Brunn-Minkowski Inequalities for Contingency Tables and Integer Flows

Given a non-negative mxn matrix W=(w_ij) and positive integer vectors R=(r_1, >..., r_m) and C=(c_1, ..., c_n), we consider the total weight T(R, C; W) of mxn non-negative integer matrices (contingency tables) D with the row sums r_i, the column sums c_j, and the weight of D=(d_ij) equal to product of w_ij^d_ij. In particular, if W is a 0-1 matrix, T(R, C; W) is the number of integer feasible flows in a bipartite network. We prove a version of the Brunn-Minkowski inequality relating the numbers T(R, C; W) and T(R_k, C_k; W), where (R, C) is a convex combination of (R_k, C_k) for k=1, ..., p.Comment: 16 page

Volume of the steady-state space of financial flows in a monetary stock-flow-consistent model

We show that a steady-state stock-flow consistent macro-economic model can be represented as a Constraint Satisfaction Problem (CSP).The set of solutions is a polytope, which volume depends on the constraintsapplied and reveals the potential fragility of the economic circuit,with no need to study the dynamics. Several methods to compute the volume are compared, inspired by operations research methods and theanalysis of metabolic networks, both exact and approximate.We also introduce a random transaction matrix, and study the particularcase of linear flows with respect to money stocks

Network dependence in multi-indexed data on international trade flows

Faced with the problem that conventional multidimensional fixed effects models only focus on unobserved heterogeneity, but ignore any potential cross-sectional dependence due to network interactions, we introduce a model of trade flows between countries over time that allows for network dependence in flows, based on sociocultural connectivity structures. We show that conventional multidimensional fixed effects model specifications exhibit cross-sectional dependence between countries that should be modeled to avoid simultaneity bias. Given that the source of network interaction is unknown, we propose a panel gravity model that examines multiplenetwork interaction structures, using Bayesian model probabilities to determine those most consistent with the sample data. This is accomplished with the use of computationally efficient Markov Chain Monte Carlo estimation methods that produce a Monte Carlo integration estimate of the log-marginal likelihood that can be used for model comparison. Application of the model to a panel of trade flows points to network spillover effects, suggesting the presence of network dependence and biased estimates from conventional trade flow specifications. The most important sources of network dependence were found to be membership in trade organizations, historical colonial ties, common currency, and spatial proximity of countries.Series: Working Papers in Regional Scienc

Conventional versus network dependence panel data gravity model specifications

Past focus in the panel gravity literature has been on multidimensional fixed effects specifications in an effort to accommodate heterogeneity. After introducing conventional multidimensional fixed effects, we find evidence of cross-sectional dependence in flows. We propose a simultaneous dependence gravity model that allows for network dependence in flows, along with computationally efficient Markov Chain Monte Carlo estimation methods that produce a Monte Carlo integration estimate of log-marginal likelihood useful for model comparison. Application of the model to a panel of trade flows points to network spillover effects, suggesting the presence of network dependence and biased estimates from conventional trade flow specifications. The most important sources of network dependence were found to be membership in trade organizations, historical colonial ties, common currency and spatial proximity of countries.Series: Working Papers in Regional Scienc

Internal Migration between US States - A Social Network Analysis

In this paper we use the novel (at least in regional science) technique of social network analysis and apply it to one of the most analyzed topics in the discipline, US internal migration. We want to see whether social network analysis can yield any new insights into this well known process. We want to compare the technique to more conventional methods of analysis in migration. The paper will give an overview of recent literature about internal migration between US states and summarize the main findings. It will then present an overview of social network analysis, define key concepts and describe the main components of the technique. This discussion will also involve a discussion of currently available software for social network analysis. Then, we will apply the technique to the official data about internal migration between US states as published by the US bureau of the census, to see whether the technique can reproduce the main results of the traditional techniques and whether it can yield any new insights.