**Working Papers**

**“Gravitational Networks and International Trade”**

The architecture of the international trade network is complex and dynamic, implicitly made up of many coalescent layers of effects. These structures can be classified into three categories based on their scope: Micro-, Meso-, and Macro-scale network effects.

### Different Scales of Network Effects

**Micro-Scale**

**“The trees in the forest”**

Micro-scale network analysis focuses on the smallest possible unit of analysis, which, in most cases, is the *node*.

This definition can be a double-edged sword, however:

- The smallest unit of analysis in a trade network is called a
*node.* - The
*node*is whatever you define the smallest unit of analysis to be.

Dangerously over-generalizing the entire field of trade literature into two bullet points:

- Aggregate-level trade models consider the
*countries*to be*nodes.* - Micro-level studies consider individual
*firms*or perhaps specific*industries within a country*to be*nodes*

Indeed, gravity models in international trade take things in a different direction, implicitly considering the *edges* of the network to be the *nodes* of interest. Within the greater gravity framework, there are, again, two different generalized subclasses of models:

*Digraph Models*are concerned with the*direction*of trade flow across bilateral pairs of countries.- Edges (
*E*) in digraph models are known as*arcs*and carry directional information. *E*⊆ {(*x*,*y*) | (*x*,*y*) ∈*V*^{2},*x*≠*y*}

- Edges (
*Network Models*contain undirected edges. Such trade models capture, or are primarily concerned with, aggregate trade activity at the bilateral pair level.

**Meso-Scale**

**“The Glade within the forest”**

The behavior of groups of connected nodes and/or edges is often of interest to those who seek to understand the evolution of trade networks.

This term is not yet widely accepted by either the trade or networks literatures, however for the purposes of this analysis, is it imperative to define this extremely useful group.

For example, a study of a country and how its set of trading partners evolve would be a *meso-analysis*.

For the purposes of my research, *meso-scale* can refer to the following:

- Individual countries and their degree-N neighborhoods
- Sets of connected countries such that at least one country that exists within the entire network is not included within the set.
- Countries connected along a specific path, such that each country is connected by edges to form a chain.
- Cliques of countries, which are connected sets of nodes that share a common behavioral characteristic, or that engage with each other more significantly along extensive and/or intensive margins.
- Club networks in
*digraph*cases are subsets of a directed network that form a closed subset. Club networks are defined by having a*principle node*(or a*bouncer*) which regulates the flow of activity into, and out from the club.- In international trade, club networks are more commonly observed when trade at the industry or firm-level is concerned.
- Countries, industries, or firms may join or leave club networks.
- Club network structures are also common artifacts when studying inverted graphs, or when the object of the study (
*i.e., the node*) is the connection between countries instead of the countries themselves.

**Macro-Scale**

**“The forest itself”**

Macro-scale analyses focus on the network graph or digraph as a whole along some latent dimension. Within the context of international trade, some examples of macro-scale studies could include:

- Analyses of the evolution of an industry across the globe over time.
- Tracking the relationship between migration and trade flows over time.
- Gravity model estimations of distance elasticities in trade flow over time.
- Estimations of the effects of trade agreements on trade in a general equilibrium setting.

**“Exploring Time-Varying Population-Weighted Distance Measures in the Gravity Model Framework”**

**Exploring Time-Varying Population-Weighted Distance Measures in the Gravity Model Framework **

**(Co-Author: Elizaveta Gonchar)**

**Abstract:**The distribution of population across and within countries naturally relates to the distribution of economic production. In this paper we explore differences in gravity model estimates of trade that take into account spatial factors of population distributions, introducing a novel measure of geodesic distance between countries using population-weighted centroids as endpoints for bilateral distance measures. Canonical gravity models of international trade have relied on time-invariant measures of bilateral distance between nations, including distance between national capitals, geographic centroids, and weighted centroids based on the N largest population centers. By using annual global population density rasters to identify the central spatial tendency of the population, the location of any country’s weighted centroid changes each year. This time-varying distance measure introduces a source of variation into the standard gravity model framework that captures.