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==Dynamics of the Product Space==

==Dynamics of 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. [[File:ProductSpaceLocalization.png|frame|right|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. [[File:ProductSpaceLocalization.png|frame|right|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.

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 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。

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，'''<font color="#ff8000">工业化国家 industrialized countries</font>'''出口核心产品，如机械，化学品和金属产品。同时，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。从这些分析中可以清楚地看出，每个区域都显示出一个在产品空间中容易识别的专业化模式。

===Empirical diffusion===

===Empirical diffusion===

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.”

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”

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的产品。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”

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

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

“密度”的定义是指一种新产品接近某一国家当前的产品组合:

“密度”的定义是指一种新产品接近某一国家当前的产品类集:

:<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>

<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:

一个较高的密度反映出一个国家一个国家围绕未使用的产品j有许多已开发的产品。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>

 

<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.

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。

<math>H_j</math>反映了以第j项产品为过渡产品的所有国家的平均密度和未开发第j项产品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，这表明该密度值可能预示着向新产品的过渡。

===Simulated diffusion===

===Simulated diffusion===

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.

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。

产品空间结构的影响可以通过在一个国家反复转向邻近程度高于某一阈值的新产品的模拟中来评估。在接近度等于0.55的临界值时，各国能够扩散经过产品空间的核心，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产品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。

 

 

==Future work==

==Future work==