Complex economies have a lateral escape from the poverty trap
Emanuele Pugliese, Guido L. Chiarotti, Andrea Zaccaria, Luciano Pietronero
CComplex economies have a lateral escape from the poverty trap
Emanuele Pugliese, Guido L. Chiarotti, Andrea Zaccaria ∗ , and Luciano PietroneroISC-CNR, Via dei Taurini 19, 00185, Rome, ItalyDipartimento di Fisica, Sapienza Universit`a di Roma, P.le Aldo Moro 2, 00185, Rome, ItalyOctober 18, 2018 Abstract
We analyze the decisive role played by the complexity of economic systems at the onset of the industrializationprocess of countries over the past 50 years. Our analysis of the input growth dynamics, based on a recentlyintroduced measure of economic complexity, reveals that more differentiated and more complex economies facea lower barrier (in terms of GDP per capita) when starting the transition towards industrialization. Moreover,adding the complexity dimension to the industrialization process description helps to reconcile current theorieswith empirical findings.
The industrialization of a country is an impressive process, deeply changing the population and the institutions ofthe country while new and old resources are tapped to achieve growth. During this transition the growth rate ofthe economy is much higher than the global average and much higher than the past and future growth rate of thatcountry. It is however a transition and, as such, limited in time. When the process of industrialization has touchedall the sectors, when the population is educated and near full employment, when all the scale economies have beenfulfilled, the process loses its revolutionary power and the new society now sits among the developed countries.Two questions haunted economists since the beginning of the discipline, since Adam Smith and Max Weber. Thefirst question is about the drivers of this sudden sprout of growth, how an entire society changes dramatically in fiftyyears after thousands of years of stillness. Related to this, why the process is as suddenly interrupted while the growthslows down after catching-up with the other developed countries. There are many competing answers to this part ofthe puzzle, the most basic being the poverty trap due to multiple equilibria that was already in Solow (1956): thephenomenon is sudden because there is a barrier, a country wealth that has to be reached to start a quick transition toa different equilibrium. Many alternative explanations are there, most notable increasing returns and demand, as inRosenstein-Rodan (1943) and - more formally - Murphy et al. (1988), in which the barrier to overcome is a minimuminternal demand to allow for returns to scale in manufacturing.The second question is about the heterogeneity of the process among countries. England experienced its IndustrialRevolution in the second half of the XVIII century, followed by other Western countries. In the XIX century theUnited States industrialized too, and other countries followed in the XX century. Other countries did not. Whatare the countries lagging behind missing to move toward prosperity? There are many alternative explanations, fromcultural (Weber et al. (2002), McCloskey (2010)) to geographic (Diamond and Ordunio (1997)), even biological (Ashrafand Galor (2011)). Another explanation is political : to achieve growth the population has to be empowered throughinclusive political institutions, leading to more inclusive economic institutions and diffused prosperity (Acemoglu et al.(2005)).In this paper, we address both of the questions above by exploring the nature of the barrier to industrializationand its correlation to the complexity of the economy at the onset of the industrialization process. Indeed, alongthe industrialization path, the industrial capabilities of the country, the corresponding products and the consumerpreferences, are completely reorganized, leading to the population’s freedom to pursue their own interests in unexpected(new) sectors and entrepreneurial activities. This fact dramatically increases the diversification and the complexityof the underlying economy. We quantitatively measure the complexity of an economy through a new dimension,the fitness of the country, that has recently been introduced in the study of social and economic systems (Tacchellaetal.2012). The latter share with traditional complex systems the emergence of unexpected collective behaviors comingfrom the non-trivial interactions between their basic components (Anderson 1972). The industrialization of a countryis a dynamic process in which a complex network reinforcing production capabilities and product demand emergesat the country scale. The prosperity and the potential of a country can then be characterized (Cristelli et al. 2013)by considering this new dimension, which takes into account the diversification and the complexity of the production ∗ [email protected] a r X i v : . [ q -f i n . E C ] N ov ystem. In this paper, we investigate the role played by this new measure in the countries’ industrialization process.In order to perform this analysis we look at the empirical growth patterns of countries having different levels of fitness.As it will emerge, fitness, which is a quantity tuned on the diversification and complexity of the country’s exportbasket, carries important information with regard to the onset of the industrialization process. In particular we willsee how a higher value of the fitness is associated with a lower barrier toward industrialization of a country. Thisempirical finding will motivate an attempt to build a full-fledged model of industrialization taking fitness endogenouslyinto account as a proxy for the growth potential of countries. However, this will only be outlined in the conclusionsas its mathematical formulation goes beyond the purpose of this paper.The following essay will be divided in four sections in addition to this introduction. In the next section we willdescribe the economic complexity approach. We will then briefly sketch a simple poverty trap model, a basic renditionof Solow (1956), to fix notation. In the following section we will show some empirical shortcoming of this basic idea ofpoverty trap and we will show the promising role of our Fitness index to solve these shortcoming. Finally, in section 5we will show that introducing the Fitness in the basic poverty trap narrative helps the models to describe the empiricalevidence. The data used for our analysis is described in the appendix. In most of countries that will eventually join the other developed nations, the early stages of economic growth arecharacterized by a period of fast growth. The growth of the Soviet Union that scared the United States administrationand economists Krugman (1994), the growth of Japan and Southern Europe in the ’50s, the growth of the Asian Tigersin the ’70s: every country emerging from of an agriculture based economy has experienced a decade or more of extremelyhigh growth while it is catching up with the other developed countries. The spike of high growth is characterized by astrong increase in investments, both in physical and human capital. While the population experiences new incentivesand opportunities for education and investment, the factors of production rise inflating the economic growth. This iswhat we define as industrialization: the moment in which there is a sudden spike in the factors of production availablein the country.Since the influential Solow (1956) this sudden transition from mere subsistence to a complete industrializationhas been described with the presence of a trap that could be avoided by overcoming a barrier in terms of wealth, orphysical capital. More formally the usual picture makes use of the presence of multiple equilibria in the time evolutionof physical capital. In this picture, the presence of multiple equilibria is due to the non linear relation between thecountry investments in physical capital and GDP due to the presence of a threshold in the saving rate. The dynamicevolution results in a non linear increase of the available capital at successive times. The main ideas behind Solow(1956) are presented in appendix B for the interested reader.This kind of explanation, being related to investments, is said “supply side”, since it implies that the the lack ofenough investments is the missing variable for achieving industrialization. In this picture what is missing to injectgrowth are plants able to produce more profits to be reinvested again: overcoming a threshold level of physical capital isnecessary to start a expansive cycle. There are many competing explanations however, typically marked as “demandside”, where the lacking variable is enough internal demand to kick-start industrialization, Murphy et al. (1988),Rosenstein-Rodan (1943). In this kind of explanations, often referred as “The Big Push”, one sector industrializingincreases the wages of part of the population, that requires more goods and, therefore, pushes for the industrializationof other sectors in a cascade dynamics. While to address the issue of these different competing narratives is animportant research question, it is not the question we want to answer in this analysis.Therefore any explanation, both demand and supply side, can be assumed in the following, as long as it allows fora threshold of resources needed to start industrialization. Since GDP per capita - required as a threshold by a demandside model of poverty trap with increasing returns - and the physical capita - required as a threshold by a traditionalmodel of poverty trap - correlate very strictly , we will be able to keep the same fuzziness also in the next, moreempirical, analysis. Economic theory is used in our empirical analysis only to separate the contribution to growth dueto innovation from that due to inputs, as illustrated in the next section. To understand the role played by the complexity of the economy in the industrialization process we decompose therelative growth of output of the country production structure (GDP) into its main components: the one related tovariation of technological efficiency and those related to variation of inputs, namely asset capital and human capital.This decomposition is standard in economic literature since the seminal work of Solow (1957), and its mathematicalformulation can be derived from the model presented in appendix B. In this setting the GDP per capita growth ratecan be written as: y c,t = a c,t + αk c,t + (1 − α ) e c,t + (1 − α ) h c,t . (1) In our sample, over the period 1963-2000, the Spearman’s rank correlation between GDP and physical capital is 96.2%. a c,t is the growth rate of GDP per capita due to the (exogenous) technological efficiency of the country c attime t , αk the growth due to the increase of physical capital per capita, (1 − α ) e the growth due to an increase of thelabor force share in population, (1 − α ) h is the growth due to an increase the human capital (education) of workersof the country, and α is the output elasticity of capital, where the output elasticity of labor is assumed to be (1 − α ).These last three addenda form our definition of input growth, being it a physical investment in new machinery ( k ),an increase in labor force participation( e ), or additional education ( h ).Since the growth rate of inputs is quantifiable, to compute the different parts of growth in equation 1 we need onlyto estimate α . Economic theory is handy in this case. If each factor of production is paid for at its marginal value,the share of national income going to capital will be α and the share going to labor 1 − α . Since these shares areobservable numbers, we will use them to estimate α . Finally, the efficiency part a can be recovered as the residualafter removing the inputs component from the total GDP per capita growth.While the overall measure of GDP growth can be deceiving and influenced by the price and discovery of naturalresources and the happening of any external factor, the sudden investments in physical and human capital and theincrease in labor force participation are the clear fingerprints of a structural change, a movement from an equilibriumto another. Why are we interested in input growth, and not in total per capita GDP growth? Much of the academic world focusedonly on efficiency and productivity, assessing that most of the long term growth is due to productivity growth (Halland Jones 1999). This is obvious: input growth is intrinsically limited. While a country can double its employmentrate from 30% to 60% in the first 20 years of industrialization, it cannot double it again in the following 20 years. Whilea country can quickly increase literacy rate to 90%, further efforts cannot give similar payoffs. Even if physical capitalcould, in principle, grow without bounds, its effectiveness in terms of increasing labor productivity would decline oncetechnological progress is included in the description. As a consequence, input growth suffers from decreasing returns,and it cannot be the focus for long-term growth in developed countries. However, the growth due to inputs is indeeda powerful force at the onset of a country’s industrialization.Analyzing for example the case of industrialization of Singapore during its high growth phase, the excess growthrequired to catch up with the developed world was obtained through input growth. In the year of maximum growthfor Singapore, 1970, out of an impressive 11% growth rate of real per capita GDP, 8% was due to input growth.Even without decomposing the growth, the transforming effect of industrialization on Singapore is visible by simplylooking at the changes in the descriptive statistics in the time span of one generation. In 1966, at the beginning ofSingapore’s industrialization, 27% of the country population was employed, and 39% of the new entrants in the jobmarket had no formal education. Only 16% of the new entrants in the job market had at least a secondary degree.Furthermore, investments in physical capital were modest, with only 10% of saving rates. The generation enteringthe job market in 1990 were confronted with a deeply changed country. Female workers had entered massively inthe job market, and 51% of the population was now working, almost twice as much as in the previous generation.Among entrants in the job market, only 10% do not have any formal education (one fourth compared with the previousgeneration) and 54% have at least a secondary degree (a threefold increase). Saving and investing has become commonamong the population, the savings rate has increased fourfold reaching 39% (Krugman 1994, Mukhopadhaya 2002).Not surprisingly, in the same years Singapore’s GDP has increased by almost 9 times and the per capita GDP hasincreased by almost 6 times. Of this exceptional growth, only a modest 25% (around 1% per year, in line withdeveloped countries), can be assigned to a growth in productivity (data from Penn Table 8.1). In conclusion, the inputgrowth defines the trend of per capita GDP growth, while the residual productivity increase acts mostly as noise overthe growth signal.
As mentioned in the introduction, we expect economies showing different levels of complexity (different fitness values)to behave differently in the industrialization process. The idea that economic indicators can be used to summarize theaffluence and growth potential of nations dates back to the seminal work of Kuznets (1946), which introduced the GDPas a measure of nations’ productivity in the Thirties in order to better understand how to tackle the Great Depression.Since then a notable number of economic indicators have been proposed (Stock and Watson (1989)). In recent yearsparticular attention has been dedicated to non-monetary indicators (Costanza et al. (2009), Diener and Suh (1997)).All these indicators look deeply in the characteristics of the economy to unveil the hidden potential of a single country.However in a complex system, as for the economic system of a country, the characteristics of single elements areusually less important than their mutual interactions. A stark example is the evaluation of the relative authority ofwebpages done by Google through the PageRank algorithm (Page et al. (1999)), in which the ranking reflects theproprieties of the reference network connectivity. Modern goods markets constitute a network of products similar tothe one formed by the nodes of the world wide web: ranking algorithms can then be efficiently used to characterizethe network properties, and in particular to rank nations according to their manufacturing capabilities and productcomplexity. In other words, the basket of manufacturing capabilities of each country, which is representative of the3ocial, cultural and technological structure of the underlying economy (Dosi et al. (2000), Lall (1992)) (intangible andnot directly measurable) is expressed by the basket of products the country is able to produce (Hidalgo et al. (2007)).Hidalgo and Hausmann (2009) have pioneered this kind of approach for the economic science, and kindled a richliterature on the subject. In particular Tacchella et al. (2012) applied this view to introduce a novel non-monetaryindicator based on the properties of the network formed by interstate goods exchanges in which non-linear interactionsplay a fundamental role. In this work we will follow this later approach. The information of the country growthpotential can be extracted from the properties of the worldwide export network as expressed by the structure of thematrix M whose entries M cp take the value 1 if the country c shows a Revealed Comparative Advantage (Balassa(1965)) in the export of a (physical) product p and 0 otherwise. This choice has a number of advantages: i) anytrivial correlation with export volumes is removed, thus allowing comparison of countries of different size; ii) themethod allows comparison of countries with very different shares of manufacturing sectors of total GDP, since onlyits composition is relevant, while the aggregate volumes of export does not matter. Finally iii) while the matrix“binarization” necessarily implies a loss of information, it has been shown that this kind of treatment is far moreresilient with respect of the possible presence of noise in the data (Battiston et al. (2014)). To measure the countryexport competitiveness (directly related to the country’s capabilities, in the spirit of Hausmann et al. (2007)) usingonly the above defined export network linking countries and products, could be sufficient to take into account thenumber of products exported by a given country, i.e. its diversification. However this would be simplistic, since onecannot assume that products are all equals in terms of the capabilities required to produce them: some products mayin fact require a higher number of (or more exclusive) capabilities to be produced (and exported). In this sense wedefine a product to be complex if it requires a higher number of capabilities (or a more sophisticated set of capabilities)to be produced. Indeed what is required is a way to measure, although indirectly, the countries’ capabilities signaledby the production (and export) of a given product. Being the capabilities not directly measurable, we will summarizethe capabilities needed to export a single product as a single value, that we call product complexity, computed onlyrelying on the structure of the country-product network. Let us suppose for the moment this numeric value to beknown. Given these product complexities, the fitness of a country will simply be defined as the sum of the complexitiesof its exported products (mathematical expression below) and it will be representative of the country’s capabilities.We will show in the following how this measure of fitness empirically relates to the industrialization of the country. Inturn, product complexity can be defined through the fitness of the countries exporting them: a product is consideredcomplex if low fitness countries do not export it. Consider this simple case: only highly developed countries exporttransistors, while both more industrialized and less industrialized countries export nails. Therefore the low complexityof nails can be deduced directly by the fact that low fitness countries are also able to produce and export them. As aconsequence low fitness countries are more informative in assessing the complexity of products. All these considerationsyield to a non-linear relation between fitness of countries and complexity of products.More formally, to calculate the fitness of countries F c and the complexity of the exported products Q p we iterateupon convergence the following set of non-linear coupled equations:˜ F ( n ) c = (cid:88) p M cp Q ( n − p (2)˜ Q ( n ) p = 1 (cid:80) c M cp F ( n − c (3) F ( n ) c = ˜ F ( n ) c < ˜ F ( n ) c > c (4) Q ( n ) p = ˜ Q ( n ) p < ˜ Q ( n ) p > p (5)where the normalization of the intermediate tilted variables is made as a second step, n is the iteration index, andthe <> x symbol stands for the arithmetic mean with respect to the possible values of x .The fixed point of these maps has been studied with extensive numerical simulations and it is found to be stableand not depending on the initial conditions. We refer to Cristelli et al. (2013) for a detailed description of the algorithmand a comparison with the one proposed by Hidalgo and Hausmann (2009). The convergence properties of the fitnessand complexity algorithm are not trivial and have been studied in Pugliese et al. (2014). This methodology hasbeen applied to both the study of specific geographical areas, such as the Netherlands (Zaccaria et al. (2015)) andthe Sub-Saharan countries (Cristelli et al. (2015b)), and general features of growth and development (Cristelli et al.(2015a), Zaccaria et al. (2014)).Once countries and products are arranged according to their respective fitness and complexity, the matrix M isroughly triangular, as shown in 1. This structure implies that developed countries tend to have a highly diversifiedexport basket, since they export both complex and not complex products, while poor or less developed countriesexport fewer and less complex products. While diversification may lead to an immediate (zero-order) estimate of thefitness of a country commensurate with the number of different products it exports, the evaluation of the products’complexity is more subtle: a product exported by low-fitness countries should be assigned a lower score since it isreasonable to expect that a lower level of capabilities is required to produce it. Clearly a linear page-ranking type ofanalysis cannot handle this point, while a nonlinear ranking approach – as the one presented above – will be moreappropriate. 4igure 1: Binary matrix identifying countries producing a specific product. Countries (rows) are ordered according totheir Fitness, Products (columns) are ordered according to their Complexity. A clear triangular structure emerges. While economic theory is mostly related to equilibrium processes, studying balanced growth at the equilibrium ratio,industrialization is obviously a dynamic process occurring between different growth paths, while the country movesfrom one equilibrium ratio to another. Although growth in equilibrium is driven by the growth in productivity, theidea that there can be multiple equilibrium ratio of balanced growth and a barrier to overcome to shift from oneequilibrium ratio to another was already present in Solow (1956). In the transition the country experiences highGDP growth through input growth. There can be a capital barrier, like in Solow (1956), or a demand barrier, like inMurphy et al. (1988). Still, there is a threshold to overcome in order to access the input driven out-of-equilibriumgrowth spike. Even in models considering the evolution of a country as a unified process, like Galor and Weil (2000),there are variables that must reach a tipping point in order to move the society into a high growth regime, driven byincentives to invest in production inputs. Given this, two stylized facts should then be expected to emerge by lookingat empirical data:First, if the catching up of developing countries is the result of the dynamics of inputs to a new equilibrium, weshould expect high input growth among the developing countries, sharply declining for the developed ones. We shouldtherefore expect a negative relation between the GDP growth due to input and the level of GDP for the countries thathave started the transition: the growth should slow down for developing countries while the level of inputs approachesthe new equilibrium and the developing countries catch up with the developed ones.Second, we should expect a certain level of GDP (or physical capital, in Solow’s perspective) per capita to berequired to trigger the transition if the barrier to start the industrialization is demand driven as in Rosenstein-Rodan(1943) (or capital driven, in Solow’s perspective Solow (1956)). We should therefore find a positive relation betweenper capita GDP growth due to inputs and the level of per capita GDP for low levels of per capita GDP, whereadditional per capita GDP means additional internal demand and implies higher per capita physical capital. To checkthese expected empirical behaviors we compute the average growth rate due to input versus the country related percapita GDP. We do so by pooling all the countries and years. In particular, we will use a non parametric Gaussiankernel estimation (Nadaraya 1964, Watson 1964) to compute the expected value of the per capita GDP growth ratedue to input and the corresponding confidence interval for different values of per capita GDP. We plot the results infigure 2.The results in figure 2 do support the existence of a barrier to growth, since there is for sure a certain role playedby prosperity to kick-start investments. Data do not seem however to support the first hypothesis: if any catching upmechanism is visible from the data, it is not an awe-inspiring event. The slow down for very high level of GDP percapita, while statistically significant, has poor economic meaning due to the presence of the plateau at medium large5igure 2: Non parametric kernel estimation of growth rate of per capita GDP due to inputs versus relative per capitaGDP. The shadowing indicates 90% of confidence interval of the expected value, computed with bootstrap. Differentcountries-years in the range 1963-2000 have been pooled after removing the global trend. While the low performanceof low GDP countries in increasing their input is clearly visible (left site of the figure), the slowing down of inputgrowth expected after catching-up (right side) is modestlevels. For sure it does not support the image of calm after the storm that we tried to evoke in the previous sections.Clearly, at this level our analysis is missing a crucial ingredient: we are not able to pinpoint the possibly differentgrowth potentials among countries.As it is well known, some countries have started an impressive growth process, from an industrial and a socialpoint of view, while others simply rely on the exploitation of natural resources. For the same level of physical capitalor GDP, two different countries could live a moment of intense investment and shared opportunities for the whole ofthe population, favoring investments both in physical and human capital, or a moment of stillness and complacence,often characterized by exploitive economic institutions and high inequality. We need a quantitative measure in orderto discriminate among these and others situations; from a practical point of view, a new dimension to disentangledifferent economies, possibly independent from the ones which are usually taken into account in mainstream economics.We believe that concepts taken from the economic complexity approach may be of help. In particular we believe thatthe fitness of a country, being both a quantitative measure of the number and of the quality of capabilities of a nationand a measure of diversification in advanced and complex products, is a useful indicator of the potential for growthof the country.We will therefore replicate the exercise dividing the countries in three sets accordingly to their fitness, to see if ithelps disentangling the different regimes. In figure 3 we show the results for the high fitness countries compared withthe low fitness ones.When data are split in this way, two different patterns emerge. What was confused when clubbing all the countriestogether is now visible and in agreement with the predictions from section 2.1. The high fitness economies, the onesable to differentiate their production in advanced products, present a clear downward slope of the growth of GDP percapita due to input growth with respect to the level of GDP per capita. The countries with lower fitness instead haveissues to start the transition. They experience an higher barrier and they need a very high level of GDP per capita toexperience the mobilization of resources expected by economic theory.The complexity based measure of country fitness seems to lower the barrier to start the transition, and we will seeit in more detail in the next session. 6igure 3: Non parametric Gaussian kernel estimation of growth rate of per capita GDP due to input versus percapita GDP for the lowest and the top tertile of the fitness distribution. The shadowing indicate the 90% confidenceinterval of the expected value, computed with bootstrap. Different countries-years in the range 1963-2000 have beenpooled after removing the global trend. Dividing the countries in sets depending on their fitness values highlights verydifferent behaviors and reconciles the theory with the empirical observation.
In the previous section we observed different behaviors for countries with different fitness levels, hinting at a possibleexplanation for the industrialization process of a country, which is fostered by high fitness levels. The complexity of thecountry’s economy brings down the barrier to industrialization and allows for investments in inputs. This hypothesis,however, requires further investigation. The different behavior of countries grouped according to their high (solid line)or low (dashed line) fitness levels (figure 3), needs to be generalized to a continuous description. This is the aim ofthe present section in which we compare the growth rate of per capita GDP due to inputs, with both the detrendedper capita GDP Y and the fitness F. This is achieved by a non parametric estimation of a two dimensional Gaussiankernel (Nadaraya 1964, Watson 1964) obtained by pooling all the countries and years for the time period in question.At difference with the analysis in figure 3, in which we compared only the behavior of the highest and the lowestfitness countries, we here explore the complete range of fitness values. This is equivalent to adding a further dimensionto the analysis. The results are reported in figure 4. To represent the three dimensions, the dependent variable, thegrowth due to inputs, is visualized as a color map. To further explain the relation between the two representations,we notice that the leftmost part of figure 4 is populated by the same countries belonging to the dashed line in figure3 (low growth potential countries), while the rightmost part is populated by the countries belonging to the solid line(high growth potential countries). This analysis strongly supports our argument: the complexity and diversificationof a country’s economy acts as a catalyst in triggering the transition by significantly reducing the necessary per capitaGDP. The catching up phenomenon is barely observable in Figure 2 since the plot represents the average of differentfitness levels for each level of per capita GDP, thereby mixing up different states of the transition. Even when startingfrom very low levels of per capita GDP, high fitness, more complex, countries are able to start the transition, withincreasing investments causing increasing input growth levels. On the contrary, low fitness countries characterized byexports concentrated in few low complexity sectors, require very high levels of per capita GDP to start the transitionand attract investments. It is trivial to adapt this result to a demand-side explanation: there is a complementarity inkindling the industrialization process of a country between fitness, which is a proxy for export competitiveness, andper capita GDP, which is a proxy for internal demand.However, even a supply-side explanation is consistent with our empirical results, since the opening of new export7igure 4: The color map represents the part Per Capita GDP Growth due to inputs, for different values of Fitness andGDP per Capita. Different countries-years in the range 1963-2000 have been pooled after removing the global trend.Both the role of the fitness of the country in lowering the threshold to enter in the high endogenous GDP growthregime (the blue band in the center) and the slowing down of the process for developed countries (the top-right corner)are evident.sectors increases the incentives to invest. One would expect this increase in incentives to be even more visible lookingat the residual productivity growth (a). However, if the new accessible sectors allow new - intrinsically different -inputs to be used and accumulated, the scale of production can increase without a corresponding increase in thefactor productivity, consistently with an input driven growth. Low fitness countries with poorly diversified economiesdo not start the endogenous transition until they have reached an extremely high level of capital, staying stuck inthe so-called poverty trap. In this sense the poverty trap can be seen as a 2 dimensional object in which both thepopulation wellness (per capita GDP) and the complexity of the national economy (country fitness) play a role.A different point of view to explain the same empirical data would be a demand side explanation imagining acontinuous transition between internal and external demand, proxied respectively by the GDP per capita and thefitness of the country, that is a measure of the complexity and value added of the exported goods.Finally we add some comments about the trajectories of the countries we considered in Fig.4. The depicted countriesare an the extended set of Asian Tigers, originally including South Korea, Singapore, Hong Kong and Taiwan, a wellknown set of countries studied for their model of industrialization. In particular, South Korea and Thailand representa paradigm for what we intend with a lateral escape from poverty trap. Taking advantage of the two-dimensionalstructure of the trap, they have increased their fitness first, and when their economy reached a high level of complexitythey started the upward movement towards a balanced and richer society, reaching a higher level of GDP per capita.The careful reader will note that the case of China is complementary: even if the fitness of China was high even in thesixties, the extreme poverty of a large share of its population prevented this country to overcome the barrier and startto grow in a sustained way. From this point of view, the industrialization of China from the sixties to nowadays can bedescribed in terms of the neoclassical poverty trap, in which only one dimension is needed. However, this consideration8an only move our story back to the sixties: we still need to understand how China reached, fifty years ago, such a levelof Fitness. This investigation will be the subject of a future work. We end this section with an analogy between thissubtle, country-dependent interplay between fitness and GDP per capita and phase transitions, such as the transitionof water from the liquid state to the gaseous one. When water is heated, in general, its temperature increases. This isanalogous to a country which is already out of the poverty trap, and whose efforts are entirely reflected in an increaseof its GDP per capita. However, during a phase transition the absorbed heat is used to break the bonds among themolecules, and even if the temperature does not increase, this process is fundamental to change phase. Similarly, whena country exits from the poverty trap by increasing its fitness the consequences of its efforts do not give immediateresults in terms of GDP per capita, but they are firmly grounding the requirements for a future, sustained growth.
We shown in the paper that simple toy models of countries’ growth (in particular models assuming that all countriesare homogeneous objects characterized only by one state variable, being it the per capita GDP or per capita physicalcapital) are not able to catch the different patterns of industrialization and, therefore, to predict the starting point ofindustrialization, the moment in which they will come out of the poverty trap. We also shown that the measure ofFitness is able to properly disentangle these different patterns, highlighting countries that are ready to take off andto industrialize and countries that, even with similar standard of living, are far from the threshold.These findings suggest a possible role for the complexity of the economy to drive opportunities and attract internalor external sources of investment. The increased number of complex production sectors, proxied by the fitness, leadsto an open array of possibilities allowing the individual to invest in physical and human capital in order to exploit newand additional opportunities. This effect of fitness on savings and education could be modeled in terms of a dynamicalprocess in which a multi-sector economy goes from one equilibrium to another after overcoming a threshold that canbe lowered by increasing the complexity and diversification of the economy. We believe that this out of equilibriumdynamics is the one performed by countries emerging from the poverty trap.Indeed, this analysis does not scrap the concept of poverty trap: if anything, it makes the original point stronger.As can be seen from figure 4, not only is the barrier real but, for countries with low fitness, it is extremely high; tothe point that the figure seems to imply the paradox that in order emerge from the poverty trap a low fitness countrymust first become rich. However, it also suggest a different way to overcome both the trap and the paradox, loweringthe threshold to industrialization by diversifying exports and making its economy more complex.We think that our analysis is particularly relevant for policy makers interested in the first steps of development, inparticular for the ones interested in countries that are unable to complete their industrialization process even if theyenjoy moderately good standards of living thanks to the presence of natural resources.
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Dataset
In the following we will use mostly simple national statistics, other than the Fitness measure previously described.We use for all the national statistics data the Penn World Table 8.0. The data on physical capital is produced witha perpetual inventory method, as described in Inklaar and Timmer (2013), while the proxy for the human capital isthe average number of years of education in the population. The exogenous growth has been computed as the residualof the total growth after removing the input growth.Countries’ fitness evaluations are based on the import-export flows as registered in the UN-NBER database,reconstructed and edited by Feenstra et al. (2005). This database includes the (discounted) imports of 72 countries andcovers more than 2577 product categories for a period ranging from 1963 to 2000. Exports are reconstructed startingfrom these imports, which cover about the 98% of the total trade flow. There are many possible categorizations forproducts; we will base our study on the Sitc v2, 4-digits coding. After a data cleaning procedure, whose aim is toremove obvious errors in the database records, and to obtain a consistent collection of data, the number of countriesfluctuates between 135 and 151 over the years, while the number of products remains equal to 538.
B Basic Solow Model of Growth and Growth Accounting
In this appendix we give a simple version of the models of economic growth based on Solow (1956) and Solow (1957).Even if the aim of the paper is an empirical analysis, we thought it might be useful to the potential reader new tothe macroeconomic analysis to have a simple version of economic model aimed at explaining growth. Moreover thisderivation is required in our analysis to decompose the growth in input growth and exogenous growth.We start writing a production function as generic as possible, Y i,t = Y ( A i,t , I ji,t ) , (6)where Y i,t is the production of country i at time t , A i,t is an efficiency measure and, for different j s, I ji,t are thedifferent inputs of the production (Physical Capital, Labor, Human Capital, ...). The production function F gives theoutput of the economy for different levels of inputs and efficiency. The growth of output, that we will identify withGDP in the following, can therefore be the consequence of an efficiency and technological growth, i.e. a growth of A ,or an input growth.In growth models some inputs are accumulated in an endogenous way: a part of the output is invested to buildnew physical capital, a part of the working time of the laborers is spent to train new workers and accumulate humancapital. Their level in equilibrium is the result of their accumulation and their depreciation. Growth due to inputaccumulation is therefore called endogenous growth. On the opposite side, growth due to technology and efficiency, agrowth of A , is called exogenous growth .In the following we will use a minimal case. We will take a Cobb-Douglas production function with two inputs,physical capital K i,t and labor L i,t : Y i,t = A i,t K αi,t L − αi,t . (7)If a fraction s of the output Y is invested in the production of new physical capital K and a fraction δ of K decadesat each time step due to depreciation, the time evolution of physical capital is K i,t +1 = sY i,t + (1 − δ ) K i,t . (8)In figure 5(a) we show that this equation has only one stable equilibrium. The equilibrium is possible due to thedecreasing returns on capital: the more capital a country has, the less output the country gains with an additionalunit of capital. It is also worth to note that, since the equilibrium point K ∗ depends on A and L , K will still grow ifthose variables grow.However already in Solow (1956) there were the idea that multiple equilibria in the capital levels are possible. Iffor example the investing rate s is not independent from the per capita income of the country, but it depends onthe achievement on a minimal level of subsistence, the capital accumulation function becomes non linear. We can forexample assume a functional form of the investing rate like, s i,t = s i K F − K i,t (9)where s i is a country-dependent parameter and K F a minimum threshold to achieve subsistence and start investing.As a consequence of this non linearity the system can present a behavior similar to figure 5(b).After overcoming a barrier, in figure 5(b) represented by point K ∗ , the country capital would move endogenouslyto K ∗ . The out-of-equilibrium dynamics from one equilibrium to another has to be characterized by fast inputaccumulation and, therefore, fast endogenous economic growth. A way of looking the results of our analysis in section5 is that k F depends on the Fitness of the country. it is also called exogenous growth the growth of inputs that are not accumulated endogenously in the model; e.g. demographic growth a) (b) Figure 5: (a): a single equilibrium in K ∗ . The two curves δK and sY represents respectively capital depreciation andcapital accumulation. The equilibrium is achieved when the two effects are equal, i.e. K ∗ . (b): a case with multipleequilibria. When the production function has increasing returns for some scales, multiple equilibria are possible. K ∗ and K ∗ are stable equilibria, while K ∗ is unstable.In this setting we can also understand equation 1. From 7, the GDP per capita is equal to (cid:18) Y i,t P i,t (cid:19) i,t = A i,t (cid:18) K i,t P i,t (cid:19) α (cid:18) E i,t P i,t H i,t (cid:19) − α , (10)and therefore, defining with the lowercase letters the growth rates of the respective uppercase variables and with thehat the division by population, ˆ y c,t = a c,t + α ˆ k c,t + (1 − α )ˆ e c,t + (1 − α ) h c,t . (11)In equation 1 we dropped the hats notation to simplify the reading, and y , k , and ee