Applications of Optimal Transport to Economics and Related Topics

Table of Contents

1. Frontmatter

2. Theoretical Results

   1. Frontmatter

   2. Structural Model for US Gun Violence

      Arnab Bhattacharjee, Swagatam Sen

      Abstract

      The US has alarmingly high, and rising, gun violence and fatality rates. While it is generally believed that supply side policy is critical in addressing the problem, legislation has been relatively ineffective, for example the Gun Violence Prevention and Community Safety Act of 2020. Previous literature has identified hotspots and proximate determinants, particularly urban locations. Effective supply side policy would require application of optimal transport methods. We apply novel and current generation structural models to identify the spatial network for supply of guns and propagation of violence risks. This provides clean quantification of spatial supply chains and associated costs of transport between nodes, which are necessary for mitigation using optimal transport and logistics network management methods.

   3. Extending Jaynes: How Scientific and Economic Claims are Judged

      William M. Briggs

      Abstract

      ET Jaynes work on probability theory, which he subtitled the logic of science, should be much better known. We cast some light on a small segment of his work, demonstrating how logical probability can be used to analyze people judge scientific and economic pronouncements and claims of cause. This has important consequences in economics, and any area in which people are asked to believe a cause has been discovered or verified in science, especially when they are asked to act on the discovery.

   4. The A Priori Procedure for Estimating the Location Parameter Under Elliptical Settings

      Xiangfei Chen, Tonghui Wang, S. T. Boris Choy, David Trafimow, Tingting Tong

      Abstract

      The a priori procedure (APP) provides minimum sample sizes for estimating parameters of the population distribution that ensure precision and confidence in sample statistics. In this paper, we extend the APP to include the family of elliptical distributions, which is a member of a broad family of probability distributions and is an extension of the family of normal distributions. Properties of the elliptical distribution are discussed. Under the uncorrelated assumption and with a given precision and a confidence level, the desired sample size for estimating the location parameter is obtained for generalized elliptically symmetric logistic, symmetric Kotz Type, and t distributions, respectively. The confidence interval for the location parameter is constructed based on the desired sample size using elliptical distribution. Three real data examples are given to illustrate our main results. In addition, the Shinyapp program links for some of the elliptical distributions are provided for researchers and practitioners to use. In the program, the desired sample size is calculated.

   5. Estimation of Under-Reported COVID19 Cases with Susceptible-Infected-Removed Epidemiological Model via Stochastic Frontier Analysis

      Nene Coulibaly, Zheng Wei, Tonghui Wang

      Abstract

      As the COVID-19 pandemic has evolved, it has become increasingly evident that the actual number of cases has likely been underestimated. In this study, we review an econometric method to estimate the true scale of COVID-19 cases for 40 countries spanning from January 1, 2020, to November 3, 2020. The method centers around the ‘structural’ model, which is an expansion of the SIR epidemiological model, and is designed to incorporate the notion of underreporting. The findings of our analysis reveal substantial underreporting, aligning with prior research and expert opinions within the field of public health.

   6. AI and Econometric Modeling: Deep Reinforcement Learning in Predictive Modeling

      Do Huu Hai, Pham Van Tuan

      Abstract

      Artificial intelligence (AI) has significantly impacted many different industries, including finance and economics. These technologies are increasingly being used to improve economic forecasting and analysis, providing more accurate predictions and better decision-making. The article delves into the expanding use of artificial intelligence (AI) in economic forecasting and analysis, including subjects such as big data, predictive analytics, and econometrics. It will also examine the problems of using AI in econometrics research, as well as the future of these technologies. Traditional forecasting approaches rely on econometric models for economic forecasting and analysis. These models evaluate correlations between economic indicators such as GDP, inflation, and unemployment using statistical approaches and mathematical equations. However, these classic models have limitations in that they may not be able to explain more complex interactions between economic variables. Furthermore, they require a lot of data as well as certain assumptions about the structure of the model, which can affect their ability to adapt to changing economic conditions. The use of AI and Machine Learning (ML) in economics can help overcome these problems and improve the accuracy of predictions about future trends.

   7. Multivariate Quantiles: Geometric and Measure-Transportation-Based Contours

      Marc Hallin, Dimitri Konen

      Abstract

      Quantiles are a fundamental concept in probability and theoretical statistics and a daily tool in their applications. While the univariate concept of quantiles is quite clear and well understood, its multivariate extension is more problematic. After half a century of continued efforts and many proposals, two concepts, essentially, are emerging: the so-called (relabeled) geometric quantiles, extending the characterization of univariate quantiles as minimizers of an L\(_1\) loss function involving the check functions, and the more recent center-outward quantiles based on measure transportation ideas. These two concepts yield distinct families of quantile regions and quantile contours. Our objective here is to present a comparison of their main theoretical properties and a numerical investigation of their differences.

   8. Human Centered AI for Financial Decisions

      Polina Khrennikova

      Abstract

      We survey the state of the art of AI applications to financial expectations and the role quantum logic can play in further advancements of AI technologies. We discuss financial applications of such machine learning techniques as reinforcement learning and deep neural networks to the analysis of financial statements, algorithmic trading, portfolio management, and robo-advising. Next, we elaborate on the emergence and advancement of QML (quantum machine learning) and advocate for the wider exploration of the advantages of quantum inspired neural networks, steaming from the use of quantum logic that is able to capture agents’ non- classical expectations and non expected utility decisions, also coined “bounded rationality”. We would like to motivate to use human—like AI techniques that are centered on quantum, rather than classical logic to (i) represent the human brain type information processing; (ii) speed up the work of the AI algorithms; (iii) better operate in complex and uncertain environments.

   9. Digital Economy, Labor Mobility and Industrial Structure Optimization—Empirical Analysis Based on Mediating Effect and Threshold Effect

      Jianxu Liu, Zhidan Shen, Yansong Li

      Abstract

      Using the provincial panel data in China from 2014 to 2021, this paper examines the effects and paths of digital economy and labor mobility on industrial structure optimization, based on the construction of industrial structure upgrading index and digital economy comprehensive development level index. The mediation effect model and the panel threshold model are used in the analysis process. The empirical results show that: ① Digital economy can promote the optimization and upgrading of industrial structure by facilitating the mobility of labor. ② Adopting the threshold model, this paper finds that the effect of digital economy on the optimization of industrial structure presents non-linear characteristics. ③ Both digital economy and industrial structure are characterized by heterogeneity in terms of regional distribution. Therefore, we can conclude that in order to realize the goal of high-quality development, it is necessary to actively promote the balanced development of the digital economy. We are supposed to further improve the relevant labor market policies to promote the coordinated development of the industrial structure and the digital economy.

   10. Bayesian Model Selection Among Dispersed Integer-Valued Time Series Models

       Feng-Chi Liu, Cathy W. S. Chen, Hsiao-Han Hsu

       Abstract

       This research evaluates model selection within a class of integer-valued time series models that feature overdispersion and extends these models to their generalized forms. The newly introduced models include: (1) dispersed integer-valued GARCH models incorporating negative binomial, double Poisson, or generalized Poisson distributions, and (2) a Double Log-form integer-valued GARCH model. The latter model avoids over-restrictions in the parameter space. We estimate parameters and select models within the Bayesian framework using adaptive Markov chain Monte Carlo (MCMC) sampling schemes, and employ the deviance information criterion (DIC) for model selection. We also design simulation studies to examine estimation accuracy and potential model misspecification. Using monthly crime counts in Bankstown, New South Wales, Australia, for an empirical illustration, our findings highlight the ability to select the most promising models among the competing ones based on DIC.

   11. Forecasting GDP with Many Predictors Using Sparse-Group LASSO MIDAS

       Wasin Siwasarit

       Abstract

       We conducted an investigation into four econometric models designed to handle mixed-frequency data. Our primary objective is to leverage a vast array of monthly macroeconomic variables to enhance the accuracy of forecasting quarterly Gross Domestic Product (GDP). To achieve this, we compared the following models: (1) The Autoregressive (AR) model, (2) The Mixed Data Sampling (MIDAS) model, which enables the combination of data at different frequencies, (3) The Lasso-MIDAS model, as proposed by [27], aimed at addressing issues related to inconsistent data frequencies and the curse of dimensionality arising from high-dimensional data, (4) the Sparse-group LASSO model, introduced by [3], which accommodates for the mixing processes and recognizes that the financial and the macroeconomic data may have heavier than exponential tails. An empirical analysis of forecasting GDP growth reveals that the sparse-group LASSO model consistently outperforms other models when forecasting four steps ahead, both before and after COVID-19 episodes. For short-term forecasting, both the MIDAS and sparse-group LASSO models exhibit favorable performance compared to alternative approaches. When comparing our findings before and after the COVID-19 episodes, it becomes evident that the MIDAS model significantly outperforms other models when incorporating COVID-19 data. Utilizing high-frequency data without any form of regularization appears to play a substantial role in improving forecasting performance, particularly during abrupt economic downturns. In essence, these two models can serve as an alternative “benchmark” for forecasting when sudden economic fluctuations occur, rendering conventional models like the AR model quickly outdated.

   12. On Disintegration of Measures in Optimal Transport

       Hung T. Nguyen

       Abstract

       As part of a prelude to the applications of optimal transport theory to econometrics and machine learning, this tutorial paper focus on the notion of disintegration in measure theory in the analysis of Wassersrein metrics which are useful, in particular, for machine learning and financial risks. An elementary exposition on using disintegration to prove that Waserstein divergence is a bona fide metric is provided.

   13. Why Micro-funding? Why Small Businesses Are Important? Analysis Based on First Principles

       Hien D. Tran, Edwin Tomy George, Vladik Kreinovich

       Abstract

       On the one hand, in economics, there is a well-known and well-studied economy of scale: when two smaller companies merge, it lowers their costs and thus, makes them more effective and therefore more competitive. At first glance, this advantage of big size would make economy dominated by big companies—but in reality, small business remain a significant and important economic sector. Similarly, it is well known and well studied that research collaboration enhances researchers’ productivity—but still a significant portion of important results come from individual efforts. In several applications areas, there are area-specific explanations for this seemingly contradictory phenomenon. In this paper, we provide a general explanation based on first principles. Our reasoning also leads to a new explanation of the ubiquity of Zipf’s Law—a law that describes, e.g., the distribution of companies by size.

   14. Local-Global Support for Earth Sciences: Economic Analysis

       Uyen Hoang Pham, Aaron Velasco, Vladik Kreinovich

       Abstract

       Most funding for science comes from taxpayers. So, it is very important to be able to convince taxpayers that this funding is potentially beneficial for them. This task is easier in Earth sciences, e.g., in meteorology, where there are clear local benefits. The problem is that while many people support local studies focused on their region, they do not always have a good understanding of the fact that effective local benefits require also studying surrounding areas—and what should be the optimal balance between local and (more) global studies. In this paper, on a (somewhat) simplified model of the situation, we explain what is the appropriate balance. We hope that the corresponding methodology can (and will) be applied to more realistic—and thus, more complex—local-global models as well.

   15. Approximate Stochastic Dominance Revisited

       Chon Van Le, Olga Kosheleva, Vladik Kreinovich

       Abstract

       According to decision theory, in general, to recommend the best of possible actions, we need to know, for each possible action, the probabilities of different outcomes, and we also need to know the decision maker’s utility function—that describes his/her preferences. For some pairs of probability distributions, however, we can make such a recommendation without knowing the exact form of the utility function—e.g., in financial applications, we only need to know that a larger amount is preferable to a smaller one. Such situations, when we can make decisions based only on the information about probabilities, are known as stochastic dominance. The usual analysis of such situations is based in the idealized assumption that any difference in utility, no matter how small, is important. In reality, very small changes in utility value are irrelevant. From this viewpoint, if the utility corresponding to the distribution \(F_2(x)\) is always either larger or only slightly smaller than the utility corresponding to \(F_1(x)\), then we can still conclude that the second action is better (or of the same quality) than the first action. In this paper, we show how to describe such approximate stochastic dominance in precise terms.