UNIVERSITY OF PISA
SANT’ANNA SCHOOL OF ADVANCED STUDIES
DEPARTMENT OF ECONOMICS AND
MANAGEMENT
MASTER OF SCIENCE IN ECONOMICS
MASTER’S THESIS
SOCIAL CAPITAL: AN INVESTIGATION OF ITS
THEORETICAL IMPLICATIONS
Supervisor:
Candidate:
Contents
Introduction……….... 4
Chapter 1 Literature overview……….….5
1. The notion of social capital………..5
1.1 Channels of creation of social capital………10
1.2 The role of historical factors………..10
1.3 Voluntary associations………...11
1.4 Family………....12
1.5 Is there a role for the government?... 13
1.6 Measuring social capital………15
1.7 Two different views of social capital……….17
1.8 Social capital as a by-product………17
1.9 Social capital as a private good………..19
Chapter 2 Some theoretical implications of social capital………....22
The framework………...22
2.1 The Solaria syndrome: Social capital in a growing hyper-technological economy………….33
Chapter 3 Social capital, human capital and fertility……….34
Chapter 4 Social capital evolution in presence of heterogeneous agents………..…44
Conclusions………....51
Introduction
What is social capital? Social capital is not a new term in literature, but it had to wait for the ’80 to become relevant in scholars research agendas and politicians rhetoric. To this day there is no unified definition of social capi-tal. The literature is divided into two different stands. On one hand, part of the literature emphasis the accidental nature of creation of social capital as a by-product of other (relational) activities. Social scientists definitions belong to this tradition. For Coleman (1988), social capital is a resource that resides in the relationships between agents and facilitates their actions, making pos-sible the achievement of desirable outcomes. The author identifies trust as one type of resource related to membership in communities. It enables the achievement of results that would not be possible in its absence. Coleman (1988) identifies also social norms, especially the ones that impose individuals to act in the interest of the community, as they allow to overcome collective action problems. Political scientists on the other hand, consider social cap-ital as a group level attribution. Putnam (1993) defines social capcap-ital as “ features of social life - networks, norms and trust - that enable participants to act together more effectively to pursue shared objectives”. According to Put-nam, social capital is generated through repeated interaction and voluntary organizations are seen as the most important channel of creation as they of-fer a chance for people to meet and learn cooperative values and democratic attitudes. On the other hand, the economic view emphasises the private good nature of social capital, with agents rationally investing on its creation in order to maximize their economic payoff. Becker (1974) was the first to extend the neoclassical utility function in order to include the characteristics of others as a social capital variable, which presumably affect the production of a significant fraction of commodities. Individuals are assumed to have an influence on these variables and they rationally put in being actions aimed at enhancing these characteristics in order to obtain a higher payoff.
Why social capital? There is a growing empirical evidence that link so-cial capital with many economic and non economic phenomena. Knack and Keffer (1997) investigate empirically the effects of one dimension of social capital, namely trust, on annual average growth of income, using data from twenty nine different countries. Their findings show that trust is positively and significantly related to growth. Its effect is higher in poor countries. The authors identify several channels through which trust operates: it affects in-vestment levels through the facilitation of access to credit. Informal credit markets have a strong component of trust, and they act as substitutes of for-mal markets in places where these are not developed. In other cases the two coexist since individuals who are wealth constrained are normally excluded from the later. In a high trust society the promises of the government and other public authorities are trustworthy and this helps people make better decisions in terms of investment and other productive activities. In addition, trust also increases the return to education, as in low-trust societies hiring is based more on the personal knowledge of the employee, thus discriminat-ing those with similar education levels but without the right connections. Putnam (1993) studies the differences in institutional performance between north and south Italy. He finds evidence that institutional performance is higher in regions in which social capital, characterized by active participa-tion of citizens in public affairs, equality of rights and obligaparticipa-tions, solidarity, trustworthiness etc., is higher.
This work focuses on two theoretical contributions on the social capital literature. The first is an investigation on the role that technology might have in determining the dynamics of social capital accumulation. The au-thors built a model in which agents maximize a utility function depending on a private good and on a socially provided good. The rate of substitution between the two goods is a crucial determinant of the dynamics of the econ-omy and technology plays a role as it affects this rate. What the authors find is that if technology determines higher returns in the private sector and
the rate of technological change is high, than if the goods are substitutes the economy runs the risk of falling into a social povery trap, ie. a situation in which social participation is constantly low. On the contrary when the goods are complements and the rate of technological change is high, their comple-mentarity precludes the possibility of falling into the trap. When technology determines higher returns in the relational sector and the goods are substi-tutes, individuals are willing to replace material goods with relational ones, causing the stock of social capital to grow. Contrary to the popular belief that sees technology as a possible destruction to human interactions, this paper finds that it is not always the case. In some situations like the ones described above, technology can help preserve ties between individuals, in a context in which time is more and more scarce.
The second paper is an investigation of the role social capital plays in determining fertility decisions. The authors extend the traditional quantity-quality trade off framework, in order to include social capital variables which are said to have an effect on fertility through two channels. Firstly they increase the returns to education and secondly they make time spent in social participation more rewarding. In presence of time constraints and budget constraints, this implies a preference for quality over quantity. What the authors find indeed, is that social capital is negatively related to fertility. If the stock of social capital is low, the economy will fall into a social poverty trap, where people don’t invest in human capital and fertility rates are high. On the other hand, a high stock of social capital can sustain growth through the effects it has on human capital accumulation, but only in the case in which investment in education is positive. If the returns to education are low and people don’t invest, there is no role for social capital to play and the risk of falling into the trap remains present.
The last part of this thesis is an attempt to bring together the two stands of the literature, by proposing an elementary model of social capital accu-mulation in which agents are heterogeneous with respect to the way they
consider the dynamics of social capital into their utility functions. In partic-ular, some agents explicitly consider the dynamics into their maximization problem, and rationally invest in social capital in order to obtain a higher payoff. Others are more shortsighted and only obtain social capital as a by-product of other activities. What emerges from this part, is the fundamental role of expectations regarding the others behavior. In presence of negative expectations about the others’ investment in social capital, the economy will end up in a social poverty trap.
The thesis is organized as follows. Chapter one makes a literature overview, illustrating the main contributions in social capital research. Chapters 2 and 3 analyze two influential articles with the aim to understand their formal structure and implications in terms of policy prescriptions. Chapter 4 pro-poses a hybrid model for the study of the dynamics of social capital accumu-lation and presents some conclusions arising from the present work.
Chapter 1 - Literature overview
1
The notion of social capital
Social capital as a concept is all but new. The first appearance of the term is attributed to the author Lyda Hanifan. In a book published in 1916 in the United States, she defined it as “those tangible assets [that] count for most in the daily lives of people: namely goodwill, fellowship, sympathy, and social intercourse among the individuals and families who make up a social unit”. However, it wasn’t until the ’90, with the works of Coleman and Putnam, that the term started gaining increasing attention from scholars and policy makers around the world. The perfectly rational individual, making deci-sions in isolation in order to maximize his utility function, doesn’t fit very well a range of real world situations. Individuals do not act independently, but as part of networks which have influences on their behavior and whose behavior feeds back in the network. The fact that social capital has been studied by different disciplines means that there is not a single definition but a plurality of definitions, each focusing on some different aspect. Coleman (1988), defines social capital as advantages that individuals get from being members of communities. According to the author “Social capital constitutes a particular kind of resource available to an actor. It is not a single entity but a variety of different entities with two elements in common: they all consist of some aspect of social structure and they facilitate certain actions of the actors within the structure”. From this point of view, social capital is a resource that resides in the relationships between agents. The author identifies trust as one type of resource related to membership in communi-ties. It enables the achievement of outcomes that would not be possible in its absence. Knack and Keffer (1997) argue that trust becomes especially important in all those transactions in which one part has to rely in a future action of the other part. In employment contracts for example, the presence
of trust allows the completement of tasks that are difficult to monitor and reduces the monitoring costs whenever control is possible. In the case of en-terprises this is important and is argued that it helps innovation through the additional financial resources and time that are not devoted to monitoring. The promises of the government and other public authorities are trustworthy and this helps people make better decisions in terms of investment and other productive activities. In addition, trust affects investment levels through the facilitation of access to credit. Informal credit markets have a strong compo-nent of trust, and they act as substitutes of formal markets in places where these are not developed. In other cases the two coexist since individuals who are wealth constrained are normally excluded from the later. Trust also in-creases the return to education, as in low-trust societies hiring is based more on the personal knowledge of the employee, thus discriminating those with similar education levels but without the right connections. The authors in-vestigate empirically the effects of trust on annual average growth of income, using data from twenty nine different countries. Their findings show that trust is positively and significantly related to growth, through the quality of government and confidence in financial markets which facilitates invest-ment. Its effect is higher in poor countries where contracts are not efficiently enforced by the legal system and where access to formal credit markets is limited (Knack and Keffer, 1997). Trust however is not the only resource that resides in relationships between individuals. Coleman (1988) identifies also social norms, especially the ones that impose individuals to act in the interest of the community, as they allow to overcome collective action prob-lems. The effectiveness of these norms is made possible by a property of the social structure called closure. It means that given three individuals, if the actions of one of them are harming the other two, than these two have to be able to join forces to stop the harmful action. They can only do so if they are connected to each other. In this case we say that the norms are effective. Different groups adhere to different norms and some of them have negative
effects for the community or the society as a whole. Portes (1998) observes that the same ties that hold together members of a group, can prevent oth-ers from accessing, and this group closure can prevent business initiatives. Social norms can also act as constraints on individual freedoms because of the claim they put on the individual to conform.
Building on the theoretical principles suggested by Coleman, but differing from him under certain aspects, Putnam (1993) defines social capital as “ features of social life - networks, norms and trust - that enable participants to act together more effectively to pursue shared objectives”. This definition and others in the political science tradition, consider social capital as a group level attribution and not as an individual one.
In a path breaking work, Putnam studies the differences in institutional performance between north and south Italy. He finds evidence that institu-tional performance is linked to civic community, which is characterized by active participation of citizens in public affairs, equality of rights and obliga-tions, solidarity, trustworthiness etc. Civic community itself has its roots in the medieval era, when the organization of the north was based on horizontal relationships which provided mutual assistance, whereas the south was based on a hierarchical structure. Regions with higher civic engagement, as mea-sured by a set of four indicators, namely newspaper readership, voter turnout at referendum, the incidence of preference voting and associational activity have a higher institutional performance, where performance is measured by a composite index formed by twelve indicators ranging from legislative innova-tion to bureaucratic responsiveness. According to the author, this happens because when political negotiation is embedded in a network of social inter-actions, incentives for opportunism are reduced. In a later work, Putnam (1995) studies the trends of civic participation in America and finds evidence that it has been declining. Indicators such as voter turnout, attending of political meetings, participation in religious organizations or in labor unions, have all reduced. This reduction has not been compensated by new forms
of civic engagement such as tertiary organizations, non profit organizations and support groups. Putnam attributes the poor state of social conditions as well as the worsening of economic conditions in the American Society to this decline of social capital.
Social capital does not affect only economic outcomes or institutional performance. A number of studies link it directly to people’s happiness. Traditional economic theory measures well-being through utility functions depending on consumption goods and leisure. This has led to the usage of Gross Domestic Product as the main indicator of the subjective well-being of a nation. Policies have long focused on growth of GDP as a way of increasing happiness among residents. However, self declared levels of happiness show that increasing income does not always lead to more subjective well-being, the so called the Easterlin’s paradox. A large number of psychological studies have shown that happiness depends in great part on relational goods. Bec-chetti, Pelloni, Rossetti, (2008) define relational goods as goods that include companionship, emotional support, social approval, the desire to be loved or recognized by others etc. These goods are produced by family relation-ships or friendrelation-ships and in many kinds of social events (club or association meetings, live sport events, etc.). The authors use time dedicated to vol-unteering, time spent with friends, attending social gatherings and cultural and sports events as relational activity indicators and test empirically their impact on life satisfaction. Their findings show that all the above indicators of relational goods are positively associated with self-declared happiness.
Ostrom (1997) studies how decision making is different in presence of so-cial capital. The rational theory of decision making predicts that individuals will act selfishly and always choose the option that gives the highest payoff in order to maximize their utility. However, a number of real world cases as well as laboratory experiments show that it is not always the case. To illustrate it we will refer to individual behavior in social dilemmas, which are extensively studied and theorized in game theoretic framework. The term
“social dilemma” refers to a large number of situations in which individuals make independent choices in an interdependent situation. The most famous social dilemma is the prisoner’s dilemma. The rational choice theory pre-dicts that self-interested, profit maximizing individuals will choose to defect, leading to an outcome which is worse off with respect to the case in which they choose to cooperate. Thus, a Pareto-superior alternative exists, but rational participants making isolated choices are not predicted to realize this outcome. This is so because it is assumed that participants have no opportu-nity to punish each other, their decisions don’t affect their future reputation and no external actor (or central authority) is present to enforce agreements about their choices. However experimental results don’t fit the predictions of this theory. Most experimental studies of social dilemmas find levels of cooperative actions to be higher than zero, in one-shot games, or in the first rounds of a repeated game. Walker, Gardner, and Ostrom (1990), find that when groups of eight subjects made appropriation decisions in repeated common-pool resource experiments of 20 to 30 rounds, the unique symmet-ric Nash equilibrium strategy was never played. Why do people cooperate? Bowles (2016) argues that they do so because they have social preferences. “Social preferences refer to motives such as altruism, reciprocity, intrinsic pleasure in helping others, aversion to inequity, ethical commitments, and other motives that induce people to help others more than is consistent with maximizing their own wealth or material payoff”. The main determinant of defecting, as assessed by playing the prisoners dilemma game sequentially, is not higher payoff but the possibility that own cooperation might not be repaid by the other. Although the author doesn’t use the term social capital we can recognize in his argument some of its main dimensions. Theoretical models that depart from perfectly rational individuals have been developed. In these models individuals are boundedly rational, they use heuristics and norms, including reciprocity norms, hence responding to the positive actions of others with positive actions and to the negative actions with negative ones.
The existence of one of the forms of social capital then – norms of reciprocity – affects the behavior of individuals by making them more cooperative than they would be in its absence. Trust - another form of social capital - is important for the willingness of an individual to initiate cooperation in the expectation that it will be reciprocated.
1.1
Channels of creation of social capital
While a lot of research work has been done on the outcomes of social cap-ital, the determinants of its creation are under theorized. There are two main theories concerning the creation of social capital. The fist puts empha-sis in the operating of the civil society, with particular focus on voluntary organizations, whereas the other focuses on the role of government.
The first view can be found in the works of Putnam and Fukuyama. According to Fukuyama (2001), social capital is the by-product of religion, tradition, shared historical experience and other types of cultural norms.
1.2
The role of historical factors
The role of historical factors in generating social capital can be found in the work of Putnam. Putnam (1993) attributes the differences between north and south Italy to their different conditions during the middle ages. While southern Italy was built as a monarchy based on hierarchical relationships, the north developed as a republic, with organization mostly based on hori-zontal relationships, which provided mutual assistance and promoted coop-eration among the population. Putnam postulates that it is this differences that determined the different endowments of social capital one can observe to this day, although he doesn’t provide an explanation of their transmission or their strong persistence over time. An attempt in this direction is made by Tabellini (2008), who adopts a definition of social capital as “good” culture - in other words, a set of beliefs and values that facilitate cooperation among
the members of a community. The author develops a model of cultural trans-mission of cooperative values where parents optimally choose which values to pass to their children, but do so based on their own experience. This creates path dependence because if parents are faced with poor institutional contexts they will transmit values of non cooperation and will choose limited enforcement. When faced with more favorable contexts they will transmit cooperative values and opt for strong enforcement. Guiso, Sapienza e Zin-gales (2007) on the other hand, model the inter-generational transmission of beliefs about the trustworthiness of others. Children acquire probability distributions over unknown events (priors) mostly from their parents. These priors are conservative because of the parent’s desire to protect their children from costly mistakes and the failure to fully internalize the value for their children to learn from experience. Successively, by engaging in cooperation children will update their prior depending on their experience. If their trust was repaid they will transmit a more optimistic prior to their own children and vice-versa. A society starting from a situation of diffused pessimistic priors can be trapped in an equilibrium of non cooperation and the only way to escape from it would be a shock in the benefit of cooperation. The au-thors simulate the distribution of priors and show that even a brief shock, in the form of historical experience, can have permanent effects. This finding supports Putnam’s intuition that free city state experience in the medieval era has an effect on today’s trust.
1.3
Voluntary associations
The operating of voluntary associations is seen as the most important factor in creating social capital. This is so because social capital, according to Put-nam, is generated through repeated interaction and voluntary organizations offer a chance for people to meet and learn cooperative values and demo-cratic attitudes. In places where such associations are less frequent, people have fewer chances to cooperate and learn to trust each other. However the
mechanism that allows trust from within the group to expand and become generalized trust is not explored and is often assumed. Different types of associations produce different levels of social capital. The associations of members coming from different segments of society, allow for bridging inter-actions (Putnam) and are said to be more efficient in creating social capital as opposed to more homogeneous organizations. The lack of a micro theory of the formation of social capital has brought several scholars to question the effect of voluntary associations to create generalized trust. Opponents point to the possibility of self selection: individuals with a higher level of trust become members while low trust individuals choose not to join. The causality in this case would be reversed (Hooghe, 2003).
1.4
Family
The family can be seen as another source of social capital, especially trust and norms of reciprocity. Stole (2003) argues that the way a child is raised -more individualistic and self oriented or -more community oriented - and the frequency with which parents told them to be careful toward strangers, is a strong predictor of child trust towards others in adulthood. In general the author argues, parents affect the social capital formation of their children in at least three ways:
By providing a trusting and tolerant atmosphere: research shows that children who grew up in such an environment are more likely to be trusting and willing to reciprocate.
By teaching their children how to judge others and with whom to co-operate.
By acting as arenas where children experience cooperation and defec-tion for the first time.
The changes that have interested the family in the last decades are identified by Putnam (1995) as one of the causes of declining social capital in America. First of all the role of women, which have been for centuries the main actors in child education, has dramatically changed. The fact that more women are now having paid jobs outside the home means they are dedicating less time to typical socializing activities like participating in parent teacher associations. In addition, the loosening of family bonds and the rise in divorce rates and single-parent families adds to the problem inasmuch as the levels of trust among married people are 15%-20% higher as compared to single ones.
1.5
Is there a role for the government?
The society based approach recognizes a limited role for the government to affect the accumulation of social capital, given the strong path dependence which characterizes it. According to Fukuyama (2001) government cannot replicate the role of the channels of creation of social capital. It can only indirectly affect its accumulation by providing property rights and general safety because it is more likely for people to interact with one another and to create trust if they don’t fear for their own life or property. However, the most effective way for government to affect social capital is through education. It has been acknowledged that schools provide not only intellectual knowledge but serve also as platforms for students to learn values, be it from formal curricula or direct interaction with others.
The previous approach, which views social capital exclusively as the prod-uct of civil society, has been criticized by several scholars giving rise to an institutional approach which recognizes the possibility for the government to exert an independent influence on the creation of social capital. One of the relations that has been stressed in the literature is the one between democ-racy and trust. Democratic states have higher levels of trust. According to Levi (1999, 82), states build trust through “the use of coercion” and that “democratic states may be even better at producing generalized trust than
are nondemocratic institutions . . . because they are better at restricting the use of coercion to tasks that enhance rather than undermine trust.” Uslaner (2003) reports several correlations between the level of trust and measures of democracy like political freedom and civil liberties. The correlations are robust and positive in many cases, but yet in former communist countries for example, a negative relation can be observed. This is for the author a proof that democracy not neccessary breeds trust, and if it does it takes a long time for it to do so because the only correlations that are positive and significant even after a simultaneous equation estimation are the ones between the years of continuous democracy and trust. The length of time needed to move a country from below the mean of trust to above it is forty-six years. The au-thor retains however, that there is another more effective way for government to affect the levels of trust, and that is through government policies that pro-mote a more equal distribution of resources. Several research has shown that inequality discourages the creation of social capital. Alesina and La Ferrara (2006) use individual level data drawn from US localities and find that one of the strongest factors associated with low trust is living in a racially mixed community or in one with a high degree of income disparity. More precisely an increase in Gini coefficient by one standard deviation decreases the like-lihood of trust by 2.5 percentage points. This finding is consistent with the argument that people distrust those who are not similar to them. Economic equality is a strong determinant of trust. In addition, government can af-fect the accumulation of social capital by investing in social infrastructure. Social infrastructure refers to the provision, both by the public and private sectors, of areas for actors to connect to others and develop the interpersonal linkages which are regarded as the essence of social capital. Examples of social infrastructure include community facilities, leisure facilities, parks and other landscapes areas. Roskruge, Grimes, McCann and Poot Motu (2010), conduct an empirical research to determine the effect of social spending on trust using World Value Survey data and data for annual local government
spending. Their findings show that expenditure on social infrastructure in-creases the range of social activities among people who already participate, whereas the decision to participate in social activities is negatively correlated with the level of social infrastructure expenditure.
1.6
Measuring social capital
In a critique to several theoretical approaches to social capital, Solow (1995) observes that: ‘If “social capital” is to be more than a buzzword, something more than mere relevance or even importance is required. ... the stock of so-cial capital should somehow be measurable, even inexactly’ (1995, 36). The empirical literature on social capital has been developed in parallel with the theoretical strand. The multi-faced nature of social capital as a concept and its somehow blurry definition has led to the usage of different indicators for its measure. Although there is no final agreement between scholars, it is possible to identify three main dimensions of social capital, namely trust, membership in various types of networks and norms of reciprocity. On the empirical grounds studies have focused on measuring one or more of these dimensions. Engbers, Thompson and Slaperg (2015) make an overview of the main measures of social capital. According to the authors, one of the most common and widely used indicator is the level of trust prevailing in a society, which can be either generalized trust - trust in other members of the community with whom one interacts, or trust in institutions. Its level is assessed through surveys, as for example the World Value Survey, in which participants answer the following question: “Generally speaking, would you say that most people can be trusted or that you need to be very careful in dealing with people?” with ’Most people can be trusted’ and ’Need to be very careful’ as possible answers. Another way to measure is by using indirect indicators as for example crime levels, having in mind the negative relation-ship that exists between these and trust. The concept of social capital as networks, is measured by membership in community groups. The number of
organizations in which an individual is active or the number of hours he dedi-cates to such activity and in community level, the number of institutions in a country, are used as indicators of civic participation and social capital since being part of them creates opportunities for establishing both strong and weak ties. Political participation is one of the most widely used indicators of social capital because it is seen as a source of it, through the connections that individuals can develop, and as a consequence in the sense that be-ing part of social networks fosters political participation (Brehm and Rahn 1997). Guiso, Sapienza and Zingales (2004) adopt a twofold measure of social capital given by electoral participation - more specifically voter turnout in referenda - and blood donation as indirect indicators, because both decisions are made only as a consequence of internal norms and do not result from legal obligations. Other studies have focused on measuring norms using proxies such as demographic homogeneity or inequality within a community. The use of indirect indicators as a measure of social capital has been criticized by several authors. Sabatini (2006) observes that this has led to a confusion between the concept of social capital and its outcomes. The term has come to mean every aspect of the social structure that makes markets work better and agents cooperate, but this way every empirical analysis will find that social capital fosters cooperation and efficiency. The goal of the theoretical literature on the contrary is to investigate the role of socio-cultural factors on growth. The author goes on observing that the measurement of trust through indexes built from surveys, the most famous of which is the World Value Survey, is problematic since the individual responses reflect personal perceptions of the environment and are influenced by the status the individ-ual has in the society. Their aggregation is an indicator of social trust, but the link with the social context in which such individual beliefs were created is lost in the process, and if social capital is context-dependent, like Fine (2001) argues, than this undermines the possibility to make generalizations starting from any conclusions.
1.7
Two different views of social capital
Social capital as a concept, has been studied by scholars of different disci-plines, from anthropology, philosophy, sociology, political science etc. Economists have included social capital on their research agendas in light of the effects that it has on economic performance of countries. The economic framework to the study of social capital is not a unified one. Indeed we can identify two different ways in which economists have approached the problem. The first one which considers social capital as community attribute, was originally developed in other disciplines and successively employed also in economic analyses of social capital, whereas the second one is the traditional neoclassi-cal framework, in which the utility function is enriched with new elements to take into account the effect of the social environment. Below we will briefly discuss each of them.
1.8
Social capital as a by-product
This view was first pioneered by Coleman (1988) who argued that social capi-tal is created as a by-product of other activities, without any ones willingness. The author makes the example of an obligation of a person B towards a per-son A. When B makes the choice to ask a favor to A and incur an obligation, he does so based on his own cost-benefit analysis, without taking into con-sideration that this obligation also adds to the stock of social capital of A. Social capital has the characteristics of a public good because the benefits of the actions that bring it into being are not enjoyed only by the person that does the effort, but also by others. Hence, it is not always in his best interest to bring it into being. This leads to under investment and free riding. For example the parent teacher associations are formed in most cases by parents who don’t have a job in the formal market. However, they benefit the whole community of students and parents, regardless of their participation.
author focuses on one aspect of the micro level interactions - the strength of interpersonal ties between individuals - and uses network analysis in an attempt to explain how macro level patterns like diffusion of information. Network theory distinguishes between bonding and bridging social capital. Although the distinction was formally made by Putnam (2000) it is useful in this context. Bonding social capital refers to ties that hold together in-dividuals within groups whereas bridging social capital crosses social divides and links individuals from different groups. Bonding social capital is charac-terized by strong ties, where the strength of a tie as defined by Granovetter (1973), is given by the amount of time, emotional intensity and reciprocal services which characterize it. Strong ties are important because they fos-ter cooperation inside the group and make possible the pursuing of common objectives. In his article however, Granovetter shows that weak ties play a much more important role than could be thought, because by linking people from different groups they serve as information transmitters. In egocentric networks weak ties link ego with contacts which are not connected to one an-other and in addition are connected with people not connected to ego. These ties are bridges through which information distant from ego can reach him. The author supports his point with a job market study. While the natural idea he argues, is that people with whom we have strong ties are motivated to help with job information, it is those with whom we hold weak ties that moving into circles different from our own have access to information differ-ent from that which we receive. In a sample of professional, technical, and managerial job changers he asked those who found a job through contacts, how often they saw the contact around the time that they passed the in-formation to them and the reported frequencies were: 16.7% often, 55,6% occasionally and 27,8% rarely. Taking the frequency of meeting as a proxy for the strength of the tie it means that most of the respondents only held weak ties. Notice that, in his approach, information diffusion as a form of social capital is a by-product of networking between individuals, which takes
place for reasons that are different from acquiring this type of information.
1.9
Social capial as a private good
The reason why it took economists so long to consider social capital as a relevant variable and consequently to study its implications, even when other disciplines widely acknowledged its crucial importance can be attributed to the neoclassical tradition. Neoclassical economics focuses on individuals only, without considering the general context within which they operate. History and social relations, all lose importance in front of mathematical models which aim to explain individual behavior in response to certain events. The framework consists of self interested utility maximizing agents, where utility is a function of consumption goods and leisure. Becker (1974) article was a break with this tradition. The author employs the neoclassical framework but extends it in order to analyze interactions between the behavior of some persons and the different characteristics of other persons. The characteristics of other persons are treated as intermediate goods in the production of the final goods. According to the modern theory of household behavior, the utility function of the i − th person is given by:
Ui = Ui(Z1, .., Zm)
and Z1, ..., Zm are the basic wants or commodities. Each person also has a set of production functions that determine how much of these commodities can be produced with the market goods, time, and other resources available to him:
Zj = fji(xj, tj, Ei, R1j, ...., R r j)
where xj are quantities of different market goods and services, tj are quan-tities of his own time, Ei stands for his education, experience, and ”envi-ronmental” variables, and R1
j,..., Rrj are characteristics of other persons that affect his output of commodities. For example, if Z1 measures i0s
distinc-tion in his occupadistinc-tion, R1
1,.. .,Rrj could be the opinions of i held by other persons in the same occupation. Presumably, characteristics of others affect the production of a significant fraction of commodities. The author assumes that i can change Rj by his own efforts. In such a framework, assuming one single commodity is produced with one single good, the individual problem becomes: M ax x,h Ui(x, R) R = Di+ h pxx + prh = Ii
where h measures the effect of i effort, Di is the level of R when i makes no effort, Ii is his money income and prh is the amount of money which must be spent to influence R. R1...Rj. influence the social sphere of the individual and are a means for the pursuit of his personal interest. They are Becker’s social capital and in this setting they are treated as a private good, a resource that individuals use to maximize their utility.
Becker’s work led the foundations of what is now considered the economic approach to social capital. Many subsequent authors extended the same framework to study the determinants of social capital formation. In an in-fluential work, Glaeser, Laibson, Sacerdote (2002) treat social capital as a property of individuals, which is created through their deliberate choice to invest on it in order to maximize their utility function. The authors define social capital as:
“ ...a person’s social characteristics - including charisma, social skills and the size of his network - which enables him to reap market and non market returns in his interactions with others”.
They built a model of individual investment in social capital which has the following formal structure:
Social capital is assumed to be a stock variable and each individual possesses a certain level of such stock. In each period, individuals receive a utility
of S*R( ˆS) from their stock of social capital, where R( ˆS) is a differentiable function of the aggregate per-capita level of social capital, and bear a cost of C(It), which rapresents the time cost of investment in social capital. The opportunity cost of time equals w, which can be seen as forgone wage or the value of leisure time in the cases in which labor supply is inelastic. The stock of social capital evolves according to St+1 = δSt+ It, where δ ∈ (0, 1) is the depreciation factor. The individual problem is then to:
max I0,I1...It T X t=0 βthS ∗ R( ˆS) − wC(It) i s.t St+1= δφSt+ It, ∀t
where φ rapresents the depreciation factor of social capital deriving from mobility, since the authors argue that social capital investment is community specific. φ = (1−θ)+θλ, with θ being the probability to leave the community.
ˆ
St is assumed to be fixed.
The first order condition associated with this problem is:
wC0(It) =
1 − (βδθ)T −t+1 1 − βδθ R( ˆS)
and it gives rise to the following comparative static results. The investment in social capital:
1. increases with the discount factor β,
2. decreases with mobility θ,
3. decreases with the opportunity cost of time w,
4. increases with the occupational returns to social skills R(.) ,
5. decreases with the rate of social capital depreciation (1 − δ),
7. decreases with age t.
Two of the above results merit special attention. First of all, social capital decreases with mobility. This means that residential mobility must be a key determinant of investment in social capital. The authors test this implication against empirical data. They estimate a regression using organization mem-bership as a measure for social capital and an indicator of expected mobility, and find a statistically strong relationship which is also quantitatively signifi-cant. Second, social capital investment is higher in individuals who belong to groups with more social capital, which means that there are complementari-ties among individuals. The authors test also this implication of the model, by forming an indicator of average organization membership in ones group and estimating the relationship between such indicator and individual social capital. The coefficient is positive and significant, meaning there is a peer group effect. However, when the Instrumental Variables approach is used (with individual characteristics like marital status and age acting as instru-ments for the group social capital) to account for problem like endogeneity, the effect of average group social capital is not significant anymore. This is a further proof in favor of the individual investment in social capital model as it implies that it is individuals only who make decisions regarding social capital investment in order to maximize their utility, and not groups.
Chapter 2 - Some theoretical
implications of social capital
2
The framework
shed light on the role that social capital could play and to understand the possible implications that an ever-changing environment could have on social capital itself. To do so, we will analyze two articles, “ Social capital, human capital and fertility” and “The Solaria syndrome: Social capital in a growing hyper-technological economy” in order to understand their formal structure and their implications in terms of policy prescriptions. Before we move on to analyze the articles, we will briefly describe the problems that form the object of their research.
Fertility rates have been low in most of European countries, starting from the ’90 (Marczak, Sigle, Coast, 2018). Population aging is linked with numerous social and economic problems. Bloom, D., Canning, D., Fink, G., Finlay, J. (2009), study the relationship between fertility and the size of the workforce. They argue that if fertility rates stay at current levels, the working age population share can be expected to decline to 55% from the current 70%, with a reduction of the number of workers per-capita of expected 25%, which would clearly have detrimental effects to growth. This is why the issue has been on the agenda of the European Union, which has implemented policies aimed at reducing the cost of childbearing, a direct application of the cost benefit model of fertility. However, fertility rates remain low in most European countries, even after these interventions, suggesting that other factors may have an influence on the decision.
Moreover, technological change has become a much discussed topic in recent times. While there is no doubt on the positive effects of technological advancement ie. greater connectivity, reducing distances, new goods that facilitate living, its negative effects are causing much concern throughout all the world, especially in developed countries. Technological unemployment is what everybody fears, and it seems that we have reached a point where humans are becoming ever more obsolete, as their jobs are being executed by automated systems. Furthermore, in a world where we seem all connected, it could well be that we are in fact becoming disconnected, as technology
substitutes for direct interaction.
2.1
The Solaria syndrome: Social capital in a growing
hyper-technological economy
The aim of the paper is to analyze the evolution of social capital and so-cial participation in a world characterized by technological progress. The rationale for that is the central role that technology has in the lives of to-day’s people. In a society where time is more and more scarce the diffusion of internet and social networks, often acts as a substitute for face to face interaction. Could such substitution process lead to a social povery trap, ie. a self reinforcing mechanism which causes the stock of social capital in the society to be persistently low? In this paper the authors show this need not be always the case, since they identify a set of parameters where growth and technological progress are reconciled with social participation. In what follows we describe the model.
To start, the authors assume that in each instant of time t, the well-being of the representative agent depends on the consumption of a private good and on social participation, ie. the consumption of a socially provided good, also called relational good.
U (C, B) =λC−θ+ (1 − λ)B−θ−1/θ
with C being the private good, B the socially provided good and parameter values θ ∈ (−1,+∞) and θ6= 0.
Material and relational goods serve different needs. Yet, material goods can substitute for relational goods. Think of the cases when the environment is poor of social participation opportunities and this induces people to make use of technology to interact with others whom they may not know personaly. The rate of substitution is costant and given by ρ = 1/1 + θ. When θ>0, the rate of substitution between the two goods is low. In this case we say that
the goods are complements. When θ < 0 the rate of substitution is high and in this case we say that the goods are substitutes.
Following Coleman, the stock of social capital, here meaning durable ties, is created as a by-product of social participation. The social capital stock is considered as a factor of production since its presence facilitates social participation, as well as the production of the private good. The production functions of the private and relational goods are the following:
Y (t) = [1 − s(t)]Ksα(t) (1)
B(t) = sβ(t)¯s1−β(t)Ksγ(t) (2) with s(t) being the time agent spends on social participation and ¯s the society wide average time spent in social participation. The parameter α rapresents the elasticity of Y with respect to Ks, and the parameters β, 1-β and γ rap-resent the elasticity of B with respect to s, ¯s and Ks. The elasticity values vary between zero and 1 ( 1 > β > 0 and γ > α ≥ 0 ). By assumption, the elasticity of the production of the relational good with respect to the stock of social capital is greater than the elasticity of the private good be-cause following the empirical literature, the stock of social capital is more important in the production of relational goods although it plays a role in the production of private goods as well. The stock of social capital can play indeed an essential role in the production of the private goods. A Ks equal to zero would lead to zero production, in case the elasticity α > 0 . And furthermore a positive average social participation is always neccessary for the production/consumption of the relational goods, because if no one par-ticipates, production will be zero even in presence of a positive stock of social capital Ks.
The time evolution of social capital depends on average social participation and on the stock of social capital. In particular, the time derivative of social
capital is given by: ˙
Ks = I(¯s, Ks) − ηKs = ¯sδKs − ηKs (3) <
The parameter η indicates the depreciation rate of Ks. 0 < η < 1 because social ties need care to be preserved over time. The parameter δ measures the elasticity of the “investment function” I in social capital with respect to the average social participation ¯s and 0 < δ < 1 holds. The exponent of Ks in the function I(¯s, Ks) is assumed to be equal to 1 since the authors aim at analyzing a context in which the unbounded growth of Ks is possible. The evolution of social capital depends on its current level, to account for the path dependence highlited by many authors who emphasize its cultural nature. The individual problem becomes:
max s(t)
Z +∞ 0
U (C, B)e−rtdt (4)
subject to the constraints (1),(2).
Given that agents are a continum, the individual choice of s(t) has no effect on the average social participation ¯s or on the stock Ks. Hence, in every moment the solution s(t) of the above problem coincides with the solution of the static maximization problem:
max s {λ[(1 − s)K α s] −θ + (1 − λ)(sβs¯1−βKsγ)−θ}−1/θ (5)
subject to the constraint s(0, 1).
The first order conditions of (5), together with the fact that agents are iden-tical and make the same choices causing the average social participation ¯s to coincide ex post with the individual choice s, imply that the Nash equilibrium value s∗ of s is:
s∗ = β(1−λ) λ 1/(θ+1) Ksθ(α−γ)θ+1 1 +β(1−λ)λ 1/(θ+1) Ksθ(α−γ)θ+1 (6)
where 1 > s∗ > 0 always holds.
“Proposition 1. The Nash equilibrium value s* of social participation is increasing in Ks if θ < 0 and decreasing if θ > 0 ”.
By taking the derivative of s∗ with respect to Ks we have:
ds∗/dKs = −β(−1+λ)λ 1/(θ+1)Ksθ(α−γ)θ+1 θ (α − γ) −β(−1+λ)λ 1/(θ+1)Ksθ(α−γ)θ+1 2 (θ + 1) Ks
The sign of the derivative depends on the sign of θ, in particular it is posi-tive(negative) when θ is posiposi-tive(negative). The reason social participation behaves in this way is the following: an increase in Ks makes the time spent in social participation more productive since by assumption γ > α. In the case in which θ < 0 ( B and C are substitutes) agents will dedicate more time to social participation because they are willing to replace the private good with the relational one. In the case in which θ > 0 (B and C are comple-ments) an increase in Ks, will induce a decrease in social participation since agents want a balanced growth between their private and relational spheres. If we replace the solution s∗ to ¯s in problem (3) then the resulting dynamics of the stock of social capital is given by:
˙ Ks = hKs θ(α−γ) θ+1 1 + hKsθ(α−γ)θ+1 !γ Ks − ηKs (7)
where h = (β(1 =λ )/λ)1/θ+1> 0.
Equation (7) has two stationary states, respectively: Ks0 = 0 and Ks1 =
η1/δ h (1 − η1/δ)
θ(α−γ)θ+1
and the following holds:
1. “If θ< 0, then the stationary state Ks0 is locally attractive and Ks1 is repulsive. The economy follows a growth trajectory along which Ks +∞ if it starts from an initial value Ks(0) greater than the threshold value ¯K1
s”.
2. “If θ> 0, then the stationary state Ks0 is repulsive and Ks1 is globally attractive. The economy cannot follow a trajectory along which Ks grows without bound”.
according to Proposition 1, s∗ and Ks are positively correlated. This means that an increase in Ks will lead to an increase in s∗which will further increase Ks (the opposite holds in the case in which Ks decreases). The mechanism is self reinforcing and it explains the coexistence of paths approaching 0 and ∞. In the case in which θ > 0 an increase in Ks will lead to a decrease in s∗ and the economy will neither approach 0 nor ∞.
In conclusion, from this first part of the paper we see that the rate of sub-stitutability between the two goods plays a crucial role in determining the social capital dynamics of the economy. When material and relational goods act as substitutes, then the stock of social capital approaches either 0 or +∞, depending on its initial value. When the two goods are complements, then the stock of social capital approaches a positive finite critical value, independently of its initial level.
Exogenous technological progress
In the second part of the paper the authors introduce an exogenous tech-nological shock to the model, which affects the rate of substitution between the two goods. In this part the aim is to study the role of technology in determining the trajectories of social participation and social capital, and establish if the solaria syndrome ie. a growing social isolation, is an actual risk.
Starting from the assumption that technical progress raises the productivity both in the private and relational sector, the production functions of the two goods are modified as follows:
Y (t) = [1 − s(t)]Ksα(t)Tπ(t)
B(t) = sβ(t)¯s1−β(t)Ksγ(t)Tψ(t) (8)
elas-ticity of Y and B, with respect to T . The evolution of T is given by:
˙
T = µT (9)
where µ > 0 is the exogenous growth rate of technology.
The FOC yield the following Nash equilibrium time allocation choice and capital dynamics: s∗ = hT θ(π−ψ)/(θ+1)Ksθ(α−γ)/(θ+1) hTθ(π−ψ)/(θ+1)Ksθ(α−γ)/(θ+1)+ 1 (10) ˙ K = hTθ(π−ψ)/(θ+1)Ksθ(α−γ)/(θ+1) hTθ(π−ψ)/(θ+1)Ksθ(α−γ)/(θ+1)+ 1 δ Ks − ηKs (11)
where h = (β(1=λ )/λ)1/θ+1> 0. In order to analyze (11) the authors define the variable:
H = Ksθ(α−γ)θ+1 T θ(π−ψ)
θ+1 (12)
whose time derivative is:
˙ H =
Hθ(α − γ) hH+1hH δ
− η+ (π − ψ) µ
θ + 1 (13)
The above equation admits at most one stationary state with H>0 and the condition for its existence is given by:
1 > η(α − γ) − µ(π − ψ) α − γ > 0
The stationary state is:
H∗ = 1 h
[(η(α − γ) − µ(π − ψ))/(α − γ)]1/δ 1 − [(η(α − γ) − µ(π − ψ))/(α − γ)]1/δ
In order to obtain ˙H > 0 in the long run the following condition must hold:
θ
θ + 1H[(1 − η)(α − γ) + µ(π − ψ)] > 0 Equation (13) has the following dynamics:
1. If 1 > η(α−γ)−µ(π−ψ)α−γ > 0 and θ+1θ [(1 − η)(α − γ) + µ(π − ψ)] > 0 then an interior stationary state H∗ exists and this stationary state is repulsive in that H→ 0 starting from an initial state H(0) < H∗ and H→ ∞ starting from an initial state H(0) > H∗.
2. If 1 > η(α−γ)−µ(π−ψ)α−γ > 0 and θ+1θ [(1 − η)(α − γ) + µ(π − ψ)] < 0 then an interior stationary state exists and it is globally attractive.
3. If η(α−γ)−µ(π−ψ)α−γ < 0W ∨η(α−γ)−µ(π−ψ)α−γ > 1 and θ
θ+1[(1−η)(α −γ)+µ(π − ψ)] > 0 then an interior stationary state doesn’t exist and H→+∞ for every initial value H(0) > 0.
4. η(α−γ)−µ(π−ψ)α−γ < 0Wη(α−γ)−µ(π−ψ)
α−γ > 1 and θ
θ+1[(1−η)(α−γ)+µ(π−ψ)] < 0 then an interior stationary state doesn’t exist and H→ 0 for every initial value H(0) > 0.
Figure 2: Graphical representation of the four cases
The above dynamics can give rise to the following scenarios:
1. H = Ksθ(α−γ)θ+1 T θ(π−ψ) θ+1 → 0 then Ks → 0 for t → +∞ 2. H = Ksθ(α−γ)θ+1 T θ(π−ψ) θ+1 → +∞ then Ks → +∞ for t → +∞ 3. H = Ksθ(α−γ)θ+1 T θ(π−ψ)
θ+1 → H∗ then the behavior of Ks depends on the
sign of π − ψ. If π − ψ > 0 then Ks → 0 and Ks → +∞ in the other case.
The stock of social capital as we can see from above can tend either to zero or to ∞. The introduction of technology into the model has changed things a bit compared to the first case, as it is now impossible for Ks to converge to a positive finite value.
“Proposition 5. Under dynamics (16), there exist trajectories along which +∞ if and only if:
π − ψ > 0 and either 1. or 2. hold 1. θ < 0,µ < (1 − η)(γ − α)/(π − ψ)
2. θ > 0,µ > (1 − η)(γ − α)/(π − ψ)
π − ψ < 0, θ < 0”
A number of conclusions arise from the above proposition. Firstly, if the returns to technology are higher in the production of the private good and the two goods are substitutes, in order to keep social capital growing in the long run, technology has to change slowly. If it is not the case, then there is a risk of falling into a social poverty trap where Ks tends to zero. On the contrary, when the goods are complements, technology has to grow at a high rate in order to prevent the economy from falling into the trap. In the scenario in which technology has higher returns in the production of the relational good, the substitutability between the two goods is a condition for the unbounded growth of social capital. If the rate of technological change is high enough then the possibility of contracting the Solaria syndrome is precluded.
Chapter 3 - Social capital,
human capital and fertility
The paper we are going to analyze here is an investigation on the role that so-cial capital may have regarding fertility decisions. The most renowned model employed by economists to study fertility is the traditional Quality-Quantity tradeoff (hereafter QQ), first developed by Becker. In a setting where par-ents derive utility both from the quantity and the quality of their children and face budget constraints, the QQ predicts an inverse relationship between economic growth and fertility. Subsequent authors argued that technology plays a role in that it increases the returns to human capital accumulation, thus leading parents to prefer quality over quantity. The authors extend the QQ model to include social capital variables that are claimed to have an effect on fertility dynamics through the following two channels:
One direct channel consisting of the effect social capital has in increasing the returns to human capital accumulation. As argued by Knack and Keefer, this can happen in a number of ways. For instance, by facilitating access to credit social capital can increase the rates of school enrolement. In addition, in trusting societies hiring decisions are made based on a candidates skills and not personal knowledge, further increasing the returns to education. One indirect channel consisting of the effect that social capital has on parents decision making with regard to human capital investment on their children. This decision depends on parents own human capital endowment and on the average level of human capital in the society, which are in turn affected by social capital. In what follows we describe the model.
The economy is composed by individuals and firms. The authors start from the assumption that agents live for three periods: childhood, adulthood and old age. They derive utility from consumption, which for simplicity is as-sumed to occur only in time t + 1, the number of children nt and their
quality ht+1, and leisure time lt whose utility depends on the stock of social capital Kst, and on average leisure time ¯lt that is enjoyed in the society. Formally, the utility function of the single agent is given by:
U (t) = ρlnCt+1+ γlnnt+ βlnht+1+ Ksωtln(1 + ltπl¯t 1−π
) (1)
Parameters ρ, γ, β, ω are strictly positive, whereas π ∈ (0, 1). The budget constraint of adults is:
st= ωt(1 − ntz − lt)ht− etnt (2)
where st are agents’ life-cycle savings, ωt is the wage rate for labor, z > 0 is the time devoted to rearing children, and et is per child educational expenditure.
The budget constraint of the elderly is given by:
Ct+1 = rt+1[(ωt(1 − ntz − lt)ht− etnt] (3)
where rt+1 is the interest rate in period t + 1. Consumption is financed entirely by the returns to savings.
Education is assumed to consist of two parts. One part is the result of spillover effects from parents and depends only on their level of human cap-ital, not requiring any time investment. The other consists of formal edu-cation, delegated by parents to the educational system. This second part requires investment of resources and is subject to budget constraints. The human capital of an individual working in time t + 1 is given by:
With , θ > 0 and φ, δ ∈ (0, 1). The parameter indicates the technology of production of human capital, δ indicates the role of the human capital of parents and their expenditure for the education of the offspring, 1 − δ is the productivity of the average level of human capital in the economy, φ expresses the importance of social capital in increasing the effectiveness of education, Kst is the stock of social capital which is assumed to have an effect through the two channels described above and ¯htis the average level of human capital in the society, which is assumed to play a role through spillover effects. The problem for the individual of generation t is to choose savings st, leisure time lt, the number of children nt, old age consumption Ct+1 and the educa-tional expenditure et, in order to maximize his lifetime utility U (t) defined in (1), subject to (2), (3), (4) and considering htand Kst as given. The solu-tions to this maximization problem will be different according to the values of the stock of social capital and wage. Four cases are possible:
CS1 : et= 0; lt= 0 nt = z(γ+ρ)γ ; st= ρhγ+ρtwt Ct+1 = ρhγ+ρtwtrt+1 if wt < wtand Kst < Ks (5) CS2 : et = 0; lt= πKsω t−γ−ρ πKsω t+γ+ρ nt= z(πKs2γω t+γ+ρ); st= 2ρhtwt πKsω t+γ+ρ Ct+1= πKs2ρhωtwt t+γ+ρrt+1 if wt< wt and Kst> Ks (6)
CS3 : et= htβδωtz−Ks −φ t γθ γ−βδ ; lt = 0 nt = wtKsωt(γ−βδ) (γ+ρ)(zKsω twt−θ); st = ρhtwt γ+ρ Ct+1= ρhγ+ρtwtrt+1 if wt> wtand Kst< Ks (7) CS4 : et= htβδωtz−Ks −φ t γθ γ−βδ ; lt= πKsωt−γ−ρ πKsω t+γ+ρ nt= 2wtKsφt(γ−βδ) πwtzKsω+φt +zwt(γ+ρ)Ksφt−θ(πKsωt+γ+ρ) ; st= πKs2ρhωtwt t+γ+ρ Ct+1 = πKs2ρhωtwt t+γ+ρrt+1 if wt> wt and Kst> Ks (8)
where Ks= γ+ρπ and wt = zβδ(Ksγθ t)φ are critical levels of social capital stock
and wage. It is possible to see that agents will invest in their children’s formal education only if the wage is above the threshold. Otherwise they choose to rely only on spillover effects from own human capital to their offspring. On the other hand, agents will devote time to social participation only if the stock of social capital is above the threshold. Indeed, in CS1, where both the wage rate and the social capital stock are below the threshold agents neither invest on formal education nor spend time in social participation. The opposite holds in CS4 where both expenditure and leisure time assume positive values. In CS2, the wage rate lies below the threshold and hence agents don’t find it convenient to invest in the human capital of their children. However given that the stock of social capital is above the threshold, they will spend time on social participation, thus contributing to the creation of social capital. In CS3 we have that the wage rate lies above the critical threshold and hence agents will chose to invest resources on their children’s education. However they will not participate in social activities, given that the stock of social capital is low. With respect to fertility choices, except for the first case where fertility is costant, in all other cases an increase in the
stock of social capital decreases fertility through the two channels described above. An increase in social capital will make leisure time more rewarding and in presence of time constraints, agents will choose to reduce the number of children they are willing to have. Furthermore, as argued earlier, social capital increases the returns to education. Hence a greater stock will lead parents to prefer quality over quantity.
On the production side, the economy is populated by firms that operate in perfect competition and make use of a constant returns to scale technology. The production function is assumed to be Cobb-Douglas:
F (Kt, Lt) = AKtαL 1−α
t (9)
where Kt denotes physical capital, Lt the labor force and A is a productivity parameter. The profit maximization conditions are the following:
wt= A(1 − α)Kα t Lα t (10) rt = AαKtα−1 Lα−1t (11)
The stock of social capital in the economy evolves according to:
Kst+1 = B(Kst)λlt1−λ+ (1 − ζ)Kst (12)
where ζ ∈ (0, 1), is a parameter capturing the depreciation, λ ∈ (0, 1) and B > 0 is a parameter capturing the productivity of social participation in the accumulation of social capital. In this setting, social capital is created as a by-product of social participation. This is why, in communities that
are poor in social participation opportunities the stock of social capital will constantly diminish until complete erosion.
The equilibrium condition in the labor market is given by:
Lt= Nt(1 − ntz − lt)ht (13)
where Nt is population of generation t and evolves according to:
Nt+1= ntNt (14)
The equilibrium condition in the capital market is given by:
Kt+1= ntst (15)
In equilibrium, the values of et,lt, nt, st are determined in CS1, CS2, CS3 and CS4 and equations (4), (12), (13), (14) and (15) hold. According to the values of the state variables Kt, Kst, Nt, ht+1 equilibrium dynamics are described by four systems, whose dimension is reduced by introducing the variable vt= hKtNtt . The threshold values of vt corresponding to w are given by: ¯ v1t = ( γθ Aβδz(1−α)) 1/α ρ (γ+ρ)Ksφ/α if Kst < Ks ¯ vt 2 = (1−ntz−lt)γθ(πKsωt+γ+ρ) Ksφβδz(πKsω t−γ−ρ) if Kst > Ks
In the first scenario, when the values of Ks and income are below the thresh-old, equilibrium dynamics are described by the following system:
S1 : vt+1= A(1−α)vα t( γ+ρ ρ )αρz θγγ Kst+1 = (1 − ζ)Kst
which has a unique steady state, given by (v1∗, Ks∗1) = hAρz(1−α) θγγ ( γ+ρ ρ ) αi1−α, 0 . (v∗1, Ks∗1) is locally asymptotically stable.
In the case in which the wage rate is below the threshold allowing for invest-ment in the education of children, and the social capital stock is above the threshold, equilibrium dynamics are described by:
S2 : vt+1 = zA(1−α)ρ1−2α(πKsω t+γ+ρ)α 2αθγγ vtα Kst+1 = BKsλt πKsω t−γ−ρ πKsω t+γ+ρ + (1 − ζ)Kst
whose solutions depend on the value of the parameter B. There exist a thresh-old value of B, ¯B such that for B < ¯B no fixed points exist while for B > ¯B two fixed points exist. The fixed point associated to the lower level of Ks is unstable while the one associated with the higher level is locally asymptoti-cally stable.
In the case in which the wage rate is above the threshold while the stock of social capital is below it, we have that equilibrium dynamics is given by:
S3 : vt+1= ((γ+ρ)nA(1−α)ρt(1−ntz−lt)α γ−βδ [AKsθ tvαtz(1−α)(1−ntz−lt)−α+θ]δβ δ vα t Kst+1= (1 − ζ)Kst
There are no fisible fixed points in that no positive value of expenditure can be associated with Ks=0. This system describes only a transitory phase of the economy in which at time t, the stock of social capital falls below the threshold and from that time on the dynamics of the economy will be given by S1.
