While spatial autoregressive (SAR) models are increasingly used in population-level psychological studies, researchers often overlook the crucial step of parsing effects into direct, indirect and total impacts, a standard practice in spatial econometrics. In this paper, we demonstrate the necessity of this practice by re-analyzing Gruda et al.'s (2024) U.S. Dark-Triad and health dataset with heteroskedasticity-robust SAR models and full impact decomposition, revealing significant changes. The previously observed direct protective effect of state-level narcissism on hypertension mortality disappeared when accounting for interstate spillovers. Conversely, the association with lower cancer prevalence and depression strengthened. Several health-behaviour findings reversed direction, indicating naïve regressions conflated within- and between-state effects. Machiavellianism and psychopathy coefficients also shifted. These results demonstrate that spatial spillovers can dilute, negate or reverse local effects, cautioning against policy inferences based solely on direct estimates.

Amid slowing urbanisation, tightening climate constraints and growing fiscal pressures, the spatial consequences of public policy have become a central concern in urban and regional research. Yet most empirical studies still represent policy exposure with coarse buffers, administrative units or stylised scenarios, which makes it difficult to disentangle the effects of overlapping instruments and governance arrangements. This review synthesises peer-reviewed work published mainly between 2020 and 2025 that explicitly links public policies—particularly land-use regulation, transport and mobility interventions, environmental and climate policies, and selected social and health measures—to spatially explicit outcomes such as land prices, urban form, emissions and socio-spatial inequality. Drawing on Web of Science and Scopus searches complemented by targeted snowballing, we retain studies that (i) conceptualise policy as a spatially delimited intervention and (ii) employ explicit spatial indicators of exposure and outcome. Within this corpus, the Policy Spatial Footprint (PSF) framework is highlighted as one representative approach that converts legal and planning clauses into auditable geometries with time stamps and intensity levels and, in the Yangtze River Delta case, combines network-time exposure with staggered difference-in-differences models to identify land-value capitalisation effects. Across domains, we find persistent sectoral fragmentation, short time horizons and a marked geographical bias towards large cities in Europe, North America and China, with small cities, peri-urban areas and the Global South under-represented. Methodologically, recent studies advance spatial econometrics, quasi-experimental designs, remote sensing and digital-twin infrastructures, but open, standardised spatial policy datasets remain rare. The review proposes a policy–space–outcome framework anchored by PSF, outlines priorities for multi-scale causal designs, open PSF repositories and comparative governance research, and argues that integrating resilience, justice and digitalisation is essential for evaluating how policy packages shape spatial development trajectories.

Aquavoltaics policy has been introduced in Taiwan to promote the integration of solar photovoltaic facilities on aquafarms. To explore the effects of the aquavoltaics policy on aquafarm price and small-scale aquaculture, we collected data on aquaculture and renewable energy materials. Subsequently, three groups of factors that influence the use of aquafarms (land, aquaculture, and renewable energy attributes) were analyzed using the hedonic price model to examine the effects of the aquavoltaics policy on aquafarm prices. We employed spatial econometrics models to estimate each variable's influence and analyze the factors that affect aquafarm prices, as well as the possible effects of implementing an aquavoltaics policy. The empirical results indicate that the implementation of the Two-Year Solar Promotion Plan has led to an approximately 10% increase in aquafarm prices, reflecting the policy’s influence on land valuation and market expectations. Variables such as distance to urban areas, proximity to feeder lines, shellfish farming and empty ponds were found to significantly affect aquafarm prices. These findings suggest that when aquavoltaics policies are implemented in regions dominated by small-scale aquaculture, a systematic approach to aquafarm use and pricing is required. Moreover, developing integrated energy blueprints and aquavoltaic plans that balance economic, environmental, and fishery objectives is essential for achieving synergy between the fishery and renewable energy sectors.

Modeling Active Transportation Demand using GIS-Integrated Spatial Econometrics to Evaluate Infrastructure Accessibility, Sustainability, and Equity in Urban Mobility

Empirical studies on the geography of digital economic activities are currently lacking. This is due to digital economic activities remaining largely undefined in official economic statistics. This paper introduces a novel empirical pipeline to examine the spatial characteristics of the digital economy while addressing the challenges of data missingness. Firstly, we identify digital economic activities by using commercial websites and Natural Language Processing (NLP). Secondly, we study the geographical distribution of digital firms, as well as the mechanisms causing this distribution, through considering firms as the realisation of a latent spatial Poisson Point Process. In doing so, this paper enhances our understanding of urban processes by combining data created through advanced NLP techniques with spatial econometrics. Focusing on the case of London, UK, we identify digital economic activities by applying contextualized weak supervision to text scraped from firms’ websites. By doing so, we showcase how websites can complement, or even substitute official economic statistics, leading to a more complete understanding of the digital economy. Using this data, we proceed to inferring the causes of firms’ locations in space: indeed, firms can locate in space for exogenous reasons, such as the presence of infrastructure and public incentives, or endogenous reasons, such as knowledge spillovers. We base our analysis on estimating the inhomogeneous K-function, quantifying the spatial dependency between firms. Our study reveals a tendency for digital firms to cluster due to the importance of in-person interactions that cannot be explained simply by exogenous factors such as the attractiveness of the location. To our knowledge, the paper provides the first empirical evidence uncovering the persisting relevance of space and face-to-face interactions in the digital economy, prompting reflections on the geographical footprints of digitality.

ABSTRACT In this paper, we attempt to introduce peer effects as a new channel in pricing emerging markets credit default swap spreads and study the impact of peer effects on 17 countries for the period 2006–2022. Unlike spillover models, we exploit spatial econometrics to distinguish between direct (country‐specific) and indirect (non‐country‐specific) effects in the credit default swap spreads. We are motivated by the fact that the connectedness among emerging market credit default swaps is proportionally high based on the similarity concerning the dimensions of economic development, governance and uncertainty. Adopting a spatial modelling strategy allows us to consider such similarity to unravel non‐country‐specific channels driving the shifts in sovereign credit risk. On top of documenting significant spatial interactions, we find that indirect effects are roughly as important as the direct ones in explaining the credit default swap spread movements. Our findings are robust to a set of additional analyses and modelling choices. The findings underpin a plethora of attempts on the importance of coordinated policy actions in the international regulatory fora to alleviate sovereign risk. This paper also calls for careful use of credit default swap spreads as a sovereign credit risk indicator. After all, these measures are already a cost indicator but the idiosyncratic risk may be quite different.

This study combines spatial econometric models with intelligent optimization algorithms to explore the spatial distribution characteristics of China’s carbon emissions and their optimization and regulation mechanisms. It aims to improve the operational efficiency of regional multi-microgrid systems under the constraints of energy conservation and emission reduction. The Moran index is used to analyze spatial autocorrelation based on China’s carbon emission data from 2013 to 2023. The results show that the spatial agglomeration of carbon emissions is strengthening year by year. In addition, the study constructs a three-layer multi-microgrid control system and adopts an improved whale optimization algorithm for scheduling optimization. On 10 standard test functions, the average error value of the improved algorithm is less than 0.0023, which is about 31.4% lower than that of the original algorithm. Meanwhile, the improved algorithm’s performance is better than other similar algorithms on most functions. In the actual scheduling simulation, during daytime hours with abundant renewable energy, Microgrid 1 achieves a minimum operating cost of 214.9 yuan, which is 1.3% lower than that of Microgrid 2 (217.65 yuan). Moreover, the environmental emission cost is reduced to 54.47 yuan. This study enhances the low-carbon scheduling capability of multi-microgrid systems; it also provides theoretical support and policy references for realizing regional collaborative emission reduction and the national carbon neutrality strategy.

The article examines the production function with Constant Elasticity of Substitution (CES), particularly its special case – the Cobb-Douglas production function – which assumes an elasticity of substitution equal to unity. In many works, the assumption of a unitary elasticity of substitution is challenged, and it is noted that estimates vary depending on the characteristics of the economy under study and the analysis horizon, and can be both significantly lower and higher than unity. The purpose of the study is to test the hypothesis about the possibility of using the Cobb-Douglas production function to model economic processes at the regional level in the Russian Federation. The CES production function, which depends on two factors – labor and capital (accounting for Hicks-neutral technological progress) – is examined. The assumption that the constant elasticity of substitution of production factors equals unity is tested using statistical data from the Rosstat website for 80 regions of the Russian Federation for the period from 2010 to 2022. The methodology includes panel data analysis to determine the elasticity of substitution between capital and labor, as well as the application of spatial econometrics models that allow spatial effects to be taken into account to minimize bias in estimates due to interregional heterogeneity. The results of the evaluation of panel data models with the inclusion of spatial effects and control variables do not reject the proposed hypothesis and indicate the applicability of the Cobb-Douglas production function for modeling the economic development of Russian regions.

ABSTRACT Frequent global geopolitical conflicts, climate change and food security are threatening the global human living environment. This study aims to investigate the spatial and temporal dynamic evolution and spatial correlation between agricultural mechanization and agricultural energy efficiency in China in the context of sustainable development, and to explore whether agricultural mechanization in China can contribute to the improvement of agricultural energy efficiency in China. Based on panel data from 30 provinces in China from 2010 to 2022, this study calculated China's agricultural energy efficiency and agricultural mechanization levels, and used spatial analysis methods to explore the spatiotemporal dynamics of these two factors. Furthermore, the Spatial Durbin Model (SDM) was used to analyze the impact of agricultural mechanization on agricultural energy efficiency at the provincial level. The results show that China's total agricultural energy consumption has been increasing annually, with a shift in energy structure from indirect to direct energy. Agricultural energy efficiency has generally improved, but significant regional differences persist. Between 2010 and 2022, agricultural mechanization exhibited clear spatial correlation and agglomeration effects. Prior to 2014, agricultural energy efficiency showed no spatial correlation, but after 2014, spatial correlation gradually emerged. A U‐shaped relationship exists between agricultural mechanization and agricultural energy efficiency: initially, higher mechanization is negatively correlated with energy efficiency, but after reaching a critical point, this correlation becomes positive. This study innovatively combines the EBM‐DEA model with spatial econometrics to more comprehensively capture efficiency measures and spatial spillover effects. It identifies and verifies the U‐shaped nonlinear relationship between agricultural mechanization and agricultural energy efficiency in China. The study also reveals significant regional differences and spatial agglomeration patterns in both agricultural mechanization and agricultural energy efficiency, enriching theoretical and empirical research in the field of agricultural energy efficiency. The study concludes that the promotion of agricultural mechanization should be combined with the promotion of energy‐saving equipment, the utilization of renewable energy, and regionally differentiated policies to achieve the goal of sustainable agricultural development.

Identifying the determinants of the energy transition in departments in Colombia: An analysis with spatial econometrics

With the rapid advancements in technology for data collection, the application of the spatial autoregressive (SAR) model has become increasingly prevalent in real-world analysis, particularly when dealing with large datasets. However, the commonly used quasi-maximum likelihood estimation (QMLE) for the SAR model is not computationally scalable to handle the data with a large size. In addition, when establishing the asymptotic properties of the parameter estimators of the SAR model, both weights matrix and regressors are assumed to be nonstochastic in classical spatial econometrics, which is perhaps not realistic in real applications. Motivated by the machine learning literature, this article proposes quasi-score matching estimation for the SAR model. This new estimation approach is developed based on the likelihood, but significantly reduces the computational complexity of the QMLE. The asymptotic properties of parameter estimators under the random weights matrix and regressors are established, which provides a new theoretical framework for the asymptotic inference of the SAR-type models. The usefulness of the quasi-score matching estimation and its asymptotic inference is illustrated via extensive simulation studies and a case study of an anti-conflict social network experiment for middle school students.

ABSTRACT Terrorism and the resulting shocks in a country can likely trigger feelings of insecurity, apprehension, and fear among investors. Thus, the intensification of terrorist activities in a particular region is likely to increase the rate of investment outflows in neighboring countries. As a result, the present study aimed to investigate the impacts of terrorist activities on investment security in a select group of 18 countries from 2005 to 2020 by using spatial econometrics. Therefore, we conducted the necessary tests to determine the spatial effects before estimating the model. Once we confirmed the existence of spatial effects, we selected the Spatial Durbin Model from competing spatial models to apply it to the selected group of countries. The model estimation results revealed a significant impact of terrorism and related activities on the outflow rate of foreign direct investment in the selected group of countries, both in the target country and its neighboring areas. In other words, the escalation of insecurity in a particular region posed a threat to investment security, resulting in the outflow of investors from the target country and its surrounding areas. Furthermore, the study demonstrated a significant negative impact of the democracy index on outward foreign direct investment in the target and neighboring countries, while the structural vulnerability index, political risk, and corruption indices significantly influenced the Outward Foreign Direct Investment rate.

Water and soil resources (WSRs) determine the healthy development of the socio-economic systems. This research seeks to clarify the spatiotemporal evolution characteristics, spatial spillover effects, and key constraint factors influencing the comprehensive carrying capacity (CCC) of WSR in the Yellow River (YR) Basin from 2012 to 2023, thereby supporting the healthy development of the river basin. Based on the structural relationships among the internal elements of this system, the entropy method and an extensible cloud model are employed in this study to evaluate the WSR-CCC. Based on the estimation theory and spatial econometrics methods, the temporal and spatial evolution process of WSR-CCC was explored, and the obstructive factors were analyzed. We made the following discoveries: (1) The WSR-CCC demonstrates a fluctuating upward tendency, gradually moving from critical overload level IV to sustainable level II, but inter-provincial disparities expand. (2) The spatial pattern exhibits a gradient of higher levels in the western region, lower levels in the eastern region, stronger intensity in the northern region, and weaker intensity in the southern region, with weak spatial correlation. However, the spatial spillover effect is significant, with club convergence and the Matthew effect coexisting. (3) The obstacle factors exhibit a drive–influence–state three-stage dominant characteristic. The findings provide actionable insights for coordinating WSR optimization and ecological conservation.

The administration of the Measles, Mumps, and Rubella (MMR) vaccination has had a substantial impact on controlling the spread of measles on a global scale. Nevertheless, the COVID-19 pandemic caused major disruptions to normal immunization schedules, causing the omission or delay of routine immunizations. Expanding on previous research that simulated measles outbreaks using a detailed agent-based model, this study integrates epidemiological forecasts with spatial econometrics analysis. Our objective is to quantify the household-level direct and indirect health and economic impact of measles outbreaks caused by reduction in MMR vaccine uptake. A network-based SEIR (susceptible-exposed-infected-recovered) model is used to simulate the transmission of measles over a synthetic social contact network of Virginia, under various scenarios. Household-level costs of measles outbreak, encompassing MMR vaccine expenses, treatment costs, and productivity losses, are estimated from the simulation results. A Generalized Spatial Autoregressive (GSAR) model is used to estimate the spatial ‘spillover effect’ on neighboring counties. Our findings indicate that reduced MMR vaccination rates are associated with increased measles cases and related economic costs, which are intensified by disease transmissibility and moderated by home quarantine. The GSAR model, with spatial lag coefficients, shows significant spatial interdependencies. A small decrease in vaccination rate in an urban region like Richmond, Virginia, has significant economic and epidemiological spillover effect, while similar reductions in rural regions like Highland County, Virginia, have a negligible impact. A decline in MMR vaccination rate has ramifications for both disease incidence and the economy, presenting diverse consequences influenced by regional disparities. Policymakers should acknowledge the interconnectedness of health and economic outcomes across regions. This research underscores the necessity of implementing broad, region-wide policy measures in response to fluctuations in vaccination rates, prioritizing overarching strategies over localized interventions.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-21097-0.

This study investigates the transformative impacts of the 15th National Games and the National Para Games on the evolution of cultural and tourism industries across Guangdong, Hong Kong, and Macao—marking the first mega-sporting event jointly staged under the "one country, two systems" framework. Drawing upon event system theory and spatial econometrics, the paper constructs a Spa-tial Event Spillover Framework (SESF) to capture how infrastructural enhance-ment, cultural valorization, and institutional coordination interact to generate both direct growth and interregional diffusion effects. Using dynamic spatial Durbin models and five-year panel data (2020–2025), the findings reveal a 12.7% increase in cultural–tourism value-added in host cities and a significant 3.8% positive spillover within a 50-kilometer radius, driven largely by cross-boundary connectivity and governance collaboration. Mediation analysis further shows that 41% of the total effect operates through improved transport accessibility and digital integration, while the intensity of institutional coopera-tion amplifies these gains. The results illuminate a "dual-core radiation" pattern centered on Guangzhou and Foshan, signaling a structural shift from fragmented local development toward an integrated, polycentric cultural economy. The study advances theoretical discourse by embedding spatial dependency into event system theory and offers a replicable methodological framework for eval-uating how mega-events catalyze sustainable cultural transformation in mul-ti-jurisdictional regions.

Spatial spillovers and ecological awareness (EPI) in EU renewable energy transition: Implications for environmental management.

Sustainable tourism development has emerged as a strategic priority across ASEAN countries, yet the role of green innovation and environmentally responsible investment in shaping tourism outcomes remains underexplored. Existing studies often overlook the spatial interdependencies that characterize regional integration and cross-border environmental dynamics. This study investigates how green patents and green foreign direct investment (FDI) influence sustainable tourism development, both within and across ASEAN nations. Drawing on endogenous growth theory, ecological modernization, and FDI spillover frameworks, the analysis employs a Spatial Durbin Model (SDM) using panel data from 2000 to 2023. The findings reveal that green innovation and green FDI significantly enhance tourism development, with notable spatial spillover effects that benefit neighboring countries. These effects are most pronounced in leading ASEAN economies, where institutional capacity and absorptive readiness amplify the impact of green practices. The relationship is further shaped by economic growth, human capital, and political stability, while environmental degradation and inflation pose constraints. The study underscores the nonlinear and regionally heterogeneous nature of green tourism development, offering policy insights for fostering inclusive, resilient, and environmentally sustainable tourism strategies across ASEAN.

Rural entrepreneurship is a key way to combat rural decline and promote the revitalization of rural areas and their sustainability, and also a key area of research in agricultural and rural geography, economics, and management. We combined spatial econometrics models such as spatial clustering, cold and hot spot analysis, geographical weighted regression and Geodetector to carry out empirical research on geographical distribution of rural entrepreneurship in Anhui province, in an attempt to provide scientific basis for rural policy design, spatial planning and evidence-based decision-making. The findings showed an increasing trend of the spatial heterogeneity and autocorrelation of rural entrepreneurship in Anhui, with geographic clustering of high, medium and low values as well as cold and hot spots. And the diversification of rural entrepreneurship changes led to a very complex driving mechanism for the generation and evolution of rural entrepreneurship spatial patterns, and the factors showed significant spatial and composite effects. The enlightening value of the analysis results lies in the fact that rural entrepreneurship management not only needs to delineate geographical zones and design differentiated policies, but also needs to jointly build rural entrepreneurship alliances in similar or adjacent areas to integrate regional entrepreneurial resources. In addition, rural entrepreneurship management should be guided according to the situation, and policy design should take into account both quantity and speed control, with establishment of policy combinations based on the spatial and composite effects of different factors.

Cross-border mergers and acquisitions activity in the tourism industry: A spatial econometrics analysis

ABSTRACT This study examines the impact of production network clusters (PNCs), derived through network science methods, on German counties’ economic development using a complex systems approach, conceptualising trade as information flows that guide economic agents’ decisions. Employing spatial econometrics, it finds that PNC trade flows predict regional economic synchronisation, though effects are not always positive. While results indicate that PNCs synchronise agents’ decisions within the same cluster, they may desynchronise their decisions with agents in spatially linked areas. These findings contribute to advancing a complexity economics framework for understanding regional development dynamics and disparities in Germany.