Spatial econometrics has been widely used in the Chinese literature for more than 20 years. Spatial econometric models can be found in many disciplinary fields, which on the one hand denotes the rapid popularity of spatial econometric models and on the other hand indicates the wide range of applications of spatial econometric models. However, because spatial econometrics covers a wide range of knowledge in geography, econometrics, and geographic information systems, it is a typical interdisciplinary discipline. Hence, quite a lot of problems have arisen in its application. This paper systematically summarizes the most common problems of spatial econometric models in empirical studies, as well as more in-depth explanations in these problems, in an effort to help economics and social sciences researchers correctly apply these spatial econometric models. This paper first introduces the concept of spatial effects, which are the core of spatial data analysis and spatial econometric models; then discusses some problems of spatial weight matrices in empirical analysis, including the advantages and disadvantages of various types of spatial weights matrices, as well as the importance of matrix standardization; then summarizes the most common problems in drawing thematic choropleth maps, especially the advantages and disadvantages of various classification methods. The article then focuses on spatial autocorrelation analysis, including the important notes in application of the Moran's I test and the differences and linkages between Moran's I statistic and spatial autoregressive coefficient. Finally, it summarizes and analyzes the main problems of spatial econometric models in empirical analysis, including the scope of application of different spatial econometric models, whether to consider multiple spatial interaction effects in the models, and how to select the appropriate spatial weights matrix to construct spatial econometric models. In addition, it also introduces the scale and hypothesis testing of the GWR model in empirical applications.

Spatial econometric models can be used to capture spatial dependence within data. These models have found extensive application in disciplines such as economics, management and network analyses. Bayesian methods, such as Markov Chain Monte Carlo algorithms, have addressed many limitations of classical approaches, hence significantly advancing both theoretical and applied research. With the growing availability of large datasets and advancements in computational methods, Bayesian estimation methods are required not only to provide accurate estimates but also to balance computational efficiency. This study examines three state-of-the-art Bayesian methods, i.e., Hamiltonian Monte Carlo (HMC), Integrated Nested Laplace Approximations (INLA), and Variational Inference (VI). Various Monte Carlo simulation experiments were conducted to evaluate the performance of them under different sample sizes and key parameters. The results demonstrate that all three methods exhibit good performance. HMC excels for small sample sizes, whereas INLA demonstrates superior computational efficiency for large datasets. The VI method serves as an effective complement to the first two methods. This study provides theoretical guidance for researchers applying Bayesian techniques to spatial econometric models and practical insights for empirical analysts selecting suitable estimation methods based on computational constraints.

Understanding and grasping the spatial pattern of China's population aging and the factors influencing it is of great significance for optimizing the allocation of elderly care resources, and targeting the formulation of population development strategies. Under the perspective of spatial heterogeneity, the spatial and temporal patterns of population aging and influencing factors of Chinese cities at prefecture level and above are studied based on three national census data in 2000, 2010 and 2020, using multiple linear regression models and multi-scale geographically weighted regression models. The results show that: 1. China's population overall aging accelerated and deepened during the study period, most notably in Jiangsu and Sichuan provinces, with strong positive spatial correlation characteristics of the aging pattern among cities, and the overall pattern remained stable; 2. Chinese cities in general shifted from adult to senior across types, with senior cities transitioning from early to mid-late stage; 3. The hot and cold spots of aging showed spatial evolution characteristics, with the hot spots showing a "two-cluster" pattern and the cold spots gradually shrinking; 4. Ageing was affected by demographic, economic, public service, education and environmental factors, with birth rate, death rate and migration rate acting as the dominant factors, and other factors changing in stages; 5. The influence of demographic factors on population aging has shifted from global to local and from robust to non-robust, the spatial heterogeneity of the influence of economic, medical and educational factors on aging has undergone periodic changes; and the significance of environmental factors has gradually emerged.

The optimization of industrial spatial structure is pivotal for urban economic growth. This study introduces an innovative framework to evaluate the optimization of industrial spatial structures and assesses the levels of such optimization across 284 Chinese cities from 2003 to 2021, utilizing three geographical matrices—latitude and longitude distance, commuting time, and commuting distance—to develop a spatiotemporal weight matrix based on the Kronecker product concept. Building on this foundation, the research employs panel spatial econometric models, complemented by robustness checks, endogeneity treatments, and heterogeneity analyses, to dissect the economic growth effects stemming from the optimization of industrial spatial structures. The results underscore the significant role that optimizing industrial spatial structures plays in fostering economic growth, an impact that surpasses that of traditional input factors like capital and labor. Nonetheless, the pace of improvement in the optimization of industrial spatial structures across China has been gradual during the period under review, with noticeable regional disparities in the economic growth effects of such optimization. In light of these findings, the study advocates for elevating the level of industrial spatial structure optimization, harnessing the synergistic interactions between macro and micro dimensions of industrial spatial structures, and stimulating inter-regional collaborative development in optimizing industrial spatial structures to propel sustained economic growth.

Based on an unbalanced panel composed of 3 222 observation samples of 267 cities and a balanced panel composed of 3 808 observation samples of 238 cities constructed by the random forest method from 2003 to 2018, we construct both the unbalanced and balanced panel spatial Durbin error models to study the spatial evolution and influencing factors of urban construction land in China. The study reveals the following spatiotemporal evolution characteristics: 1. Since 2003, China's per capita urban construction land has generally exhibited a continuous upward trend. Even based on the underestimated values defined in this study, it has approached the upper limit (115 m²/person) stipulated in the 2012 updated Urban Land Classification and Planning Construction Land Standard. 2.With the exception of megacities, where per capita urban construction land has shown an overall decline, the other six city categories demonstrated significant growth trends.Regarding influencing factors: 1. Urban scale expansion significantly reduces per capita urban construction land. 2. Current economic development and urbanization rates still promote the increase of per capita urban construction land, indicating that these drivers have not yet transitioned to a phase of promoting intensive land use. 3. Per capita urban construction land is also influenced by neighboring cities'urban scales, economic development levels, industrial structures, and openness.