# Colombian Export Capabilities: Building the Firms-Products Network

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## Abstract

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## 1. Introduction

## 2. Data

#### 2.1. Colombian Export Data

#### 2.2. World Trade Web Data

#### 2.3. Data Cleaning Procedure

## 3. Methods

#### 3.1. Measuring Nodes Similarity

#### 3.1.1. Quantifying the Significance of Nodes Similarity

#### 3.1.2. Validating the Projection

#### 3.1.3. Testing the Projection Algorithm

#### 3.1.4. Statistical Analysis

## 4. Results

#### 4.1. Node Degree and Strength Distributions

#### 4.2. Nodes Degrees and Strengths Correlation

#### 4.3. Specialization vs. Diversification at a National and International Level

#### 4.4. Nestedness

#### 4.5. Projecting the Colombian Firms-Products Network

#### 4.6. Comparison with the WTW

## 5. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Percentage of validated links by the RCA on the Colombian export dataset (

**left**) and the WTW (

**right**). While the RCA behaves as a selective filter on the World Trade Web, it is much less effective on the network of Colombian exports.

**Figure 2.**Distributions of firms strengths (

**left**) and products strengths (

**right**) for the CFP network in 2010, before applying the threshold at ${10}^{4}$ USD (

**bottom**panel) and after applying such a threshold (

**top**panel): from a qualitative point of view, results do not change. A KS test does not reject the hypothesis that strengths are log-normally distributed.

**Figure 3.**

**Top**panel: distributions of firms degrees (

**left**column) and products degrees (

**right**column) for the CFP network in 2010.

**Bottom**panel: distributions of countries degrees (

**left**column) and products degrees (

**right**column) for the WTW in 2010. All distributions refer to the thresholded dataset. A KS test does not reject the hypotheses described in the insets.

**Figure 4.**Degree vs. strength heatmap for the firms (

**left**panel) and products (

**right**panel) of the CFP network, after (

**top**panel) and before (

**bottom**panel) applying the threshold at ${10}^{4}$ USD. The heatmaps were obtained counting the number of points falling in sliding windows in log-log scale, and the color goes from blue to red as the density of points increases. The Spearman coefficient, computed on the thresholded dataset, is around 0.65 for products and 0.40 for firms. In the WTW case, it rises to 0.90 for countries and 0.73 for products.

**Figure 5.**Biadjacency matrices of the WTW in the year 2010 (

**top**panel) and of the CPF in the year 2010 (

**central**and

**bottom**panel). The ratio between the x- and y-axes was modify to permit an easier comparison between the shape o the matrices. Columns represent products and rows countries (WTW) or firms (CFP). In the central panel, rows and columns of the biadjacency matrix are ordered according to the FiCo ranking, while in the bottom panel the (bipartite) communities found via the Barber algorithm are highlighted [44]. The FiCo algorithm, thus, hides the block-structure characterizing the national exports of Colombia.

**Figure 6.**Evolution of the empirical nestedness (NODF) values and of the BiCM-induced ensemble distributions of the same quantity, compactly represented by the box-plots (showing the 0.15th, the 25th, the 50th, the 75th and the 99.85th percentiles). The CFP network is characterized by a nestedness whose empirical value is significantly less than expected.

**Figure 7.**Projection of the CFP network on the products layer and detected communities for the years 2010 (

**top**panel) and 2014 (

**bottom**panel), found after the projection of the network (

**left**panel) or found via the Barber algorithm on the original bipartite network, and then projected (

**right**panel). The legend used for the communities on the left is as follows: •—clothes; •—fuels, metals and other industrial products; •—fabrics; •—soaps, body care products and related chemicals; •—food; •—electronic components; •—chemicals and medicines; •—furniture for the house and ornaments, in wood and plastic; •—domestic products, small plastic/metal objects; •—stationery, mixed printed products and kids’ toys; •—small tools for construction companies (chains, hammers, etc.); •—refrigerators and other domestic appliances; •—stone, marble and chemicals for construction companies; •—bed linens.

**Figure 8.**Projection of the CFP network on the firms layer and detected communities for the years 2010 (

**left**panel) and 2014 (

**right**panel).

**Figure 9.**Evolution of the Spearman correlation coefficient between the degree of Colombian firms and their fitness values (dark green, dashed,

**left**panel) and between products degree and complexity values (light green, dot-dashed,

**left**panel). As a comparison, the Spearman correlation coefficient between the degree of countries and their fitness values (dark green, dashed,

**right**panel) and between products degree and complexity values (light green, dot-dashed,

**right**panel) is shown.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Bruno, M.; Saracco, F.; Squartini, T.; Dueñas, M.
Colombian Export Capabilities: Building the Firms-Products Network. *Entropy* **2018**, *20*, 785.
https://doi.org/10.3390/e20100785

**AMA Style**

Bruno M, Saracco F, Squartini T, Dueñas M.
Colombian Export Capabilities: Building the Firms-Products Network. *Entropy*. 2018; 20(10):785.
https://doi.org/10.3390/e20100785

**Chicago/Turabian Style**

Bruno, Matteo, Fabio Saracco, Tiziano Squartini, and Marco Dueñas.
2018. "Colombian Export Capabilities: Building the Firms-Products Network" *Entropy* 20, no. 10: 785.
https://doi.org/10.3390/e20100785