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**The Product Space** is a network that formalizes the idea of relatedness between products traded in the global economy. The network first appeared in the July 2007 issue of *Science* in the article "The Product Space Conditions the Development of Nations,"^{ [1] } written by Cesar A. Hidalgo, Bailey Klinger, Ricardo Hausmann, and Albert-László Barabási. The Product Space network has considerable implications for economic policy, as its structure helps elucidate why some countries undergo steady economic growth while others become stagnant and are unable to develop. The concept has been further developed and extended by The Observatory of Economic Complexity, through visualizations such as the Product Exports Treemaps and new indexes such as the Economic Complexity Index (ECI), which have been condensed into the Atlas of Economic Complexity.^{ [2] } From the new analytic tools developed, Hausmann, Hidalgo and their team have been able to elaborate predictions of future economic growth.

* Science*, also widely referred to as

**Ricardo Hausmann** is the former Director of the Center for International Development currently leading the Center for International Development growth lab and is a Professor of the Practice of Economic Development at the John F. Kennedy School of Government at Harvard University. He is also a former Venezuelan Minister of Planning and former Head of the Presidential Office of Coordination and Planning (1992–1993). He co-introduced several regularly used concepts in economics including original sin, growth diagnostics, self-discovery, dark matter, the product space, and economic complexity.

**Albert-László Barabási** is a Romanian-born Hungarian-American physicist, best known for his work in the research of network theory.

- Background
- The forest analogy
- Building the Product Space
- The concept of ‘proximity’
- Source data
- Matrix representation
- The Product Space network
- Maximum spanning tree
- Network layout
- Node and link attributes
- Properties of the Product Space
- Dynamics of the Product Space
- Empirical diffusion
- Simulated diffusion
- Future work
- See also
- References

Conventional economic development theory has been unable to decipher the role of various product types in a country's economic performance.^{ [3] }^{ [4] }^{ [5] } Traditional ideals suggest that industrialization causes a “spillover” effect to new products, fostering subsequent growth. This idea, however, had not been incorporated in any formal economic models. The two prevailing approaches explaining a country's economy focus on either the country's relative proportion of capital and other productive factors^{ [6] } or on differences in technological capabilities and what underlies them.^{ [7] } These theories fail to capture inherent commonalities among products, which undoubtedly contribute to a country's pattern of growth. The Product Space presents a novel approach to this problem, formalizing the intuitive idea that a country which exports bananas is more likely to next export mangoes than it is to export jet engines, for example.

**Economic development** is the process by which a nation improves the economic, political, and social well-being of its people. The term has been used frequently by economists, politicians, and others in the 20th and 21st centuries. The concept, however, has been in existence in the West for centuries. "Modernization, "westernization", and especially "industrialization" are other terms often used while discussing economic development. Economic development has a direct relationship with the environment and environmental issues. Economic development is very often confused with industrial development, even in some academic sources.

In economics, a **model** is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes. Frequently, economic models posit structural parameters. A model may have various exogenous variables, and those variables may change to create various responses by economic variables. Methodological uses of models include investigation, theorizing, and fitting theories to the world.

An **export** in international trade is a good or service produced in one country that is bought by someone in another country. The seller of such goods and services is an *exporter*; the foreign buyer is an *importer*.

The idea of the Product Space can be conceptualized in the following manner: consider a product to be a tree, and the collection of all products to be a forest. A country consists of a set of firms—in this analogy, monkeys—which exploit products, or here, live in the trees. For the monkeys, the process of growth means moving from a poorer part of the forest, where the trees bear little fruit, to a better part of the forest. To do this, the monkeys must jump distances; that is, redeploy (physical, human, and institutional) capital to make new products. Traditional economic theory disregards the structure of the forest, assuming that there is always a tree within reach. However, if the forest is not homogeneous, there will be areas of dense tree growth in which the monkeys must exert little effort to reach new trees, and sparse regions in which jumping to a new tree is very difficult. In fact, if some areas are very deserted, monkeys may be unable to move through the forest at all. Therefore, the structure of the forest and a monkey's location within it dictates the monkey's capacity for growth; in terms of economy, the topology of this “product space” impacts a country's ability to begin producing new goods.

There exists a number of factors that can describe the relatedness between a pair of products: the amount of capital required for production, technological sophistication, or inputs and outputs in a product's value chain, for examples. Choosing to study one of these notions assume the others are relatively unimportant; instead, the Product Space considers an outcome-based measure built on the idea that if a pair of products are related because they require similar institutions, capital, infrastructure, technology, etc., they are likely to be produced in tandem. Dissimilar goods, on the other hand, are less likely to be co-produced. This a posteriori test of similarity is called “proximity.”

In economics, **capital** consists of an asset that can enhance one's power to perform economically useful work. For example, in a fundamental sense a stone or an arrow is capital for a caveman who can use it as a hunting instrument, while roads are capital for inhabitants of a city.

The Product Space quantifies the relatedness of products with a measure called proximity. In the above tree analogy, proximity would imply the closeness between a pair of trees in the forest. Proximity formalizes the intuitive idea that a country's ability to produce a product depends on its ability to produce other products: a country which exports apples most probably has conditions suitable for exporting pears: the country would already have the soil, climate, packing equipment, refrigerated trucks, agronomists, phytosanitary laws, and working trade agreements. All of these could be easily redeployed to the pear business. These inputs would be futile, however, if the country instead chose to start producing a dissimilar product such as copper wire or home appliances. While quantifying such overlap between the set of markets associated with each product would be difficult, the measure of proximity uses an outcome-based method founded on the idea that similar products (apples and pears) are more likely to be produced in tandem than dissimilar products (apples and copper wire).

**Proxemics** is the study of human use of space and the effects that population density has on behaviour, communication, and social interaction.

The RCA is a rigorous standard by which to consider competitive exportation in the global market. In order to exclude marginal exports, a country is said to export a product when they exhibit a Revealed Comparative Advantage (RCA) in it. Using the Balassa^{ [8] } definition of RCA, *x(c,i)* equals the value of exports in country *c *in the *i*th good.

If the RCA value exceeds one, the share of exports of a country in a given product is larger than the share of that product in all global trade. Under this measure, when *RCA(c,i)* is greater than or equal to 1, country c is said to export product *i*. When *RCA(c,i)* is less than 1, country *c* is not an effective exporter of *i*. With this convention, the proximity between a pair of goods *i* and *j* is defined in the following way:

is the conditional probability of exporting good *i* given that you export good *j*. By considering the minimum of both conditional probabilities, we eliminate the problem that arises when a country is the sole exporter of a particular good: the conditional probability of exporting any other good given that one would be equal to one for all other goods exported by that country.

The Product Space uses international trade data from Feenstra, Lipset, Deng, Ma, and Mo's *World Trade Flows: 1962-2000* dataset,^{ [9] } cleaned and made compatible through a National Bureau of Economic Research (NBER) project. The dataset contains exports and imports both by country of origin and by destination. Products are disaggregated according to the Standardized International Trade Code at the four-digit level (SITC-4). Focusing on data from 1998-2000 yields 775 product classes and provides for each country the value exported to all other countries for each class. From this, a 775-by-775 matrix of proximities between every pair of products is created.

Each row and column of this matrix represents a particular good, and the off-diagonal entries in this matrix reflect the proximity between a pair of products. A visual representation of the proximity matrix reveals high modularity: some goods are highly connected and others are disconnected. Furthermore, the matrix is sparse. Five percent of its elements equal zero, 32% are less than 0.1, and 65% of the entries are below 0.2. Because of the sparseness, a network visualization is an appropriate way to represent this dataset.

A network representation of the proximity matrix helps to develop intuition about its structure by establishing a visualization in which traditionally subtle trends become easily identifiable.

The initial step in building a network representation of product relatedness (proximities) involved first generating a network framework.

Here, the maximum spanning tree (MST) algorithm built a network of the 775 product nodes and the 774 links that would maximize the network's total proximity value.

The basic "skeleton" of the network is developed by imposing on it the strongest links which were not necessarily in the MST by employing a threshold on the proximity values; they chose to include all links of proximity greater than or equal to 0.55. This produced a network of 775 nodes and 1525 links. This threshold was chosen such that the network exhibited an average degree equal to 4, a common convention for effective network visualizations. With the framework complete, a force-directed spring algorithm was used to achieve a more ideal network layout. This algorithm considers each node to be a charged particle and the links are assumed to be springs; the layout is the resulting equilibrium, or relaxed, position of the system. Manual rearranging untangled dense clusters to achieve maximum aesthetic efficacy.

A system of colors and sizing allows for simultaneous assessment of the network structure with other covariates. The nodes of the Product Space are colored in terms of product classifications performed by Leamer^{ [10] } and the size of the nodes reflects the proportion of money moved by that particular industry in world trade. The color of the links reflects the strength of the proximity measurement between two products: dark red and blue indicate high proximity whereas yellow and light blue imply weaker relatedness.

There are also other types of classifications applied to the Product Space methodology,^{ [11] } as the one proposed by Lall^{ [12] } which classificates the products by technological intensity.

In the final Product Space visualization, it is clear that the network exhibits heterogeneity and a core-periphery structure: the core of the network consists of metal products, machinery, and chemicals, whereas the periphery is formed by fishing, tropical, and cereal agriculture. On the left side of the network, there is a strong outlying cluster formed by garments and another belonging to textiles. At the bottom of the network, there exists a large electronics cluster, and at its right mining, forest, and paper products. The clusters of products in this space bear a striking resemblance to Leamer's product classification system, which employed an entirely different methodology. This system groups products by the relative amount of capital, labor, land, or skills needed to export each product.

The Product Space also reveals a more explicit structure within product classes. Machinery, for example, appears to be naturally split into two clusters: heavy machinery in one, and vehicles and electronics in the other. Although the machinery cluster is connected to some capital-intensive metal products, it is not interwoven with similarly classified products such as textiles. In this way, the Product Space presents a new perspective on product classification.

The Product Space network can be used to study the evolution of a country's productive structure. A country's orientation within the space can be determined by observing where its products with RCA>1 are located. The images at right reveal patterns of specialization: the black squares indicate products exported by each region with RCA>1.

It can be seen that industrialized countries export products at the core, such as machinery, chemicals, and metal products. They also, however, occupy products at the periphery, like textiles, forest products, and animal agriculture. East Asian countries exhibit advantage in textiles, garments, and electronics. Latin America and the Caribbean have specialized in industries further towards the periphery, such as mining, agriculture, and garments. Sub-Saharan Africa demonstrates advantage in few product classes, all of which occupy the product space periphery. From these analyses, it is clear that each region displays a recognizable pattern of specialization easily discernible in the product space.

The same methods can be used to observe a country's development over time. By using the same conventions of visualization, it can be seen that countries move to new products by traversing the Product Space. Two measures quantify this movement through the Product Space from unoccupied products (products in which a given country has no advantage) to occupied products (products in which that country has an RCA>1). Such products are termed “transition products.”

The "density" is defined as a new product's proximity to a given country's current set of products:

A high density reflects that a country has many developed products surrounding the unoccupied product j. It was found that products which were not produced in 1990 but were produced by 1995 (transition products) exhibited higher density, implying that this value predicts a transition to an unoccupied product. The “discovery factor” measurement corroborates this idea:

reflects the average density of all countries in which the *j*th product was a transition product and the average density of all countries in which the *j*th product was not developed. For 79% of products, this ratio exceeds 1, indicating that density is likely to predict a transition to a new product.

The impact of Product Space's structure can be evaluated through simulations in which a country repeatedly moves to new products with proximities above a given threshold. At a threshold of proximity equal to 0.55, countries are able to diffuse through the core of the Product Space but the speed at which they do so is determined by the set of initial products. By raising the threshold to 0.65, some countries, whose initial products occupy periphery industries, become trapped and cannot find any near-enough products. This implies that a country's orientation within the space can in fact dictate whether the country achieves economic growth.

Although the dynamics of a country's orientation within the network has been studied, there has been less focus on changes in the network topology itself. It is suggested that "changes in the product space represent an interesting avenue for future work."^{ [13] } Additionally, it would be interesting to explore the mechanisms governing countries' economic growth, in terms of acquisition of new capital, labor, institutions, etc., and whether the co-export proximity of the Product Space is truly an accurate reflection of similarity among such inputs.

In linear algebra, the **determinant** is a scalar value that can be computed from the elements of a square matrix and encodes certain properties of the linear transformation described by the matrix. The determinant of a matrix *A* is denoted det(*A*), det *A*, or |*A*|. Geometrically, it can be viewed as the volume scaling factor of the linear transformation described by the matrix. This is also the signed volume of the *n*-dimensional parallelepiped spanned by the column or row vectors of the matrix. The determinant is positive or negative according to whether the linear mapping preserves or reverses the orientation of *n*-space.

In mathematics, a **product** is the result of multiplying, or an expression that identifies factors to be multiplied. Thus, for instance, 6 is the product of 2 and 3, and is the product of and .

In linear algebra, a symmetric real matrix is said to be **positive definite** if the scalar is strictly positive for every non-zero column vector of real numbers. Here denotes the transpose of .. When interpreting as the output of an operator, , that is acting on an input, , the property of positive definiteness implies that the output always has a positive inner product with the input, as often observed in physical processes.

In linear algebra, the **trace** of an *n* × *n* square matrix **A** is defined to be the sum of the elements on the main diagonal of **A**.

In machine learning, **support-vector machines** are supervised learning models with associated learning algorithms that analyze data used for classification and regression analysis. Given a set of training examples, each marked as belonging to one or the other of two categories, an SVM training algorithm builds a model that assigns new examples to one category or the other, making it a non-probabilistic binary linear classifier. An SVM model is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible. New examples are then mapped into that same space and predicted to belong to a category based on which side of the gap they fall.

In mathematics, a **Hermitian matrix** is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j:

In linear algebra, a **linear functional** or **linear form** is a linear map from a vector space to its field of scalars. In **ℝ**^{n}, if vectors are represented as column vectors, then linear functionals are represented as row vectors, and their action on vectors is given by the dot product, or the matrix product with the row vector on the left and the column vector on the right. In general, if *V* is a vector space over a field *k*, then a linear functional *f* is a function from *V* to *k* that is linear:

In linear algebra, an *n*-by-*n* square matrix **A** is called **invertible** if there exists an *n*-by-*n* square matrix **B** such that

In graph theory and computer science, an **adjacency matrix** is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph.

High-dimensional data, meaning data that requires more than two or three dimensions to represent, can be difficult to interpret. One approach to simplification is to assume that the data of interest lie on an embedded non-linear manifold within the higher-dimensional space. If the manifold is of low enough dimension, the data can be visualised in the low-dimensional space.

**Multidimensional scaling** (**MDS**) is a means of visualizing the level of similarity of individual cases of a dataset. MDS is used to translate "information about the pairwise 'distances' among a set of n objects or individuals" into a configuration of n points mapped into an abstract Cartesian space.

In mathematics, a **unimodular matrix***M* is a square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over the integers: there is an integer matrix *N* which is its inverse. Thus every equation *Mx* = *b*, where *M* and *b* are both integer, and *M* is unimodular, has an integer solution. The unimodular matrices of order *n* form a group, which is denoted .

**Multi-task learning** (MTL) is a subfield of machine learning in which multiple learning tasks are solved at the same time, while exploiting commonalities and differences across tasks. This can result in improved learning efficiency and prediction accuracy for the task-specific models, when compared to training the models separately. Early versions of MTL were called "hints"

In combinatorics, especially in analytic combinatorics, the **symbolic method** is a technique for counting combinatorial objects. It uses the internal structure of the objects to derive formulas for their generating functions. The method is mostly associated with Philippe Flajolet, and is detailed in Part A of his book with Robert Sedgewick, *Analytic Combinatorics*. Similar languages for specifying combinatorial classes and their generating functions are found in work by Bender and Goldman, Foata and Schützenberger, and Joyal. The presentation in this article borrows somewhat from Joyal's combinatorial species.

In mathematics, **subshifts of finite type** are used to model dynamical systems, and in particular are the objects of study in symbolic dynamics and ergodic theory. They also describe the set of all possible sequences executed by a finite state machine. The most widely studied shift spaces are the subshifts of finite type.

In mathematics, **Welch bounds** are a family of inequalities pertinent to the problem of evenly spreading a set of unit vectors in a vector space. The bounds are important tools in the design and analysis of certain methods in telecommunication engineering, particularly in coding theory. The bounds were originally published in a 1974 paper by L. R. Welch.

**The Observatory of Economic Complexity** is a data visualization site for international trade data created by the Macro Connections group at the MIT Media Lab. The goal of the observatory is to distribute international trade data in a visual form. At present the observatory serves more than 20 million interactive visualizations, connecting hundreds of countries to their export destinations and to the products that they trade.

The **Economic Complexity Index** (**ECI**) is a holistic measure of the productive capabilities of large economic systems, usually cities, regions, or countries. In particular, the ECI looks to explain the knowledge accumulated in a population and that is expressed in the economic activities present in a city, country, or region. To achieve this goal, the ECI defines the knowledge available in a location, as the average knowledge of the activities present in it, and the knowledge of an activity as the average knowledge of the places where that economic activity is conducted. The product equivalent of the Economic Complexity Index is the Product Complexity Index or PCI.

In the field of statistical learning theory, **matrix regularization** generalizes notions of vector regularization to cases where the object to be learned is a matrix. The purpose of regularization is to enforce conditions, for example sparsity or smoothness, that can produce stable predictive functions. For example, in the more common vector framework, Tikhonov regularization optimizes over

- ↑ C.A. Hidalgo, B. Klinger, A.-L. Barabási, R. Hausmann,
*Science***317**(2007). - ↑ "OEC - Books". atlas.media.mit.edu. Retrieved 16 August 2016.
- ↑ A. Hirschman,
*The Strategy of Economic Development*(Yale University Press, New Haven, CT, 1958). - ↑ P. Rosenstein-Rodan,
*Econ. J***53**, 202 (1943). - ↑ K. Matsuyama,
*J. Econ. Theory***58**, 317 (1992). - ↑ E. Heckscher, B. Ohlin,
*Heckscher-Ohlin Trade Theory,*H. Flam, M. Flanders, Eds. (MIT Press, Cambridge, MA, 1991). - ↑ P. Romer,
*J Polit. Econ.***94**, 5 (1986). - ↑ B. Balassa,
*The Review of Economics and Statistics***68**, 315 (1986). - ↑ R.R. Feenstra, H.D. Lipsey, A. Ma, H. Mo,
*HBER Work. Pap 11040*(2005). - ↑ E. Leamer,
*Sources of Comparative Advantage: Theory and Evidence*(MIT Press, Cambridge, MA, 1984). - ↑ J. Romero, E. Freitas, G. Britto, C. Coelho (2015). The great divide: the paths of industrial competitiveness in Brazil and South Korea (No. 519). Cedeplar, Universidade Federal de Minas Gerais.
- ↑ S. Lall, "The Technological structure and performance of developing country manufactured exports, 1985‐98." Oxford development studies 28.3 (2000): 337-369.
- ↑ C.A. Hidalgo, B. Klinger, A.-L. Barabási, R. Hausmann,
*Science***317**485 (2007).

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