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Conventional economic development theory has been unable to decipher the role of various product types in a country's economic performance. 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 or on differences in technological capabilities and what underlies them. 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.
Conventional economic development theory has been unable to decipher the role of various product types in a country's economic performance. 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 or on differences in technological capabilities and what underlies them. 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.
传统的'''<font color="#ff8000">经济发展 economic development</font>'''理论无法解释各种产品类型在一国经济绩效中的作用。传统观点认为，'''<font color="#ff8000">工业化 industrialization</font>'''会对新产品产生“溢出”效应，从而促进后续增长。然而，这个想法并没有被纳入任何正式的'''<font color="#ff8000">经济模型 economic model</font>'''。解释一个国家的经济，要么侧重于该国资本和其他生产要素的相对比例，要么侧重于技术能力的差异及其基础。这些理论都没有抓住产品之间固有的共性，这无疑有害于一个国家的增长模式。产品空间提出了一个解决这个问题的新方法，很直观地想，例如，一个出口香蕉的国家，下一次出口的产品更有可能是芒果，而不是喷气式发动机。
传统的'''<font color="#ff8000">经济发展 economic development</font>'''理论无法解释各种产品类型在一个国家中经济的表现。传统观点认为，'''<font color="#ff8000">工业化 industrialization</font>'''会对新产品产生“溢出”效应，从而促进后续增长。然而，这个想法并没有被纳入任何正式的'''<font color="#ff8000">经济模型 economic model</font>'''。解释一个国家的经济，要么侧重于该国资本和其他生产要素的相对比例，要么侧重于技术能力的差异及其基础。这些理论都没有抓住产品之间固有的共性，而这些产品之间的联系往往都会影响一个国家经济的增长。产品空间的建立提出了一个解决这个问题的新方法，很直观地想，例如，一个经常出口香蕉的国家很可能会出口芒果，而不是喷气式发动机。
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.
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.
产品空间的概念可以由以下方式解释: 将一个产品视为一棵树，将所有产品的集合视为一片森林。一个国家由一系列企业组成ーー用这个比喻来说，就是猴子ーー它们开发产品，生活在树上。对于猴子来说，生长的过程意味着从森林中较为贫瘠的，树木很少结果的地方搬到森林中较富饶的地方。为了达到这个目的，猴子们必须在森林中跳跃迁徙; 也就是说，重新调配(物理、人力和机构)资本来生产新产品。传统的经济理论忽视了森林的结构，认为总有一棵树伸手可及。然而，如果森林是不均匀的，就会有树木生长茂密的地区，猴子不必费多大力气就能够找到新的树木，而在树木稀少的地区，跳到一棵新的树上是非常困难的。事实上，如果一些地区非常贫瘠，猴子可能根本无法穿越森林。因此，森林的结构和猴子在森林中的位置决定了猴子的生长能力; 就经济而言，这种“产品空间”的拓扑结构影响一个国家生产新产品的能力。
产品空间的概念可以由以下方式解释: 如果将一个产品视为一棵树，将所有产品的集合视为一片森林。一个国家则可以想象成y由一片片森林组成的庄园，而生活在里面的猴子负责使用产品——树上的果子。对于猴子来说，生存意味着从森林中较为贫瘠的地方搬到森林中较富饶的地方。为了达到这个目的，猴子们必须在森林中跳跃迁徙; 也就是说，重新调配(物理、人力和机构)资本来生产新产品。传统的经济理论往往忽视了森林的结构，认为总有一棵树伸手可及。然而，如果森林是不均匀的，就会有树木生长茂密的地区，在这里猴子不必费多大力气就能够找到新的树木，而在树木稀少的地区，跳到一棵新的树上是非常困难的事情。事实上，如果一些地区非常贫瘠，猴子可能根本无法穿越森林。因此，森林的结构和猴子在森林中的位置决定了猴子的生长能力; 就经济而言，这种“产品空间”的拓扑结构会影响一个国家生产新产品的能力。
==Building the Product Space==
==Building the Product Space==
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.”
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.”
有许多要素可以描述一对产品之间的关系: 例如，生产所需的'''<font color="#ff8000">资本 capital</font>'''数量，技术复杂程度，或者产品价值链中的投入和产出。选择研究其中一个概念，假定其他概念相对不重要; 相对的，产品空间考虑一种基于结果的衡量方法，这种方法的基础是，如果一对产品因为需要相似的机构、资金、基础设施、技术等而相互关联，那么它们很可能是一起生产的。另一方面，不同种类的产品则不太可能共同生产。这种相似性的后验测试被称为“邻近度”
有许多要素可以描述一对产品之间的关系: 例如，生产所需的'''<font color="#ff8000">资本 capital</font>'''数量，技术复杂程度，或者产品价值链中的投入和产出。选择研究其中一个概念，假定其他概念相对不重要; 相对的，产品空间考虑一种基于结果的衡量方法，这种方法的基础是，如果一对产品因为需要相似的机构、资金、基础设施、技术等而相互关联，那么它们很可能是一起生产的。另一方面，不同种类的产品则不太可能共同生产。这种相似性的后验测试被称为“邻近度”。
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).
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).
产品空间用一种称为'''<font color="#ff8000">邻近度 proximity</font>'''的度量方法来量化产品之间的相关性。在上面的树的类比中，邻近意味着森林中两棵树之间的接近。一个国家生产一种产品的能力取决于它生产其他产品的能力，这种直觉的接近正式化了: 一个出口苹果的国家最有可能拥有适合出口梨的条件: 这个国家已经有了土壤、气候、包装设备、冷藏卡车、农艺学家、植物卫生法和工作贸易协定。所有这些都可以很容易地重新部署到梨业务上。然而，如果该国转而选择生产铜线或家用电器等不同产品，这些投入将是徒劳的。虽然量化与每种产品相关的一系列市场之间的重叠是很困难的，但衡量邻近程度使用的是一种基于成果的方法，其基本思想是，类似产品(苹果和梨)比不同产品(苹果和铜线)更有可能同时生产。
产品空间用一种称为'''<font color="#ff8000">邻近度 proximity</font>'''的度量方法来量化产品之间的相关性。在上面的树的类比中，邻近度意味着森林中两棵树之间的接近程度。一个国家生产一种产品的能力取决于它生产其他产品的能力，临近度直觉得认为——一个出口苹果的国家最有可能拥有适合出口梨的条件：这个国家已经有了合适的土壤、气候、包装设备、冷藏卡车、农艺学家、植物卫生法和工作贸易协定。所有这些都可以很容易地重新部署到运营梨的业务上。然而，如果该国转而选择生产铜线或家用电器等不同产品，这些投入将是徒劳的。虽然量化与每种产品相关的一系列市场之间的重叠是很困难的，但衡量邻近程度使用的是一种基于成果的方法，其基本思想是，类似产品(苹果和梨)比不同产品(苹果和铜线)更有可能同时生产。
The Product Space uses international trade data from Feenstra, Lipset, Deng, Ma, and Mo's World Trade Flows: 1962-2000 dataset, 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.A. The Product Space matrix sorted by SITC4 classification. B. The Product Space hierarchically sorted reveals modularity and that 775 products are actively traded.
The Product Space uses international trade data from Feenstra, Lipset, Deng, Ma, and Mo's World Trade Flows: 1962-2000 dataset, 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.A. The Product Space matrix sorted by SITC4 classification. B. The Product Space hierarchically sorted reveals modularity and that 775 products are actively traded.
产品空间使用来自 Feenstra、 Lipset、 Deng、 Ma 和 Mo 的世界贸易流动: 1962-2000数据集的国际贸易数据，通过'''<font color="#ff8000">国家经济研究局 National Bureau of Economic Research</font>'''(NBER)项目进行了清理和兼容。数据集包含了起源国和目的地的导出和导入。产品按照《标准化国际贸易守则》的四位数分类(SITC-4)。以1998-2000年的数据为重点，得出了775个产品类别，并为每个国家提供了每个类别向所有其他国家出口的价值。由此，得到了每对产品之间的775 * 775的相似度矩阵。A.按 SITC4分类排序的乘积空间矩阵。B.产品空间按层次分类揭示了模块性，775种产品被积极交易。
产品空间使用来自 Feenstra、 Lipset、 Deng、 Ma 和 Mo 的世界贸易流动: 1962-2000数据集的国际贸易数据，清洗并且兼容'''<font color="#ff8000">国家经济研究局 National Bureau of Economic Research</font>'''(NBER)的项目。数据集包含了起源国和目的地的进口数据和出口数据。产品按照《标准化国际贸易守则》的四位数分类(SITC-4)。以1998-2000年的数据为重点，得出了775个产品类别，并为每个国家提供了每个类别向所有其他国家出口的价值。由此，得到了每对产品之间的775 * 775的相似度矩阵。A.按 SITC4分类排序的乘积空间矩阵。B.产品空间按层次分类揭示了模块性，775种产品被积极交易。
===Matrix representation===
===Matrix representation===
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.
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.
这个矩阵的每一行和每一列都代表一个特定的商品，这个矩阵中的非对角线项反映了一对产品之间的接近程度。邻近矩阵的可视化表示显示了高度模块化: 一些商品高度连接，而其他商品是不连接的。此外，矩阵是稀疏的。5% 的元素等于0,32% 小于0.1,65% 的条目小于0.2。由于数据集的稀疏性，网络可视化是一种比较合适的数据集表示方法。
这个矩阵的每一行和每一列都代表一个特定的商品，这个矩阵中的非对角线项反映了一对产品之间的接近程度。邻近矩阵的可视化表示显示了高度模块化: 一些商品高度连接，而其他商品是不连接的。此外，这个矩阵是稀疏的。5% 的元素等于0,32% 小于0.1,65% 的条目小于0.2。由于数据集的稀疏性，网络可视化是一种比较合适的数据集表示方法。
==The Product Space network==
==The Product Space network==
网络布局
网络布局
[[File:ProductSpaceFDSL.png|thumb|left|upright=2|The force-directed spring layout above includes the links from the MST and any edge with a proximity greater than 0.55. To achieve the final Product Space design, the dense clusters were manually untangled and attributes were added in terms of node/link size and color.上面的力定向弹簧布局包括来自MST的连接和邻近度大于0.55的任何边缘。为了实现最终的产品空间设计，人工解除稠密的集群，并根据节点/链接的大小和颜色添加属性。]] 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 visualization]]s. 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.
[[File:ProductSpaceFDSL.png|thumb|left|upright=2|The force-directed spring layout above includes the links from the MST and any edge with a proximity greater than 0.55. To achieve the final Product Space design, the dense clusters were manually untangled and attributes were added in terms of node/link size and color.上面的力定向弹簧布局包括来自MST的连接和任何邻近度大于0.55的边缘。为了实现最终的产品空间设计，手动拆解相对稠密的集群，并根据节点/链接的大小和颜色为其添加属性。]] 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 visualization]]s. 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.
The force-directed spring layout above includes the links from the MST and any edge with a proximity greater than 0.55. To achieve the final Product Space design, the dense clusters were manually untangled and attributes were added in terms of node/link size and color. 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.
The force-directed spring layout above includes the links from the MST and any edge with a proximity greater than 0.55. To achieve the final Product Space design, the dense clusters were manually untangled and attributes were added in terms of node/link size and color. 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.
上面的力定向弹簧布局包括来自MST的连接和任何邻近度大于0.55的边缘。为了实现最终的产品空间设计，手动拆解相对稠密的集群，并根据节点/链接的大小和颜色为其添加属性。该网络的”骨架”是最强链接形成的，这些最强链接不局限于中心MST，也会选择包括大于或等于0.55的所有邻近链接。这产生了一个由775个节点和1525个链接组成的网络。阈值的选择使得网络的平均度等于4，这是一个已知的有效的'''<font color="#ff8000">网络可视化 network visualization</font>'''的常见规则。随着框架的完成，用一个力导向的弹簧算法实现更理想的网络布局。该算法将每个节点视为带电粒子，并假定每个连杆为弹簧，布局为系统的平衡位置或松弛位置。手动重新排列整齐的密集集群，以获得最大的美学效果。
===Node and link attributes===
===Node and link attributes===