# Economics and Network Science

## Network Centrality Measures

There are a variety of network centrality measures that are vaguely similar to PrinceRank, including PageRank. Of particular interest are measures that address signed (aka ternary) graphs, or those with negative links. Some representative lines of inquiry include:

- Bonacich (1987) defines a function c(α, β) which provides a generalized measure of network centrality. While not directly applicable to quantitative realism, this is a seminal article in eigenvector centrality, which is similar to PrinceRank. Bonacich centrality seems to work with negative edges, although the meaning is not entirely clear.
- Friedkin (1991) argues that it is preferable for centrality measures to be theoretically grounded.
- Kaur (2016) provides a very good summary of centrality measures in signed networks.
- Smith, et al, in
*Power in Politically Charged Networks*, define the Political Independence Index, which quantifies political power as a function of network structure. The PII is based on the idea of adding up the centrality of positive links to each node and then subtracting the centrality of the negative links. The motivation here is very similar to that of quantitative realism. - Tai (2005) uses a dummy node to represent aggregate effects of negative relations.
- Tang (2016) discusses the handling of negative links by subtracting the PageRank of the negative links from that of the positive links, effectively breaking the network in two.
- Traag (2010) describes "exponential ranking," which accounts for negative links by analogy to trust and reputation metrics.
- Valente (2008) observes that despite the variety of network centrality measures, they are strongly correlated, especially in non-directed graphs.

## Models of International Trade

The international trade network provides clues to the nature of the world power structure. The literature on this subject seems to be clustered around four general types of models:

- Gravity models and the study of trade frictions
- Application of statistical network analysis to trade networks
- Network wealth/asset exchange and input-output models, which have a similar flow concept to quantitative realism
- Regression (correlation) models between GDP and trade

### Gravity Models

- Almog (2019) tries to improve upon gravity models using a probability distribution related to bilateral trade volume.
- Garlaschelli (2007) infers a fitness function between two nodes indicating the likelihood of connection and finds that this fitness function is related to GDP.

### Statistical Properties of the International Trade Network (ITN)

- Algarra (2019) uses a stochastic network formation model to approximate empirical trade network data.
- Benedictis (2009) summarizes history of network analysis for international trade, which dates back to the 1940s, and then analyzes the ITN over time using common network statistics.
- Ermann (2011) applies PageRank-CheiRank to the ITN, sorting countries into three tiers.
- Fagiolo (2009) applies statistical network theory to trade networks.
- Hokkanen (2012) applies common graph metrics to the ITN and finds correlations between some of these metrics and GDP.

### Asset Exchange and Input-Output Models

In an asset exchange model, agents trade resources stochastically to see how they become distributed. This exchange concept is similar to the way the law of motion handles constructive transfers. Economic input-output models, particularly those based upon a single commodity, also bear a resemblance to the flow of power in the law of motion. Of note are:

- Coquide (2020) models a contagion doomsday scenario using PageRank-CheiRank, considering both countries and products.
- Galbusera (2018), describing ways that I-O models can be used “in reverse” to quantify the impact of some disaster on production.
- Krapivsky (2010), while not specifically about the international trade network, tries to account for the wealth distribution that results from random exchanges among agents. Unlike quantitative realism, this model "neglects the possibility of wealth growth...by both agents benefiting in exchanges."
- Luo and Tsang (2020), which uses input-output analysis to determine labor supply shock to China's GDP from Covid-19 and then calculates the effects on other countries' GDPs.
- United Nations (1999), providing a primer on the mathematics of I-O models.

### Relationship Between Trade and GDP

Does international trade tend to cause a state's GDP to rise? In one sense, the question is a tautology, because the expenditure method of calculating GDP takes into account net exports (exports minus imports), so by definition trade has a causal effect on GDP. That technicality aside, does trade expand a nation's economy?

- Bhattacharya (2009) examines distribution of bilateral trade flows and finds some positive relationship between trade volume and GDP exists
- Garlaschelli (2007) discusses effects of GDP on the trade network, and vice versa. For the latter, hypothesizes a stochastic network wealth exchange model as the cause of GDP distribution.
- Zestos (2002) applies time series causality tests between trade and growth, for the U.S. and Canada. Does not look at network effects.

## The Relationship between Trade and War

One of the assumptions of liberalism is that the benefits of trade creates a disincentive for conflict. Is this sound?

- Barbieri and Levy (1999) and (2001) look at case studies and conclude that “there is no consistent, systematic, and substantial reduction in trade between belligerents during wartime, and trade between adversaries appears to recover quickly after the termination of war.”
- On the other hand, Glick (2005) concludes: “We search for and find a very strong impact of war on trade volumes. Moreover this effect has two important aspects: first, it is persistent, meaning that even after conflicts end, trade does not resume its pre-war level for many years, exacerbating the total costs; second, the effect has a multilateral dimension and, unlike direct costs, which largely effect only the belligerents, trade destruction affects neutral parties as well, generating a negative externality.”