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Mathematics
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Mathematical Economics and Spatial Econometrics
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Mathematical Economics and Spatial Econometrics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: 1 September 2024 | Viewed by 4358

Special Issue Editors

Dr. Long Liu

E-Mail Website
Guest Editor
Department of Economics, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA
Interests: panel data econometrics; high-dimensional econometrics; applied microeconomics
Dr. Donald Lien

E-Mail Website
Guest Editor
Department of Economics, College of Business, University of Texas at San Antonio, One University Circle, San Antonio, TX 78249, USA
Interests: finance; econometrics; development economics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, spatial econometrics has attracted the interest of many researchers in fields such as economics, finance, accounting, management, and statistics. The purpose of this Special Issue is to contribute to the development of new methods in spatial econometrics and to their rapid diffusion in the scientific community. Theoretical and applied studies with methodological advances in spatial econometrics and statistics can be submitted. We invite authors to submit original research articles and high-quality review articles in areas of interest including but not limited to the following: spatial models and social network effects, spatial weight matrix, testing on spatial dependence, the factor loading model, interactive fixed effects in panel data, time series correlation in the spatial model, the static and dynamic spatial panel data model, Bayesian spatial econometric models, and computational and software issues relevant to spatial econometrics.

Dr. Long Liu
Dr. Donald Lien
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • spatial models and social network effects
  • spatial weight matrix
  • testing on spatial dependence
  • factor loading model
  • interactive fixed effects in panel data
  • time series correlation in the spatial model
  • static and dynamic spatial panel data model
  • Bayesian spatial econometric models
  • computational and software issues relevant to spatial econometrics

Published Papers (4 papers)

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Research

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33 pages, 4891 KiB  
Article
Advancing Green TFP Calculation: A Novel Spatiotemporal Econometric Solow Residual Method and Its Application to China’s Urban Industrial Sectors
by Xiao Xiang and Qiao Fan
Mathematics 2024, 12(9), 1365; https://doi.org/10.3390/math12091365 - 30 Apr 2024
Viewed by 406
Abstract
The Solow residual method, traditionally pivotal for calculating total factor productivity (TFP), is typically not applied to green TFP calculations due to its exclusion of undesired outputs. Diverging from traditional approaches and other frontier methodologies such as Data Envelopment Analysis (DEA) and Stochastic [...] Read more.
The Solow residual method, traditionally pivotal for calculating total factor productivity (TFP), is typically not applied to green TFP calculations due to its exclusion of undesired outputs. Diverging from traditional approaches and other frontier methodologies such as Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA), this paper integrates undesired outputs and three types of spatial spillover effects into the conventional Solow framework, thereby creating a new spatiotemporal econometric Solow residual method (STE-SRM). Utilizing this novel method, the study computes the industrial green TFPs for 280 Chinese cities from 2003 to 2019, recalculates these TFPs using DEA-SBM and Bayesian SFA for the same cities and periods, and assesses the accuracy of the STE-SRM-derived TFPs through comparative analysis. Additionally, the paper explores the statistical properties of China’s urban industrial green TFPs as derived from the STE-SRM, employing Dagum’s Gini coefficient and spatial convergence analyses. The findings first indicate that by incorporating undesired outputs and spatial spillover into the Solow residual method, green TFPs are computable in alignment with the traditional Solow logic, although the allocation of per capita inputs and undesired outputs hinges on selecting the optimal empirical production function. Second, China’s urban industrial green TFPs, calculated using the STE-SRM with the spatial Durbin model with mixed effects as the optimal model, show that cities like Huangshan, Fangchenggang, and Sanya have notably higher TFPs, whereas Jincheng, Datong, and Taiyuan display lower TFPs. Third, comparisons of China’s urban industrial green TFP calculations reveal that those derived from the STE-SRM demonstrate broader but more concentrated results, while Bayesian SFA results are narrower and less concentrated, and DEA-SBM findings sit between these extremes. Fourth, the study highlights significant spatial heterogeneity in China’s urban industrial green TFPs across different regions—eastern, central, western, and northeast China—with evident sigma convergence across the urban landscape, though absolute beta convergence is significant only in a limited subset of cities and time periods. Full article
(This article belongs to the Special Issue Mathematical Economics and Spatial Econometrics)
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22 pages, 356 KiB  
Article
Effect of Collaborative Innovation on High-Quality Economic Development in Beijing–Tianjin–Hebei Urban Agglomeration—An Empirical Analysis Based on the Spatial Durbin Model
by Jing Deng, Tiantian Chen and Yun Zhang
Mathematics 2023, 11(8), 1909; https://doi.org/10.3390/math11081909 - 18 Apr 2023
Cited by 5 | Viewed by 1205
Abstract
High-quality economic development is an innovation-driven economy, and collaborative innovation is key to maximizing its effects. In terms of the influence of cooperative innovation of urban agglomerations on high-quality economic development, urban agglomerations are of considerable relevance to the coordinated development of China’s [...] Read more.
High-quality economic development is an innovation-driven economy, and collaborative innovation is key to maximizing its effects. In terms of the influence of cooperative innovation of urban agglomerations on high-quality economic development, urban agglomerations are of considerable relevance to the coordinated development of China’s regional economy. This research established an evaluation system of high-quality economic development indicators for the Beijing–Tianjin–Hebei urban agglomeration based on panel data of 13 cities from 2003 to 2020, and then estimated the level of high-quality development of each city’s economy. The spatial Durbin model was used in this article to examine the effects of collaborative innovation on the high-quality development of the economy. The findings indicated that, although high-quality economic development was increasing across the board in the Beijing–Tianjin–Hebei urban agglomeration, it varied greatly between the individual cities. Beijing and Tianjin had much higher levels of high-quality economic development than the other cities in Hebei, and there was some variation within the Hebei cities as well. The high-quality economic development of the Beijing–Tianjin–Hebei urban agglomeration exhibited no spatial correlation characteristics under the weight of geographical distance. However, there was an aggregation effect on the differential relationship of economic development, which was also significant under the dual influence of economic geography. The collaborative innovation of Beijing–Tianjin–Hebei urban agglomeration could promote the high-quality economic development of both the inner and surrounding cities, and could also improve the high-quality economy development level of the overall urban agglomeration. Full article
(This article belongs to the Special Issue Mathematical Economics and Spatial Econometrics)
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16 pages, 435 KiB  
Article
High-Dimensional Distributionally Robust Mean-Variance Efficient Portfolio Selection
by Zhonghui Zhang, Huarui Jing and Chihwa Kao
Mathematics 2023, 11(5), 1272; https://doi.org/10.3390/math11051272 - 6 Mar 2023
Cited by 2 | Viewed by 1468
Abstract
This paper introduces a novel distributionally robust mean-variance portfolio estimator based on the projection robust Wasserstein (PRW) distance. This approach addresses the issue of increasing conservatism of portfolio allocation strategies due to high-dimensional data. Our simulation results show the robustness of the PRW-based [...] Read more.
This paper introduces a novel distributionally robust mean-variance portfolio estimator based on the projection robust Wasserstein (PRW) distance. This approach addresses the issue of increasing conservatism of portfolio allocation strategies due to high-dimensional data. Our simulation results show the robustness of the PRW-based estimator in the presence of noisy data and its ability to achieve a higher Sharpe ratio than regular Wasserstein distances when dealing with a large number of assets. Our empirical study also demonstrates that the proposed portfolio estimator outperforms classic “plug-in” methods using various covariance estimators in terms of risk when evaluated out of sample. Full article
(This article belongs to the Special Issue Mathematical Economics and Spatial Econometrics)
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Review

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31 pages, 472 KiB  
Review
A Survey of Spatial Unit Roots
by Badi H. Baltagi and Junjie Shu
Mathematics 2024, 12(7), 1052; https://doi.org/10.3390/math12071052 - 31 Mar 2024
Viewed by 468
Abstract
This paper conducts a brief survey of spatial unit roots within the context of spatial econometrics. We summarize important concepts and assumptions in this area and study the parameter space of the spatial autoregressive coefficient, which leads to the idea of spatial unit [...] Read more.
This paper conducts a brief survey of spatial unit roots within the context of spatial econometrics. We summarize important concepts and assumptions in this area and study the parameter space of the spatial autoregressive coefficient, which leads to the idea of spatial unit roots. Like the case in time series, the spatial unit roots lead to spurious regression because the system cannot achieve equilibrium. This phenomenon undermines the power of the usual Ordinary Least Squares (OLS) method, so various estimation methods such as Quasi-maximum Likelihood Estimate (QMLE), Two Stage Least Squares (2SLS), and Generalized Spatial Two Stage Least Squares (GS2SLS) are explored. This paper considers the assumptions needed to guarantee the identification and asymptotic properties of these methods. Because of the potential damage of spatial unit roots, we study some test procedures to detect them. Lastly, we offer insights into how to relax the compactness assumption to avoid spatial unit roots, as well as the relationship between spatial unit roots and other models, such as the Spatial Dynamic Panel Data (SDPD) model and Lévy–Brownian motion. Full article
(This article belongs to the Special Issue Mathematical Economics and Spatial Econometrics)
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