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{{Other uses|Product space}}

{{Other uses|Product space}}

The Product Space is a network representation of the relatedness or proximity between products traded in the global market. 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. The clusters of products in this space bear a striking resemblance to Leamer's product classification system.

The Product Space is a network representation of the relatedness or proximity between products traded in the global market. 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. The clusters of products in this space bear a striking resemblance to Leamer's product classification system.

产品空间是在全球市场上交易的产品之间的关系或接近程度的网络表示。网络表现出异质性和核心-外围结构: 网络的核心由金属产品、机械和化学品组成，而外围则由渔业、热带和谷物农业组成。这个领域的产品集群与利默的产品分类方案有着惊人的相似之处。

产品空间是在全球市场上交易的产品之间关系或接近程度的网络表示。网络表现出异质性和核心-外围结构: 网络的核心由金属产品、机械和化学品组成，而外围则由渔业、热带和谷物农业组成。这个领域的产品集群与利默的产品分类方案有着惊人的相似之处。

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," 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. From the new analytic tools developed, Hausmann, Hidalgo and their team have been able to elaborate predictions of future economic growth.

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," 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. From the new analytic tools developed, Hausmann, Hidalgo and their team have been able to elaborate predictions of future economic growth.

产品空间是一个网络，形式化的概念之间的关系的产品贸易在全球经济。该网络最早出现在2007年7月的《科学》杂志上，由 Cesar a. Hidalgo，Bailey Klinger，Ricardo Hausmann 和 albert-l szl barab si 撰写的文章《产品空间条件国家的发展》中。产品空间网络对经济政策有相当大的影响，因为其结构有助于说明为什么一些国家经济稳步增长，而另一些国家停滞不前，无法发展。经济复杂性观察站进一步发展和扩展了这一概念，通过产品出口树状图等可视化和经济复杂性指数等新指数，这些指数被压缩成了《经济复杂性地图集》。通过开发新的分析工具，Hausmann，Hidalgo 和他们的团队已经能够详细预测未来的经济增长。

产品空间是一个网络，形式化的概念之间的关系的产品贸易在全球经济。该网络最早出现在2007年7月的《科学》杂志上，由 Cesar a. Hidalgo，Bailey Klinger，Ricardo Hausmann 和 albert-lászló Barabási 撰写的文章《产品空间条件下国家的发展》中。产品空间网络对经济政策有相当大的影响，因为其结构有助于说明为什么一些国家经济稳步增长，而另一些国家停滞不前，无法发展。经济复杂性观察站进一步发展和扩展了这一概念，通过产品出口树状图等可视化和经济复杂性指数等新指数，这些指数被压缩成了《经济复杂性地图集》。通过开发新的分析工具，Hausmann，Hidalgo 和他们的团队已经能够详细预测未来的经济增长。

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.

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通过以下方式概念化: 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，或者说在这里，生活在树上。对于猴子来说，生长的过程意味着从森林中比较贫穷的地方搬到森林中比较好的地方，因为那里的树很少结果。要做到这一点，猴子必须跳过距离; 也就是说，重新配置(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，假设总是有一棵树伸手可及。然而，如果森林不是均匀的，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，而在稀疏的地区，跳到一棵新的树上是非常困难的。事实上，如果一些地区非常荒凉，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开始生产新产品的能力。

产品空间的概念可以通过以下方式概念化: 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，或者说在这里，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地方搬到森林中较好的地方，因为那里的树很少结果。为了做到这一点，猴子们必须跳跃距离; 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，如果森林不是均匀的，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，而在稀疏的地区，跳到一棵新的树上是非常困难的。事实上，如果一些地区非常荒凉，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开始生产新产品的能力。

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.”

有许多因素可以描述一对产品之间的关系: 例如，生产所需的资本数量，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; 相反，“产品空间”考虑的是一种基于结果的衡量方法，其基本思想是，如果一对产品因为需要相似的制度、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，不同的产品不太可能共同生产。这种相似性的后验测试被称为“接近性”

有许多因素可以描述一对产品之间的关系: 例如，生产所需的资本数量，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; 相反，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“接近性”

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“邻近度”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亲近。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，这种直观的观点正式化了: 一个出口苹果的国家很可能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，如果中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。虽然难以量化与每种产品相关的一系列市场之间的这种重叠，但衡量邻近程度所使用的是一种基于成果的方法，其基本思想是相似产品(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“邻近度”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亲近。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，如果中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。虽然难以量化与每种产品相关的一系列市场之间的这种重叠，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 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 definition of RCA, x(c,i) equals the value of exports in country c in the ith good.

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 definition of RCA, x(c,i) equals the value of exports in country c in the ith good.

Rca 是一个严格的标准，用以考虑在全球市场上的竞争性出口。为了将边际出口排除在外，一个国家如果出现显示比较优势，就称之为出口。使用巴拉萨的 RCA 定义，x (c，i)等于 c 国在第 i 货物中的出口价值。

RCA 是一个严格的标准，用以考虑在全球市场的竞争性出口。为了将边际出口排除在外，一个国家如果出现显示比较优势，就称之为出口。使用巴拉萨的 RCA 定义，x (c，i)等于 c 国在第 i 货物中的出口价值。

<math>\text{RCA}_{c,i}=\frac

<math>\text{RCA}_{c,i}=\frac

{{\sum_c x(c, i)}/{\sum_{c,i}x(c,i)}}</math>

{{\sum_c x(c, i)}/{\sum_{c,i}x(c,i)}}</math>

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:

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:

如果区域能力评估值超过1，一国在某一产品中的出口份额就大于该产品在全球贸易中的份额。根据这一措施，当 RCA (c，i)大于或等于1时，国家 c 被称为出口产品 i。当 RCA (c，i)小于1时，c 国不是有效的出口国。根据这个惯例，一对货物 i 和 j 之间的接近度定义如下:

如果区域能力评估值超过1，一个国家在某一产品中的出口份额就大于该产品在全球贸易中的份额。根据这一措施，当 RCA (c，i)大于或等于1时，国家 c 被称为出口产品 i。当 RCA (c，i)小于1时，c 国不是有效的出口国。根据这个惯例，一对货物 i 和 j 之间的接近度定义如下:

:<math>\phi_{i,j} = \min\{\Pr(\text{RCA} x_i \geq 1 \mid \text{RCA} x_j \geq 1), \Pr(\text{RCA} x_j \geq 1 \mid \text{RCA} x_i \geq 1)\}</math>

:<math>\phi_{i,j} = \min\{\Pr(\text{RCA} x_i \geq 1 \mid \text{RCA} x_j \geq 1), \Pr(\text{RCA} x_j \geq 1 \mid \text{RCA} x_i \geq 1)\}</math>

<math>\phi_{i,j} = \min\{\Pr(\text{RCA} x_i \geq 1 \mid \text{RCA} x_j \geq 1), \Pr(\text{RCA} x_j \geq 1 \mid \text{RCA} x_i \geq 1)\}</math>

<math>\phi_{i,j} = \min\{\Pr(\text{RCA} x_i \geq 1 \mid \text{RCA} x_j \geq 1), \Pr(\text{RCA} x_j \geq 1 \mid \text{RCA} x_i \geq 1)\}</math>

数学 phi i，j } min  Pr ( text { RCA } x geq 1) ， Pr ( text { RCA } x geq 1) mid text { RCA i geq 1) / math

1 mid text { RCA } x j geq 1) ，Pr (text { RCA } x j geq 1 mid text { RCA } x i geq 1)} </math >

<math>\Pr(\text{RCA}_i \geq 1 \mid \text{RCA}_j \geq 1)</math> 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.

<math>\Pr(\text{RCA}_i \geq 1 \mid \text{RCA}_j \geq 1)</math> 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.

<math>\Pr(\text{RCA}_i \geq 1 \mid \text{RCA}_j \geq 1)</math> 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.

<math>\Pr(\text{RCA}_i \geq 1 \mid \text{RCA}_j \geq 1)</math> 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.

Math  Pr ( text { RCA } i geq 1 mid text { RCA } j geq 1) / math 是导出货物的条件概率，如果你导出货物的话。通过考虑这两个条件概率的最小值，我们消除了当一个国家是某一特定商品的唯一出口国时出现的问题: 假定该国出口的所有其他商品的出口条件概率等于该国出口的所有其他商品的出口额。

1) </math > Pr (text { RCA } i geq 1 mid text { RCA } j geq 1) </math > 是输出好的条件概率，因为你输出好的 j。通过考虑这两个条件概率的最小值，我们消除了当一个国家是某一特定商品的唯一出口国时出现的问题: 假定该国出口的所有其他商品的出口条件概率等于该国出口的所有其他商品的出口额。

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年数据集》的国际贸易数据，通过国家经济研究局(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。按 SITC4分类排序的乘积空间矩阵。乙。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，通过国家经济研究局(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。按 SITC4分类排序的乘积空间矩阵。乙。产品空间按层次分类揭示了模块性，775种产品被积极交易。

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代表一个特定的商品，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，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，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。

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.

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. The maximum spanning tree represents the first step in visualizing the Product Space network.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 initial step in building a network representation of product relatedness (proximities) involved first generating a network framework. The maximum spanning tree represents the first step in visualizing the Product Space network.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.

构建产品相关性(邻近性)的网络表示的第一步涉及到首先生成一个网络框架。最大生成树表示可视化 Product Space 网络的第一步。 在这里，最大生成树(MST)算法建立了一个网络的775个产品节点和774个链接，将网络的总邻近值最大化。

构建产品相关性(邻近性)的网络表示的第一步涉及首先生成一个网络框架。最大生成树表示可视化 Product Space 网络的第一步。在这里，最大生成树(MST)算法建立了一个网络的775个产品节点和774个链接，将网络的总邻近值最大化。

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.

上面的力导向弹簧布局包括链接的 MST 和任何接近大于0.55的边缘。为了实现最终的 Product Space 设计，人工解除了稠密的集群，并根据节点 / 链接大小和颜色添加了属性。网络的基本”骨架”是通过对邻近值设定一个阈值，将不一定在最小安全系数中的最强链接强加于网络; 这些链接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。选择这个阈值使得网络的平均度等于4，这是有效的网络可视化的一个常见规则。随着框架的完成，一个力导向弹簧算法被用来实现一个更理想的网络布局。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。

力导向的弹簧布局上面包括链接从 MST 和任何接近大于0.55的边缘。为了实现最终的 Product Space 设计，人工解除了稠密的集群，并根据节点/链接大小和颜色添加了属性。网络的基本”骨架”是通过对邻近值设定一个阈值，将不一定在最小安全系数中的最强链接强加于网络; 这些链接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。选择这个阈值使得网络的平均度等于4，这是有效的网络可视化的一个常见规则。随着框架的完成，一个力导向的弹簧算法被用来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。

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 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.

Product Space 还揭示了产品类中更明确的结构。例如，机械似乎自然地分为两类: 一类是重型机械，另一类是车辆和电子设备。尽管机械集群与一些资本密集型金属产品相关联，但它并未与类似分类的产品(如纺织品)交织在一起。这样，产品空间为产品分类提供了一个新的视角。

Product Space 还揭示了产品类中更明确的结构。例如，机械似乎自然地分为两类: 一类是重型机械，另一类是车辆和电子设备。虽然机械集群与一些资本密集型金属产品相关联，但它并未与类似分类的产品(如纺织品)交织在一起。这样，产品空间为产品分类提供了一个新的视角。

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. Localization of the productive structure for different regions of the world. The products for which the region has an RCA > 1 are denoted by black squares. 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 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. Localization of the productive structure for different regions of the world. The products for which the region has an RCA > 1 are denoted by black squares. 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.

产品空间网络可以用来研究一个国家生产结构的演变。一个国家在空间内的方向可以通过观察其具有 RCA 1的产品所处的位置来确定。右边的图像显示了专业化模式: 黑色方块表示每个地区用 RCA 1输出的产品。世界不同地区生产结构的本地化。该区域具有 RCA 1的产品用黑色方块表示。可以看出，工业化国家出口的核心产品，如机械，化学品和金属产品。然而，它们也占据了周边产品，如纺织品、森林产品和畜牧业。东亚国家在纺织品、服装和电子产品方面表现出优势。拉丁美洲和加勒比地区专门从事边缘产业，如采矿业、农业和服装业。撒哈拉以南非洲在少数几个产品类别中展示了优势，所有这些产品类别都占据了产品空间的边缘。从这些分析，它是清楚的，每个地区显示一个可识别的模式专业化很容易辨别在产品空间。

产品空间网络可以用来研究一个国家生产结构的演变。一个国家在空间内的方向可以通过观察其 RCA > 1的产品所处的位置来确定。右边的图像显示了专业化模式: 黑色方块表示每个地区出口的产品 RCA > 1。世界不同地区生产结构的本地化。区域 RCA > 1的乘积用黑色方块表示。可以看出，工业化国家出口的核心产品，如机械，化学品和金属产品。然而，它们也占据了周边产品，如纺织品、森林产品和畜牧业。东亚国家在纺织品、服装和电子产品方面表现出优势。拉丁美洲和加勒比地区专门从事边缘产业，如采矿、农业和服装业。撒哈拉以南非洲在少数几个产品类别中展示了优势，而这些产品类别都占据了产品空间的边缘。从这些分析，它是清楚的，每个地区显示一个可识别的模式专业化很容易辨别在产品空间。

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 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.”

同样的方法也可以用来观察一个国家的发展。通过使用相同的可视化惯例，可以看到各国通过遍历产品空间转向新产品。有两种措施量化这种通过产品空间从无用产品(某一国家没有优势的产品)到有用产品(该国具有 RCA 1的产品)的流动。这些产品被称为“过渡产品”

同样的方法也可以用来观察一个国家的发展。通过使用相同的可视化惯例，可以看到各国通过遍历产品空间转向新产品。有两种措施量化这种通过产品空间从未使用的产品(某一国家没有优势的产品)到占用的产品(该国具有 RCA > 1的产品)的流动。这些产品被称为“过渡产品”

<math>\omega_j^k = \frac{ {\displaystyle \sum_i x_i \phi_{ij} } }{ {\displaystyle\sum_i \phi_{ij} } }</math>

<math>\omega_j^k = \frac{ {\displaystyle \sum_i x_i \phi_{ij} } }{ {\displaystyle\sum_i \phi_{ij} } }</math>

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:  

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:  

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:  

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:  

高密度反映了一个国家有很多已经开发的产品围绕着未使用的产品。研究发现，1990年未生产但1995年生产的产品(过渡产品)密度较高，这意味着这一数值预示着向无人使用的产品过渡。“发现因素”测量证实了这一观点:

高密度反映了一个国家有很多已经开发的产品围绕着未使用的产品。研究发现，1990年没有生产但1995年生产的产品(过渡产品)密度较高，这意味着这一数值预示着向无人使用的产品过渡。“发现因素”测量证实了这一观点:

:<math>H_j = \frac{ {\displaystyle \sum_{k=1}^T \omega_j^k / T} }{ {\displaystyle \sum_{k=T+1}^N \omega_j^k / (N - T)} }</math>

:<math>H_j = \frac{ {\displaystyle \sum_{k=1}^T \omega_j^k / T} }{ {\displaystyle \sum_{k=T+1}^N \omega_j^k / (N - T)} }</math>

<math>H_j = \frac{ {\displaystyle \sum_{k=1}^T \omega_j^k / T} }{ {\displaystyle \sum_{k=T+1}^N \omega_j^k / (N - T)} }</math>

<math>H_j = \frac{ {\displaystyle \sum_{k=1}^T \omega_j^k / T} }{ {\displaystyle \sum_{k=T+1}^N \omega_j^k / (N - T)} }</math>

数学 h  frac { displaystyle  sum { k 1} ^ t omega j ^ k / t }{ displaystyle  sum { k t + 1} ^ n omega j ^ k / (n-t)} / math

{显示风格 sum { k = 1} ^ t omega j ^ k/t }{显示风格 sum { k = t + 1} ^ n omega j ^ k/(n-t)}} </math >

<math>H_j</math> 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.

<math>H_j</math> 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.

<math>H_j</math> reflects the average density of all countries in which the jth product was a transition product and the average density of all countries in which the jth 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.

<math>H_j</math> reflects the average density of all countries in which the jth product was a transition product and the average density of all countries in which the jth 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.

数学 h / math 反映了所有国家的平均密度，其中 jth 产品是一个过渡产品，而所有国家的平均密度没有开发 jth 产品。对于79% 的产品来说，这个比率超过了1，这表明密度可能预示着向新产品的过渡。

反映了所有国家的平均密度，其中 jth 产品是一个过渡产品，而不是 jth 产品开发的所有国家的平均密度。对于79% 的产品来说，这个比率超过了1，这表明密度可能预示着向新产品的过渡。

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.

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.

产品空间结构的影响可以通过模拟来评估，在模拟中，一个国家反复转向临近程度高于给定阈值的新产品。在接近度为0.55的门槛值上，各国能够扩散通过产品空间的核心，但扩散的速度取决于初始产品集。一些国家的初始产品占据了周边产业，通过将门槛提高到0.65，这些国家陷入了困境，找不到任何接近足够的产品。这意味着一个国家在空间范围内的定位事实上可以决定该国是否实现经济增长。

产品空间结构的影响可以通过模拟来评估，在模拟中，一个国家反复转向临近程度高于某一阈值的新产品。在接近度等于0.55的临界值时，各国能够扩散通过产品空间的核心，但扩散的速度取决于初始产品集。通过将门槛提高到0.65，一些最初的产品占据周边产业的国家陷入困境，找不到任何接近足够的产品。这意味着一个国家在空间范围内的定位事实上可以决定该国是否实现经济增长。

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." 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.

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." 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.