Maximum Entropy for the International Division of Labor

Abstract

As a result of the international division of labor, the trade value distribution on different products substantiated by international trade flows can be regarded as one country’s strategy for competition. According to the empirical data of trade flows, countries may spend a large fraction of export values on ubiquitous and competitive products. Meanwhile, countries may also diversify their exports share on different types of products to reduce the risk. In this paper, we report that the export share distribution curves can be derived by maximizing the entropy of shares on different products under the product’s complexity constraint once the international market structure (the country-product bipartite network) is given. Therefore, a maximum entropy model provides a good fit to empirical data. The empirical data is consistent with maximum entropy subject to a constraint on the expected value of the product complexity for each country. One country’s strategy is mainly determined by the types of products this country can export. In addition, our model is able to fit the empirical export share distribution curves of nearly every country very well by tuning only one parameter.

Structure of international trade hypergraphs

“…In Appendix A, we project the trade hypergraphs onto the subspace in which either of importers or products are neglected, and obtain the pairwise trade networks [26][27][28][29][30][31][32][33][34]. Both the mean degree of the importers adjacent to an exporting country in the exporter-importer (EI) networks and that of the products adjacent to an exporter in the exporter-product (EP) networks decrease with the degree of the exporter suggesting negative correlations [33,34].…”

“…An individual trade is specified by the exporter country, the importer country, and the product, and their collection can be represented by a hypergraph consisting of triangular hyperedges connecting an exporter, an importer, and a product. So far most studies have considered the pairwise networks in the projected space including the country-country networks [26][27][28], the product-product networks [29,30], and the country-product networks [31][32][33][34].…”

Skewness of local logarithmic exports

“…We have just argued that the skewness of local exports γ v;c are influenced by the exporter c via the c-dependent mean v c . Individual local exports v cc ′ 's and v cp 's must be dependent also on the importer country c ′ and the product category p [5]. Exporters have different sets of partners and export products, possibly depending on the exporters' out-degrees, which might be influencing the skewness of local export distributions.…”

“…What products and to what countries a country exports and how large its value is may depend on the domestic industrial landscape of the exporter itself but also on the characteristics of the partner importers and product categories such as the economic development of and the social and political relationship with the partner countries, and the technology level of products, and so on. Among them, how many countries export to a country and how many countries export a product category can be used as important information when an exporter country constructs its product portfolio, as they represent the popularity in international trade, reflecting the collective evaluation by countries [5]. They correspond to the in-degrees of a country c ′ and of product p in the EI and the EP network, defined as…”

“…Individual countries, though equipped with different resources for production and put in different environments, commonly fine tune the strategies on how to allocate resources, invest capital, and make international trade partnership towards the economic development [1][2][3][4][5][6]. Such efforts are universal and thus can be imprinted in the patterns of domestic production, consumption, and international trade.…”