The Zipf's law and the effects of free trade: The case of Guatemala

Orellana Aragón, Jorge Alberto; dos Santos Queiroz, Vívian Article The Zipf's law and the effects of free trade: The case of Guatemala EconomiA Provided in Cooperation with: The Brazilian Association of Postgraduate Programs in Economics (ANPEC), Rio de Janeiro Suggested Citation: Orellana Aragón, Jorge Alberto; dos Santos Queiroz, Vívian (2014) : The Zipf's law and the effects of free trade: The case of Guatemala, EconomiA, ISSN 1517-7580, Elsevier, Amsterdam, Vol. 15, Iss. 1, pp. 82-99, https://doi.org/10.1016/j.econ.2014.03.007 This Version is available at: https://hdl.handle.net/10419/179565 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/3.0/ Available online at www.sciencedirect.com ScienceDirect EconomiA 15 (2014) 82–99 The Zipf’s law and the effects of free trade: The case of Guatemala Jorge Alberto Orellana Aragóna,∗, Vívian dos Santos Queirozb aPhD candidate in Economics with Emphasis on Development Economics at Universidade Federal do Rio Grande do Sul (PPGE/UFRGS), Brazil bPhD candidate in Economics with Emphasis on Applied Economics at Universidade Federal do Rio Grande do Sul (PPGE/UFRGS), Brazil Available online 27 March 2014 Abstract The aim of this study is to investigate the impacts of trade policy changes on the order of the size of cities and economic growth of Guatemala between 1921 and 2002. The Pareto coefficient was estimated and an index was used to measure the degree of urban concentration. Finally, a model of the impact of trade liberalization on economic growth was estimated. The main results obtained showed a slight growth in inequality and divergence, although the urban concentration index showed a gradual decline since 1964 (the golden age of the CACM by the year 2002). It was found that the urban concentration has an inverse relationship with the commercial opening and positive economic growth during the period from 1921 to 1964. It was concluded that major cities reduced their growth and that small and medium-sized cities grew at a faster rate than big cities, driven by the growth of international trade. © 2014 National Association of Postgraduate Centers in Economics, ANPEC. Production and hosting by Elsevier B.V. All rights reserved. JEL classification: F15; R11; R12 Keywords: Cities; Pareto distribution; Zifp’s law Resumo O objetivo desse estudo é investigar os impactos das mudanc¸as na política comercial sobre a ordem no tamanho das cidades e crescimento econômico da Guatemala entre 1921 e 2002. Foi estimado o coeficiente de Pareto e utilizado um índice para medir o grau da concentrac¸ão urbana. Por fim, estimou-se um modelo de impacto da abertura comercial sobre o crescimento econômico. Os principais resultados obtidos apontaram um leve crescimento na desigualdade e divergência, apesar de que o índice de concentrac¸ão urbana mostrou uma queda gradual desde o ano de 1964 (época de ouro do MCAC) até o ano de 2002. Verificou-se que a concentrac¸ão urbana tem uma relac¸ão inversa com a abertura comercial e positiva com o crescimento econômico do período 1921-1964. Concluise que as maiores cidades reduziram seu crescimento e as pequenas e medianas cidades cresceram a um ritmo mais acelerado do que os grandes centros, impulsionadas pelo crescimento do comércio internacional. © 2014 National Association of Postgraduate Centers in Economics, ANPEC. Production and hosting by Elsevier B.V. All rights reserved. Palavras-chave: Cidades; Distribuic¸ão de Pareto; Lei de Zipf ∗Corresponding author. E-mail address: [email protected] (J.A.O. Aragón). Peer review under responsibility of National Association of Postgraduate Centers in Economics, ANPEC. 1517-7580 © 2014 National Association of Postgraduate Centers in Economics, ANPEC. Production and hosting by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.econ.2014.03.007 J.A.O. Aragón, V.d.S. Queiroz / EconomiA 15 (2014) 82–99 83 1. Introduction There is a particular importance in investigating the effects of free trade agreements on urban and regional growth, because the life-span of a free-trade agreement can affect the size of cities, favoring a drop in urban concentration and reverberating on the size of the less unequal population. Guatemala participated in several free trade agreements, over the decades, which especially involved Central American countries, and also with countries in other regions. Such trade liberalization favored Guatemala by stimulating the economic growth of the country because, in recent years, there has been a significant change in the size of the population of the major cities of Guatemalan departments due to emigration, mainly toward the United States, and to the relocation of industries within the country. According to the New Economic Geography (NGE), the size distribution of cities can be represented by a Pareto distribution, which derives from an empirical regularity called Zipf’s law. This law explains how agglomeration forces interact in urban centers promoting economic activity and international trade in general. In recent decades, surveys were published seeking explanations for an empirical verification of Zipf’s law. Among the most important are the works of Rosen and Resnick (1980), written more than 20 years ago, which are based on demographic data of the 1970s. Recently, the work of Soo (2005) became prominent by making various econometric models with current data to explain how changes in urban centers in various parts of the world can be explained by Zipf’s law. In this work, the author applies a “test” for Guatemala and it was found that it did not empirically corroborate with the Zipf’s law. Other important empirical works are by Monasterio (2004) for the State of Rio Grande do Sul and Oliveira (2004) for all Brazil. For the case of the effects of a free trade treaty on economic growth are the studies of Azevedo (2004), who worked on the case of the Mercosul and, for the specific case of Guatemala, emphasized by the works of Naranjo (2003), Rodriguez (2005) and that of the Banco de Guatemala (2006a,b).1 Accordingly, the aim of this study is to investigate empirically how the life of a free-trade agreement can affect the size of cities (the population of urban areas) and how this influenced the overall economic growth of Guatemala between 1921 and 2004. The data is provided by the Census of the National Institute of Statistics (INE) and the Latin American Demographic Centre (CELADE). Specifically, this work focused on the economic and urban specificities and tries to find correlations between the rule of the order of the cities, free trade or trade liberalization, and the effects of agglomeration forces over the urban concentration and economic growth. Taking into account that for Guatemala there is no shortage of studies that address urban growth related to trade liberalization, thus it is relevant to such investigation since this study may serve to provide guidance on the formulation of public policies to promote the economic growth of this country. This work is divided into six parts aside from this introduction (part one). The second part is a summary about the performance of the Guatemalan economy. The third part discusses the Guatemalan trade integration. The fourth part closes the theoretical review, urban economic geography models, free trade impact models on economic growth and the database. The fifth part exposes the empirical evidence and, finally, the last part is devoted to the final conclusions. 2. Guatemalan economy During the fifties, Guatemala joined the model promoted by the United Nations Economic Commission for Latin America and the Caribbean (ECLAC)2and the economic model in force in the country was known as an “import substitution” and aimed to improve the country’s external position. This model was upheld during the process of Central American economic integration that began in the 1960s and later was known as the “Central American Common Market” (CACM). In the late eighties, Guatemala began changing to a model based on a more open trade with the rest of the world and, at the beginning of the 1990s, it began a diversification process of its economy based on a trade policy that was geared to negotiate free trade agreements with other countries.3The exchange-rate policy has changed permanently: 1Among the studies about the new economic geography (NGE), Fujita et al. (2002), Gabaix (1999), Henderson (2000, 2003), Ades and Glaeser (1994), Ottaviano and Marti (2001), Venables (2003), Meardon et al. (2001), Brakman et al. (2005) are included. 2For more details, see Estrelha (2007). 3More in line with the 1986 “Uruguayan Round”. 84 J.A.O. Aragón, V.d.S. Queiroz / EconomiA 15 (2014) 82–99 -6 -4 -2 0 2 4 6 8 10 12 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 percent year GDP Pol yno mial (GDP) Fig. 1. Change of GDP 1960–2005-Guatemala. Source: Bank of Guatemala-BANGUAT. the exchange rate and the interest rate were no longer regulated by the Monetary Authority as they were until 1989. The prices of the basic basket of goods were released in 1986 and completed the process in 1991. Then, taxes were gradually eliminated on exports contained within the Central American System (SAC).4Fiscal deficits were financed by the Monetary Authority until the end of the 1980s and in 1994 a constitutional norm was issued which banned the Monetary Authority the right to finance the fiscal deficit. In the external sector, there was a current account deficit of the payment balance, with a structural character and, the main sources of financing of the current account deficit, used by successive Governments until the eighties, were the International Monetary Reserves (RIN) and the External Public Debt, but these were changed in the 1990s, when the flow of private capital was the main source of funding and the reserves were increased considerably reaching record levels. It is worth mentioning that the Guatemalan economy, compared with most of the countries of Latin America, did not experience very severe inflationary processes or hyperinflation, mainly in the 1980s. Two significant inflationary spikes can be highlighted in 1985 and 1986 that have been associated with the excess liquidity in the economy, caused by the high fiscal deficits described earlier and the expansive policies of unsustainable spending. However, the highest inflation was registered in December 1990 due to the expansive monetary policy and the inconsistent democratic Government of President Vinicio Cerezo Arévalo (1986–1990). From the nineties, the monetary policy generally restricted the monetarist line and, the obsession in the fiscal deficit reduction, allowed to achieve smaller inflation rates and mainly to reduce the volatility, but achieved GDP growth rates of 3.9% average from 1990 to 2006. 2.1. Economic performance during the period between 1960 and 2006 Guatemala’s economic growth rate for the period 1960–2006 can be seen in Fig. 1, below. The growth rate of gross domestic product (GDP) shown in Fig. 1 allows the observing of five subperiods of development in Guatemalan economic activity: 1960–1980; 1981–1986; 1987–1998; 1999–2003 and 2004–2006. In the mid-seventies, the first oil crisis, due to the increase in oil prices imposed by the Organization of Petroleum Producing Countries (OPPC), was experienced. This fact deteriorated the terms of Exchange, causing a big drop in the economic activity (about 2.0% in 1975). There was a second oil crisis in 1979 and a mass flight of private capital in 1980, which caused a sharp drop of private domestic investment (−12.3% in 1979 and −22.4% in 1980). During 4Official document where the nomenclature of all classified products, with all of the records of import tariffs, for the Central American countries. J.A.O. Aragón, V.d.S. Queiroz / EconomiA 15 (2014) 82–99 85 this period, the balance of foreign debt grew by approximately $ 2000 million and became known as the External Debt Crisis. 3. Regional opening: commercial trade integration policy 3.1. Guatemala: Central American Common Market (CACM) The duration of the Treaty for the creation of the Central American Common Market (CACM) began in June 4, 1961, initial date for Guatemala, El Salvador and Nicaragua. In April 27, 1962 it started for Honduras and on September 23, 1963 for Costa Rica. The CACM has its origin in the General Treaty for Central American Economic Integration (1960) and the Central American countries undertook the establishment of a five-year common market, to adopt a uniform Central American import policy and to establish free trade for products originating in their respective territories, with some exceptions. According to Rosenthal (2005), the most obvious results of this regional integration process were expressed in the growth of intra-regional trade which increased from 30 million dollars in 1960 to 136 million in 1965 and rose successively to 286 million in 1970, 536 million in 1975 and, finally, to more than 1100 million in 1980. However, due to the mix-up of economic and political agents that participated in this process, the goals and objectives were not fulfilled, such as the conformation of a common external tariff due to the fact that Honduras suspended its activities from the integration process. Also, it was not possible to undertake the creation of the “integration industries”5due to the influence of the opposing interests of foreign capital and, in particular, of multinational companies. In addition, the crisis of the 1980s, known as the “Debt Crisis”, was more serious in Central America because of the civil war that not only diverted investment incentives, but also led to the decline of intra-regional trade, agreements and instruments adopted to strengthen integration. In 1980 several initiatives were established between the Central American Presidents to reactivate the conformation of the CACM process, and signed the “Declaration of San Jose”, with the aim of coordinating the actions of the Ministers and Deputy Ministers for restructuring the CACM. In the year 1988, Honduras proposed to study the possibility of multilateralizing the bilateral agreements they already had with the Member countries of the Central American Common Market, which, in fact, meant to request their return to the CACM. In 1990, it was agreed with an Economic Action Plan for Central America (PAECA), whose objectives were: (a) the restructuring, strengthening and reactivating of regional economic integration, (b) evolution for an integrated production system at a regional level, (c) delineation of the external debt problem and, (d) a better distribution of social costs and of necessary adjustment of economies. The signing of this agreement by the Presidents of Central America has resulted in a series of efforts directed toward strengthening the Central American integration. In 1993, the Protocol of the General Treaty on Central American integration was approved, whose goal was to reach the Central American Economic Union. From there on, the advancement in the liberalization of trade in the Central American market has been substantial, because practically all the products produced in the CACM have zero tax and more than 90% of the import record tariffs applied the same Common External Tax. When comparing the CACM with other regional integration processes, such as the MERCOSUR, the trading has been much more complicated due to conflicts between national interest and the Bloc’s standards (Azevedo, 2003). 3.2. Bilateral preferential agreements In recent years, the countries of Central America started making bilateral free trade negotiations with other countries, which are shown in Fig. A1, in the Appendix. Specifically in the case of Guatemala, several free trade agreements were signed (bilateral, in whole or partially) with Colombia (1980), Venezuela (1985), France (1988), Cuba (1999), Panama 5The “integration industries” are defined as all those composed of one or more manufacturing plants, which require having access to all the Central American market to work at least at their minimum capacity. 86 J.A.O. Aragón, V.d.S. Queiroz / EconomiA 15 (2014) 82–99 (1999), Chile (1999), Mexico (2000), and Taiwan (2005). Guatemala has also actively participated in various working groups of the Free Trade Area of the Americas (FTAA) and has also signed several agreements for the protection and promotion of investment, particularly with France, in 1998. At the beginning of the year 1984, Guatemala also benefited from unilateral trade preferences granted by the United States, by the so-called “Caribbean Basin Initiative” (CBI). The United States granted a unilateral tax free treatment of selected products that followed the “strict rules of origin” and Guatemala took advantage of the trade preferences granted by the United States. Consequently, this explains a major proportion of export growth registered during the 1990s due to those standards. The main effects of DR-CAFTA are the ability to diversify the export products basket of the country and thus achieve an expansion of trade levels; a profit derived from the “advantage of distance”,6an improvement of the investment climate, which allows a faster growth, and poverty reduction. The huge growth potential embedded in the DR-CAFTA is due to a combination of two complementary forces: the Treaty as a magnet for investment and as a catalyst for institutional change. 4. Theoretical review 4.1. The New Economic Geography (NGE) The New Economic Geography (NGE) is a field of study within the regional economy itself, but it is also a descendant of the theory of international trade, with the models featured increasing incomes of mobility and transport costs. According to Brakman et al. (2005), with the NGE, began a shift in thought about the regional policy, which perhaps should not continue focusing on the outskirts lagging behind, but to channel funds to the local settlements that have a realistic opportunity to hold on to the economic activity. Companies and workers are subject to centripetal and centrifugal market forces and the location of the decisions depends on the balance of those forces that, in turn, depend on the cost of trade. The agglomeration of equilibrium is characterized by a salary structure. The advantages of agglomeration materialize in higher wages in major regions. On the other hand, the causality of the selection is that the balance is circular, that is to say: first, that companies and workers prefer the central core, as it has the largest market and is home to many companies and workers. Therefore, if the agglomeration of balances is the rule, regional disparities are difficult to contract with traditional regional policy. Second, Brakman et al. (2005) say, the explanation is that the peripheral regions lack natural resources and institutional conditions to keep within the economic activity, so the regional policy can succeed temporarily to attract economic activity to the periphery, but in the long run, end in the central core. 4.2. International trade and agglomeration Venables (2003) indicates that the spatial inequality in developing countries is due to the natural advantages of some regions in relation to others and to the presence of agglomeration forces, leading to the Group of activities. The presence of increasing returns to scale in the cities gives rise to urban structures that are not great in size. For Ades and Glaeser (1994), the factors that explain the concentration of an urban population of a nation in a single city are the high taxes, high costs of internal trade and the low levels of international trade that increase the degree of concentration. According to Ades and Glaeser (1994), countries with high GDP percentages and low trade barriers and tariffs for imports (including an intensity of a constant level), rarely have their population concentrated in one city. Urban centralization also falls into the development of transport networks. Wheaton and Shishido (1981) and Rosen and Resnick (1980) argue that the urban concentration is negatively related to the country’s population. Ades and Glaeser (1994) are in complete agreement with Krugman and Elizondo (1996) 6“Remote” understood the capacity to respond quickly, such as fashion trends and delivery demands “Just in time”, besides the obvious geographical closeness to the United States. J.A.O. Aragón, V.d.S. Queiroz / EconomiA 15 (2014) 82–99 87 hypothesis about the fact that the urban concentration is negatively related with international trade, because in the first place, commerce and cities are connected, although it may be that the urban concentrations are causing low levels of trade, contrary to the assumption that the low levels of trade lead to concentration. For Brakman et al. (2005) the program logic of the single market rests mainly on the exploitation of comparative advantage, resulting in a change of economic activity among the Member States in such a way that the location of the production is in accordance with the location of the factors of production. According to these authors, companies want to be where the biggest markets are and, in turn, the large markets, where many companies are located, so there is a “circular causation” and free trade is crucial, where the intermediate levels of crowding tend to be stable. 4.3. Urban and economic geography models and database 4.3.1. Size distribution models of cities When trying to perform an empirical description of an urban system you can check the rank size rule called “rule of countries”. In the case of many countries, cities can be small, with successive larger cities that gradually come to be so. The result can be a function of the distribution of urban areas that are classified or sorted according to the size of each individual urban area, and which will tend to be induced to the left. According to McCann (2001) the extensive urban areas have crucial importance in the behavior and overall performance of the economy due to the presence of agglomerated economies. The result of this is that those urban and regional economies put a great emphasis on the behavior and performance of these larger urban groupings, which are relatively small in number. Within the theories of urban growth in the economic literature, with an emphasis on regional economy, a way of explaining how these changes happen in city sizes is through “Zipf’s law”, which is used to refer to the idea that the size of cities follows a Pareto distribution. George Kingsley Zipf (1902–1950)7improved the inspiring work of Auerbach (1913), which proposes that the distributions of sizes of cities are much wider depending on the original idea of Pareto, but always keeping the original idea that the same has an exponent equal to 1. The same became known as Zipf’s law, which is simply the product of the population of any city multiplied by its position in the ordering of a region of the geographical territory and product that shall be equal to the population of the largest city. Therefore, the second-largest city has half the population, and the third will have a third, and so on. Monasterio (2004) explains that, according to Zipf, there is a diversification force in the way in which the cities are distributed due to the location of the population in the vicinity of areas supplying raw materials as a means of minimizing costs and, another force, is unification of space, which derives from the minimization of transport cost of goods of final products to the consumer markets. These two agglomeration forces would be opposed. Diversification or centrifugal forces lead to an increasing number of cities with declining population, while the unified messaging or centripetal force leads to a smaller number of cities with growing population. As a result of the tension of the two forces the hierarchical system of cities can be deduced. According to Zipf’s considerations, this phenomenon makes it possible to have a linear relationship with regard to the relationship between the rank or the order of cities and its size. Thus, the size distribution of cities is determined by a Pareto distribution as follows (Oliveira, 2004): y = Axα(1) where the variable x indicates the population size of a given city; the variable y is the number of cities with a population greater than x; the coefficient A is the value of a constant and the Pareto exponent is α. The original idea is born of a Pareto cumulative distribution, where the size of the population of a city is a random variable X, with one act x, such that the probability of discovering a city, less than x is given by a cumulative distribution function Prob(X ≤ x) = F(x) = 1 − (A/xα). Therefore, the probability of discovering a city with a population greater than x is given by: Prob(X ≤ x) = 1 − F(x) =A xα(2) 7See: Zipf (1949). 88 J.A.O. Aragón, V.d.S. Queiroz / EconomiA 15 (2014) 82–99 If y = 1 − F(x) and getting the logarithms of Eq. (2), the size of urban areas can be calculated by means of logarithmic transformation econometrically: log y = log A − α log x(3) The model that will be estimated in this work is based on Eq. (3) and is prepared as follows: log yit = log Ait − α log xit + εit (4) where, i = 1, . . ., n represents the cities; t = 1921, 1950, 1964, 1981, 1999, 2000, 2001, 2002, 2003 and 2004 are the census dates and the periods in which the regression is estimated; x is the population of a specific city; y represents the number of cities with a population greater than the same x. The constants or estimated model parameters are A and α and, finally, εit is the error normally distributed with zero mean and constant variance σ2 δ. According to Monasterio (2004), to check the Zipf’s law, there is a requirement that α is near −1. So, the crucial question about the empirical evidence of the size of the cities is: why, in any area, the number of large cities is low in relation to the number of small towns? 4.3.2. Variation of the Pareto exponent In accordance with Soo (2005), the Pareto exponent can be seen as a measure of inequality, the exponent to a higher value would have to understand how populations more equal in urban systems (in the limit α = ∞, all cities have the same size). For Brakman et al. (2003), the Zipf’s law holds if, and only if α = 1, the largest city is k times larger (as the biggest city being k). The α signal should always be negative, because the greater the population of an urban center the lower the probability or the chance to find a city with a larger population. Additionally, for the higher the α value, there is a small inequality for distribution of cities, and when α → ∞ all the cities in the region have the same size. In contrast, the smaller the α value, there is great inequality in the distribution of the size of cities, and when α → 0 there is a full migration to the larger urban centers. Finally, α = 1, you can check the rule of the order of the cities rules, where the parameter A the means the population of the largest urban centers in the region or country of study. To evaluate the possibility that there is a linear relationship between the order of cities, the following Rosen and Resnick (1980) model is proposed: log yit = log Ait + α log xit + β(log x)2+ εit (5) This modified version must evaluate the parameter β, it means to evaluate the signal of the ∂ log y2/∂ log x, so, if β > 0, the curve that relates the order and size of the cities has a convex shape. Then, there is a larger population in the larger urban centers and smaller towns are more numerous in the original proposal known as Zipf’s law or the rule of the order of the cities size law. If β < 0, the interpretation would be that the order and size of the cities has a concave shape where the biggest urban centers or cities are less populous and the smaller towns are less numerous. To conclude, if β = 0, it turns out as Gibrat’s law, in which the evolution in the growth of a city is independent of its size. 4.3.3. Models of impact of free trade on economic growth The model proposed by the Bank of Guatemala aims to estimate the effect on the country’s economic growth rate, derived from the DR-CAFTA in 2006: GDPt= α1+ α2GDPt−1+ α3Xt+ α4Mt+ α5DFIt+ εt(6) where, GDPtis the rate of change in real GDP in the year t; GDPt–1is the rate of change in real GDP in the year t–1; Xtis the rate of change of the exports of goods in the year t; Mtis the rate of change of the importation of goods in year t; DFItis the rate of change in direct foreign investment in the year t; αiare the parameters to estimate (i = 1, 2, . . ., 5) εtis the error term. J.A.O. Aragón, V.d.S. Queiroz / EconomiA 15 (2014) 82–99 89 Table 1 Guatemala-population distribution (2006). Regions Towns More than 100 thousand inhabitants More than 50 thousand inhabitants More than 25 thousand inhabitants More than 25 thousand inhabitants Less than 5 thousand inhabitants Number of intermediate cities Republic 331 4 11 24 153 139 16 Metropolitan 17 3 5 3 5 1 0 North 24 0 1 0 14 9 1 Northeast 34 0 1 2 12 19 3 Southeast 38 0 0 3 17 18 2 Central 45 0 2 4 34 5 4 Southwest 109 1 1 9 46 52 4 Northwest 52 0 0 2 16 33 2 Peten 12 0 0 1 9 2 0 Source: Moran (2006, p. 4). 4.3.4. Urban concentration To measure the urban concentration the Herfindahl-Hirschman Index (HHI) is used, which is built from the sum of the square of every town in the country’s urban population. This index is commonly used to measure the degree of concentration of markets in industrial economy and to estimate the degree of concentration of a variable is as follows: HHI =PJ Ptot × 1002 (7) where the population of a country is formed by j = 1, . . ., n towns and cities in particular (PJ) and the total urban population of a country Ptot. If the index reaches a maximum value of 10,000, the value is completely concentrated in one city when the value tends to zero there is no concentration. So, when approaching zero, there is a greater weight in the medium and small localities. 4.3.5. Database Census data were obtained through the National Institute of Statistics (INE) of Guatemala, that belongs to the Direction of Censuses and Surveys in the records of the National Census of Population and Housing. The census data used corresponded to the urban populations of municipalities for the years 1921, 1950, 1964, 1973. 1981, 1994 and 2002. The data of the censuses designed jointly by the INE and the Latin American Demographic Centre (CELADE) for the years 1999, 2000, 2001, 2003 and 2004 were also used. The data can be seen in Table A1 in the Appendix. 5. Empirical results 5.1. Zipf model test Table 1 shows the distribution of the Guatemalan population. It is seen that in the metropolitan region there are 3 cities over 100 thousand inhabitants and the smallest towns are in the Southeast and Northwest of the country. The following will be exposed to the results of Eqs. (4) and (5) estimated by means of the statistical method known as Ordinary Least Squares (MQO).8The regressions obtained are presented in Table 2 and show that Zipf’s law is not the case. For the coefficient α = −1.11 the hypothesis is rejected that α = –1. In the following 20 years, the distribution of city sizes is more egalitarian until 1950, but then begins to become more unequal. This result is contrary to Gabaix (1999) explanations, which proposes that the order of the cities rule remain stable over time. 8In order to check for heteroscedasticity in the models, the White Test was made with cross-terms that confirmed the rejection of the null hypothesis. 96 J.A.O. Aragón, V.d.S. Queiroz / EconomiA 15 (2014) 82–99 Table A2 Number of countries: urban concentration (HHI). Country Census Herfindahl-Hirschman Index (HHI) Costa Rica 1984 2.468611 2000 5.562983 2006 5.580318 El 1992 7.141112 Salvador 2007 3.812698 1980 2.596704 Estados 1990 2.324380 Unidos 2000 1.893696 2007 1.817705 Guatemala 1921 4.768669 1950 2.595683 1964 16.662702 1973 14.627715 1981 14.863320 1994 9.042273 1999 7.489174 2000 7.798124 2001 7.610005 2002 7.411744 2003 7.208777 2004 6.991733 Honduras 1974 19.420835 1998 18.430050 2001 16.696744 Nicaragua 1971 25.659417 1995 18.545451 2005 15.275473 Mexico 1990 6.938736 1995 5.610312 2000 5.259623 2006 4.828907 Source: Developed by authors. Table A3 Guatemala-results of Eq. (4) to the largest cities. Cities Years A α R2Adjusted N Population of the 13 largest cities in Guatemala 1921*8.877387 −0.795089 0.867695 13 (0.844798) (0.093610) 1950*1.021330 −0.838772 0.688329 13 (1.724627) (0.170176) 1964*7.995465 −0.643998 0.821466 13 (0.884990) (0.090522) 1973*8.872373 −0.683684 0.911791 13 (0.672599) (0.064116) 1981*8.396302 −0.647450 0.786977 13 (1.049984) (0.101565) 1994*9.761984 −0.732482 0.941124 13 (0.607744) (0.055239) 1999 1.027127 −0.754857 0.948118 13 (0.604204) (0.053241) 2000 1.014134 −0.743233 0.955059 13 (0.551838) (0.048611) 2001 1.018107 −0.744760 0.956253 13 J.A.O. Aragón, V.d.S. Queiroz / EconomiA 15 (2014) 82–99 97 Table A3 (Continued) Cities Years A α R2Adjusted N (0.546670) (0.048029) 2002*1.021848 −0.746101 0.957161 13 (0.957161) (0.047591) 2003 1.025870 −0.747705 0.958889 13 (0.534049) (0.046680) 2004 1.029642 −0.749102 0.960205 13 (0.527381) (0.045981) Population of 100 largest cities in Guatemala 1921*1.507774 −1.457578 0.916968 100 (0.348790) (0.044306) 1950*1.926633 −1.706372 0.883961 100 (0.572889) (0.062452) 1964*1.348906 −1.184066 0.920155 100 (0.294333) (0.035234) 1973*1.314757 −1.082291 0.957989 100 (0.202084) (0.022895) 1981*1.443094 −1.209977 0.914056 100 (0.335444) (0.037479) 1994*1.418513 −1.129596 0.957005 100 (0.226666) (0.024186) 1999 1.466746 −1.135697 0.965786 100 (0.210422) (0.021593) 2000 1.294775 −0.964665 0.757598 100 (0.533967) (0.055120) 2001 1.295517 −0.962783 0.757722 100 (0.534209) (0.054994) 2002*1.296094 −0.960665 0.756788 100 (0.535895) (0.055013) 2003 1.296042 −0.957980 0.755739 100 (0.537389) (0.055015) 2004 1.231168 −0.892046 0.703082 100 (0.571688) (0.058558) Source: Developed by authors. *Year of the official census of the National Institute of Statistics (INE) of the Republic of Guatemala. Table A4 Guatemala-results of Eq. (5). Cities Years A α β R2Adjusted N Population of the 13 largest cities in Guatemala 1921*37.94216 −6.751540 0.300138 0.978494 13 (4.065064) (0.830803) (0.041816) 1950*120.9439 −20.95627 0.901819 0.965887 13 (1.229036) (2.231042) (0.099977) 1964*38.71868 −6.365624 0.260514 0.988400 13 (2.572040) (0.477577) (0.021717) 1973*31.61958 −4.724226 0.176613 0.989613 13 (2.639080) (0.467369) (0.020404) 1981*48.21069 −7.673939 0.303905 0.957531 13 (6.301895) (1.109795) (0.047956) 1994*27.44219 −3.777804 0.129646 0.970539 13 (5.613616) (0.964662) (0.041031) 1999 26.46692 −3.476205 0.113205 0.966528 13 (6.924563) (1.161251) (0.048271) 2000 23.60810 −3.009584 0.094417 0.968650 13 (6.485694) (1.089289) (0.045346) 2001 22.94606 −2.889809 0.089247 0.968072 13 (6.652904) (1.115760) (0.046388) 2002*22.22452 −2.760749 0.083717 0.967259 13 98 J.A.O. Aragón, V.d.S. Queiroz / EconomiA 15 (2014) 82–99 Table A4 (Continued) Cities Years A α β R2Adjusted N (6.854836) (1.148052) (0.047672) 2003 21.60388 −2.648882 0.078909 0.967576 13 (6.949200) (1.162343) (0.048210) 2004 20.90448 −2.524511 0.073609 0.967488 13 (7.105194) (1.187007) (0.049181) Population of the 100 largest cities in Guatemala 1921*32.89423 −5.593167 0.236284 0.980655 100 (1.011257) (0.232421) (0.013222) 1950*52.93112 −8.512012 0.340695 0.968134 100 (2.124666) (0.426437) (0.021284) 1964*26.82237 −4.071818 0.153232 0.984471 100 (0.677903) (0.144921) (0.007645) 1973*23.81157 −3.292161 0.112364 0.994127 100 (0.443032) (0.090858) (0.004599) 1981*30.13977 −4.405178 0.159709 0.97888 100 (0.925620) (0.186117) (0.009256) 1994*28.20426 −3.883324 0.133144 0.992876 100 (0.641111) (0.124999) (0.006025) 1999 27.64016 −3.606574 0.116094 0.991098 100 (0.788554) (0.149193) (0.006991) 2000 29.21781 −3.921532 0.131132 0.993078 100 (0.696608) (0.131763) (0.006166) 2001 29.18236 −3.904054 0.130107 0.993223 100 (0.695448) (0.131267) (0.006130) 2002*29.20808 −3.897172 −3.897172 0.993167 100 (0.705737) (0.132914) (0.006194) 2003 29.15831 −3.876994 0.12839 0.993316 100 (0.704580) (0.132422) (0.006158) 2004 29.06109 −3.848569 0.126894 0.993282 100 (0.712821) (0.133705) (0.006206) Population of all cities in Guatemala 1921*4.746776 0.953452 −0.137106 0.936734 351 (0.407563) (0.116553) (0.008279) 1950*0.740534 2.060582 −0.18824 0.936734 310 (0.967791) (0.228215) (0.013449) 1964*7.204587 0.176429 −0.07828 0.90289 324 (0.360978) (0.098050) (0.006417) 1973*7.309062 0.166925 −0.064627 0.950874 325 (0.346595) (0.085568) (0.005244) 1981*6.185634 0.486103 −0.084586 0.929269 326 (0.435701) (0.107180) (0.006567) 1994*6.241948 0.475524 −0.078993 0.954143 329 (0.401386) (0.093475) (0.005406) 1999 5.375186 0.666002 −0.08552 0.963998 330 (0.381593) (0.086009) (0.004809) 2000 5.840287 0.56704 −0.080575 0.959575 330 (0.403297) (0.090809) (0.005075) 2001 5.801971 0.574931 −0.080705 0.960379 330 (0.401615) (0.090192) (0.005027) 2002*5.749898 0.585691 −0.08098 0.961124 330 (0.399997) (0.089599) (0.004981) 2003 5.698872 0.596224 −0.081248 0.961963 330 (0.397827) (0.088886) (0.004928) 2004 5.643700 0.607559 −0.081555 0.962767 330 (0.395668) (0.088181) (0.004876) Source: Developed by authors. *Year of the official census of the National Institute of Statistics (INE) of the Republic of Guatemala. J.A.O. Aragón, V.d.S. Queiroz / EconomiA 15 (2014) 82–99 99 References Ades, F., Glaeser, E.L., 1994. Series trade and circuses: explaining urban giants. NBER Working Paper No. 4715., pp. 1–5, 21. Auerbach, F., 1913. Das Gesetz der Bevölkerungskonzentration. Petermann’s Geographische Mitteilungen 59, 74–76. Azevedo, A.F.Z., 2004. Mercosul: ambitious policies, poor practices. Rev. Econ. Pol. 24 (4), 584–601, -São Paulo: Ed. 34. Azevedo, A.F.Z., July 2003. Análise Empírica do Econômico da ALCA e da Consolidac¸ão do Mercosul sobre o Brasil. Discussion Paper, No 12, Programa de Pós-Graduac¸ão em Economia (PPGE). Universidade Federal de Rio Grande do Sul (UFRGS), Porto Alegre. Banco de Guatemala. Estudio Económico 2006. Available in: <http://www.banguat.gob.gt>. Accessed: 28.03.13. Banco de Guatemala, 2006b. Evaluación de la política monetaria, cambiaria y crediticia a noviembre de 2006. Anexo 2, 159–166, Anexo 3 p. 186–191, 2006. Available in: <http://www.banguat.gob.gt>. Accessed: 12.12.13. Brakman, S., Garretsen, H., Marrewijk, C.V., 2003. An Introduction to Geographical Economics. Cambridge University Press (Chapter 7). Brakman, S., Garretsen, H., Gorter, Joeri, J., Van der Horst, A., Schramm, M., May 2005. New Economic Geography, Empirics, and Regional Policy. CPB Netherlands Bureau for Economic Policy Analysis No. 56., pp. 8–11. Cifuentes, I., 2006. La red Vial como Indicador del Proceso de Urbanización. Centro de Estudios Urbanos y Regionales (CEUR), Universidad de San Carlos de Guatemala. Estrelha, L.F., 2006. Notas de aula para discussão: Economia das relac¸ões Internacionais. Programa de Pós-Graduac¸ão em Economia (PPGE). Universidade Federal de Rio Grande do Sul (UFRGS), Porto Alegre. Fujita, M., Krugman, P., Venables, A., 2002. Economia Espacial. Urbanizac¸ão, prosperidade econômica e desenvolvimento humano no mundo. Futura (Chapter 2 and 12). Gabaix, X., 1999. The Zipf’s law for cities: an explanation. Q. J. Econ. 114 (3), 738–767. Henderson, J.V., 2000. How Urban Concentration Affects Economic Growth. World Bank, Development Research Group, Infrastructure and Environment, 42, Policy research working papers, Washington, DC. Henderson, V., 2003. The urbanization process and economic growth: The So-What Question. J. Econ. Growth 8 (1), 47–71. Krugman, P., Elizondo, L.R., 1996. Trade policy and third world metropolis. J. Dev. Econ. 49, 137–150. LARRAIN, F., SACHS, J., 2002. Macroeconomía en La Economía Global, 2nd ed. Pearson Educationl, Buenos Aires, pp. 162 (Chapter 6). McCANN, P., 2001. Urban and Regional Economics. Oxford University Press, Oxford, pp. 78–81 (Chapter 3). Meardon, s.j.M., January 2001. Modeling agglomeration and dispersion in City and Country Gunnar Myrdal, Franc¸ois Pewoux, and the New Economic Geography. Am. J. Econ. Soc. 60 (1), 25–57. Monasterio, L., 2004. A Lei de Zipf: Rio Grande do Sul. 2◦Encontro de Economia Gaúcha. UFRGS, Porto Alegre. Moran, M.A., 2006. Las ciudades intermedias en Guatemala. Centro de Estudios Urbanos y Regionales (CEUR), Universidad de San Carlos de Guatemala. NARANJO, F., 2003. Principales efectos inacroecor-icímicos para Centroamérica de un Tratado de Libre Comercio con los Estados Unidos de América. CEFSA. Informe de Consultoría, Proyecto SG-SICA/CEPAL. Oliveira, C.A., 2004. A Evoluc¸ão da Distribuic¸ão do Tamanho das Cidades Brasileiras 1936–2000. In: Anais do Fórum BNB de Desenvolvimento e IX Encontro Regional de Economia - ANPEC Nordeste, Fortaleza. Ottaviano, P., Martin, P., 2001. Growth and agglomeration. Int. Econ. Rev. 42 (4), 947–949, 967–968, November. Rodriguez, M., 2005. Impactos de TLCAUSA. Revista Centro-Americana na Economia Mundial do século XXI, n. 1. Tratado de Libre Comercio Estados Unidos - Centroamérica (CAFTA), Guatemala. ROSEN, K.T., RESNICK, M., Sep 1980. The size distribution of cities: an examination of the Pareto law and primacy. J. Urban Econ. 8 (2), 165–186. Rosenthal, G., July 2005. Pros y contras del TLC sobre la integración Centroamericana. Sistema de Información Tratado Libre Comercio – Republica Dominicana – Estados Unidos. Revista Centroamérica en la Economía Mundial del Siglo XXI, n. 8., pp. 11. Soo, K.T., May 2005. Zipf Law for the cities: a cross country investigation. Reg. Sci. Urban Econ. 35 (3), 239–263. Venables, A., 2003. Spatial disparities in developing countries: cities, regions and international trade. London School of Economics and Centre for Economic Policy Research, pp. 1–3, 24, 25. Wheaton, W., Shishido, H., 1981. Urban concentration, agglomeration economies, and the level of economic development. Econ. Dev. Cult. Change 30, 17–30. Zipf, G.K., 1949. Human Behavior and the Principle of Least Effort. Addison-Wesley Press.