Social Capital, Union Bargaining Power and Economic Growth: The Role of Political Participation

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UNIVERSITA’ DEGLI STUDI DI PISA SCUOLA SUPERIORE SANT'ANNA

DEPARTMENT OF ECONOMICS AND MANAGEMENT MASTER OF SCIENCE IN ECONOMICS

MASTER THESIS

SOCIAL CAPITAL, UNION BARGAINING POWER AND ECONOMIC GROWTH: THE ROLE OF POLITICAL PARTICIPATION

SUPERVISOR CANDIDATE

Prof. Simone D'ALESSANDRO Ekin YURDAKUL

ACADEMIC YEAR 2016-17

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Acknowledgments

I want to first thank my parents and my brother for always being there with me. And I want to thank Mert Mutlusoy and Umut Türk, who deserve much more than a reference in this page for their support to this work. I would also like to thank Prof. Mauro Sodini for his

contributions. Lastly, I would like to thank my supervisor who has been a great teacher and coach by sharing his ideas, and more with me before, during, and after the writing of this thesis.

To AYLAN KURDI

“I tried to catch my wife and children but there was no hope. One by one, they died.” Abdullah Kurdi " For sale: baby shoes. Never worn."

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Abstract

This thesis investigates presumptive effects of the political participation on the economic growth through social capi-tal accumulation. Following introduction, we discuss pre-vious developments and discussions for social capital and political participation within economic theory in the sec-ond chapter. In the third chapter, by using an endogenous growth model, we examine the issue with a comparison of two economic systems: Decentralized and centralized economy. In the latter, in contrast to the decentralized economy, the representative household internalizes all ex-ternalities in social, productive and private sector.

In the chapter 4, we approach the same issue by adopting an efficient bargaining model in which we assume that the average level of political participation is a contributor to the labour union’s bargaining power. We develop a com-parative analysis by solving the representative household optimization problem in two different scenarios, with and without efficiency-wage hypothesis.

We demonstrate that there exists an effect of the political participation resulting in a positive stationary growth rate in all models. Moreover, we found that, in the bargaining model, the average level of political participation is pos-itively correlated with wage and employment rate under the efficiency-wage hypothesis.

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List of Figures

1 Participating in political activities by the blue-collar employees over the period 2001-2016. . . 5

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2 Hourly index of blue-collar employees’ wages according to collec-tive labour agreements over the period 2005-2016. . . 6 3 Employees waiting for renewal of wage contract per 100 employees. 7 4 Numerical illustration of the steady state equilibrium in the

de-centralized economy. . . 28 5 Illustration of the effect of some parameters on the equilibrium

level of growth. . . 29 6 Numerical illustration of the steady state equilibrium in the

so-cially planned economy. . . 36 7 Illustration of the effects of some parameters on the equilibrium

level of growth. . . 37 8 Numerical illustration of the relationship between the bargained

employment rate and average level of the allocated leisure time to political participation in the unionized economy under the efficiency-wage hypothesis, ζ ∈ (0, 1). . . 54 9 Numerical illustration of the relationship between the bargained

employment rate and average level of the allocated leisure time to political participation in the unionized economy in the absence of the efficiency-wage hypothesis, ζ = 0. . . 55 10 Numerical illustration of the steady state equilibrium along the

balanced growth path in the presence of the efficiency-wage hy-pothesis. . . 57 11 Numerical illustration of the steady state equilibrium along the

balanced growth path in the absence of the efficiency-wage hy-pothesis. . . 58

List of Tables

1 Numerical examination of the changes in the steady state levels of l_p∗, g∗, L∗and K_S∗ with respect to variations in the parameters γ and the difference between β and ζ and z. . . 59

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1

Introduction

Effort for the explanation of social capital continues to be relevant in the social science literature. Social capital has been discussed from many perspectives by many social scientists thus far. There still exists a crucial conflict related to social capital concept as the social capital theory has become a highly controversial topic within the economic development and the economic growth literature. Particularly, social capital comes into the economic theory from the perspective of economic growth. In this sense, many researchers have strived to develop a social capital accumulation model which is integrated into the economic growth model.

Although there have been some attempts to incorporate social cap-ital theory into the growth theory, it is still open to improvement since social capital takes many forms in the economic literature. The existing theoretical framework conclusively indicates that social cap-ital has an accumulation process and it is a capcap-ital that depreciates over time and it is also affected by the stock of its kind cumulated in the past. Even so the social capital theory plays a crucial role to explain the shortcomings of the economic growth theories.

On the other hand, political participation is not only a phenomenon in political science, but it is also related to the economic theory. As we are going to see, political participation may be a source of happiness in a community or among individuals, besides being con-nected with economics. It has already been shown that political participation (e.g. political party membership, joining in political movements or being an activist) influences economic growth. There-fore, it does make sense within the economic theory that political participation creates some utility for individuals and it has posi-tive externalities. Following that, we make an effort to investigate how political participation affects economic growth and household well-being through a particular attention to collective bargaining.

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Figure 1: Participating in political activities by the blue-collar employees over the period 2001-2016.

In this regard, the data, we have gathered from The National In-stitute for Statistics (ISTAT), indicates the possible role of political participation on wage.

Figure 1 presents evaluation of the political participation by blue-collar employees in Italy during the period 2001 and 2016. The vertical axis stands for political participation per 100 people with same characteristics and the blue and orange dash line indicate the time trend of political participation. It can be seen that partic-ipating in political activities (in a mass-meeting and in a march) moderately decreased in Italy over the period 2001-2016.

On the other hand, Figure 2 shows the blue-collar employees’ bar-gained wage level in Italy over the period 2005-2016. According to that, wage level determined in the collective bargaining rose from 2005 to 2016. We are aware that there are many explanatory fac-tors, which we do not discuss for this evidence that have important effects on wage. Nevertheless, participating in marches goes up from 2007 to 2009, while participation in mass meetings by employees is on the rise over the period 2008-2009. At the same time, it is ap-parent from this figure that increment in the bargained wage has

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Figure 2: Hourly index of blue-collar employees’ wages according to collective labour agreements over the period 2005-2016.

been at higher level in the 2008 and 2009 in comparison to other years. Moreover, increment in the wage and political participation level have been at their lowest in 2016.

Besides that, Figure 3 shows the blue-collar employees’ waiting time to contract renewals where a worker might have an increase in his/her wage in the industry sector and in the private services. The black dash line indicates the increase in waiting time for the renewal of contracts. It is clear to see that, the the waiting time for renewal increases over the period 2010-2016. Although there is no adequate resources for the related data to explain importance of po-litical participation on economic growth and human well-being, we present a number of studies which found the relationship between

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Figure 3: Employees waiting for renewal of wage contract per 100 employees.

political participation, economic growth and human well-being in the chapter 2.

The previous studies for social capital consider that individuals’ time allocation is between the consumption of private or material goods and leisure which implies participating in social activity or partici-pating in associational activity. Furthermore, individuals invest in accumulation of social capital through leisure which is used to im-prove social ties.

Our first investigation in the chapter 3 for the decentralized and socially-planned economy models assumes, by expanding previous studies, that each individual decides to devote their time between political and social participation. By this means, we present partic-ipating in political activities as a dynamic of social capital accumu-lation, in the process of generation of social capital in the economic theory. The theoretical framework we used in the thesis is similar

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to the approach of Bilancini and D’Alessandro (2011), yet we also included political participation into the scope.

In the chapter 2, we will see the previous developments and dis-cussions for social capital within economic theory. In the sequel, we will present the findings from various researches, which examine possible impacts of the political participation on human welfare (e.g. economic performance, economic and social inequality, democracy and happiness). Lastly, previous empirical studies, which argue the relationship between political participation and social capital will be presented.

Following that, we will analyse the effects of time allocation to po-litical participation on collective bargaining and on the economic growth in the chapter 4. When famine of studies for the political perspective of barganing power is considered, we expect that this investigation fills the void in the related literature since there are no previous studies noticeably interested in determinant of the bar-gaining power.

In this sense, our model analyses the possible role of political partic-ipation in the economic growth process and aims to take the current literature further by doing so. Besides that, we expect that this ex-pansion becomes a theoretical background for the related empirical studies.

2

Literature Review

Numerous scholars have conducted a large number of studies to ex-plain the possible role of social capital in economics. In this line, we make an effort to demonstrate the importance of social capital for the economic growth. Considering that, we are going to confine the existing social capital literature to those approaching the mat-ter from an economic perspective. Following that, we are going to

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discuss the role of political participation on economic development and economic growth. Finally, in the chapter 2, we present existing literature which are studied on the relationship between political participation and social capital.

2.1 Theoretical Background in Social Capital

Up to now, there has been no consensus on the definition of social capital. Many scholars have interpreted the concept of social capital from various backgrounds (Putnam, 1995; Bourdieu, 1986; Coleman, 1988; Lin, 1999). Bourdieu (1986, p. 246) has defined social capital as "the aggregate of the actual potential resources which are linked to possession of a durable network of more or less institutionalized relationships of mutual acquaintance or recognition".

Thinking of social capital in terms of social networks enables to ex-amine social capital at the individual level and brings the concept into the economic idea of capital (Munasip, 2007). The concept of social capital has been theoretically argued within the economic lit-erature by many scholars: Zak and Knack (2001) have generated a general equilibrium growth model in which an expansion in het-erogeneity of a society affects adversely the investment to reveal economic growth. Their theoretical model has been supported by empirical evidence as well.

The argument that participating in a social network is a means of so-cial capital investment has been integrated into the economic growth theory by many authors. Antoci, Sacco and Vanin (2007) have con-structed a social capital accumulation model, where social capital is considered as relational networks and social norms. These types of networks and norms, which increase are positively correlated with social interactions promote accessibility to social activities. Addi-tionally, Antoci, Sabatini and Sodini (2011) demonstrate that social networks and social norms are boosted by the existing stock of

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so-cial capital and by increased time allocation to soso-cial participation. They also claim that individual utility is determined by private con-sumption of goods and by the leisure devoted to social participation. Consequently, individual’s social capital increases when individual allocates more time to social activities through building new social networks in a given social environment.

The finding of Glasser, Laibson and Sacerdote (2002) has opened a new door within the economic literature. They have contributed some arguments to the social capital theory from the economic point of view. They have formulated a social capital accumulation model where social capital is characterized as an asset. It has been demon-strated that a higher level in the cost of time results in a lower level of accumulated social capital. They have found that participating in a social network within the society is a means of social capital investment.

On the other hand, human capital has an important place in the eco-nomic growth literature. It has been proven that social capital has a strong impact on the accumulation of human capital (Coleman, 1988; Buchel and Duncan, 1998). There have been some theoreti-cal contributions to the neoclassitheoreti-cal growth model by Chou (2006) and Dinda (2008) incorporating social capital, which is linked with human capital, into the economic growth model. They have theo-retically showed that marginal productivity of social capital, as a contributor to human capital accumulation, has a positive impact on economic growth.

In addition to studies of Chou (2006) and Dinda (2008), Palma, Lopes and Sequeira (2009) have developed a social capital accumu-lation model to argue the possible effects of human, natural, physi-cal and social capital to the process of economic growth. They have also acknowledged the effect of the available stock of social capi-tal on the accumulation of human capicapi-tal. Additionally, Thompson

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and Robert (2015) have presented a growth model which is fostered by innovation. Their finding implies that social capital, which they claims to be based on trust, positively affects the innovation activity. Moreover, Knack and Keefer (1997) claim that the concept of social capital is a matter of economic outcome in which there is no strong relationship between associational activity and economic growth, al-though generalized trust fosters economic growth. However, Beugels-dijk and Smulders (2009) have presented an economic growth model which has been derived from the relationship between social interac-tions and economic growth. Their finding, which has been supported by empirical evidence shows that while bonding social capital has a negative impact, there is a positive relationship between bridging social capital and economic growth.1

Furthermore, it has been empirically demonstrated that there exists a significant correlation between social capital, defined in terms of generalized trust and associational activity, and economic growth (Whiteley, 2000; Beugelsdijk and Schaik, 2004). In contrast, Bar-tolini and Bonatti (2008) have developed an endogenous growth model which implies that there is a negative relationship between the level of social capital and the economic growth.

Bassetti and Favaro (2015) have presented an economic growth model, in which they have brought socio-political participation into the their model. They show that there is a relationship between socio-political participation and educational activities. According to their model, while time allocation for socio-political participation increases, time devoted to educational activities diminishes in the stationary state.

1_{Bonding social capital reflects a homogeneity in the social network. This kind of networks,}

which increase the cost of leisure come from close solidarity or family, while bridging social capital is referred as heterogeneity in the social networks (Beugelsdijk and Smulders, 2009; Putnam, 2000).

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2.2 Political Participation and Welfare

Political participation is a phenomenon which is discussed from var-ious perspectives. Many scholars have made efforts to explore indi-viduals’ behaviour with respect to political participation. Uhlaner (1989) has theoretically investigated why rational individuals par-ticipate in political activities (e.g. voting). The paper approaches the political participation in terms of relational goods. She has con-ceived the concept of relational goods as " Relational goods can only be enjoyed if shared with some others" (Uhlaner 1989, p. 254). Furthermore, Frey, Benz and Stutzer (2004) introduced the proce-dural utility. They formulate proceproce-dural utility as "Proceproce-dural util-ity means that there is something beyond instrumental outputs as they are captured in a traditional economic utility function. People may have preferences about how instrumental outcomes are gener-ated. These preferences about processes generate procedural util-ity." (Frey, Benz and Stutzer 2004, p. 379) It has conclusively been shown that a correlation exists between political participation and the quality of life in which political participation is a source of the procedural utility in Shapiro and Winters (2008). The finding shows that there is a significant positive relationship between voting and life satisfaction at individual level. However, this is a one-way cor-relation where the individuals’ level of happiness causes to political participation, not vice-versa, as supported by empirical evidence gathered throughout Latin America.

Another contribution to explain the sources of political participa-tion has been made by Brady, Verba and Schlozman (1995). They identify time, money and civic skills as the main resources for in-vestment in political participation. The empirical results indicate that the identified resources are significant predictors of political participation.

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other than the the utility perspective by some authors in the eco-nomic literature. There are some studies that investigate possible relationship between political power and economic growth, based on the distinction between de jure political power and de facto politi-cal power2 _{(Ellis and Fender, 2009; De Luca, Litina and Sekeris,}

2015). On the other hand, Ades (1995) presents a theoretical eco-nomic model on political participation and ecoeco-nomic development, where political participation has been treated as any political action, which affects the choice of political decision-maker (for instance, professional lobbyists and interest groups). The model is generated by integrating two approaches, political participation is regarded as exogenous within the first approach and the second approach consid-ers economic development as exogenous. The findings indicate that there exists a positive relationship between political participation and the economic performance.

When discussing the subject of what the linkage between political participation and economic growth is, we need to consider political ideology and its possible influences on economic growth as well. It has been demonstrated that political ideology creates difference in the economic performance and also that political ideology has an im-pact on the economic growth (Facchini and Melki, 2013; Bjornskov, 2005).

Identity in the sense of collective action has already been discussed as "the production of identities corresponds to the emergence of new networks of relationships of trust among movement actors, operat-ing within complex social environments. Those relationships guar-antee movements a range of opportunities. They are the basis for the development of informal communication networks, interaction and mutual support." (Porta and Diani, 2006, p. 94) Further,

iden-2_{De jure political power expresses a political power emerges from the political institutions,}

while de facto political power indicates a power comes from collective actions (Acemoglu and Robinson, 2006).

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tity may result in economic outcomes, for instance to be in solely a feminist movement or participating in another identity-based po-litical movement may influence economic outcomes, where this kind of social and political actions generate a utility for individuals. Ak-erlof and Kranton (2000) have published a crucial study in which they have approached identity from different dimensions and have presented a utility function in which individual’s utility increases or diminishes with acquisition or loss of identity. It is shown that there exists a strong correlation between the expansion of women’s rights and economic development (Doepke, Tertilt and Voena, 2011). Lesbian, gay, bisexual, transgender and queer (LGBTQ) people are also affected politically by their identity. Exclusion of LGBTQ peo-ple from the social and political interactions damages the economic development. Lee, Sheila, Kess and Yana (2014) have carried out a study for possible effects of inclusion of LGBTQ people on economic development. The finding implies that expansion of the LGBTQ people’s rights, which enable them to better integrate to the labour market, social and political activities fosters the economic develop-ment. Additionally, it may be important that immigrants’ political participation (for example voting) has an impact on economic out-comes (Bevelander and Pendakur, 2007).

Many authors have presented arguments on the relationship between democracy and the economic growth. Dasgupta (1990) has stud-ied with data from 55 less developed countries over the period of 1973-1979 where the average of the level of political rights and civil liberties has been used to measure the maturity of democracy. It is shown that there is a strong and positive correlation between democracy and economic growth. In contrast, Marsh (1988) has found that there is no relationship between democracy and the eco-nomic growth.

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devel-opments in Japan after World War II. It has been found that a high level of political participation of people, who have been relatively poor after World War II, has promoted greater economic equality in Japan. Besides that, Cicatiello, Ercolano and Gaeta (2015) empir-ically show how income inequality generates variety in the political evolvement. In addition to that, They have found that, individuals with higher income levels also have a higher level of participation in political activities as well, while relatively richer people’s par-ticipation in the political activities, e.g. voting or political party membership, increases the income inequality.

Being a strong supporter of political groups or of a political idea re-sults in happiness. This kind of sense of belonging may be a source of discrepancy in happiness of a society. Di Tella and Macculloch (2005) have examined how various political ideological groups con-tribute to happiness of the society differently. The data is generated from approximately a quarter million people, living in 10 OECD countries, over the period of 1975 to 1992. The finding demon-strates that whereas people in the left-wing of the political spectrum attach more importance to unemployment than inflation, those on the right-wing care more about inflation than unemployment. Fur-thermore, the people with right-wing opinions have expressed an increase in their happiness over the period when the government’s policies tended toward the right ideologically, meanwhile left-wing individuals have indicated a decrease in their level of happiness. Protests by social movements have a solid influence to change eco-nomic actors’ perception and may have negative effect on firms. Calveras, Ganuza and Llobet (2007) have formulated a model in which protest by consumers against a firm changes the production decisions of the firm in question. The model implies that activism by consumers prompts firms to produce socially optimal goods. In addition to all these, political participation can be matter for the

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labour union’s bargaining power. “The outcome of bargaining is not the result of the characteristics of either party, but rather is a func-tion of their resources relative to each other, their relafunc-tionship with third parties, and other factors in the environment.” (Burstein, Ein-wohner and Hollander, 1995, p. 280) Although, there are not many studies to examine the possible relationship between participating in political activities and labour union’s bargaining power, Ashen-felter and Johnson (1969) present an alternative bargaining model, in which there are three actors in the bargaining, their setting differs from other bargaing models by taking trade union’s ranks into con-sideration as well. They empirically illustrate that industrial strike activity by a labour union’s members makes a positive contribution to labour union’s bargaining power. Besides, Hick (1966) illustrates the relationship between duration of the strike and percentage in-crease in wage and concludes that in line with the strike duration, labour union’s resistance decreases, when employer’s wage offer in-creases and negotiated wage becomes higher simultaneously.

2.3 Empirical Evidence

What we know about the relationship between political participation and social capital is largely based upon empirical studies that inves-tigate how political participation may foster social capital through its dynamics. "Taking part in the life of several organizations and coming into contact with their activists and supporters, individu-als construct a series of unique social relationships. In these, the political dimension of action intersects and overlaps with the pri-vate dimension, to generate the foundations of a specific form of subculture." (Porta and Diani, 2009, p.131)

Regarding the relationship between social capital and political par-ticipation, the majority of studies indicate a strong correlation

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be-tween the two social capital and political participation. Teney and Hanquinet (2012) have analysed the data from seven municipalities of the Brussels region to investigate possible correlations between political participation and social capital among young people. The sample has been classified into six classes with respect to different forms of social capital. They point out that different classes which comprise of differently characterized social capital, display distinct-ness with regard to political participation. In this sense, the class that is formed by people with high social interaction levels present a high level of political participation. In other terms, individuals who allocate more time to social activities such as going to the cinema, cafes, concerts and meeting with friends are more likely to attend political meetings, discussions about political issues and reading political news, while the relatively isolated group is inactive with respect to political participation.

Lake and Huckfeldt (1998) identify social capital as "politically rel-evant social capital" where social capital is generated as a result of political expertise and political knowledge which emerges from social networks. The article was positioned on politically relevant social capital and analysed its impacts on political participation and concluded that individual political participation increases in conjunction with political expertise within a given social network and also with frequency of political interaction within a given social network. One question that needs to be asked, however, is whether the causality is from politically relevant social capital to political participation or the opposite way.

Political party membership plays an important role to create so-cial networks, as many scholars have already argued. Savage, Tam-pubolon, and Warde (2004) have studied with two local branches of political groups, Labour Party and Conservation Group, in the British political party system. It has been shown that

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participa-tion in activities of Labour Party and Conservaparticipa-tion Group produces social capital. On top of that, Savage, Tampubolon, and Warde (2004) indicate that the members of Labour party display a higher level of political activism, (a higher involvement in social activities) which generates a higher level of trust as opposed to the members of Conservation Group. The result can be interpreted as two po-litical groups at similar physical conditions generate different levels of social capital because of the different network structuring inside their parties.

Quinteiler, Stolle and Harell (2011) show that political participation expands the divergence in social network. They have studied the data generated from 4235 young people in Belgium and examined how political participation leads to divergence in young people’s social networks. The findings imply that since there is more diversity in political participation in a social network, this network generates more political participation as well. Moreover, Quinteiler, Stolle and Harell (2011) present a causality mechanism in which a higher level of political participation increases network diversity and then the increased network diversity fosters political participation.

There is a considerable amount of research, which studies how com-puter mediated communication can foster the political participation and social capital (Diani, 2000; Zuniga, Jung and Valenzuela, 2012; Tsatsou and Zhao, 2016). Zuniga, Jung and Valenzuela (2012) have approached determinants of social capital in terms of social network sites. It has conclusively been shown that social network sites used for news and political discussion networks have a significant positive connection with civic participation and offline political participation in the shape of protests, marches, political party membership or vot-ing in election. On the other hand, it has been empirically argued that individuals who participate in movements, protests, sit-in acts, improve social capital via social media e.g. Facebook in Taiwan

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(Tsatsou and Zhaou, 2016).

Social capital can take various forms, one of which is generalized trust. Besides the researches on the connection between political participation and social network, some authors have already dis-cussed the possible impact of political participation on trust (Pons and Navarro, 2010; Wollebaek and Selle, 2003).

Pons and Navarro (2010) have investigated how political participa-tion generates social capital, treated as generalized trust and they have conducted the research at individual level. They have gathered data from European Social Survey, which measures political partic-ipation by using some information about respondents (e.g. whether they worked in a political party or action group, signed a petition, boycotted certain products). It is concluded that political partici-pation has a significant positive impact on generalized trust. More-over, since political participation magnifies exchanges in society, the social ties increase with political participation.

3

Simple Framework

3.1 Assumptions

3.1.1 Households and Technology

We start setting the model by assuming that individual’s utility de-pends on consumption of the final goods and on consumption of the relational goods. Each household devotes his time, time endowment is normalized to one, between production of the final goods (1- li)

and production of the relational goods (li). In addition to that,

each household allocates his leisure time (li) among participating in

political activities (lP,i) and participating in social activities (lS,i),

where total leisure time li = lP,i+ lS,i and 0 < lP,i+ lS,i< 1, lP,i > 0

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utility function in terms of consumption of the final goods (ci) and

consumption of the relational goods (xi)

The instantaneous utility function for each household i ∈ [1, ..., N ] is given by: Ui(ci, xi) = " c1−β_i xβ_i 1 − σ #1−σ (1) where σ > 0 and σ 6= 1. ci is consumption of the final goods for each

household i and xi is consumption of the relational goods for each

household i. The elasticity parameter β refers both consumption of the final goods and the relational goods have a positive impact on each household i’s utility in which 0 < β < 1. We assume that each individual has an infinite horizon and for simplicity, we assume that total population in the economy is constant.

The Cobb Douglas production function for the final goods, by fol-lowing Romer (1986), in terms of allocated leisure time preferences by each household i is given by:

Yi = Akiα[1 − (lS,i+ lP,i)]1−α (2)

where kiis each household i’s physical capital and [1 − (lS,i+ lP,i)] is

each household i’s labour for the production of the final goods. The parameter A is a time independent productivity parameter and A > 0. On the other hand, the parameter α is the elasticity parameter, where 0 < α < 1. The parameter A is determined at the aggregate level and it is taken as given by all firms in the economy. Therefore, the parameter A can be expressed as A = eA¯k1−α , where ¯k refers the average level of physical capital stock in the economy. Since all firms in the economy behave identically in the production process, ¯

k = k.

In the competitive market equilibrium, the physical capital for each household i and the labour for each household i are supplied with

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their marginal products: ∂Y_∂k = r = αAkα−1_{[1 − (l} S+ lP)]1−α and ∂Y ∂(1−(lS+lP)) = w = (1 − α)Ak α_{[1 − (l} S+ lP)] −α .

3.1.2 Relational Goods and Social Capital

Social capital, in line with Putnam (2000), is considered as social and political ties and contacts, which emerge from interactions among individuals in a particular environment. In this sense, we consider social capital is a stock variable. We assume that each household i allocates his leisure time between participating in political activities (e.g. in the political party activities or in the protest movements) and participating in social activities (e.g. meeting with people). We describe the production function of relational goods in line wtih Uhlaner (1989). Accordingly, participation in political activities and participation in social activities by individuals are not only engine of the production of relational goods, but also participating in political and social activities promotes to generate new social and political networks, which are sources of positive externalities. We assume that leisure time for political and social participation directly comes into the existing political and social participation, generating pro-cess of new political and social ties. In this sense, leisure time for both political and social participation are sources for producing re-lational goods and accumulation of social capital.

The production function of relational goods xi for each household i:

xi = [lγS,il 1−γ P,i ]

1−θ_Kθ

S (3)

where KS is the current stock of social capital in the economy and

initial stock of social capital in the economy is not zero, KS > 0. The

parameter γ ensures the marginal productivites of both allocated leisure time to social and political participation are positive and decreasing in the production process of the relational goods, 0 <

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γ < 1. Likewise, marginal productivity of the current stock of social capital is positive and decreasing in the process of production of relational goods, where 0 < θ < 1.

i ) ∂xi ∂lS,i = γ(1 − θ)l (γ(1−θ)−1) S,i l (1−γ)(1−θ) P,i KSθ > 0 and ∂2_x i ∂2_l S,i = γ(1 − θ)(γ(1 − θ) − 1)l (γ(1−θ)−2) S,i l (1−γ)(1−θ) P,i KSθ < 0, ii) ∂xi ∂lP,i = (1 − γ)(1 − θ)l γ(1−θ) S,i l ((1−γ)(1−θ)−1) P,i K θ S > 0 and ∂2xi ∂2_l P,i = (1 − γ)(1 − θ)((1 − γ)(1 − θ) − 1)l γ(1−θ) S,i l ((1−γ)(1−θ)−2) P,i K θ S < 0, iii) ∂xi ∂KS = θ[l γ S,il 1−γ P,i ]1−θK θ−1 S > 0 and ∂2_x i ∂2_K S = θ(θ − 1)[l γ S,il 1−γ P,i ] 1−θ_Kθ−2 S < 0,

and accumulation of social capital is expressed as: ˙ KS = P _¯ lS+ ¯lP ν − δSKS (4)

where ¯lS =PN_i=1lS,i and ¯lP =PN_i=1lP. The current stock of social

capital depreciates over time, δS > 0. We assume that social sector

is always at its stationary level, ˙KS = 0. We assume that the average

level of devoted leisure time by each household to participating in political and social activities fosters accumulation of social capital. Leisure time to political participation (social participation) stands for political (social) networks in the economy as well. The parameter P measures productivity of building social capital and it is taken as time independent. The parameter ν is the elasticity parameter and denotes externalities in the generation of social capital, ν > 1. If we rearrange the utility function for each household i, we obtain:

Ui(ci, lS,i, lP,iKS) = (c1−β_i lφ_S,il_P,iϕ Kh S)1−σ 1 − σ (5) where φ, ϕ, τ ∈ (0, 1) and φ = γ(1 − θ)β, ϕ = (1 − γ)(1 − θ)β, h = θβ.

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3.2 The Decentralized Economy

There are many firms, which have same technology in the decen-tralized economy. Additionally, the real wage (w) and rental rate of physical capital (r) are taken as given in the competitive mar-ket. We assume that each household and each firm have rational expectations for the real wage and for rental rate of physical capi-tal. We ignore uncertainty to simplify the model. Furthermore, each household i only should decide about how much they consume or save in each instant and individuals do not recognize externalities, which come from production, leisure and social capital in the decen-tralized economy. There are labour market and capital market and every identical household maximizes his utility from period zero to infinity under the budget constraint. Furthermore, the parameter ρ > 0 refers to the rate of time preference.

The representative household maximizes the utility function:3

max c,lP,lS Z ∞ 0    h c1−β_lφ Sl ϕ PKSh i1−σ 1 − σ   e −ρt dt (6)

subject to the budget constraint:

˙k = τk + wL − δk − c (7)

k(0) = k0, KS(0) = KS,0 (8)

where depreciation rate of physical capital δ > 0, k, c, lS, lP, Ks > 0,

k0> 0 and k0 and KS,0 are taken as given.

By using the following current value Hamiltonian function, we get the optimal solution for the household maximization problem:

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H = h c1−βlφ_Sl_PϕK_Shi 1−σ 1 − σ + λAk α_{(1 − (l} S+ lP))1−α− δk − c (9) where λ is co-state variable for ˙k and c, lSand lP are choice variables.

The first order conditions yield: ∂H

∂c = 0 and ∂H

∂k = − ˙λ + λρ (10)

as well as Transversality condition:

lim

t→∞λke −ρt

= 0 (11)

From the first order condition for the choice variable c, we get: λ = 1 − β

c h

c1−βl_Sφlϕ_PK_Shi1−σ (12) Transversality condition (11) can be rewritten, by combining with the equation (12), as:

lim t→∞k 1 − β c h c1−βl_Sφl_PϕK_Shi 1−σ e−pt= 0 (13)

The condition (13) must hold along the growth path. If we solve the condition for the co-state variable in (10):

˙λ = λhδ + ρ − α eA(1 − (lS+ lP))1−α

i

(14) By differentiating the equation (12) with respect to time and with equation (14), to get the growth rate of consumption:

gc=

˙c c =

α eA [1 − (lS + lP)]1−α− (δ + ρ)

1 − (1 − σ)(1 − β) (15)

The neccessary condition (15), is called Euler equation, is satisfied on any optimal path. Furthermore, to get the growth rate of physical capital:

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gk = ˙k k = eA [1 − (lS+ lP)] 1−α − δ − c k (16)

We can derive c_k in terms of lSand lP. In this sense, first order

conditions for lS and lP yield:

∂H ∂lS = 0 (17) ∂H ∂lP = 0 (18)

If we solve the first order conditions (17) and (18), respectively, for lS and lP, we get two different equations for the ratio between cand

k: φ lS h c1−βl_Sφl_PϕK_Shi 1−σ = (1 − α)λhAk [1 − (le _S+ l_P)] −αi (19) By using equation (12) to plug in for λ in equation (19), we obtain:

c k = (1 − β) eA [1 − (lS + lP)] −α (1 − α)lS φ (20)

where φ = γ(1 − θ)β and for lP:

ϕ lP h c1−βlφ_Sl_PϕK_Sh i1−σ = (1 − α)λ h e Ak [1 − (lS+ lP)] −αi (21) Likewise, by using equation (12) to plug in for λ in equation (21) we get: c k = (1 − β) eA [1 − (lS+ lP)] −α (1 − α)lP ϕ (22)

where ϕ = (1 − γ)(1 − θ)β. If we consider both equations (20) and (22), we are able to represent the relationship between lS and lP:

lS = γ 1 − γ lP (23)

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where l∗S

l∗ P =

φ

ϕ , since φ = γ(1 − θ)β and ϕ = (1 − γ)(1 − θ)β.

The relationship, in the equation (23), implies that the highest level of the allocated leisure time to political participation, lP, can not

be higher than (1 − γ). Equation (23) indicates that lP ≤ 1 − γ.

To analyse an unique balanced growth path, we take into account equation (22) and by plugging into (16) and we rewrite growth of the physical capital equation:

gk = _k˙k = eA [1 − (lS + lP)]1−α− δ−

h

(1−β) eA[1−(lS+lP)]−α(1−α)lP

ϕ

i (24)

Then by equating the equation (24) and the equation (15), and by using the equation (23), the steady state equilibrium level, where the growth rate of consumption is equal to the growth rate of physical capital is written as:

e Ah1 − l∗P 1−γ i1−α − δ−   (1−β) eA 1− l∗P 1−γ −α (1−α)l∗p ϕ  = α eA 1−l∗P 1−γ 1−α −(δ+ρ) 1−(1−β)(1−σ) (25)

The equation (25) indicates the steady state equilibrium level of the growth rate of consumption and the growth rate of physical capital4_{. The equation indicates a unique equilibrium level of the}

l∗_P. It is clear to see that the growth of the physical capital and the growth of the consumption decrease in the allocated leisure time to political participation lP.

We are able to illustrate that there exists a unique level of l∗_p ∈ [0, 1 − γ] in which the growth rate of physical capital is equal to the growth rate of consumption. In this regard, Figure 4 indicates a numerical illustration for the balanced growth path of physical

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capital and the balanced growh path of consumption in terms of the allocated leisure time to political participation. The horizontal axis shows changes in lP between 0 and 0.80 and the vertical axis

shows the growth rate of physical capital and the growth rate of consumption, where gc > 0 and gk > 0 . The red line represents the

balanced growth path of physical capital and the green line repre-sents the balanced growth path of consumption. It is clear to see in Figure 4 that the balanced growth path of physical capital is positive, where lP ∈ [0, 0.44) and the balanced growth path of

con-sumption is positive, where lP ∈ [0, 0.80). The point E∗ represents

the unique steady state equilibrum level of l_P∗ which corresponds to steady state equilibrium levels of the growth rate of physical capital and consumption. We specify all parameter values, respectively, as

e

A = 1, σ = 2.5, γ = 0.2, θ = 0.6, δ = 0.05, ρ = 0.05, α = 0.7, β = 0.5. Numerical illustration implies that the equilibrium level of allocated leisure time to political participation l∗_p is approximately 0.36, while the steady state equilibrium level of growth rate is roughly 0.18, E∗ = (0.36, 0.18).

Additionally, we investigate the effect of changes in the some param-eters on the steady state equilibrium level. On that note, Figure 5 exhibits the impact of changes in the parameters β, ρ, γ and α on the steady state equilibrium level E. The bottom right panel in Figure 5 shows that an increase in the parameter γ, stands for the marginal productivity of social participation, goes up (the parameter γ decreases the marginal productivity of political participation). It can be numerically illustrated that when the parameter γ increases from 0.10 to 0.90, where other parameters are fixed, have already specified for Figure 4, the unique steady state equilibrium level of growth (g_k∗ = g_c∗ = g∗) remains stable and level of the allocated leisure time to political participation, not surprisingly, decreases in the parameter γ.

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Figure 4: Numerical illustration of the steady state equilibrium in the decen-tralized economy.

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Figure 5: Illustration of the effect of some parameters on the equilibrium level of growth.

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Notwithstanding that, the steady state equilibrium level decreases (increases) in the marginal utility parameter of relational good (con-sumption). The top left panel in Figure 5 shows that an increase in the marginal utility parameter of relational goods β ∈ [0.1, 0.9] generates a lower steady state equilibrium level. The equilibrium level E is 0.22, where the parameter β = 0.10, while the new steady state equilibrium level E0 is 0.10, where the parameter β = 0.90. It is explicitly illustrated in the bottom left panel of Figure 5 that a rise in the time preference parameter ρ in the range of 0.02-0.2 causes a decline in the the steady state equilibrium level from 0.25 to 0.12. Lastly, the top right panel in Figure 5 means that when the marginal productivity parameter of the phyiscal capital α increases in the range of 0.20-0.90, the equilibrium level ascends from the steady state level E to E0. The steady state equilibrium level of growth rate is 0.030, when the parameter α = 0.20 and an increment in the parameter α from 0.20 to 0.90 manipulates the steady state level of the growth to 0.19.

3.3 The Social Planner Solution

We assume that the economy is socially planned rather than de-centralized. In this regard, the representative agent maximizes his utiliy by taking in consideration all the externalities in the economy. Therefore, the agent is conscious of all externalities in social, pro-ductive sector and private sector, differently from the decentralized economy. In the socially planned economy, each household maxi-mizes the utility function:

max c,lP,lS Z ∞ 0 [c1−β_lφ Sl ϕ PKSh]1−σ 1 − σ ! e−ρtdt (26)

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˙

KS = P [lS+ lP] ν

− δSKS (28)

k(0) = k0 and KS(0) = KS,0 (29)

where depreciation rate of physical capital δ > 0 and depreciation rate of social capital δS > 0. As well as, k, c, lS, lP, KS > 0, k0 > 0

and KS,0 > 0. Thus, it is shown that each household recognizes all

externalities in which k0 and KS,0 are taken no longer as given.

We set up the associated current value Hamiltonian function to solve the maximization problem:

H = [c1−βl φ Sl ϕ PK h S] 1−σ 1−σ + λ [Ak[1 − (lS+ lP)] 1−α_{− δk − c] +} µ [P [lS+ lP]ν − δSKS] (30) where λ is adjoint variable for ˙k and µ is adjoint variable for con-straint K˙S as well as c, lP, lS are choice variables. The first order

conditions yield: ∂H ∂c = 0, ∂H ∂lS = 0 and ∂H ∂lP = 0 (31) ∂H ∂k = − ˙λ + λρ and ∂H ∂KS = − ˙µ + µρ (32) The parameter ρ > 0 refers the rate of time preference and Transver-sality condition: lim t→∞λke −ρt = 0 (33) lim t→∞µKSe −ρt = 0 (34)

By differentiating H, in the equation (30), with respect to the con-trol variable c, we obtain:

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λ = 1 − β c h c1−βl_Sφlϕ_PK_Shi 1−σ (35) Likewise, for both control variables lS and lp:

φ lS h c1−β_lφ Sl ϕ PKSh i1−σ = λ(1 − α) [Ak[1 − (lS+ lP)]−α] − µν[P [lS+ lP]ν−1] (36) and ϕ lP h c1−βlφ_Sl_PϕK_Sh i1−σ = λ(1 − α) [Ak[1 − (lS+ lP)]−α] − µν[P [lS+ lP]ν−1] (37)

By differentiating H, in the equation (30), with respect to the state variable k, the result:

˙λ = λ δ + ρ − A[1 − (lS+ lP)]1−α

(38) and, in the same way, we differentiate H with respect to the state variable KS: ˙ µ = µ(δS+ ρ) − τ KS h c1−βlφ_Slϕ_PK_Shi 1−σ (39) If we differentiate the equation (35) with respect to time and substi-tute for ˙λ in the equation (38) in which the steady state equilibrium holds lP˙ lP = ˙ lS lS = ˙ KS

KS and since the growth rates of leisure for

polit-ical and social participation should be equal to zero as well as the growth rate of social capital must be equal to zero along the bal-anced growth path. We obtain the neccessary condition for choosing consumption along the balanced growth path:

gc=

˙c c =

A[1 − (lS+ lP)]1−α− (δ + ρ)

1 − (1 − β)(1 − σ) (40)

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gk=

˙k

k = A[1 − (lS+ lP)]

1−α_{− δ −} c

k (41)

and the growth rate of social capital is equal to:

gKS = ˙ KS KS = P [lS+ lP] KS ν − δS (42)

Furthermore, we are able to express co-state variable µ in terms of lP and lS, by plugging the equation (35) into the equations (36) and

(37) for the variable λ, we get two equations for µ in terms of lS and

lP, respectively: µlS = h c1−β_lφ Sl ϕ PK h S i1−σ ν[P [lS+ lP] ν−1 ]lS (1 − β)(1 − α)A[1 − (lS+ lP)]−αlS k c − φ (43) and µlP = h c1−β_lφ Sl ϕ PKSh i1−σ ν[P [lS+ lP]ν−1]lP (1 − β)(1 − α)A[1 − (lS+ lP)]−αlP k c − ϕ (44)

Transversality condition (34) can be rewritten, by combining with the equation (44): lim t→∞ ˙ h c1−β_lφ Sl ϕ PKSh i1−σ ν[P [lS+lP]ν−1]lP (1 − β)(1 − α)A[1 − (lS+ lP)] −α_l Pk_c − ϕ ˙ KSe−ρt= 0 (45)

The condition (45) must hold along the growth path. The steady state equilibrium satisfies that lP˙

lP = ˙ lS lS = ˙ KS KS = 0. In this case,

current stock of social capital can be shown as KS =

P [lS+lP]ν

δS . By

taking time derivatives of the equations (43) and (44) respectively and by substituting for the µ_µ˙ in the equation (39), we obtain:

c k = (1−β)(1−α)A[1−(lS+lP)]−αlP ϕ n (1−β)(1−σ) 1−(1−β)(1−σ)[A[1−(lS+lP)]1−α−(δ+ρ)]−(δS+ρ) o − υhlP δS P (lp+lS ) n (1−β)(1−σ) 1−(1−β)(1−σ)[A[1 − (lS+ lP)] 1−α_{− (δ + ρ)] − (δ} S+ ρ) o (46) and

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c k = (1−β)(1−α)A[1−(lS+lP)]−αlS φn_{1−(1−β)(1−σ)}(1−β)(1−σ) [A[1−(lS+lP)]1−α−(δ+ρ)]−(δS+ρ) o − νhlS δS P (lP +lS ) n (1−β)(1−σ) 1−(1−β)(1−σ)[A[1 − (lS+ lP)] 1−α_{− (δ + p)] − (δ} S+ ρ) o (47)

since l∗_S = h_1−γγ il∗_P in the steady state, where φ = γ(1 − θ)β and ϕ = (1 − γ)(1 − θ)β and h = βθ. In the steady state equilibrium, the growth rate of physical capital:

gk= A 1 − l∗P 1−γ 1−α − δ −nΩhA[1 − l∗P 1−γ] 1−α_{− (δ + ρ)}i_{− (δ} S+ ρ) o (1−β)(1−α)A[1−l∗P 1−γ] −α_l∗ P ϕ Ω A[1−l∗P 1−γ]1−α−(δ+ρ) −(δS+ρ) −νβθδS(1−γ) (48)

where, Ω = _{1−(1−β)(1−σ)}(1−β)(1−σ) . And the growth rate of consumption:

gc = A1 − lP∗ 1−γ 1−α − (δ + ρ) 1 − (1 − β)(1 − σ) (49)

In the steady state equilibrium, the growth rate of physical capital should be equal to the growth rate of consumption, g_k∗ = g_c∗ = g∗and the steady state equilibrium ensures that there exists a unique level of l_P∗ ∈ (0, 1 − γ)5_{. As in the decentralized economy, a higher level}

of allocation of leisure time to political participation decreases the growth rate of physical capital and the growth rate of consumption as well. At the some levels of lP, the growth rate of physical capital

and the growth rate of the consumption are greater than zero. Proposition 1 The growth rate of physical capital decreases in the marginal productivity parameter of total level of allocated leisure time ν.

Proof From the equation (48):

∂gk ∂ν = − (1−β)(1−α)AlP[Ω " A− 1−l∗P 1−γ 1−α −(δ+ρ) # −(δS+ρ)]βθδS(1−γ) " ϕ ( Ω " A 1− l∗P 1−γ 1−α −(δ+ρ) # −(δS+ρ) ) −νβθδS (1−γ)_P #2 P < 0. The result indicates that the growth rate of physical capital decreases in

5_{See Appendix B for the existence of the steady state equilibrium in the socially planned}

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the parameter ν.

The system defined by optimality conditions in the centralized econ-omy is quite hard to be studied, because of its dimension. Nonethe-less we have found numerical evidence of the existence and the uniqueness of stationary solution. Figure 6 displays the balanced growth paths of physical capital and consumption in terms of the al-located leisure time to political participation, where lP ∈ [0, 1 − γ].

Figure 6 below clearly exhibits that there exists a unique steady state equilibrium level, where l∗_P ∈ [0, 0.8]. The parameter values are specified as eA = 1, σ = 2.5, γ = 0.2, θ = 0.6, δ = 0.05, δS =

0.2, α = 0.7, β = 0.5, ρ = 0.05, ν = 2. The horizontal axis repre-sents the variation of lP between 0 and 0.80 and the vertical axis

depicts the balanced growth paths of physical capital and consump-tion. Figure 6 shows that gc > 0, where lP ∈ [0, 0.80) and gk > 0,

where lP ∈ [0, 0.58). In the the steady state equilibrium level E∗,

the growth rate of physical capital is equal to the growth rate of con-sumption. Numerically, it is presented that the steady state level of political participation l_P∗ is equal to 0.44 and the steady state equilibrium level of the growth rate is equal to 0.22 in the socially planned economy.

Figure 7 displays the impact of changes in the some parameters on the steady state equilibirum. The top left panel in Figure 7 shows that when other parameters are fixed, the steady state levels of the growth rate of physical capital and the growth rate of consumption decrease in the marginal utility parameter of relational goods β ∈ [0.1, 0.9]. The steady state equilibrium level E is 0.35, when the parameter β = 0.1, however the steady state equilibrium level is 0.15, where the parameter β = 0.9.

The top right panel in Figure 7 indicates that an increase in the marginal productivity parameter of physical capital α generates a lower steady state equilibrium level. When the parameter α = 0.2,

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Figure 6: Numerical illustration of the steady state equilibrium in the socially planned economy.

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Figure 7: Illustration of the effects of some parameters on the equilibrium level of growth.

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the steady state equilibrium level is equal to 0.41, while the equi-librium level is equal to 0.15, when the parameter α = 0.90. Fur-thermore, the bottom left panel in Figure 7 discloses that a rise in the rate of time preference ρ ∈ [0.02, 0.2] causes a lower level of the steady state equilibrium level. The steady state equilibrium level goes down from 0.33 to 0.20, when the parameter ρ rises from 0.02 to 0.20.

Lastly, the bottom right panel in Figure 7 shows that the marginal productivity parameter of the allocated leisure time to participating social activities γ does not have any remarkable impact on the steady state equilibrium level, relatively a lower steady state level of the political participation maintains the same steady state level of the growth rate.

3.4 Comparative Statistics

Heretofore, we have discussed the economic growth from the point of view of political participation through social capital. Our findings show that political participation is a matter of the economic growth. In that sense, our results determine that the steady state equilibrium level of the growth rate in the socially planned economy is higher in comparison to the steady state level of the growth rate in the decentrally planned economy.

Furthermore, the steady state equilibrium level of the political par-ticipation in the socially planned economy is higher than the steady state equilibrium level of the political participation in the decen-tralized economy. Eventually, when households are aware of the externalities, they allocate a higher portion of their leisure time to political participation and at the same time they have a higher growth rate in the steady state equilibrium. A comparison of the two results reveals that:

i) g∗_k,s > g_k,d∗ and g_c,s∗ > g_c,d∗ where the notation s stands for the growth rate in the socially planned economy and d refers the growth

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rate in the decentralized economy. The steady state equilibrium level in the socially planned economy is equal to 0.22, while the steady state level of the growth rate is equal to 0.18 in the decentralized economy.

ii) l_P,s∗ > l∗_P,d. l_P,s∗ is the steady state equilibrium level of the allo-cated leisure time to political participation in the socially planned economy and it is equal to 0.44 whereas l∗_P,d is the steady state level of the allocated leisure time to political participation in the decen-tralized economy and it is equal to 0.36.

4

The Unionized Economy

Several attempts have already argued the growth effect of unioni-sation within the endogenous growth framework. Chang, Shaw and Lai (2007) have demonstrated that a labour union’s preferences be-tween wage and employment are determinative on the unemploy-ment and the economic growth. They have emphasized that labour union’s bargaining power has an positive impact on employment and economic growth in the case of labour union is employment oriented rather than wage oriented. Contrary, a higher level of union’s bar-gaining power composes a lower level of growth and employment, when labour union is wage oriented. On the other hand, it has been already shown that, even if labour union is wage oriented, unionisa-tion may have positive effect on employment and economic growth (Bhattacharyya and Gupta, 2015).

Following Chang, Shaw and Lai (2007), Chang and Hung (2016) and Bhattacharyya and Gupta (2015), we further our theoretical investigation with an unionized economy is composed of households, firms and a labour union.

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4.1 Basic Structure

4.1.1 Firms

We assume that each firm consumes a certain amount of physical capital and a certain amount of labour to produce a final good Y in the competitive product market. The Cobb-Douglas production function for each household i:

Yi = Akiα[(1 − lP,i− lS,i)Li]β (50)

where 0 < α < 1, 0 < β < 1 and 0 < α + β < 1. Moreover, A > 0 is time independent productivity parameter, ki and Li respectively

denotes physical capital and labour for each household i. Number of the workers is defined by L and (1 − lP − lS) stands for the total

working hours. Number of the workers L and the households’ time endowment are normalized to one for the model. On the other hand, allocated leisure time to political participation by each household i is denoted by lP,i and lS,i represents the allocated leisure time of

households to social participation.

As we have already specified before, the time independent parame-ter A is expressed as A = eA¯k1−α_{where ¯}_{k denotes the average level of}

physical capital stock in the unionized economy. Moreover, marginal productivity of physical capital r in the competitive market equilib-rium: τ = ∂Y ∂k = αAk α−1_{[(1 − l} P − lS)L] β (51) and each firm desires to maximize it’s profit π:

π = Y − w(1 − lP − lS)L − τ k (52)

where r is the rental rate of capital and w presents the each house-hold i’s wage per each hour.

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4.1.2 Labour Union and Collective Bargaining

Labour union’s utility depends on the net wage premium, which is given by the difference between wage and unpaid working hours rate and number of union’s member. In this line, Labour union’s utility function is expressed as:

U = {[w(1 − lP − lS) − b] Lz} with 0 < z < 1. (53)

where w(1 − lP − lS) − b represents the net wage premium. The

parameter b ∈ (0, 1) refers the opportunty cost of working and it is taken as given. We assume that the labour union is a closed shop labour union6_{. Therefore, all workers are members of the labour}

union and it represents employment rate as well.

The union seeks to maximize it’s utility in the collective bargaining with respect to whether the union is more wage-oriented or it is more employment-oriented. We assume that the labour union is more wage-oriented, since 0 < z < 1. Negotiated wage and employment are a result of the efficient bargaining between the labour union and the employer’s federation7_{. According to that, the level of wage}

and employment level are determined in the collective bargaining between a labour union and the employers.

Following that, the generalized Nash product is written as:

max ψ = [(w(1 − lP − lS) − b)Lz]p(lP)[Y − wL − τ k]1−p(lP) (54)

The first order conditions of the efficient bargaining game yield:

6_{Closed shop union represents that all employees in the economy are members of the union}

as well. In return, it is not required that all employees are members of the labour union in the open shop labour union. See also Hoagland (1918).

7_{We assume that labour union’s objective is specified as efficient contracts (bargaining over}

wage and employment) instead of right-to-manage (bargaining only for the determination of wage). Chang and Hung (2016) have considered labour union’s barganing objective as managerial labour union, the former, while Bhattacharyya and Gupta (2015) have assumed the union’s bargaining objective as right-to-mdel, the latter.

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∂ψ

∂w = 0 (55)

∂ψ

∂L = 0 (56)

where each firm’s profit is given by π = Y − wL − τ k and p(lP) ∈

(0, 1) represents the labour union’s relative bargaining power. We assume, in line with Checchi and Corneo (1998), that employed workers’ political participation (e.g. participating in strike, net-working activities with political institutions) has a positive impact on the labour union’s bargaining power. In this regard, average level of political participation in the economy strengthens labour union’s bargaining power. We are able to specify bargaining power of the labour union:

p(lP) = p ¯lP = p

PN

i=1lPL

L = ϑ (57)

The equation (57) implies that bargaining power of the labour union increases in average level of the allocated leisure time to political participation.

In our model, labour union and employer federation bargain over the wage level and the employment rate. To find optimal level of wage and employment, the first order conditions of the maximization problem with respect to w and L yield:

∂ψ ∂w = ϑ(1 − lP − lS) w(1 − lP − lS) − b = (1 − ϑ)(1 − lP − lS)L Y − w(1 − lP − lS)L − τ k (58) and ∂ψ ∂L = ϑz L + (1 − ϑ) Y − w(1 − lP − lS)L − τ k w(1 − lP− lS) − Y β L (59)

By combining the equations (58) and (59), contract curve is given by:

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w(1 − lP − lS) − b = 1 ν w(1 − lP − lS) − Y β L (60) By solving the equation (59) with the marginal productivity of phys-ical capital condition (51), we obtain the negotiated wage level:

w = β(1 − ϑ) + (1 − α)ϑz (1 − ϑ) + ϑz Y (1 − lP − lS)L (61) Proposition 2 Each household i’s shared wage income increases in the barganing power of the union, ϑ.

Proof From the equation (61), we are able to show the equation of households’ share income,

wL(1 − lP − lS)

Y =

β(1 − ϑ) + (1 − α)ϑz

(1 − ϑ) + ϑz (62)

and by taking first derivative of the equation (62): ∂ h wL(1−lP−lS) Y i ∂ϑ = z(1−α)−β− [zϑ(1 − α) + (1 − ϑ)β] (−1 + z) (1 − ϑ) + ϑz > 0 where the parameter z ∈ (0, 1). Moreover, second derivative of the equation (62) with respect to ϑ:

∂2hwL(1−lP −lS ) Y i ∂2_ϑ = −z(1 − α) − β+ [zϑ(1−α)+(1−ϑ)β](−1+z) (1−ϑ)+ϑz < 0

The result implies that a higher level of labour union’s barganing power ϑ generates a higher level of workers’ share income.

On the other hand, it is possible to derive bargained employment rate. In this sense, by plugging the equation (62) into the equation (61) and by assuming b = sY , s is the ratio between the opportunity cost b and Y , the bargained employment rate L∗:

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L∗ = T s 1 − 1 z + β zs < 1 (63)

where T = zϑ(1−α)+(1−ϑ)β_(1−ϑ)+ϑz , and T ∈ (0, 1). Negotiated employment rate is designated as fixed and it holds, L∗ ∈ (0, 1). We need a parametric restriction to ensure that 0 < L∗ < 1:

s > T (1 − z) z + β z and β T > (1 − z) (64) Proposition 3 Negotiated employment rate decreases in the bar-ganing power of the union, ϑ.

Proof By taking first derivative of the equation (63), we are able to show that employment rate decreases in the labour union’s bargaining power ϑ, ∂L∗ ∂ϑ = [z(1 − α) − β] z−1 z − [zϑ(1−α)+(1−ϑ)β](−1+z) z−1_z (1−ϑ)+ϑz < 0 (65) where the parameter 0 < z < 1. Furthermore, second derivative of the equation (63) with respect to the parameter ϑ:

∂2_L∗ ∂2_ϑ = − [z(1 − α) − β] z−1 z + [zϑ(1−α)+(1−ϑ)β](−1+z) z−1_z (1−ϑ)+ϑz > 0 (66) So far, we have shown that while bargained wage, determined in the collective bargaining, increases in the labour union’s bargain-ing power, negotiated employment level decreases in the bargainbargain-ing power of the labour union.

4.1.3 Households

As we have specified before, each household i derives utility from consumption of the final good ciand consumption of relational goods

xi. In this sense, the instantaneous utility function for each

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Ui(ci, xi) = (ci)1−a(xi)a 1 − σ 1−σ (67) where xi = [(lS,iγ l 1−γ P,i )]1−ηK η S, 0 < a < 1 and σ > 0 and σ 6= 1. If we

rewrite the representative household’s utility function:

U (c, lS, lPKS) = " c1−a_lφ Sl ϕ PKSb 1 − σ #1−σ (68) where φ = γ(1 − η)a, ϕ = (1 − γ)(1 − η)a and b = aη.

We are able to rewrite the representative household’s dynamic op-timization problem in the unionized economy:

max c,lP,lS Z ∞ 0    h c1−alφ_Sl_PϕK_Sbi 1−σ 1 − σ   e −ρt dt (69)

˙k = τk + w(1 − lP − lS)L + π − c (70)

k(0) = k0 and KS(0) = KS,0 (71)

where time preference parameter ρ > 0. We assume that k, c, lS, lP, KS >

0 and k0 > 0, KS,0 > 0. Furthermore, k(0) = k0 and KS(0) = KS,0

are given. Furthermore, employment rate is determined in the col-lective barganing and the constant rate of negotiated employment rate is denoted by L∗. When we consider the budget constraint, we are able to rearrange the accumulated wealth constraint of the unionized economy, by plugging the equation (52) into the budget constraint:

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By using the following current value Hamiltonian function8_: H = h c1−a_lφ Sl ϕ PKSb i1−σ 1 − σ + λ h Akα[(1 − lP − lS)L∗]β − c i (73) where λ is co-state variable for ˙k is the co-state variable for ˙K and c, lS and lP are choice variables as well. The first order conditions

yield: ∂H ∂c = 0 ∂H ∂lS = 0 and ∂H ∂lP = 0 (74) ∂H ∂k = − ˙λ + λρ (75)

and Transversality condition: lim

t→∞λke −ρt

= 0 (76)

By differentiating H with respect to the control variable c: λ = 1 − a

c h

c1−alφ_Sl_PϕK_Sbi1−σ (77) And from the first order condition (75):

˙λ = λhρ − α eA [(1 − lP − lS)L∗]β

i

(78) The steady state equilibrium should satisfy the following property,

˙ lP lP = ˙ lS lS = ˙ KS

KS = 0. If we differentiate the equation (77) with respect

to time and substitute for ˙λ in the equation (78), then the balanced growth path of the consumption:

gc = ˙c c = α eAh(1 − lP− lS) h_{zϑ(1−α)+(1−ϑ)β} ((1−ϑ)+ϑzs 1 − 1 z + β zs iiβ − ρ 1 − (1 − σ)(1 − a) (79)

where constant rate of employment L∗ is given by

L∗ = zϑ(1−α)+(1−ϑ)β_{s((1−ϑ)+ϑz))} 1 − 1_z + _zsβ. Furthermore, the accumulation of physical capital:

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gk= ˙k k = eA (1 − lP − lS) zϑ(1 − α) + (1 − ϑ)β ((1 − ϑ) + ϑz)s 1 − 1 z + β zs β − c k (80)

The first order conditions for the control variables lS and lP

respec-tively yield: ∂H ∂lS = φ lS h c1−al_Sφl_PϕK_Sb i1−σ = λ " β eAk(1 − lP − lS)βL∗ β (1 − lP − lS) # (81) and ∂H ∂lP = ϕ lP h c1−alφ_Slϕ_PK_Sϑi 1−σ = λ " β eAk(1 − lP − lS)βL∗ β (1 − lP − lS) # (82) By substituting the equation (77) in the equation (81):

c k = (1 − a) eAβ(1 − lP − lS)βL∗ β lP ϕ(1 − lP − lS) (83) Likewise, by substituting the equation (77) in the equation (82):

c k = (1 − a) eAβ(1 − lP − lS)βL∗ β lS φ(1 − lP − lS) (84) If we consider both equations (83) and (84), as we have already shown, we get the relationship between allocated leisure time to polical participation and social participation, lS =

h

γ 1−γ

i

lP. When

we rewrite the equation (80) by considering the equation (83) and with the relationship lS =

h