Ca Foscari University of Venice

Transcription

1 Ca Foscari University of Venice M.Sc programme in Economics (A.Y ) Large countries are better off in an open economy and small countries are better off in a closed economy - with empirical evidence Candidate: Mumu Ayesha Sugandhi Student ID: Supervisor: Prof. Federico Etro Assistant Supervisor: Elisabetta Lodigiani

2 Abstract Two of the fundamental political and economic phenomena of the last century have been the break up of nations into smaller states and the increased economic integration of international markets. This dissertation reviews the theoretical literature on these topics. The purpose of this dissertation is to study the relationship between size, government consumption and trade openness. We present empirical results that show that of open economy are positively and statistically significant and are economically sizable for small countries, and country size is negatively related to the government spending and most of the government spending items. The results are robust to different time periods and country samples, different econometric techniques and to several sets of control variables. 2

3 Contents Abstract 2 Contents 3 List Of Tables 5 Executive Summary 6 Chapter One: Introduction Determinant of borders Determinant of Size of countries The benefits of size The cost of size Chapter Two: Theoretical Presentation Of The Models Alesina, Spolaore and Wacziarg(2000) : basic structure Production and trade Capital accumulation and growth Steady state income/output Equilibrium analysis Equilibrium analysis part 1: The main Alesina and Spolaore (1997,2003) Trade, growth and openness theory Equilibrium analysis part 2: Etro (2006) theory Equilibrium welfare Equilibrium government spending and public spending provision 3

4 2.3. Summary and Conclusions Chapter Three: Empirical Evidence The relationship between size and openness The relationship between government consumption and size Summary and Conclusions Chapter Four: Summary And Concluding Remarks 53 REFERENCES 55 Theoretical part Empirical part 4

5 List of Tables 2.1. Comparison between the utility function of endogenous and exogenous government spending models Comparison between the optimal size of our distinct models Descriptive statistics ( averages) Pairwise correlations for the main variables of interest ( averages) Conditional correlation ( ) Constrained SUR estimate (size =log pop, openness=n. openness) Descriptive statistics ( averages) Pairwise correlations for the main variables of interest ( averages) a Table 3.2.3(b) OLS regression for various control variables of government consumption (size=log of population)- Demographic size b. Table 3.2.3(b) OLS regression for various control variables of government consumption (size=log of total GDP)- Economic size Cross- sectional time- series FGLS regression tail p- value test for sasabuchi test

6 Executive summary A large body of literature deals with the economic determinants of government size, the relationship of government consumption with size of country and the determinants of trade openness. Recent studies of the economics of country formation, by Alesina, Spolaore and Wacziarg (2003); Etro (2006) suggest that country size, government size and trade openness are interconnected and Rodrik (1996) suggest that, size is negatively correlated with government spending. Normally size of countries has always been considered an exogenous variable. Nevertheless, the borders of countries and therefore their size change in response to economic factors such as the pattern of international trade. For instance smaller countries have a greater stake in maintaining free trade because of the larger market space it gets through open economy while for a close economy, being large is considered as a benefit. There exists a trade- off between heterogeneity costs and benefits from scale economies, and both increase in the size of a country. Trough these trade- off, size effects the share of its public spending, which is maximized at an intermediate size and the higher the heterogeneity cost the larger are the size. The main inspiration of my research is the theoretical work of Alesina and Spolaore (1997,2005), who have introduced that; there is a trade- off between heterogeneity (in preferences) and scale economies (in public good provision). And this trade- off works as the determinant of the political geography. Their implications of openness and heterogeneity cost pointed out towards political secessions and lots of small countries. My second, paper of references are Rodrik (1996), who determined a negative relationship between government consumption and size and Etro 1 who has reconstructed and renovated the AS 2 theory. Etro, in his paper, pointed out the limits of the Alesina and Spolaore (1997,2005) model, that is considering public spending per nation as an exogenous and fixed variable. Which limited the countries from choosing the size of their public spending and constrained the countries to provide same amount of public goods independently from their dimension. Considering size of countries 1 Etro refers to Etro(2006) 2 AS refers to Alesina and Spolaore (1997,2005) model 6

7 and public spending as endogenous variables, he explained the relationship between government consumption and size. And argued that, the optimal geography 3 might not be a stable equilibrium because it may imply too large countries from which citizens at the borders would prefer to escape. In particular, these papers have put forward two hypotheses: Large countries are better off in a closed economy and small countries are better off in an open economy Smaller countries have a larger share of public consumption in GDP We will be reviewing both of the above- discussed hypotheses empirically. The empirical relationship of size and openness has already been proved by Alesina, Spolaore and Wacziarg (2003). Notwithstanding, to the best of my knowledge, the impact of the size of nations upon the determination of government spending has not yet been empirically discussed in the literature after Rodrik(1996). These two facts, taken together, may account for the observation that open countries have larger governments. This paper is organized as follows; In the first chapter, we discuss some of the stylized facts concerning the determinants of size of a country. Chapter 2 presents the theoretical models specifying our targeted relationship. And chapter 3 empirically checks and confirms the results of both AS and relationship between government consumption and size. Basically we show that, small countries are better off in an open economy and larger countries are better off in a closed economy. Chapter four concludes the findings of overall discussion. 3 The one that AS proved in their theory by considering the public spending exogenous. 7

8 Chapter 1 Introduction Countries come in all size, some are large and some are small. The five largest countries (by population) in the world are China, India, the USA, Indonesia, and Brazil. Among them only the USA is a rich country. Basically, many of the richest countries in the world are small. In fact the richest country in the world in 2010, in terms of income per capita, was Luxembourg that had inhabitants. According to World Bank, of the ten richest countries in the world in terms of GDP per capita (indicator of a country s standard of living), six have population above one million. They are the United States (313.9 million people), Australia (22.32 million), Austria (8.424 million), Switzerland (7.912 million), Norway (4.953 million), and Singapore (5.184 million). And of these six countries, two are below average in terms of population. The largest increase in the number of independent countries in the post II world war has been accompanied by an expansion of world trade and by a sharp increase in economic integration. Basically today s countries are smaller in size than the countries that got independence decades back. This independence depends on various facts such as regional separatism and ethnic conflicts. Some big countries are getting divided like Quebec or Catalonia and some are reuniting like Germany and Yemen. Actually, economic integration works better with political disintegration. Quebec s separatism is a good example. These results gives arise to the following questions: Why is this difference? Why do country size varies? What are the determinants of country size? What are the cost and benefit of size? Well in the following subsections, we will be exploring the solution of these questions. 1.1.Determinant of borders Size is a relative concept; land area, population and GDP can derive it. Based on AS, we have pointed out the trade- off between size and heterogeneity, majority voting and trade regime as the determinant of border (namely cause of political disintegration), across countries. The following part describes briefly these factors: 8

9 Trade- off between size and heterogeneity Trade- off between size and heterogeneity of certain public goods determine the borders of countries. Usually public goods are a basic financial system, tax collection and fiscal institutions, legal juridical system, government infrastructure, public libraries, national parks and embassies. In most instances the provision of these public goods include fixed costs. In this world, everyone pays certain amount of taxes to the government for enjoying the facilities of these public goods. And different people have different views about how the policy should spend their tax money. In general, public good have both ideological and political dimension, which means cost, is negatively correlated with the distance. (Ex: public school) for example: in Italy concerning the location of hub of the main national airline had substantial implications for the distribution of travel costs in different parts of Italy. There exist two dimensions of heterogeneity: Geography (how distant an individual is from a public good): jurisdictions are generally geographically compact because there is administrative cost in disjoint countries. Ideology (how close are public good and policies to the individual preference): individuals who are close together in a space are also more alike in preference because of the following reasons: 1. Sorting: individuals of same attitudes, ideology, preference, income and religion attempts to live close to each other. 2. Uniformity: hundreds of years of proximity generate more uniformity of beliefs and preferences. (Ex: a common language that evolves from geographical proximity) 3. Degree of heterogeneity: which itself do explicit policy decisions influence. 9

10 Majority voting: Apart from the fact of tradeoff between heterogeneity and size, the formation of democratic institutions within countries of borders can also be decided by majority voting. The formation is also defined between the evolution of optimal country size and the country that results from majority vote on its borders. Basically in an one person vote, everyone equally contributes to the decision on borders however in that case individual will have the authority to vote to break up of a country just because they were not experiencing the benefits of public goods as much as closer regions in preference to government policy making. While in majority voting it is everyone s mutual duty to compensate the distant region with favorable interests through fiscal policy in order to avoid inefficient secessions. Trade regime The size of the market (or the border) for any country also depends on the trade regime and on the state of its international economic relations. When all borders are close each country s market is determined equivalent to its size two extremes: 1. (All country) without international trade size of the market economy large country advantage 2. (All country) open to trade in goods small and large countries compete in the same market through factors of production and financial instruments. 1.2.Determinant of Size of countries This subsection of chapter one describes the trade- off of economies of scale and scale trade- off of political and market size as the determinants of country size (namely- economic integration). 10

11 Trade- off of economies of scale If there are economies of scale to the size of the market, larger countries can be expected to do better economically than smaller countries (considering all other things being equal such as natural resources, geographical size, population etc). Political size becomes less relevant as economic integration increases, because it reduces the limit of certain country. In other words, the stable size of country reduces economic integration. If we see the evidence, it is clear that even in world of free trade national borders do not turn into inappropriate. The evidence on Canadian and U.S. trade is striking. In spite of distance being strong determinant of trade flows, U.S. states and Canadian provinces trade much less than two distant Canadian provinces. Which enlightens the fact that free trade just makes borders more fact that free trade just makes borders more open in return of huge cost in terms of trade flows cost in terms of trade flows. The bottom line is that small countries can prosper as long as they are open to international trade. Conversely, small countries are more open towards free world trade regime. The empirical evidence gathered by Alesina, Spolaore, and Wacziarg (2000) is consistent with implications. The substitution effect of public and private goods The historical process of the last century toward smaller size nations may be a consequence of the increased substitutability between private and public goods. One may view publicly provided private goods, as close substitutes with private goods while pure public goods are less substitutable with private goods. It is a well known fact that the diffusion of Communism around the world since the first half of the twentieth century and the diffusion of the welfare state in western countries in the second half of the twentieth century have extended government activity toward publicly provided private goods as education, health and social security. Since scale economies are much less powerful and heterogeneity of views is more accurate for these kinds of activities a tendency toward a decreasing size of nations emerged during the twentieth century. The other crucial factor in the secular decline of the size of nations is the increase in openness. Openness plays a very crucial role in determining both the size and growth of countries. 11

12 Scale tradeoff of political and market size Basically a country s market size coincides with its domestic size only if the country s economy is perfectly integrated domestically but completely closed to the rest of the world. In short in a world of complete autarky, political size and market size of a country coincide. That is a world without any economic relationships among the countries has a small market and thus low demand for output and low production. It follows that if a country is small it has a small market. But we have to keep in mind that what matters is the total income not the population size. Whereas there exists also economically integrated world, where the market size of a country is larger than its political size. In this economically integrated world borders are totally irrelevant for economic interactions, the market size defines the world, where free trade, political borders are irrelevant. But true fact is that, people have contrived ways to deprive themselves and one another; and prefer agglomerated animosities to singular happiness. Market size=political size has the following intuitions in different situations: Autarkic world: small country smaller market low demand low production (from the point of view of market size where income matters not population) Economically integrated world: larger market size than its political size. (A country s economic prosperity completely depends on its economic integration with rest of the world) Extreme case: the market size of the country is whole world (borders are completely irrelevant) Free trade world: political borders are irrelevant. After discussing the formal reason of economic integration (1.2) and political disintegration (1.1) we can summarize our findings as follows: Two configurations of trade and size are; 1. Large and closed economy little interest in promoting trade liberalization (free trade) 2. Small countries promote free trade 12

13 Both democratization and opening of international trade accompany political separatism and the breakups of large countries. According to functional theory: Economic integration in political integration (both regional and global levels) 1.3.The benefits of size This section of chapter one emphasizes the benefits of size. According to AS the benefits of size are the followings: 1. The first motivation is the importance of Economies of scale in running the public sector. 2. The second one is defense against foreign aggression. If we neglect the term peaceful world, than it is notable that the larger the country the more valuable it is. In fact, being large is especially valuable if much has to be spent on defense and economies of scale. Obviously small county size has coincided with an explosion of political separatism. In short, Political borders and political size are very important for the growth of a country as they are incorporated with obstacles to economic exchange and political barriers to trade. 3. The size of a country affects the size of its economy. So larger countries have larger markets hence larger economy and smaller countries have the smallest economy. Which effects in the productivity of the countries, the number of individuals and the amount of spending in an economy depends on the trade openness of a country. An economically integrated country has the whole world as its market, which reflects in its economic success. So, the economic benefits of size depend on the openness of country. 4. Large countries have the redistribution scheme advantage, which allows them to redistribute schemes from richer to poorer individuals and regions, thereby achieving distributions of after- tax income that wouldn t have been possible in independent economy acting at its own. 5. And the last one deals with the creation of a common market, 13

14 1.4.The cost of size If there were only benefits from size, then the whole world should have been organized in a single country. Well here comes the cost of size. In principal, larger countries entails administrative and congestion costs which offsets the benefits of size pointed in the previous section. But these costs are not same for all large countries. Actually larger countries have diverse preferences, cultures and languages within the population. A country s heterogeneity of preference increases as it becomes larger because more people gets added to the country and more people means more preference. Basically, belonging to a country implies agreeing to a set of policies and these policies could be any kind of redistributive scheme, public goods or foreign trade. Heterogeneity implies every individual of that specific country comes to an agreement on these matters. Of course certain policies can be delegated to localities, in order to allow local preference but the same does not work for every policy. Because with increased heterogeneity their increases number of individuals who are less satisfied by the central government policies. Indeed, many violent domestic conflicts around the world are associated with this type of racial, religious, and linguistic heterogeneity, which have literally threatened the stability of national governments. Apparently, in a large republic the common good gets sacrificed to a thousand of considerations while in a small republic the presence of public good is more recognized, better known and are more closer to each citizen. Summary In summary, at one extreme, market size coincides with political size in an autarky world whereas at other extreme political size is smaller than the market size in a world of free trade. In general, the viable size of country decreases with international openness because country s market is defined by its domestic market and foreign market 4. In presence of economies of scale to the size of market, larger countries can be expected to do better economically than smaller countries (all other things being equal) when international openness is low and vice versa. 4 Depending on the country s degree of international trade openness 14

15 Chapter 2 Theoretical presentation of the models The theories of this chapter linking country size, international trade and economic growth is built upon AS, Alesina, spolaore and Wacziarg(2000) and Spolaore and Wacziarg(2005) Alesina, spolaore and Wacziarg (2000): Basic static model Alesina,Spolaore and Wacziarg constructed a simple static model of a world economy with a large number N of identical countries and a continuum [0, 1] agents and N economic units which are basic entities(countries) carrying out economic activities. Each country produces differentiated goods, and countries are specialized in different varieties. Consumers enjoy utility from the consumption of differentiated goods and a country- specific public good. Governments set policies unilaterally so as to maximize utility of domestic citizens Production and trade If we consider the following utility function, where the world population N=1, and each population is living at location i ϵ 0,1 : U ( c!" )=!!!!!!"!!!! e!!! dt (1) Where c!" denotes the consumption at time t, with σ > 0 and ρ > 0, K! (t) and L! (t) denotes aggregate capital and labor at location i. And both inputs are elastically supplied and are not mobile. At each location i a specific intermediate input X! (t) is produced using the location- specific capital according to the linear production function X! (t) = K! (t) (2) If each location i produces Y! t units of the same final good Y (t), then according to the production function we can write;!! Y! t = X!!" t dj L!!!! (t).. (3) 15

16 Assuming, 0<α < 1, X!" t denotes the amount of intermediate input j used in location i at time t. Intermediate inputs can be traded across different locations in perfectly competitive markets by profit- maximizing firms without any cost (assuming open economy). Conversely if one unit of intermediate good i is shipped to a location i of a different country then (1- β) units of the good i will arrive due to the extensive political borders that entail trading cost. (Assuming 0 β 1) This trading costs varies as following: 1) Open economy, where intermediate goods can be traded across locations without inducing any cost. 2) Closed economy, the transfer of intermediate goods across different location incurs cost. If we consider, D! (t)=the intermediate inputs produced in either at location i or another location that belongs to the same country as location i. F! (t)= The units of input i shipped to a location that doesn t belong to the same country as location i. Then due to the border cost assumption, only (1- β) F! (t) units will be used for production 5. Therefore, P i t =αd i α- 1 t =α(1- β) α F i α- 1 (t) (4) Where P! t is the market price of input i at time t. at each time t the resource constraint for each input i is given by, s i D i (t)+ W- s i F i (t)=k i (t) Where, s i denotes size of country at location i that it belongs to; 5 We know that, in equilibrium, markets are perfectly competitive (p=mc) 16

17 The intuition of these equation states that barriers to trade increases the domestic use of the intermediate output to discourage foreign trade. For the simplicity of analysis we will assume uniform barriers to trade across countries. Let s now introduce openness "ω" to our model, Assuming 0< ω < 1, and the lower the barriers to trade the higher is the openness, we can define it as following; ω (1 β)!!!!. (4) ω = 1 when there are no barriers to trade β = 0 - Open economy ω = 0 when there are barriers to trade, complete autarchy β = 1 closed economy Thus our domestic D! t and foreign F! t inputs simplifies as follows: D i t = K i t ω+(1- ω)s i And F i t = K i t ω+(1- ω)s i Capital accumulation and growth Lets now assume, in each location i, consumers net household assets are identical to the stock of capital K! (t). Since each unit of capital yields one unit of intermediate input X! (t), the net return to capital is equal to the market price P!". 17

18 From intertemporal optimization 6 we get, dc it dt 1 C it = P i t - ρ = α ω+(1- ω)s i 1- α K i α- 1 t - ρ The Solow s model steady state level of capital at each location i of a country size S!, will be; K i ss =K i ss 1- ρ + α ω+(1- ω)s i 1- α K i ss(α- 1) K i ss = α ρ α 1- α ω+(1- ω)s i (5) Steady state income/output:. With N number of identical countries of size s: The steady- state level of output in each unit of a country size s! is given by; Y!!! = s! (D!!! )! + s! (1 β)! (F!!! )!!!! by substituting D!! ss! and F i into the equation above, we obtain the following; Y!!! = α α 1- α ω+(1- ω)si (6) ρ 6 c t c t = π t- ρ, γ(c γ(c t ) t)= - u'' c c Here ρ is the efficiency parameter. u'(c) 18

19 PROPOSITION 1 : By far, we can say that steady- state output per capita is increasing in openness and size, which means they both have positive effect in economic growth of a country. But openness is less important for large countries. Which summarizes as follows: The smaller the effect of country size s! is, the larger is the openness ω Apparently, the growth rate of output around the steady state can be approximated by; dy dt. 1 Y =ξe- ξ (lny ss - lny 0 ) Where, ξ =!! α α And Y (0) is initial income 7 PROPOSITION 2: Around the steady sate, the growth rate of income per capita increases in size and openness and decreases in size time s openness. These results, how ever are the evidence of the fact that, economic benefits from size decreases in openness and economic benefits from openness decreases in size Equilibrium analysis Equilibrium analysis part 1, AS Based on the same normalization assumption, lets consider the world has at least one government, thus N 1, N denoting number of countries in the world. And to avoid complexity a country s government cost is assumed to be k, regardless of the size of the country. If every individual has the same 7 The derivation of this result can be found in appendix 2B, Barro and Sala- i- Martin (1995, Chapter 2) 19

20 exogenous income y and pays taxes t i = k, (where i stand for individual s identity) than the utility of individual i is: U! = g al! + y k s Where g and a are two positive parameters and l i is the distance from individual i to his/her government. The utility function is linear to private consumption. g= measures the maximum utility of the public good at l! =0. a= measures the loss in utility due to the distance of his/her preferred government. Based on the above assumptions, the social planner maximizing the sum of individual utilities would choose the number of countries N ; N = a 4k If public good is located in the middle of each country and if each citizen pays same taxes in its own country and enjoys the benefits from public spending according to his or her distance from the public good than s*=!! is the size of each country. Hence the utility in steady state for an individual living at location i become: u i =g- al i + α ρ α 1- α ω+(1- ω)si - k s (7) Therefore, the number of equally sized countries that maximizes average utility is; * dw =- a ds 4 + α ρ α 1- α (1- ω)- s 2 k=0 20

21 N * = a- 4(1- ω) α ρ 4k α 1- α (8) And the equilibrium size 8 of countries: s =! (9)! Optimizing the welfare on openness gives us the following: dw dω = α ρ α 1- α (1 s) We can summarize the findings of this theory as following: This theory explained the relationship of country size, openness, and income per capita through a model that benefits of country size decrease by an increasing economic integration between different political borders. But this benefits gets bigger by the increasing trade openness and economic integration in smaller countries. The theory also argued a positive relationship between economic and political integration. It proved that as the economy becomes more integrated, scale effect of large country starts to vanish due to the shift of increasing trade- off between size and heterogeneity of smaller countries. So overall summary of this theory reflects the fact of two possible worlds; one world of large and relatively closed economies, and another of many smaller and open economies Equilibrium analysis part 2, ETRO After the basic theoretical part of AS, let s begin by finding the social planner equilibrium solution in an integrated economy as stated by Etro, where the number and sizes of countries and location of the public good can be individually chosen. Assuming that the social planner maximizes the sum of individual utilities, the social planner problem is: Max 1 U i di 0 1 s. t. t i di=nk..(9) 0 8 For the derivation of the results see AS(ch 3) 21

22 Where, a social planner maximizing the sum of individual utilities locate the government in the middle of each country, chose N* countries of equal size, such that; In the world there are many countries each one with a capital city set in the middle of the country. So utility for agent i in country j have the following functional form: U ij =u C j +α ij H g j, given α ij =λ- al i Here H (g! ) = utility from public spending g! in country j and u(c j )= utility from private consumption, which is income net of effective taxation, α ij = Heterogeneity cost across citizens in a way discussed below. Any assumption on the utility from public goods is not necessary as we are going to focus on the necessary taxation of each agent to finance the latter. Since this part is going to endogenize public spending, we need to be more precise. Although the following results will also hold within a general well- behaved utility function, but for the sake of closed form solutions, we will focus on linear utility from consumption and iso- elastic utility from public spending. Finally, some assumptions on technology of production of public goods and on the distortions induced by the corresponding individual tax t! in country j are needed. Later on we will follow, David. Ricardo s growth model of diminishing marginal returns in the production process and a distortion of taxes that is increasing and convex in the taxation level. For simplicity issue, in our model we will be summarizing both these elements with a convex cost function of taxation, and in particular a quadratic one. In conclusion, utility is the following: U ij = g 1- Θ j 1- Θ λ- al ij +y j - t 2 j. (10) 2 Θ 0,1 =the elasticity of marginal utility of public expenditure 9 9 The lower it is, the more substitutable are public and private consumption. If publicly provided goods belong to a wide range which starts with purely private goods (drugs or school s books) and arrives to purely public goods (defense), the former typology corresponds to goods with 22

23 Here, l ij =distance from the public good 10 a= cost of heterogeneity and λ=utility provided by the public good11 In this section, the tax independent output y j = y is assumed constant across countries. Let us define the size of country j as s! and the per capita provision of public goods as given by the revenue constraint. Summary From the model suggested by Etro it is clear that, there are some specific assumptions on the technology of production of public goods. The increasing cost function of taxation causes diminishing marginal returns in the production process of pubic goods, which is by the way useful because of the tractability of the first order conditions. Whereas AS s model didn t made any assumption on technology of production of public goods because their utility from the exogenous public spending is a given parameter g, and the costs of taxation is exogenous parameter. Table 2.1 Comparison between the utility function of endogenous and exogenous government spending models Utility from public spending Heterogeniety of preferences Costs of taxation/public good AS (exogenous Etro (endogenous government spending) government spending) g!!! g! 1 Θ al!" λ al!" /! t! 2 perfect substitutability with the private goods and the latter one with those that are less substitutable for the private goods 10 l!" =! if the good is situated at the capital; It is typically recognized that regions far away! from the capital of a country are the most likely to have at least different preferences from the regions close to the capital, and at most a separatist tendency (the experience of many European countries is quite clear in this direction). 23

24 Equilibrium welfare Here we define the optimal organization of the worlds as the equilibrium welfare; as we have assumed uniform distribution of citizens, the optimal equilibrium would contain countries of equal size s and the public good would be situated at the center of each country. So, the optimal welfare choosing the size of nations and the provision of national public goods would be as following; W = 0 1 g j 1- Θ 1- Θ λ- al ij +y - t 2 j 2 di s.t. t js=g j = g 1- Θ j λ-! s - 1 (! 1- Θ! 2! )2 +y Applying AS optimal size of the nation rule, that is maximizing welfare w.r.t s, we obtain the following; dw ds = - a g 1- Θ 4 1- Θ + g2 s 3 =0 Comparitive statics: s * = g 1+Θ 3 3 4(1- Θ) a The g s for exploiting economies of scale and a s The optimal size of a given amount of public good remains unaffected by the absolute utility from the public good. We get our very first relationship between optimal size and optimal per capita provision of public goods from this optimality condition; t=g/s 24

25 s = g 1+Θ Θ a s s 1+Θ 3 g1+θ 3 = s 1+Θ Θ a t * = s 2- Θ 1+Θ. a 4 1- Θ 1 1+Θ =ψ * (s) PROPOSITION 1: Optimal size of nations is an increasing and concave function of the provision of public good (government consumption). Equilibrium government spending and public spending provision Now if we consider a modified samuelson rule for optimal public good provision t, (Samuelson, 1955) than the function of size of countries satisfying the first order condition becomes; dw dg =g- Θ λ- a 4 s - g s 2 g 1+Θ = s 2 λ- a 4 s g * = s 2 1+Θ. λ- a 4 s 1 1+Θ The optimal provision g is an inverted function of s. So, the second relationship between g and s can be written as following; Given, 25

26 g * = s 2 1+Θ. λ- a 4 s 1 1+Θ g* s * = s 2 1+Θ s. λ- a 4 s 1 1+Θ t * = s 1- Θ 1+Θ. λ- a 4 s 1 1+Θ =Φ * (s) Comparative statics: The cost of benefitting from the public spending 12 is higher if there exists less taxation hence less public spending in the economy. t is first increasing in s and then decreasing, with a peak!!!!!!!!!. Henceforth it is clear that, tradeoff between heterogeneity costs and scale of economies both increase in the size of a country. And given intermediate size of country, the net benefit from public good provision is the higher at the costs of heterogeneity. PROPOSITION 2: The optimal per capita provision of public good is non- monotonic function of size, which means that, large and small countries should impose lower taxes and countries of intermediate size should impose higher taxes. 26

27 In a real world this kind of monotonic relationship varies with the nature of the public good. If the good is pure public good (defense), there exists negative relationship between size and taxes and scale economies become more relevant for the overall equilibrium. But if the good is private (schools), then the relationship between size and taxes becomes positive offsetting the importance of scale economies. Solving the system of optimality conditions we get; ψ * s = Φ * s s 2- Θ 1+Θ. a 4 1- Θ 1 1+Θ = s 1- Θ 1+Θ λ- a 4 s 1 1+Θ s * = 4λ 1- Θ a. 2- Θ Plugging s * into t we get; t * = s!!!!!!. a 4 1 Θ!!!! =!!!!!!!!!!!.!!!!!!!!!! In general, if optimal world N * = 1 s * then; N * = of Public spending; a. 2- Θ 4λ 1- Θ and total provision g * = t* s * = 4 1- Θ a 2 1+Θ λ. 2- Θ 3 1+Θ 27

28 Comparative statics: Both the optimal N and g are in a; (heterogeneity cost) and in λ (the absolute utility). Table 2.2 Comparison between the optimal sizes of our distinct models: AS Intuitions Etro Intuitions s s = 4k a- 4 (1- ω) α ρ α 1- α a s k s s = 4λ 1 Θ a. 2 Θ a s λ s t t = 4 1 Θ a!!!!!! λ 2 Θ!!!!!! a t λ t N N = a 4 1 ω h 4k a N ω N N = a. 2 Θ 4λ 1 Θ a N λ N Finally, world welfare for of our model is: W!" = g -!!!"!!! (!!!)!!!!!! +!!!!!! (ω + 1- ω 4k a- 4 (1- ω) α ρ α - k 1- α a ω h 4k W!"#$ =!!!!!!(!!!)!!!.!!!!!(!!!)!!!!!!!(!!!) + y 28

29 2.3. Summary and conclusion We can summarize the findings of this chapter as following: The steady- state output per capita is increasing in openness and size, which means they both have positive effect in economic growth of a country. But openness is less important for large countries and is less important for economic performances in an open world economy. The benefits of size go down with increasing international economic integration. Which is converse in the case of small countries. Around the steady sate, the growth rate of income per capita increases in size and openness and decreases in size time s openness. Which means, Economic integration and political disintegration are positively correlated with the fact that, increasing economic integration offsets the effect of large market size by reducing the benefits of large market size. These results, how ever are the evidence of the fact that, economic benefits from size decreases in openness and economic benefits from openness decreases in size. Optimal size of nations is an increasing and concave function of the provision of public good (government consumption). The optimal per capita provision of public good is non- monotonic function of size, which means that, large and small countries should impose lower taxes and countries of intermediate size should impose higher taxes. According to AS, these results points out that, the trade- off between size and heterogeneity shifts in favor of smaller and more homogenous countries whereas the technological progress shifts in favor of larger countries. The reverse source of causality is also possible because, the economy of small countries highly depends on international markets. In fact, Etro by considering openness as endogenous variable has extended the AS model to capture two possible worlds as equilibrium border configurations: a world of many more smaller and more open economies and one large and relatively closed economy. Spolaore (1995, 2002) provides explicit models with endogenous openness and multiple equilibria in the number of countries. Spolaore and Wacziarg (2005) also treat 29

30 openness as an explicitly endogenous variable, and show empirically that larger countries tend to be more closed to trade. Empirically, both directions of causality between country size and trade openness, which are not mutually exclusive, likely coexist (AS). AS model provides evidence about smaller countries being in favor of adopting more open trade policies and smaller countries 13. Conversely, Etro model provided a theory that theoretically proved that, when openness is endogenous there exists multiple equilibria, some with globalization backlash associated with large nations and small governments and others with smaller countries, bigger governments and high openness. 13 Are consequently more open when openness is measures using trade volumes 30

31 Chapter 3 Empirical evidence 3.1. Relationship between size and openness: A large number of empirical studies have estimated the effect of openness on size and on economic growth of a country. Vamvakis (1997) presented a regression on the interaction of our main variables of interest (of this section) and obtained a negatively significant coefficient. But he used policy measures for openness rather tan trade measures. Ades and Glaeser(1999), in a sample of poor countries, showed that the interaction between openness and country size bears a significantly negative coefficient. But they used different size measure (per capita income). Later, AS along with Wacziarg have estimated the coinciding relationship twice and have confirmed the negative correlation in both. According to them, the presence of openness offsets the existence of size on growth. Alesina, Spolaore and Wacziarg (2000) studied the interaction of size and openness on growth over 120 countries during the period 1960 to Author has found the size and openness relation is negative and approximately and statistically significant. In their next extension Alesina, Spolaore and Wacziarg (2005), explored the relationship between interaction of size and openness on growth over 114 countries during the period 1960 to Later study used the constrained SUR estimation method exploiting the within- country variations in growth and found that interaction of size and openness on growth is and statistically significant. This study uses same method of estimation as Alesina, Spolaore and Wacziarg (2000) with same dependent and control variables, but focuses on the interaction of size and openness on growth over 79 countries during the period 1970 to

32 The data Our estimation is based on panel data analysis for 79 countries 14 over 1970 to 2011 period. Annual data on annual growth, openness, investment rates, income levels, population and government consumption is derived from the Penn world table (7.1) and the data on human capital is extracted from Penn world table (8.0) [Heston and Aten (2009)], which updates their panel of PPP- comparable data to the year The rest of the data on population density and fertility rate came from World Bank. Estimation method: As an extension to their previous estimation, Alesina, Spolaore and Wacziarg (2005) have measured the country size in two ways (by the log of total GDP and by the log of total Population) in order to capture both economic size and demographic size. In their new updated analysis, they have defined the openness in two ways: Openness (Nominal)= Exports current price+imports current price GDP current price Openness (Real)= Exports exchange rate $US+Exports exchange rate $US GDP PPP $US The reason behind using two measures of openness lies in the fact that, it allows comparability with past results of Alesina, Wacziarg (2000). For the sake of simplicity, in this subsection of my empirical part we will be using the log of population as the measure of country size and the current openness as the openness measure (apart from the first three tables, that are the basic descriptive statistics). Though the relationship of my variables of interest has been tested and proved multiple times, in this section we will only update the results with most recent dataset. 14 ARGENTINA, ANTIGUA, AUSTRALIA, AUSTRIA, BAHRAIN, BANGLADESH, BELARUS, BURKINA FASO, BELGIUM, BELIZE, BERMUDA, BARBADOS, BAHAMAS, BRUNEI, BENIN, BHUTAN, BOLIVIA, BULGARIA, CENTRAL AFRICAN REPUBLIC, CAMERON, CANADA, CHINA, CONGO, COMOROS, CAPE VERDE, CUBA, CHILI, COLOMBIA, CYPRUS, GUYANA, GERMANY, GREECE, GREENLAND, GUATEMALA, GRENADA, DJIBOUTI, DOMINICA, EGYPT, FINLAND, FIJI, FRANCE, FINLAND, GRENADA, GUYANA, GUAM, HAITI, HONDURAS, HONG KONG, HUNGARY, INDIA, INDONESIA, IRAN, IRAQ, ISRAEL, ICELAND, ITALY, JORDAN, JAMAICA, JAPAN, KIRIBATI, KUWAIT, LIBERIA, LITHUANIA, KOREA, KENYA, LIBYA, LATVIA, LEBANON, LESOTHO, LUXEMBOURG, MEXICO, MACAO, MALDIVES, SWEDEN, SRI LANKA, SWITZERLAND, USA, ZIMBABWE. Total 79 countries 32

33 The model In this subsection, based on the Propositions 1 and 2 of AS [section of chapter 2], we explore the empirical evidence of their model. Which are as follows: If small countries tend to be more open to trade, and if trade openness is positively related to growth, then a regression of growth on country size that excludes openness will understate the effect of scale. Moreover, the AS theory suggests that the effects of size become less important as an economy becomes more open, i.e. the coefficient on an interaction term between openness and country size is predicted to be negative. AS predicted the following growth regression to examine the interaction of country size and openness: log y it y it- τ =β 0 +β 1 logy it- τ +β 2 logs it +β 3 O it +β 4 O it logs it +β 5 ' Z it +ε it Here, y it = Per capita income in country i at time t, GDP per capita is the gross domestic product divided by midyear population. y it y it- τ = Log measure of Growth rate of real GDP of country i at time t, S it = Measure of country size. Population is measured by thousands of inhabitants and total GDP is total PPP Converted GDP, G- K method, at current prices (in millions $) O it =Measure of openness (Openness at Current Prices % of GDP), Z it =Vector of control variables, where Human capital (Index of human capital per person, based on years of schooling (Barro/Lee, 2012) and returns to education (Psacharopoulos, 1994) and; Investment rate Investment Share of PPP Converted GDP Per Capita at current prices [cgdp], (%) 33

34 Fertility rate represents the number of children that would be born to a woman if she were to live to the end of her childbearing years and bear children in accordance with current age- specific fertility rates. Government consumption as ratio of GDP. The share of total government current expenditures (including transfers and interest payments), the share of consumption spending excluding education and defense, and the share of education related expenditures In this specification, the parameter growth estimated over openness, size of country, control variables and their interactions would be the main focus of the results. The efficiency of the estimates can potentially be improved by exploiting country variations in growth, openness and country size. Thus we will be using SUR estimator where the data are averaged over periods and estimate a system consisting of one growth equation per time period. Descriptive statistics Table display summary statistics for our main variable of interest, averaged over the period Table estimates the basic summary statistics of our 79 countries. And Table explains the correlation between size and openness. The correlation of between both measures of openness justifies examining differences in results obtained using each measure. But as stated above for the sake of simplicity we will avoid estimating both measures. The correlation between openness (both nominal and real) and country size (both log total GDP and log of population measure) is negative with a magnitude of , and , respectively. Confirming the past results of Alesina, Spolaore and Wacziarg (2005) and AS that, small countries are more open and an omission of openness in the overall regression will overpower the effect of size. However, the negative correlation of per log of total GDP and growth is however a new relation. 34

35 Table Descriptive statistics ( averages) Variable Obs Mean Std. Dev. Min Max avgannualg~h opennessn opennessr logofperca~p logofpopul~n fertilityr humancapit~g invstmnent~p govtcon~ngdp Table Pairwise correlation for the main variables of interest ( averages) annual~h logoft~p logofp~p logpop openno~l openreal annualgrowth logoftotal~p logofperca~p logpop opennominal openreal The preliminary findings of AS proposition 1 and 2 can be collected from table This table presents correlation of openness and growth conditional on country size being greater or lower than the sample median. From the table it can be noticed that, the correlation between openness and growth is 0.31 for small countries (those smaller than 6.7 million populations) and for large countries. Which means the results are consistent and qualitatively unchanged with the previous findings and provides evidence that openness and country size are substitutes 15, and the correlation between size and growth falls with the level of openness. 15 Presence of either one offsets the existence of the other. 35