the larger population Population P 2 curves and dominance of the larger population Population poverty incidence curves and dominance of the smaller population Population P 2 curves and dominance of the smaller population Canadian cumulative distributions Cumulative distributions of 976 and 996 and the critical level Relation between z + and α P s curves and dominance of the larger population P s curves and dominance of the smaller population (case ) P s curves and dominance of the smaller population (case 2) Poverty incidence curves with α = α adjusted for differences in population sizes Poverty incidence curves with α = α adjusted for differences in population sizes Non-dominance of 2005 over Dominance of 2005 over

12 List of Figures xii 5.5 World 2005 dominates world dominates 2005 for ECA and SSA The increase in the absolute number of poor leads to more poverty in SSA

13 List of Tables 4. Population sizes and upper bounds of the critical level large dominates small Population sizes and lower bounds of the critical level small dominates large Asymptotic standard errors of the bounds of the critical levels First-order dominance tests Estimates of the upper bound of ranges of critical levels over which the larger population dominates the smaller one Estimates of the upper bound of the range of critical levels over which the larger population dominates the smaller one Estimates of lower bound of the critical level Population size and average income Estimation of upper bounds: 2005 dominates Values of the utilitarian social evaluation index (in billion $) Estimation of lower bounds: 990 dominates Values of upper bounds: large dominates small for Burkina

14 Chapter Introduction Does the value of a society increase with its population size? How can we answer this in a normatively robust framework? What sort of statistical procedures can be performed to test this? What does the empirical evidence suggest? To address these questions is the main contribution of this thesis. This thesis consists of three essays, but they are quite close. All these essays deal with social evaluations when populations differ in size. The motivation for such comparisons lies in the fact that the evaluation of public policies often implies situations where the number of individuals differ from one situation to another. This is also expected when comparisons are targeted toward different societies. Finally, comparisons involving different populations sizes are certainly the most generally encountered case in empirical analysis. We therefore consider populations of different sizes and we are interested in the question of whether a society s well-being increases with its population size. In Chapter 2, we review the literature on this subject. Historically, there have been two opposite views about the ideal population size. The first one follows the Malthusian view that small is better because of limited available resources. The second one is based on Bentham s view and advocates that large is better. Although the recent literature develops some economic models to deal with this question, the results of

15 Chapter. Introduction 2 studies are sometimes ambivalent. Four different conclusions can emerge from the studies: (i) more people lead to greater human ingenuity and higher per capita income; (ii) more people are likely to bring more social happiness; (iii) more people, less welfare; (iv) more people and more poverty go together. The first conclusion derives essentially from positive arguments. The three last conclusions are based more on normative arguments. Given that most of these studies use some social evaluation objectives to deal with the question of size and value, we may be interested in knowing if such social evaluations are to be favored, for instance, in case of comparing alternative public policies involving different population sizes. Note that social evaluation rankings are easily made when populations have the same size. However, this is not the case when sizes differ. In that situation, the tradition has been to overcome the problem of variable sizes by calling on the replication invariance principle. In this case, social evaluation is made in per capita terms and then sizes do not substantially matter. However, as Blackorby, Bossert, and Donaldson (2005) have argued, population sizes should sometimes matter when comparing aggregate welfare. The thesis develops this idea and follows the critical-level principle. In the literature, Blackorby and Donaldson (984) were the first who introduced the notion of the critical-level principle. This principle suggests that further individuals with welfare above a value of the critical level to an existing population can be considered as improving the social welfare of the population. In other words, the critical level reflects how much a life must be minimally worth to contribute positively to society s welfare. The critical-level principle can be used to socially evaluate populations of different sizes. But this principle requires the choice of the value of the critical level, which remains the main problem of this approach. Until now, few studies have addressed this issue in the literature.

16 Chapter. Introduction 3 The first essay is presented in Chapter 3. It develops and presents some theoretical results for stochastic dominance with varying population sizes. The purpose is to extend traditional critical-level generalized utilitarianism (CLGU) analysis by considering arbitrary orders of social welfare dominance and ranges of poverty lines and values for the critical level. This essay draws from the procedure developed by Duclos and Makdissi (2004). Links between critical levels and orders of dominance are also investigated. We also introduce how to generalize the Blackorby and Donaldson (984) s critical-level principle. The second essay is contained in Chapter 4. This essay performs a statistical inference analysis taking into account changes in population sizes and population distributions. A few simulations are made to show the effect of population size on social evaluation. The essay also derives the asymptotic distributions of some lower and upper bounds of robust ranges of critical levels. An empirical application is made using Canadian Surveys of Consumer Finances (SCF) for 976 and 986, and Canadian Surveys of Labour and Income Dynamics (SLID) for 996 and Using asymptotic and bootstrap tests, we find that Canada s welfare has globally improved in the last 35 years despite the substantial increase in population size. The third essay, presented in Chapter 5, is primarily empirical. It aims at extending the application of the CLGU approach to regional and world scales using data from most countries in the world. The objective is to assess whether the value of humanity has increased between 990 and 2005 despite a substantial increase in world population size. We estimate the bounds of the critical levels for all developing countries, for regions and for the entire world. In addition to results obtained in Chapter 4, such estimations show how the process of demographic transition, in which a large part of humanity has recently engaged, may be assessed through a CLGU approach. We also compare the CLGU approach to the traditional per capita one.

17 Chapter 2 Population problems and social evaluations This chapter reviews the linkages between population size and population wellbeing. It explores whether societies are better off with smaller populations or bigger populations. This requires using social evaluation functions that can take account differences in population size to assess society s value as a whole. The choice of these functions is guided by economic objectives and also by some ethical and normative foundations. In such a setting, social evaluations also lead to important implications in terms of public policies. The first section summarizes the principal conclusions that emerge from the links between a population s size and its well-being. The second section discusses how changes in population size and population distribution are socially evaluated. 2. Is a bigger society a better one? This question sparks off many reactions according to our understanding of what we call a better society. Does it imply higher per capita income? A happier society?

18 Chapter 2. Population problems and social evaluations 5 We can focus on two views: those who believe that a larger population is usually better (the positive view) and those who do not (the negative view). The first view s argument is generally based on the idea that a large population favors development. This stems from the neoclassical theory of the impact of population growth on economic growth. Population growth induces infrastructure and market development, and influences positively technological change and innovation. This in turn raises per capita income and growth, and therefore leads to a higher level of welfare. The second view emphasizes that population growth leads to more deprivation in common dimensions (standards of living, education, health, etc.). The gist of the second view seems to be guided by an observable fact : poor countries are associated with rapid population growth and lower per capita income, while rich countries have lower rates of population growth and higher per capita income. The two views are motivated by both positive and normative arguments. 2.. More people leads to greater human ingenuity and higher per capita income The literature that supports this positive view relies on the arguments of Boserup (965), Boserup (98) and Simon (98) that a greater population is an important driver of technological change and innovation and encourages organizational and institutional change. A larger population also allows for scale economies in production and consumption. The historical features of Boserup and Simon s argument are the empirical investigations of Kremer (993) and Acemoglu, Johnson, and Robinson (2005). Using a model of population and endogenous technological change, Kremer supposes that technology is a pure public good. He also assumes that each individual s research productivity is independent of population size and that the population growth rate is limited by the state of food production. He suggests a linear relationship between population growth and population size. He shows that larger initial

19 Chapter 2. Population problems and social evaluations 6 populations without technological contact enjoy faster technological progress and population growth. Acemoglu, Johnson and Robinson show that the growth of urbanization between 300 and 850, with the access to Atlantic Trade and a favourable institutional environment, are the factors that explain the modern economic development of Western Europe. Using Kremer s model, Klasen and Nestmann (2006) incorporate population density as an additional positive determinant of technological change. Even if an increase in population leads to a greater number of potential suppliers of new technology, high density generates the linkages. It facilitates communication and exchange and raises the demand and the diffusion of technological innovations, which could in turn increase the quantity of available resources. This suggests why some people think that human inventiveness and ingenuity are capable of enhancing Earth s capacity to support the species indefinitely and to support it at a high standard of living (Dasgupta 2005, p. 46). Easterly and Levine (997) also emphasize the importance of population density. They argue that low density in Africa has some negative effects such as greater ethnic divisions. In addition, they conclude that ethnic divisions have something to do with Africa s poor economic development. All these models are consistent with endogenous growth models that find that the size of populations and also population density have a positive impact on the growth of per capita income (see, for instance, Grossman 99, Aghion and Howitt 992, Aghion and Howitt 998 and Jones 999). Some implications of the endogenous growth theory are the external benefits of having more people. More people means a higher level of knowledge, skills and human resources avalaible for future labor shortages. This in turn increases production. This idea may be found in the French philosophers Bodin (576) and Quesnay (758), who consider the individual as playing a central role in the production of wealth. According to them, there exists a bi-directional relation between population size and standards of living. Individuals represent the labour force and the strength of the army. According to Bodin, a large population can help a country to become rich and powerful: But one should never be afraid of having too many subjects or too many

20 Chapter 2. Population problems and social evaluations 7 citizens, for the strength of the commonwealth consists in men. Moreover the greater the multitude of citizens, the greater check there is on factions seditions. For there will be many in an intermediate position between the rich and the poor, the good and the bad, the wise and the foolish. There is nothing more dangerous to the commonwealth than that its subjects should be divided into two factions, with none to mediate between them. This is the normal situation in a small commonwealth of few citizens. (Six Books of the Commonwealth, Book V, chapter II, translated by Tooley 955) In Quesnay s point of view, it is more the availability of resources that leads to population growth: That the sovereign and the nation should never lose sight of the fact that the land is the unique source of wealth, and that it is agriculture which causes wealth to increase. For the growth of wealth ensures the growth of the population. (General Maxims for the Economic Government of an Agricultural Kingdom, translated by Meek 963, p. 232) One advantage of a larger population that Bodin underlines is the sake of defense against foreign attacks. This is consistent with the view of those who see in a better society a peaceful one. A larger population itself contributes to society s welfare, in the sense that it defends a nation against its enemies. There is some literature on this issue. For instance, McNicoll (984) reviews the positive effects of having more people on military capabilities. First, populous nations, other things equal, tend to have more influence in international decisions and world affairs. Second, as nations become alike in technology and in institutional organization, an increase in population is an important source of national power, both military and industrial. Because there is a great difference in technological levels among states in the world today, Although the strength of the commonwealth is not expressed in concrete terms in the quotation, it is apparent in Bodin s definition of the sovereignty of a nation. Hall and Clark (2002), pp See for example

21 Chapter 2. Population problems and social evaluations 8 the achievement of technological equality is a distant prospect. However, for some developing countries and moreover for developed countries that are characterized by low fertility rates, population can account for a significant power factor. When the population size is very low, the survival of human race can be threatened. Using the example of a nuclear holocaust which causes the problem of endangered species, Hurka (983) argues that it is desirable in that situation to encourage population to increase, even if average well-being decreases as population increases. De La Croix and Dottori (2008) also notice that the benefit of an increase in population size was enhanced by the need for a large army. Investigating the Easter Island s collapse and the quest for greater bargaining power between conflicting groups, the biggest group had the highest probability to win the war. Nerlove, Razin, and Sadka (986) (p. 60) go on to quote Edgeworth s benefit of being larger: being must be secured before well-being. Furthermore, they extend Edgeworth s argument to public goods and claim that a larger population has an advantage in providing pure public goods. The most interesting example is national defense, because the per capita cost of providing that public good falls as the population becomes larger. More generally, public goods such as infrastructure, electricity network, telecommunications and research are recognized as having cost-reduction benefits when there is more people. Alesina and Spolaore (2003) enumerate five types of benefits of having a large population: (i) lower per capita costs of public goods and more efficient taxation. The public goods are monetary and financial institutions, the judicial system, infrastructures for communication, police and crime prevention, public health, and so on. The second type of benefits is: (ii) greater military power and lower per capita defense and military costs; (iii) increase in productivity thanks to substantial skills and large markets (however, country openness to international market can limit this factor); (iv) providing insurance; (v) greater opportunities for income redistribution (pp. 3-4). A slow population growth also has negative consequences mainly for countries with AN ageing population. Because of large proportions of elderly, pay-as-you-go transfer systems become difficult to sustain. There are also fewer and fewer workers

22 Chapter 2. Population problems and social evaluations 9 to finance investment in public goods. 2 Kravdal (200) notes the same problems and remarks that less populated regions may experience difficulties in surviving. In 2005, the European Commission publishes an official document beginning by a rather alarming content: Europe is facing today unprecedented demographic change. In 2003, the natural population increase in Europe was just 0.04 per cent per annum (...). The fertility rate everywhere is below the threshold needed to renew the population (around 2. children per woman), and has even fallen below.5 children per woman in many Member States. (Commission of the European Communities 2005, p. 2) 3 Michel Rocard, a former French prime minister set the tone two decades ago in the following terms: La plupart des états d Europe Occidentale sont en train de se suicider, de se suicider par la démographie, sans même en avoir conscience (Michel Rocard, January 20, 989, Conférence des Familles ) More people, less welfare Although there can be external benefits and advantages in the provision of public goods as populations become larger, there can also be pernicious effects of being larger. Larger populations are likely to be more heterogeneous than homogeneous. This gives rise to more diverse preferences, cultures, religions and languages within the same population. As individuals differ in many respects, they do not share the same objectives. This can result for example in conflicts and in an inefficient use of public goods. In fact, larger populations can intensify the use of non renewable resources and non-pure public goods, namely common-pool resources and club goods. 2 Unless the country adopts migration policies to adjust labor supply and to correct imbalances, the problem will worsen. In fact, some governments in developed countries now focus on maximizing the benefits of economic migration. 3 See Bloom, Canning, Fink, and Finlay (200) for the reasons justifying the rapid decline in fertility in Europe. From society s point of view, parents do not have enough children when the social benefits of having children are higher than the private benefits. 4 The quotation is taken in

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