Do Knowledge Externalities lead to growth in Economic Complexity? Empirical evidence from Colombia.

Do Knowledge Externalities lead to growth in Economic Complexity? Empirical evidence from Colombia.

Navroop K. Sahdev Erasmus Mundus Masters Economic Policies in the Age of Globalization August, 2015 Cambridge, Massachusetts.

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Abstract We live in a Complex Economic system where externalities play a key role in fostering growth in complexity through increasing interdependence of interacting agents. The study tests this hypothesis for the case of Colombia. We ask whether knowledge externalities lead to growth in economic complexity. If yes, which variety of knowledge externalities – MAR, Porter or Jacobs? Results from our empirical investigation uphold the MAR theories of externalities or intraindustrial externalities which are maximized with high local specialization1 and local monopoly. A pattern of convergence in economic complexity of Colombian municipalities emerges from our results, supporting Schumpeterian growth theories, which advocate that knowledge externalities drive convergence. This is in line with the recent macroeconomic trends of the Colombian economy which is suffering from “Dutch Disease” leading to a contraction in its domestic economy. We show that knowledge externalities are a mechanism through which convergence dynamics are brought about and fostered in the domestic economy.

Keywords Knowledge externalities, MAR, ECI, Diversity, Competition, Convergence.

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Note that we do not add a separate variable to measure ‘Specialization’ and at the same time, neither is specialization the reciprocal of our ‘Diversity’ variable. The results we present point towards the availability of MAR externalities as inferred from the system’s characteristics, rather than a direct measurement of knowledge spillovers. This necessitates careful handling of the two concepts.

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Acknowledgments I wish to acknowledge with gratitude the constant support and guidance provided by my thesis advisors - Ricardo Hausmann, for taking the time from his busy schedule to provide invaluable guidance, and giving me the opportunity to be a part of “Team CID”, Cristiano Antonelli - whose work on Complexity inspired the thesis - for his patient counsel and insights over the past 6 months, Benjamin Coriat for his advice and delightful luncheons in Paris and Frank Neffke for weekly meetings for thesis discussion and his helpful comments on the initial drafts. I would like to thank my fellow research fellows at the Center for International Development (CID) at Harvard University - who provided extremely useful comments and inputs during the process of thesis writing. (You guys are an awesome bunch!) In particular, I would like to acknowledge inputs of Luis Espinoza, Juan Tellez, Andres Gomez, Michele Coscia, Jose Ramon and Sebastian Bustos. I thank Marcela Escobari for her kind advice. I wish to thank Forrest Rogers-Marcovitz for helping me in writing the code and Federico Bassi who provided key insights. I wish to acknowledge the resources from Harvard University and the French government towards this thesis work. I thank all faculty members and my family and friends for their constant encouragement.

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Table of contents 1. Introduction …………………………………………………………………………….. 6 2. Understanding Complex Economic Systems …………………………………………... 8 2.1 Definition ………………………………………………………………………. 8 2.2 Measuring Economic Complexity ……………………………………………... 9 2.3 The Dynamics of Complexity Growth: Externalities as a Complexity Fostering Mechanism …………………………………………………………. 10 3. Externalities in Economic Thought: A brief summary of the literature ………………. 11 4. Knowledge Externalities in Colombia ………………………………………………… 16 4.1 Data ……………………………………………………………………………. 17 4.2 Methodology…………………………………………………………………… 24 4.3 Results …………………………………………………………………………. 33 4.4 Discussion ……………………………………………………………………... 33 5. Conclusion ……………………………………………………………………………... 35 6. Appendix: A brief note on Inter-municipality spillovers …………………………...…. 38 7. References …………………………………………………………………………...… 39

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List of figures and tables Figures 1. Colombia Dutch Disease Data, 2000 – 2011. 2. Industries by ISIC 2-digit classification in Colombia, 1995 – 2011. 3. All municipalities ranked by employment, 1997. 4. ECI growth of 50 biggest Colombian municipalities (by the order of their codes), 1997 – 2011. 5. ‘Diversity’ of municipalities, 1997. 6. ‘Diversity’ of municipalities, 2011. 7. Regression of ECI 2011 on ECI 1997.

Tables 1. Summary statistics of key variables. 2. Five largest municipalities by employment. 3. Five smallest municipalities by employment. 4. Ten largest municipality-industries, by output in 1997.

5. Municipalities with the highest ECI growth over 1997 to 2011. 6. Municipalities with the lowest ECI growth over 1997 to 2011.

7. Varieties of Knowledge externalities and expected coefficients. 8. Regression results: ECI growth between 1997 and 2011.

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1. Introduction The study of complex systems has brought a renewed focus on the role of externalities. The “divergence between social and private costs or benefits” affecting other agents in the system or other subsystems necessitates the understanding of the whole system that they are endogenous to. Brewer (1975) suggests the following in his analysis of social systems: “Because social systems exhibit properties of organized complexity (my emphasis), perturbations at one point in a structure may have effects elsewhere. Participants often perceive these effects as occurring “outside” of their particular system, and almost as often, are surprised by these externalities.” More recently, Antonelli (2011) argues that the “new growth theory” that builds upon Arrow’s (1962) legacy fails to appreciate the endogenous, idiosyncratic and dynamic character of knowledge spillovers2. Starting from this gap in the literature, the motivation of this study is then twofold: on one hand, it attempts an in-depth analysis of the notion of externalities and on the other, it attempts to understand their role in a “complexity framework”. We focus on each of these three characteristics (endogeneity, idiosyncrasy and dynamism) by borrowing from the literature in proposing such a framework. Specifically, we test if knowledge externalities lead to growth in economic complexity. The literature on positive knowledge externalities has drawn particular attention towards their role in fostering growth, particularly in cities (Jacobs 1969; Bairoch 1988; Glaeser 1992). While this is simultaneously situated in the broader literature of Economic Geography, a complexity-angle might lend new insights into the same. Other scholars have vouched for them even more forcefully as “engines of growth” (Romer 1986; Lucas 1988). All these theories deal with technological externalities, whereby innovations and improvements occurring in one firm increase the productivity of the other firms without full compensation (Glaeser et al., 1992). Accordingly,

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Note that we use the terms “knowledge externalities” and “knowledge spillovers” interchangeably throughout the paper. Strictly speaking, these are ‘externalities’ because agents receive knowledge without paying for its full cost. But at the same time, the literature seems to prefer the term ‘spillovers’. This might be due to the following line of argument: Knowledge spillovers do not require any transaction between the producers and the recipients of the external effects: they can be considered the characteristic of the ‘atmosphere’ of the districts in which firms are based (Antonelli, 2011).

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knowledge externalities are expected to facilitate the recombination of different bits of productive knowledge which lead to growth. The key idea of this paper is that availability of knowledge externalities (as a specific type of externality) leads to growth in complexity. In this sense, they are a complexity fostering mechanism, albeit not the only one (section 2.3 provides a more detailed discussion). We shall test this hypothesis by regressing complexity growth - as measured by the Economic Complexity Index (ECI) - on the system’s characteristics that are said to be conducive for knowledge spillovers. Furthermore, we investigate which variety of knowledge spillovers leads to complexity growth in the case of Colombia – MAR, Jacobs or Porter. The literature stands indecisive as to whether MAR, Porter or Jacobs externalities are important for economic growth, also known as the theories of dynamic externalities (Glaeser et al., 1992). For they explain the growth in economic complexity in comparison to the theories of static externalities which focus on why industry specializes and its choice of location. Location externalities are discussed by Lichtenberg (1960), Henderson (1986, 1988), Arthur (1989), and Rotemberg and Saloner (1990), among others. Another group of static externalities - urbanization externalities – are discussed by Lichtenberg (1960), Murphy, Shleifer, and Vishny (1989), and Krugman (1991). Since it is often not possible to directly observe the origin and scale of externalities in a complex economic system, we infer from the conditions that must hold true from them to be available in the system. Which is to say that if knowledge externalities are available, diversity of the economic base and local competition within the geographical area under investigation should be significant predictors of growth in economic complexity. The equation below depicts the causal relationship we seek to test. As already mentioned, the extent and impact of externalities is very difficult to trace in a complex system due to its intricate interdependencies and in particular - emergent behavior, rendering the direct measurement of externalities a challenging task. The chain of causality is extremely hard to trace, if not completely lost. Hence, we explicitly assume that knowledge spillovers are not directly observable and infer their presence through the system’s characteristics.

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The next section clarifies the meaning of a complex system and our working definition of economic complexity, listing key characteristics of complex systems before turning to the dynamics of complexity growth.

2. Understanding Economic Complexity 2.1 Definition Neil Johnson in his 2007 book “Two's company, three is complexity” articulates complexity as ‘crowd phenomena’ through lucid examples. In turn, he defines Complexity Science as “the study of the phenomena which emerge from a collection of interacting objects”. A common example of this crowd response is a financial market or the housing market where the spontaneous formation of a crowd of people who wish to sell - and hence effectively competing for buyers - can lead to a market crash in which the price falls dramatically in a short time. Johnson’s working definition aside, there is no strict definition of complexity in the literature so far. Indeed ‘complexity’ has as many different definitions as the number of scholars working on the subject. However, there is a broad consensus on the characteristics that identify a particular system as complex or not. Once again, Johnson (2007) lists the following features/components which characterize any complex system: 1. The system contains a collection of many interacting “agents”. 2. The agents’ behavior is affected by memory or “feedback”. 3. The agents can adapt their strategies according to their history. 4. The system is typically “open”. 5. The system appears to be “alive”. 6. The system exhibits “emergent phenomena” which are generally surprising, and may be extreme. 7. The emergent phenomena typically arise in the absence of a central controller. 8. The system shows a complicated mix of ordered and disordered behavior. 8

With these characteristics in mind, it is not hard to see that we live in a complex system – the global economy – and equally complex sub systems like national economies. While a simple example of a stock market crash easily exemplifies all of these features simultaneously; this study emphasizes one fundamental aspect of complex systems: the interdependence of agents, which is fostered through interactions (point 1 above) and were it for the lack of direct interactions (as one can argue might be the case of externalities where the action of one economic agent affects the other), there is one thing that is flowing through the system that makes it complex: information3. The result is a system which appears to be “alive” (point 5 above) or as if with a life of its own. Complexity arises whenever a system - technical, social, or natural - has multiple interdependent parts. The human body, bees in a hive, a soccer team, and international banking are all examples of complex systems - they consist of many components and interdependencies that can change unpredictably and frequently. (Sull and Eisenhardt, 2015) This resonates closely with Antonelli’s (2011) criticism of the new growth theories, emphasizing the idiosyncratic character of the knowledge spillovers in complex systems which themselves exhibit such behavior. Hence, complexity behavior of a system can be understood as “interdependencies” between interacting agents (or individuals) which are the constituent parts of the system. Once the economy or an ecosystem is identified as a complex system (which depicts all of the above listed characteristics), modelling complexity can take the form of taking into account these interdependencies in understanding economic phenomena and predicting economic outcomes. Complexity Science applications to Economics or “Economic Complexity” here on, is thus the study of interdependencies among economic agents in all spheres of economic activity.

2.2 Measuring Economic Complexity The application of Complexity Sciences to Economics is relatively new, compared to other disciplines; for example, biology. No one measure of economic complexity so far can be credited with being the most robust one, exactly because what makes a system complex also makes it

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Further elaboration on this fascinating subject is outside the scope of this study. Read “The Information” by James Gleick for a flavor of the same. The author envisions future research work on the topic.

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idiosyncratic and unpredictable, embedding various levels interdependencies which are very challenging to model. A good measure of economic complexity would then be the one that can explicitly takes in account the interdependencies in the system. For not only the agents in the system are important, but equally important are the linkages between them for these linkages cannot be the property of any one individual (Blosh and Metcalfe, 2011). This invariably calls for a networks based analysis of system. Indeed, Networks Theory has become the basic warehouse of Complexity Sciences just as the IS-LM framework did for the general equilibrium models. This study employs the Economic Complexity Index (ECI) as a proxy for the measurement of economic complexity. A very specific formulation of economic complexity, where “the complexity of an economy is related to the multiplicity of useful knowledge embedded in it; expressed in the composition of its productive output and reflected in the structures that emerge to hold and combine knowledge” (Hausmann et al., 2011); it analyzes and infers the knowledge embedded in networks of individuals and organizations as reflected in the mix of products an economy is able to make. In other words, the ECI reflects the total amount of productive knowledge in an economy. Increase in economic complexity, is then, necessary for the growth of economies.

7.3 The Dynamics of Complexity Growth What does it mean for economic complexity to grow or evolve? How do we know if a system is more/less complex over time? How can we compare two systems and figure out which one is more complex than the other? The answers to these questions require a dynamic understanding of complexity.

Growth in economic complexity is then the growth of the total amount of productive knowledge in the economy. Albeit this being an oversimplification of the meaning of economic complexity, a simple parallel from the literature on the growth of knowledge can be drawn. We can ask: How does knowledge grow? Certainly through re-combinatory processes where new knowledge builds on previous knowledge along with knowledge spillovers or externalities.

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Section 3 discusses how the literature in the past 100 years has seen increasing agreement over the role of positive knowledge externalities in economic growth of geographical regions. Since we explicitly start with the assumption that the economy depicts the characteristics of a complex system, we now ask: How does the complexity of a system grow? If indeed economic complexity grows over time, there has to be a mechanism to foster complexity growth. This study suggests that externalities (both positive and negative) - the divergence or private and social costs/benefits which then become part of the utility/production function of the agents it affects - are one such mechanism4. For it creates ever increasing interdependencies between agents and various subsystems, within a system.

How are externalities a complexity fostering mechanism?

On a broad note, the presence of externalities means that the impact of the actions of one economic agent has direct or indirect bearings on the other agents in the system. Increasing interdependence is caused by the presence of external effects in the system and is in fact, the consequence of the presence of externalities. Externalities are thus endogenous to the system. They arise from the system, impacting its macro structure and in turn yield newer and greater external effects. As Brian Arthur says “the system is constantly reinventing itself”. And given that interdependence of the agents is a key feature of a complex system and greater interactions are presumed to lead to greater externalities, we can expect greater spillovers in geographical areas where interactions are higher and agents are highly interdependent. For example, in cities or similar geographical areas where production is highly specialized and no one agent is completely self-sufficient.

3. Knowledge Externalities in Economic Thought: A brief summary of the literature The literature on Externalities goes back to over a 100 years. First discussed by Marshall, in his “Principles of Economics” (1890), the idea of externalities appears as “external economies”, i.e. economies external to the firm but internal to the industry (Mishan, 1971). The notion captured 4

However, in no way it is claimed that externalities are the only mechanism for increasing or decreasing complexity of economic systems.

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increasing interest particularly after the publication of Pigou’s “The Economics of Welfare” (1920) who is credited with an early formalization of the notion of externalities, thus putting it in the center of debates concerning welfare economics. The remedy to the problem of external costs by the imposition of the so called “Pigovian tax” stood as the only ‘solution’ to negative externalities until Coase’s 1960 paper “The Problem of Social Cost” instead highlighted the reciprocal nature of the problem. Coase treats externalities as “those actions of business firms which have harmful effects on others” (Coase, 1960). So essentially, Coase’s focus remains on negative externalities. His ‘solution’ lies in clearly defining property rights and bargaining with low transaction costs (for if the cost of bargaining is too high, agents will never undertake the transaction). The simple taxonomy of externalities The conventional, and rather simple taxonomy of externalities is that of positive versus negative externalities. Barring Marshall’s notion of “external economies” (1890), the earliest literature has largely been focused on correcting negative externalities (Pigou 1920, Coase 1960, Buchanan and Tullock 1965, Browning 1977, Baumol and Oates 1977, 1985). Arguably, the distinction between positive and negative externalities demands adequate attention – not only because of the separate bodies of literature that evolved under this taxonomy – but also because of the different incentives operating behind them. Keppler (1994) briefly touches upon this distinction. Starting from the assumption that the producer of a particular externality has the best knowledge about it, the producer of a positive externality has the incentive to demand due compensation for it whereas, the producer of a negative externality has the incentive to do everything possible to avoid the cost of paying for the eternality as long as it is lower than what it costs to keep on producing it. On Negative Externalities The disagreement in the literature on the subject of negative externality is neither about the actuality of the concept nor the necessity for its treatment; the discord is rather about the means of treatment or mechanism (i.e. the degree of governmental involvement), in corrective actions. (Vorotnikova, 2013) starting from an effective evaluation of the cost of the externality. Since an externality gets diffused to a large number of agents, with sometimes the whole system/sub system bearing its cost/benefit, the marginal valuation criterion of the measurement of 12

the externality becomes extremely challenging an exercise. This is particularly true for global environmental externalities. From direct governmental intervention through taxes and subsidies (Pigou), agent to agent bargaining (Coase) and an institutions-based approach (Keppler), a wide range of policy recommendations have been advanced. Keppler, in his 1994 paper “Externalities, Fixed Cost and Information” argued that the very existence of an externality, highlights the existence of informational complexity and high transaction costs, vouching for an institutionsbased approach to address the complexity and the dynamic nature of externalities. His insight rests in clarifying that if externalities could be monetized, they would have already been internalized. On Positive Externalities The literature on positive externalities largely focuses on the role of knowledge spillovers in economic growth and the challenges in appropriation of knowledge, thus calling for policy support in terms of direct investment or subsidies along with strict property rights. The nature of information (or knowledge) as an economic good has been elaborated upon by Arrow (1962) as limited by the three classical reasons for the failure of perfect competition to achieve optimality in resource allocation: indivisibilities, inappropriability, and uncertainty. This challenge of information/knowledge5 ‘appropriability’ or the inevitable ‘divergence between private and social costs/benefits’ has been explored by the literature over the decades. Knowledge externalities directly contribute to economic growth of the local region in terms of the knowledge (technological or otherwise) that the agents receive from others without paying for it, thanks to the very nature of knowledge which is not fully appropriable. This means that not all the agents have to pay the full cost of acquiring knowledge, making this positive externality available in the system. At the same time, previous knowledge is a necessary input for creating new knowledge. Or as Antonelli et al. (n.d.) put it, “We create new knowledge by standing on the shoulders of the giants”. Importantly, the degree of the available knowledge spillovers depends on geographical

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Over the last few decades, the difference between information and knowledge has become clear. Briefly, information can be defined as “organized data” (Saint-Onge, 2002), “data endowed with relevance and purpose” (Drucker, 2001) or “interpreted data” (Probst et al, 2002), whereas knowledge can be defined with the notions of empiricism and rationalism (Gordon, 2002) i.e. knowledge can only reside in one’s mind and is the result of human experience and reflection based on a set of beliefs that are at the same time individual and collective. The high complexity of knowledge (as compared to information) lies in the critical role of human beings in processing, creating, carrying and using it.

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proximity to the producer of knowledge (Jaffe 1992, Audretsch 2004); spillovers are stronger in proximity to knowledge producers. Firms are able to appropriate only a fraction of the knowledge they produce, which then spills over into the system. The insight comes from Zvi Griliches (1979) who highlighted the role of positive knowledge externalities as the divergence between social and private returns of R&D expenditures (Antonelli, 2011). Accordingly, greater knowledge spillovers can be expected in dense areas, characterized by high interactions. The Varieties of Knowledge externalities The debate in the literature concerning spillovers that are key to economic systems, mainly focuses on three varieties of it: MAR, Porter and Jacobs. Marshall-Arrow-Romer (MAR) externalities are maximized with high local specialization and local monopoly, while according to Jacobs (1969), knowledge externalities are most easily available between industries, while local competition plays an important role in early adoption of new technology. Porter (1990), on the other hand, favors specialization along with local competition. The empirical evidence on the famed “MAR versus Jacobs” debate remains very context specific. For example, Panne (2004) finds evidence in the favor of Marshallian specialization in the Dutch case, where regional innovativeness is investigated through innovation counts, with high ‘local competition’ within an industry playing a negative role in its innovativeness. In contrast, Glaeser et al., (1992) find evidence that supports inter-industrial spillovers for the case of 170 U.S. cities, consistent with Jacobs’ views. Paci and Usai (2000) find evidence supporting both Specialization (Marshall) and Diversity (Jacobs) externalities at the same time, in the case of Italy. Antonelli, et al. (n.d.) conclude the same for their study on patent data from 27 European Union countries using the ‘size of the regional stock of knowledge’ as a proxy for Marshall externalities and the ‘Economic Complexity Index’ as a proxy for Jacobs externalities6. A related stream of literature on technological convergence or divergence (and their causes and dynamics thereof) is readily applicable to this study. It explores the possibility of convergence of productivity among firms, thanks to the knowledge externalities available from more productive

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A possible criticism of using ECI as a proxy for Jacobs externalities can be that the ECI contains much more information about the economic complexity of a region than the mere availably of inter-industrial externalities, as is assumed by Antonelli et al. (n.d.). In fact, ECI seeks to explain the total amount of productive knowledge contained in an economy as expressed in the country's industrial composition. (Hausmann, et al., 2011)

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firms to the less productive ones. These are the so-called Schumpeterian growth models where convergence is expected from knowledge spillovers. For instance, Fung (2005) shows that R&D expenditures being the same, the followers in technology will eventually catch up with the leaders, because they receive knowledge spillovers from the leaders. Another stream of literature builds on the neoclassical growth models pioneered by Solow (1956), where convergence is a result of decreasing returns in physical or human capital accumulation. Antonelli (2011) discusses the process of technological convergence among firms through knowledge recombination which exploits complementary technologies (moving more and more towards the periphery of the core technologies), with diminishing returns to recombination that eventually set in. Hence, both sets of growth models discuss convergence but different factors leading to it. Accordingly, we check only for the Schumpeterian explanation of a possible convergence in our study, which occurs due to the availability of knowledge externalities (see Section 4.4 for the discussion of results). Since the Economic Complexity Index is, in fact, a measure of the total amount of knowhow in an economy (technological or otherwise), as reflected in what it competitively produces, the literature on technological convergence or divergence (and their causes and dynamics thereof) is readily applicable to this study. Accordingly, we seek to find evidence suggestive of either variety of knowledge externalities and understand their role in the growth of complexity in Colombia.

4. Economic Complexity and Knowledge Externalities in Colombia: Empirical evidence Colombia provides an interesting case for studying growth in economic complexity. Having witnessed a steady growth rate over the past few years, Colombia had one of the highest growth rates in Latin American in 2007 at 6.9% albeit suffering from a painful depression in 1999. Since our years of comparison are 1997 and 2011, we envision a possible impact of the 1999 recession in the years following it. But the gap of 14 years is also expected to have provided adequate time for recovery. Since the case of Colombia is that of an economy which was historically agrarian, we don’t expect industries to be very mature during the period of 1997 – 2011 unlike their American or European counterparts. During the same years and more recently too, the Colombian 15

economy has seen a boom in the export of petroleum oils (crude and refined) and coal briquettes leading to an appreciation in its currency, thus presenting a classic case of ‘Dutch Disease’. Figure 1 provides an overview of Colombian exports from 2000 – 2011. Figure 1: Colombia Dutch Disease Data, 2000 – 2011.

Source: Cordaid, Extractives in Colombia. Based on World Bank and BP Stat Review, 2013.

We believe that these are important dynamics of the Colombian economy that should serve as the broader context in which the study can be situated, even though we concern ourselves with the manufacturing sector of Colombian municipalities only. More specifically, our trust remains on understanding the domestic dynamics as evident from knowledge externalities rather than the broader macroeconomic trends, which are nevertheless adequately analyzed with a consensus that the Colombian economy presents a Dutch Disease case from over the last two decades. As section 4.1 shows, the ECI growth in Colombia municipalities from 1997-2011 is in fact, negative at 0.02. This is in line with the trend of boom in natural resource export and an overall decline in manufactures export (Figure 1). The “Convergence hypothesis” is discussed as a possible explanation in the conclusion of the paper (section 5).

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4.1 Data Construction of the data set

1. Years of observation The panel dataset studied is from the Annual Manufacturing Survey or EAM7 of Colombia on output, employment, wages and number of firms per municipality per ISIC 4-digit industry classification (revision 3) for all years from 1995-2013. As per ISIC industry classification for all economic activity, 15 – 39 constitute ‘manufacturing’ activities. Hence, services are not included in this study.8 The highest difference in economic complexity is intuitively assumed to be observed over longer periods of time. Which is why longer the time frame, the more meaningful the comparison is expected to be. Our dataset compares years 1997 and 2011, rather than 1995 and 2013. Year 1995 and 1996 are dropped due to the non-availability of data on industries 15 – 30 as per the ISIC 2 digit classification. This is clear from the Figure 2 below.

ISIC 2 digit industry

Figure 2 - Industries by 2-digit classification in Colombia, 1995 – 2011.

Years

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EAM is aimed at capturing the regional distribution and geographical concentration or dispersion of industrial activity in Colombia. 8 An interesting future research area can be to study if knowledge externalities across services sector (or the whole array of economic activities) in Colombia lead to greater economic complexity over time.

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Secondly, the year 2012 witnessed the transition from the 3-digit industry classification to 4-digit classification, resulting in some significant outliers. Hence, 1997 and 2011 will serve as our years of comparison for this study.

2. Choice of municipalities The largest spillovers or externalities are expected in the biggest municipalities. For if indeed it is true that knowledge externalities are available because of interactions among agents, stronger evidence should be available in areas where interactions are high (Jacobs, 1969; Jacobs, 1984; Glaeser et al., 1992), justifying creation of a subset of municipalities. Smaller municipalities with a small number of workers are less interesting for this study. We let the data speak for itself in this case. A quick look at Figure 3 makes the point that the top 50 municipalities are an appropriate sample for testing our hypothesis.

Figure 3 - Municipalities ranked by employment, 1997.

Figure 3 ranks all municipalities (total < 250) by employment or the total number of workers (across all manufacturing industries) in each municipality, where the municipality with the highest employment is ranked 1. Clearly, there is a huge difference between the biggest and the smallest municipality, with the biggest municipality of Colombia employing over 2 million people across all manufacturing industries in 1997.

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We set the cut off at the 50 biggest municipalities of 1997 and obtain a matrix of 1100 observations (50 municipalities x 22 industries). These 50 municipalities are then matched with 2011 entries only retaining data on these 50 municipalities in order to study the dynamics in the same municipalities over time. Accordingly, we obtain a matrix of 1100 observations for 2011 as well.

3. Aggregation by industry Since the original data is disaggregated at the 4 digit industry code – which is required for calculating the ECI – we aggregate the variables ‘output’, ‘wages’, ‘employment’ and ‘number of firms’ up to the 2 digit classification of industries which is used for calculating our ‘Competition’ and ‘Diversity’ indexes. As a result, we obtain the values of these variables per municipality per 2-digit industry. This municipality-industry data is then used to test the hypothesis whether interindustrial externalities or intra-industrial externalities from the available “urban variety” along with local competition during the base year are predictors of change in complexity over time.

Since our data is at the lowest available geographical level of disaggregation, it arguably lends a very close look at the dynamics occurring at the regional level. This stands in contrast with the Glaeser et al.’s 1992 paper where they create ‘cities’ by aggregating American counties for testing the conditions for knowledge spillovers. At the same time, this study retains all 22 industries which constitute ‘manufacturing’ sector (according to the ISIC 4 digit classification), as against the 6 fastest growing city-industries in Glaeser et al., 1992.

Description of the data

To get a better sense of the data, descriptive statistics of key variables are briefly summarized in this section. Table 1 provides a summary of the variables. The values of ECI – our dependent variable – range between -9.407 and 4.620 with mean of -0.384 and standard deviation of 2.548. The negative mean of ECI growth points toward an average fall in the complexity of Colombian municipalities. Explanatory variable average “Diversity” of a municipality assumes values between 0.057 and 0.213 where the most diverse municipality has the smallest value and the least diverse municipality 19

has the highest value. The mean of the average Diversity is 0.135 with a standard deviation of 0.047. The second explanatory variable average “Competition” in a municipality across all industries has the minimum of 0.046 and the maximum of 9.835, with a mean of 2.841 and standard deviation of 2.119. Higher values of this variable point towards greater Competition across all industries in a municipality. A detailed discussion of all the variables and their construction follows later in this section.

Table 1 - Summary statistics of key variables. Mean

Variable

Standard

Minimum

Maximum

Deviation

Number of observations

-0.384

2.548

-9.407

4.620

1100

Diversity

0.135

0.047

0.057

0.213

1100

Competition

2.841

2.119

0.046

9.835

1100

Economic Complexity Index (ECI) growth

Table 2 and 3 describe the five largest and five smallest municipalities in Colombia in 1997. Interestingly, all of them saw a significant decrease in their employment from 1997 to 2011 except for two of the smallest municipalities in our sample (municipality code 76248 and 25126). Once again, this is in line with the possible ‘Dutch Disease’ hypothesis adversely affecting the manufacturing sector with a contraction in employment and exports.

Table 2 - Five largest municipalities by employment.

Municipality code

Employment 1997

Employment 2011

1001

663,412

611,684 20

5001

252,726

175,773

76001

164,275

108,999

8001

97,756

64,156

5360

93,333

60,494

Decimal points have been removed for simplification purposes.

Table 3 - Five smallest municipalities by employment.

Municipality code

Employment 1997

Employment 2011

20001

5,892

2,967

19001

5,948

3,953

76248

4,032

7,171

41001

6,032

4,195

25126

6,018

12,960

Decimal points have been removed for simplification purposes.

Table 4 below lists the ten largest municipality-industries by their output (in Colombian pesos) in 1997 in our sample. Since our data is at municipality-industry 2-digit level9 for each year, the following table gives a descriptive picture of the biggest industries with their respective districts. “Food products and beverages” in municipality 11001 is the biggest industry in Colombia in 1997. As the table shows, it is also the biggest industry in municipalities 76001, 5001 and 8001, thus appearing 4 times in the list in total. “Chemical and chemical products” is the second biggest industry in municipality 11001 and the fourth largest in municipality 76001. The remaining four largest industries are “Coke, refined petroleum products and nuclear fuel” (municipality 68081), “Motor vehicles, trailers and semi-trailers” (municipality 11001), “Textiles” (municipality 11001)

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In fact, we have data on industries at 4-digit level of classification for each municipality in Colombia. However, this is too disaggregated for purposes of this study. Since we are interested in looking at inter-industry/intraindustry knowledge externalities as a predictor of growth in economic complexity, we aggregated the variables to arrive at 2 digit industry level classification.

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and “Rubber and plastics products” (municipality 11001). Their respective outputs are listed in the table below. Table 4 - Ten largest municipality-industries, by output in 1997.

Municipality Industry

Industry name

Output (in

code

code

Colombian pesos)

11001

15

Food products and beverages

2,507,635,958

11001

24

Chemicals and chemical products

2,224,280,281

68081

23

Coke, refined petroleum products and nuclear

1,406,351,366

fuel 76001

24

Chemicals and chemical products

1,045,517,653

11001

34

Motor vehicles, trailers and semi-trailers

1,008,509,252

11001

17

Textiles

819,624,997

76001

15

Food products and beverages

753,127,408

5001

15

Food products and beverages

748,852,038

11001

25

Rubber and plastics products

719,681,675

8001

15

Food products and beverages

704,727,033

Table 5 and 6 below list the top 5 municipalities that witnessed the highest ECI growth from 1997 and 2011 and the bottom 5 municipalities that witnessed the lowest ECI growth. Table 5 – Municipalities with the highest ECI growth over 1997 to 2011.

Municipality

ECI growth

Diversity

Competition

Number of industries

41001

4.61

0.19

3.77

8

15491

4.09

0.14

0.16

2

76111

2.73

0.15

4.40

9

5212

1.61

0.09

3.02

10

66001

1.53

0.10

1.71

17

22

Table 6 – Municipalities with the lowest ECI growth over 1997 to 2011.

Municipality

ECI growth

Diversity

Average

Number of

Competition

industries

66075

-9.38

0.21

0.04

1

76130

-8.98

0.18

3.78

12

76895

-6.46

0.21

7.48

3

8758

-4.97

0.16

5.86

11

76248

-4.52

0.21

2.87

4

ECI growth

Contrary to intuition, the average complexity of the 50 largest municipalities of Colombia actually reduces from 0.071 in 1997 to 0.051 in 2011. This means a -0.02 growth in ECI. A simple plot of the ECI growth rates of all municipalities in Figure 4 below reveals the same.

This can be understood as the decrease over time in what Colombia produces competitively (as measured by ECI), rather than decrease in growth rate of municipalities in GDP. Indeed, the municipalities might in fact be growing, but with decreasing diversity of their product basket. A deeper analysis follows in the Section 4.4. Figure 4 – ECI growth of 50 biggest Colombian municipalities (by the order of their codes), 1997 – 2011.

23

4.2 Methodology The study uses regression analysis to test the stated hypothesis: Do knowledge externalities lead to growth in Economic Complexity of Colombian municipalities?

The general model is as follows: 𝐸𝐶𝐼𝑔𝑟𝑜𝑤𝑡ℎ = 𝛼 + 𝛽𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦 + 𝛾𝐶𝑜𝑚𝑝𝑒𝑡𝑖𝑡𝑖𝑜𝑛 + 𝛿𝑁𝑜𝑟𝑚𝐸𝐶𝐼1997 + 𝜃

Where, ECIgrowth is the dependent variable – a proxy for the growth in economic complexity in the system. Diversity and Competition are the two explanatory variables, as the characteristics of the system which make available dynamic knowledge externalities and NormECI1997 is the normalized (by mean) ECI of the base year (1997) of our analysis, starting from which we infer which variety of knowledge externalities – if at all – were available in Colombian municipalities. It serves as a key control in the model, but not only. Its coefficient also points out (as we shall see in the results) the unexpected but interesting and explicable negative relationship between ECIgrowth and ECI 1997 (base year) values. 𝜃 is the error term.

Construction of the variables

1. Economic Complexity Index

We measure economic complexity as in Hausmann et al. (2011). The Economic Complexity Index (ECI) is measured as: Define a Matrix 𝑀𝑐𝑝 that is I if the country 𝑐 produces product 𝑝, and 0 otherwise. Diversity and Ubiquity are measured as a sum of the rows and columns of this matrix.

(1)

𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦 = 𝑘𝑐,0 = ∑𝑝 𝑀𝑐𝑝

(2)

𝑈𝑏𝑖𝑞𝑢𝑖𝑡𝑦 = 𝑘𝑝,0 = ∑𝑐 𝑀𝑐𝑝 24

These two measures are simultaneously used to correct the other. For a given country in question, they calculate the average ubiquity of the products it exports and the average diversity of the countries that export those products. Note that they define a parallel measure for products by calculating the average diversity of the countries that make those products and the average ubiquity of the other products that these countries make. This can be expressed as follows:

(3)

𝑘𝑐,𝑁 =

(4)

𝑘𝑝,𝑁 =

1 𝑘𝑐,0

1 𝑘𝑝,0

∑𝑝 𝑀𝑐𝑝 . 𝑘𝑝,𝑁−1

∑𝑐 𝑀𝑐𝑝 . 𝑘𝑐,𝑁−1

Inserting (4) into (3), to obtain:

(5)

(6)

𝑘𝑐,𝑁 =

1 𝑘𝑐,0

∑𝑝 𝑀𝑐𝑝

1 𝑘𝑝,0

∑𝑐′ 𝑀𝑐′𝑝 . 𝑘𝑐′,𝑁−2

𝑘𝑐,𝑁 = ∑𝑐′ 𝑘𝑐 ′ ,𝑁−2 ∑

𝑀𝑐𝑝 𝑀𝑐′𝑝 𝑘𝑐,0 𝑘𝑝,0

Rewriting:

(7)

̃𝑐𝑐′ . 𝑘𝑐′,𝑁−2 𝑘𝑐,𝑁 = ∑𝑐′ 𝑀

where,

(8)

̃𝑐𝑐′ = ∑ 𝑀𝑐𝑝 𝑀𝑐′𝑝 𝑀 𝑘 𝑘 𝑐,0 𝑝,0

̃𝑐𝑐′which is Equation (7) is satisfied when 𝑘𝑐,𝑁 = 𝑘𝑐,𝑁−2 = 1. This, in turn is the eigenvector of 𝑀 associated with the largest eigenvalue. This eigenvector is a vector of 1s, hence the eigenvector

25

associated with the second highest eigenvalue captures the largest amount of variance in the system. This is Hidalgo-Hausmann (HH) measure of economic complexity.

Thus, ECI is defined as:

(9)

𝐸𝐶𝐼 =

⃗ − 𝐾 ⃗⃗⃗⃗⃗⃗⃗ 𝑠𝑡𝑑𝑒𝑣(𝐾)

(where < > represents an average, stdev stands for the standard deviation)

⃗ = Eigenvector of 𝑀 ̃𝑐𝑐′ associated with the second largest eigenvalue. And: 𝐾 The absolute values of ECI are then used to rank countries in terms of their relative complexity vis-a-vis other countries. Higher complexity renders a country a higher rank in the Economic Complexity Index and lower complexity corresponds to a lower rank. The country with the highest ECI value is ranked 1 and so on. The values of ECI are not meaningful in themselves.

For the purposes of this study, a measure of change in complexity over time is sought. And since the absolute values of ECI do not constitute a measure of complexity in themselves, we normalize these ECI values both for the base year (1997) and the current year (2011) by their mean. We divide each value of ECI (unique for each municipality) by the mean value of the distribution to arrive at the normalized values. We then calculate the growth rate of ECI from 1997 to 2011 for each municipality using these normalized ECI values. This is our measure of ECI growth. In can be expressed as following:

(10)

∆𝐸𝐶𝐼𝑖 =

(𝐸𝐶𝐼′2011 − 𝐸𝐶𝐼 ′ 1997 ) 𝐸𝐶𝐼′1997

where 𝐸𝐶𝐼’ are normalized by their means.

26

2. Competition

This measure calculates how competitive each industry is in each municipality. The study adapts Glaeser et al.’s (1992) measure of local competition in a municipality as the number of firms per worker in this industry in this municipality relative to the number of firms per worker in this industry in all 50 Colombian municipalities in our sample.

(11)

Competition =

𝐹𝑖𝑟𝑚𝑠 𝑖𝑛 𝑚𝑢𝑛𝑖𝑐𝑖𝑝𝑎𝑙𝑖𝑡𝑦−𝑖𝑛𝑑𝑢𝑠𝑡𝑟𝑦⁄𝑊𝑜𝑟𝑘𝑒𝑟𝑠 𝑖𝑛 𝑚𝑢𝑛𝑖𝑐𝑖𝑝𝑎𝑙𝑖𝑡𝑦−𝑖𝑛𝑑𝑢𝑠𝑡𝑟𝑦 𝐹𝑖𝑟𝑚𝑠 𝑖𝑛 𝐶𝑜𝑙𝑢𝑚𝑏𝑖𝑎 𝑖𝑛𝑑𝑢𝑠𝑡𝑟𝑦⁄𝑊𝑜𝑟𝑘𝑒𝑟𝑠 𝑖𝑛 𝐶𝑜𝑙𝑜𝑚𝑏𝑖𝑎 𝑖𝑛𝑑𝑢𝑠𝑡𝑟𝑦

where ‘Colombia industry’ refers to the 50 Colombian municipalities in our sample and not the total number of municipalities in Colombia.

We then take the average of the ‘Competition’ in each municipality-industry, to arrive at the average competition in each municipality across all industries. This is important to make sure that the analysis is at the same level – municipality - as the other variables in our regression equation10.

Competition hence, represents number of firms per worker per industry per municipality compared to the national average (50 biggest municipalities). Average competition represents firms per worker (across all industries) in the municipality in question, compared to the national average. Accordingly, greater average competition represents more firms per worker in a municipality and vice versa. This measure ranges from 0.04 to 9.83.

3. Diversity

This study devises a new measure of diversity in production of each municipality. Just like the ECI and Average Competition, “Diversity” of a municipality is a unique value for each municipality.

The way we derive this index is by taking the ratio of the output of a single industry in a municipality relative to the total output of that municipality across all industries, thus arriving at a

10

Both ECI and Diversity are unique values computed for each municipality, characteristic of a Colombian municipality and not a municipality-industry.

27

vector of relative shares of all industries in a municipality. Since we do not have any information about the distribution of such a vector, we simply take the Standard deviation of this distribution. The result is a unique value for each municipality that we use as a measure of “diversity” of the municipality. The closer this value is to 0 for a municipality, the more diverse the municipality and the farther it is from 0, the less diverse that municipality. The limit cases would be a municipality whose output is say, equally split between all 22 industries (for simplification purposes) and a municipality all of whose output comes from one industry. In the former case, the standard deviation of such a distribution (1/22, 1/22, 1/22…) would be 0 whereas in the latter case, the standard deviation of a municipality all of whose output comes from one industry (1, 0, 0…) would be 0.213. Suppose we are calculating the diversity of the 𝑖 𝑡ℎ municipality with n number of industries where the share of each industry’s output is denoted by 𝑂1 , 𝑂2 , 𝑂3 , … , 𝑂𝑛 and 𝑂𝑇 is the total output of the ith municipality, then,

(12)

𝑂

𝑂

𝑂

𝑂

𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦𝑖 = 𝑆𝑡𝑑𝑒𝑣 (𝑂1 , 𝑂2 , 𝑂3 , … , 𝑂𝑛 ) 𝑇

𝑇

𝑇

𝑇

Below we plot the number of municipalities against their respective diversity values, for 1997 in Figure 5 and 2011 in Figure 6.

Figure 5 - Diversity of municipalities, 1997.

28

Figure 6 - Diversity of municipalities, 2011

One criticism can be the possible endogeneity problem as a certain measure of ‘diversity’ goes in the construction of the ECI, and another is one of the key explanatory variables in our regression models. The most important thing to consider is the following: Where the HH variable of ‘diversity’ is the simple summation of the total number the products that a municipality produces (with higher value representing greater diversity), our variable is the standard deviation of the distribution of the relative shares of each industry in a given municipality, with lower values representing greater diversity and higher values representing lower diversity. So even though they are both indicators of ‘diversity’ of a municipality, they are very different variables in what they measure.

The way we address the problem of endogeneity - so as it does not distort our regression results is by using growth in ECI as our dependent variable rather than the absolute values of ECI in 2011. If there is any problem of endogeneity between ‘ECI growth’ as the dependent variable and ‘Diversity’ as the explanatory variable, it should stand corrected because we are only measuring the change in complexity. 4. Control – Normalized ECI, 1997 The normalized ECI values of the base year, 1997 – the variable NormECI1997 - serve as an important control in the regression model. Controlling for the complexity of the municipalities in 29

the base year allows the measurement of the pure the impact of externalities which in turn are due to average Diversity and average Competition within the municipalities. At the same time, the relationship between the base ECI values and the growth of ECI is clarified by the coefficient of this variable. This helps to identify the general trend of Complexity growth in Colombian municipalities, lending a bigger picture view. Varieties of knowledge externalities and expected coefficients We focus on three type of dynamic knowledge externalities from the literature: MAR, Porter and Jacobs. Introduced by Marshall (1890), and subsequently developed by Arrow (1962) and Romer (1986), the idea was consolidated by Glaeser et al. (1992) in their search for dynamic externalities as a factor explaining growth of city-industries in U.S. In spite of all of them having implications for growth, these theories differ along two lines: First, they differ in whether knowledge spillovers come from within the industry or from other industries. Second, they differ in their predictions of how local competition affects the impact of these knowledge spillovers on growth (Glaeser et al. 1992). The Marshallian thesis emphasizes the concentration of an industry in a geographical region for knowledge to spill over between firms within the industry. Feldman (1994) quotes Krugman (1991) in his proposing a new theory of economic geography as follows: “What is the most striking feature

of

the

geography

of

economic

activity?

The

short

answer

is

surely

concentration...production is remarkably concentrated in space.” At the same time, the MAR theory favors local monopoly over local competition as monopoly rights provide innovators the opportunity to internalize externalities serving as an incentives for further innovation. Porter, on the other hand, favors local competition over local monopoly. According to him, it is competition that provides the incentive to innovate, in order for firms to survive. He favors specialization over diversification. Jacobs, in her theories concerning growth of cities argues that it is the cross-fertilization of ideas across industries that sets the stage for knowledge spillovers to flow. Jacobs (1969) believes that the most important knowledge transfers come from outside the core industry (Glaeser et al, 1992).

30

In summary, MAR externalities are maximized with high local specialization and local monopoly while according to Jacobs (1969), knowledge externalities are most easily available between industries with local competition playing an important role in the early adoption of new technology. Porter (1990), on the other hand, favors specialization along with local competition. Accordingly, armed with our explanatory variables of Diversity and Local Competition (see section 4.2 for a detailed discussion of the construction of the variables), we expect negative signs of Diversity and Competition coefficients in case MAR externalities are available in the system. On the other hand, we expect positive coefficients of Diversity and Competition in case the system is characterized by Jacobs externalities. Porter externalities is an intermediary case, where we expect a negative coefficient of Diversity and a positive coefficient of Competition. Table 7 provides a quick summary of the types of knowledge externalities and their respective coefficients. Table 7 - Varieties of Knowledge externalities and expected coefficients. Type of externality

Diversity

Competition

Marshall Arrow Romer (MAR)

Negative

Negative

Porter

Negative

Positive

Jacobs

Positive

Positive

Based on Glaeser et al., 1992.

In a host of related studies, alternative variables have been used by scholars for measuring specialization, diversity and competition. Paci and Usai (2000) use the production specialization index (PS) and a separate production diversity index (PD). Panne (2004) employs the same PS and PD indexes from Paci and Usai (2000) along with the “Competition” measured on similar lines as Glaeser et al., (1992). These studies maintain that a geographical region can be simultaneously diverse and specialized in a particular industry (see Paci and Usai, 2000 and Panne, 2004). Similar analysis repeated for our study. This would likely necessitate aggregating data on Colombian municipalities into bigger geographical units so as to allow for greater variation within the unit of observation and then infer industry level specialization within economically diverse municipalities. We have chosen a relatively simpler path where we only check for the diversity and the competition of a municipality.

31

In fact, it would be interesting to find if the results we arrive at are robust upon the inclusion of an additional variable or not. This is an important limitation of our study.

4.3 Results

Our results can be explained in the following points. Table 8 summaries the results of the linear regression11 models. An in-depth discussion of the results follows in section 4.4.

1. The significant negative coefficient of Diversity points towards the inverse relationship between the average Diversity of the manufacturing base of the Colombian municipalities in 1997 and the ECI growth. Note that the range of variable Diversity is between 0.057 and 0.213 while the coefficient of Diversity ranges between -21.132 to -2.195 in our regression models. Hence, whether the municipalities were more diverse or less diverse in 1997, on an average, there is a negative relationship between ECI growth and the diversity of municipalities.

2. The significant negative coefficient of Competition underlines that higher the number of firms per worker in 1997, lower the growth in ECI. However, note that Competition is not a significant explanatory variable after controlling for Diversity (models 3 and 4). 3. The significant negative coefficient for ECI1997 depicts an inverse relationship between ECI 1997 and growth of ECI: municipalities with had high ECI values in 1997 have a low ECI growth and municipalities which had low ECI values in 1997 witness high ECI growth. This is the most interesting finding of the study and underlines a convergence pattern in Colombian municipalities (detailed discussion follows in section 4.4). Note that this is our control variable in the regression model 4.

11

Note that we tested the results by fitting Generalized Linear Models, since we have no information on the distribution of the data and the results were found to be robust up to three decimal points and the significance of the coefficients stands unaffected.

32

4. The negative signs of the “Diversity” and “Competition” coefficients provide evidence in support of MAR externalities. The results are robust and statistically significant even after controlling for ECI 1997. Table 8 – Regression Results: ECI growth between 1997 and 2011.

Constant

Diversity

(1)

(2)

(3)

(4)

2.487***

0.0455

2.484***

2.620***

(0.216)

(0.127)

(0.218)

(2.246)

-21.132***

…

-21.193***

-2.195***

(1.591)

(1.619)

-0.151***

0.004

5.421

(0.036)

(0.035)

(3.535)

…

…

-2.197*

(1.502) Competition

NormECI1997

… …

(9.010) Adjusted R2

0.152

0.014

0.151

0.155

4.4 Discussion

The results presented above allow us to arrive at some tentative conclusions, keeping in mind the specific proxy we use for measuring economic complexity. This paper attempts to measure the inferred role of knowledge externalities on the growth of economic complexity. We develop a new index for measuring diversity of the economic base of a region. The evidence - suggestive of MAR or intra-industrial variety of externalities - is useful for the understanding of Colombia’s industrial development and the agglomeration dynamics in its manufacturing sector. A possible explanation can be that specialization is important for the effective transmission of productive knowledge in the early development stages of development of industries when firms tend to co-locate and specialize (Glaeser et al., 1992). Accordingly, our results are in contrast with the works of Glaeser and Antonelli who found that greater economic diversity and local competition (and hence the availability of Jacobs externalities) played a key role in the growth 33

American cities and production of new knowledge in European regions respectively, which are mature manufacturing economies. An interesting pattern of convergence emerges from the results. Municipalities that had higher economic complexity have lower ECI growth and vice versa. We run an additional model to seek more evidence on this convergence pattern. We regress ECI 2011 values on ECI 1997, while controlling for Diversity and Competition. Figure 7 depicts the output yield from R.

Figure 7 - Regression of ECI 2011 on ECI 1997.

There is a highly significant negative correlation between ECI 2011 and ECI 1997: municipalities that who had a higher complexity in 1997 have a lower complexity in 2011. This confirms the convergence pattern among municipalities as mentioned above. At the same time, we can reasonably expect these results, as these municipalities belong to the same country! A possible explanation can be that knowledge externalities affect not only the complexity of the municipality itself, but also the complexity of other municipalities through an exchange of knowledge. The appendix to this paper highlights the Hausmann et al., (2011) framework to measure inter-municipality spillovers, which we have not checked for. Convergence in turn might be due to three possible reasons:

34

1. Diminishing marginal returns in Competition and Diversity on the amount of knowledge externalities they are able to generate (for high complexity municipalities). 2. Imitation (by low complexity municipalities). Fung (2005) shows that R&D expenditures being the same, the followers in technological knowledge will catch up with the leaders as they receive knowledge spillovers from the leader. 3. Convergence can also be due to increased absorptive capacity of low complexity municipalities. Cohen and Levinthal (1989) find that intra-industry spillovers may encourage equilibrium industry R&D investment. Building on which Aghion and Jaravel (2015) argue that the notion of absorptive capacity have important implications for convergence and divergence from knowledge spillovers. What would make all the difference is the absorptive capacity of the low complexity municipality “in selfreinforcing feedback cycles that can result in either convergence or divergence.” (Aghion and Jaravel, 2015) Finally, a word on the limitations. Since we do not have any data on cross-municipality spillovers or exchange of goods or movement of workers, we cannot test the same. Similarly, other macroeconomic variables are expected to impact ECI growth which represents the growth in the productive knowledge in the economy as reflected in what it competitively produces. Secondly, the results favoring MAR externalities might also have to do with the level of classification used for the purposes of this study (2 digit). “The probability to detect Jacobs externalities increases with the level of detail of industry classification.” (Beaudry & Schiffauerova, 2009).

5. Conclusion Externalities lead to growth in economic complexity because they increase the interdependence of interacting agents in the system. Externalities are the entry point to economic complexity (Antonelli, 2011). In the case of Colombia, which witnessed a fall in its economic complexity from 1997 – 2011, our empirical tests provide evidence in favor of MAR externalities (greater specialization and less competition) as the coefficients of our explanatory variables have a negative sign. In particular, the negative relationship between ECI growth and ECI 1997 is points towards a convergence trend 35

where municipalities which were high on the Economic Complexity Index saw the lowest growth and municipalities which were low on the ECI, saw high growth. These are very interesting findings from a complex system perspective. And can be explained both by the rich neo-classical and Schumpeterian literatures on convergence. The neoclassical growth theories attribute convergence to diminishing returns on physical or human capital accumulation while the Schumpeterian thesis attributes convergence to knowledge spillovers. Even though we have evidence that clearly points towards diminishing returns on Competition and Diversity in Colombian municipalities, further analysis would be required to confirm the neo-classical hypothesis. On the other hand, we have in fact checked for the Schumpeterian dynamics of convergence, i.e. knowledge externalities, with evidence that indeed a trend of convergence between municipalities is evident. This stands in conformity with the macroeconomic trends of the Colombian economy which has witnessed huge FDI flows in its natural resource extraction sector in the past decades, with decreasing employment in manufacturing and agriculture sectors. In light of the Colombian Dutch Disease, the municipalities show a trend of convergence towards lower levels of economic complexity – as evident from the mean -0.02 growth in ECI – due to knowledge spillovers within the municipalities, but possibly between them too. However, we do not check for intermunicipality spillovers as it is beyond the scope of this study. The study thus provides a dynamic understanding of the effects of macroeconomic trends of the Colombian economy on its domestic manufacturing sector. The added value of this study lies in an in-depth analysis of the role knowledge externalities play in complexity dynamics and that, at the lowest level of geographical disaggregation – municipalities. We also show that spillovers – albeit growth enhancing – may not also be a positive force in the long term health of the economy. This is to say that they are an important mechanism that drives the microeconomic dynamics in the economy. The literature so far only explores their contribution to economic growth which is arguably, only one side of the coin. Such an understanding is made possible because our explanatory variable is the Economic Complexity Index rather than the conventional “output growth” or “productivity growth”. While indeed, the Colombian economy is growing, its negative trend in complexity is detrimental for its manufacturing sector which is in fact, contracting as evident from the results. 36

6. Appendix: A brief note on Inter-municipality spillovers The results and conclusions discussed above open up interesting areas of future research where we can check if inter-municipality knowledge transfers can explain growth in economic complexity. The literature on the subject is rich with a variety of methods (proposed by economic geographers) for measuring knowledge spillovers in the geographical dimension12, however these are beyond the scope of this paper. We do not check for them, but it is reasonable to expect that these knowledge externalities are stronger on nearby municipalities and weaker on those which are geographically far. In other words, as Antonelli (2011) sums it up: proximity matters. This can also be extrapolated from the initial assumption in this study that geographical proximity invariably results in greater interactions among agents and we expect greater spillovers in municipalities where we witness a larger number of interacting interdependent agents. One possible way to quantify geographical spillovers or the effect of geographical proximity as reflected on the product space can be the following measures: “Distance”, the “Economic Opportunity Index” (EOI) and the “Economic Gain Index” (EGI) (Hausmann, et al., 2011). If applied to the current study, they would essentially measure the effect of Competition and Diversity within a municipality in generating spillovers on other municipalities, due to an additional/more complex product it produces over time i.e. its ECI growth. Briefly, Distance: Distance is the weighted proportion of products connected to good p that country c is not exporting, where the weights are given by proximities. Proximity measures the similarity between a pair of products. Formally, 𝑑𝑐𝑝 =

∑𝑝′(1 − 𝑀𝑐𝑝′ )∅𝑝𝑝′ ∑𝑝′ ∅𝑝𝑝′

The Economic Opportunity Index (EOI) of a country/region/municipality, is the level of complexity of the products that it is not currently producing, by how close these products are to the country’s current export suite. Mathematically,

12

Geography is only one of the dimension in which knowledge can spill over. For a detailed discussion, see Antonelli, 2011.

37

𝐸𝑂𝐼𝑐 = ∑(1 − 𝑑𝑐𝑝′ )(1 − 𝑀𝑐𝑝′ )𝑃𝐶𝐼𝑝′ 𝑝′

The Economic Opportunity Gain (EOG) index is then calculated as the change in opportunity value (EOI) that would come as a consequence of developing a new product p. Formally, 𝐸𝑂𝐼𝑐 = ∑(1 − 𝑑𝑐𝑝′ )(1 − 𝑀𝑐𝑝′ )𝑃𝐶𝐼𝑝′ 𝑝′

38

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