We describe a problem in complex networks we call the Node Vector Distance (NVD) problem, and we survey algorithms currently able to address it. Complex networks are a useful tool to map a non-trivial set of relationships among connected entities, or nodes. An agent—e.g., a disease—can occupy multiple nodes at the same time and can spread through the edges. The node vector distance problem is to estimate the distance traveled by the agent between two moments in time. This is closely related to the Optimal Transportation Problem (OTP), which has received attention in fields such as computer vision. OTP solutions can be used to solve the node vector distance problem, but they are not the only valid approaches. Here, we examine four classes of solutions, showing their differences and similarities both on synthetic networks and real world network data. The NVD problem has a much wider applicability than computer vision, being related to problems in economics, epidemiology, viral marketing, and sociology, to cite a few. We show how solutions to the NVD problem have a wide range of applications, and we provide a roadmap to general and computationally tractable solutions. We have implemented all methods presented in this article in a publicly available open source library, which can be used for result replication.
By exploiting variation both in mortgage payoffs and mortgage interest rate resets, we find that a decline in mortgage payments induces a significant increase in nondurable goods spending, even when households have substantial amounts of liquidity. Following mortgage payoff, households increase consumption expenditures by 61% of the original payment. In comparison, households increase consumption by only 36% in response to a transitory payment adjustment induced by interest rate changes. Households with a higher payment-to-income ratio have a significantly lower marginal propensity to consume (MPC). These results have practical implications for policy markers seeking to design consumption boosting policies and are important for understanding how changes in monetary policy may affect consumer spending patterns.
We use aggregated and anonymized information based on international expenditures through corporate payment cards to map the network of global business travel. We combine this network with information on the industrial composition and export baskets of national economies. The business travel network helps to predict which economic activities will grow in a country, which new activities will develop and which old activities will be abandoned. In statistical terms, business travel has the most substantial impact among a range of bilateral relationships between countries, such as trade, foreign direct investments and migration. Moreover, our analysis suggests that this impact is causal: business travel from countries specializing in a specific industry causes growth in that economic activity in the destination country. Our interpretation of this is that business travel helps to diffuse knowledge, and we use our estimates to assess which countries contribute or benefit the most from the diffusion of knowledge through global business travel.
The educational gender gap has closed or reversed in many countries. But what of gendered labour market inequalities? Using micro‐level census data for some 40 countries, the authors examine the labour force participation gap between men and women, the “marriage gap” between married and single women's participation, and the “motherhood gap” between mothers' and non‐mothers' participation. They find significant heterogeneity among countries in terms of the size of these gaps, the speed at which they are changing, and the relationships between them and the educational gap. But counterfactual regression analysis shows that the labour force participation gap remains largely unexplained by the other gaps.
As individuals specialize in specific knowledge areas, a society’s know-how becomes distributed across different workers. To use this distributed know-how, workers must be coordinated into teams that, collectively, can cover a wide range of expertise. This paper studies the interdependencies among co-workers that result from this process in a population-wide dataset covering educational specializations of millions of workers and their co-workers in Sweden over a 10-year period. The analysis shows that the value of what a person knows depends on whom that person works with. Whereas having co-workers with qualifications similar to one’s own is costly, having co-workers with complementary qualifications is beneficial. This co-worker complementarity increases over a worker’s career and offers a unifying framework to explain seemingly disparate observations, answering questions such as “Why do returns to education differ so widely?” “Why do workers earn higher wages in large establishments?” “Why are wages so high in large cities?”