Spatial Weight Matrices Research Articles

Model selection and model averaging for matrix exponential spatial models

In this paper, we focus on a model specification problem in spatial econometric models when an empiricist needs to choose from a pool of candidates for the spatial weights matrix. We propose a model selection (MS) procedure for the matrix exponential spatial specification (MESS), when the true spatial weights matrix may not be in the set of candidate spatial weights matrices. We show that the selection estimator is asymptotically optimal in the sense that asymptotically it is as efficient as the infeasible estimator that uses the best candidate spatial weights matrix. The proposed selection procedure is also consistent in the sense that when the data generating process involves spatial effects, it chooses the true spatial weights matrix with probability approaching one in large samples. We also propose a model averaging (MA) estimator that compromises across a set of candidate models. We show that it is asymptotically optimal. We further flesh out how to extend the proposed selection and averaging schemes to higher order specifications and to the MESS with heteroscedasticity. Our Monte Carlo simulation results indicate that the MS and MA estimators perform well in finite samples. We also illustrate the usefulness of the proposed MS and MA schemes in a spatially augmented economic growth model.

Impact assessment of population migration on energy consumption and carbon emissions in China: A spatial econometric investigation

Human activities are closely related to energy consumption and carbon emissions. Nevertheless, in the context of energy transition and carbon emission reduction policies, the impact of population migration on energy consumption and carbon emissions is still unclear. Based on the panel data of 30 provincial regions in China from 2000 to 2019, this paper uses the spatial Durbin model to perform a spatial econometric investigation on this issue. In particular, this study innovatively embeds two spatial weight matrices, an economic gravity weight matrix and a population migration weight matrix, into the spatial Durbin model to capture the spatial spillover effects of population migration. The results show that population migration has obvious adverse impacts on the provinces with net outward population migration. Specifically, on the one hand, population migration increases energy consumption and energy poverty, but energy poverty is more severe in provinces with net outward population migration. On the other hand, population migration increases the carbon emissions and carbon reduction barriers of the provinces with net outward population migration and has no significant impact on the carbon emissions and carbon reduction barriers of the provinces with net inward population migration. Besides, the results of heterogeneity analysis show that population migration causes gaps in the energy structure among regions and even triggers the carbon transfer to provinces with net outward population migration. On the whole, the research results of this paper all prove that population migration increases the carbon reduction barriers in the provinces with net outward population migration. These empirical insights enrich the relevant theoretical achievements of the impact of population migration on energy consumption and carbon emissions and have a high reference value for formulating more reasonable regional energy transition and carbon emission reduction policies.

Bayesian Analysis of Spatial Dynamic Panel Data Model with Convex Combinations of Different Spatial Weight Matrices: A Reparameterized Approach ⋆

Bayesian Analysis of Spatial Dynamic Panel Data Model with Convex Combinations of Different Spatial Weight Matrices: A Reparameterized Approach ⋆

Оценка пространственной неоднородности экономической деятельности хозяйствующих субъектов в муниципальных образованиях Свердловской области

Uneven socio-economic development of municipalities in various regions depends on many factors, in particular, on the peculiarities of the distribution of economic entities and their activities. We hypothesise that this heterogeneity increases due to unequal distribution of labour and investment resources. In order to test this hypothesis, the study assesses the impact of the distribution of personnel and investment resources in the municipalities of Sverdlovsk oblast on the spatial heterogeneity of economic activity. To this end, the methods of regression and spatial autocorrelation analysis were used. The developed methodology involves assessing the spatial heterogeneity of economic activities of various enterprises in territorial systems. Spatial regression analysis was applied to examine the impact of labour and investment resources on the heterogeneity dynamics, while spatial autocorrelation analysis was used to consider the distribution of these factors. Due to the systematic use of spatial autocorrelation analysis for various spatial weights matrices, as well as regression analysis based on panel data and geographically weighted regression, the degree of the influence of factors on the heterogeneity of economic activities in certain municipalities was established. Testing of the presented methodology revealed a trend towards an increase in the spatial heterogeneity of economic activity, its concentration in Ekaterinburg, Nizhny Tagil, Kamensk-Uralsky, as well as in Verkhnyaya Pyshma, Pervouralsk, Verkhnesaldinsky, Polevskoy, Revda, Kachkanarsky, Berezovsky, Zarechny and Serovsky urban okrugs in the period from 2017 to 2020. The Cobb-Douglas model showed that the main factor contributing to the increase in the spatial heterogeneity of the economic entity activity is labour costs; the volume of attracted investments plays an important role in municipalities with a high concentration of shipped goods and rendered services. Based on the model modified using geographically weighted regression, the study established a degree of spatial influence of the examined factors on the economic activity and, together with a spatial autocorrelation analysis of the distribution of human resources and investments in the municipalities of the region, to confirm the hypothesis put forward.

Оптимальные пространственные форматы межрегионального экономического сотрудничества в рамках инновационной экономики

Domestic cooperation of companies in the field of innovative economy seems to be a promising research area in Russia, especially considering recent macroeconomic events caused by sanctions, in particular, restrictions on the import of high-tech goods. Thus, the present study examines the optimal spatial scale of interregional innovation cooperation. The article presents an analysis of approaches to determining the optimal number of k-matrices of relations between innovation active regions. It is hypothesised that the innovative activity of the business sector in one region does not influence the innovative activity of its neighbours and vice versa. Stepwise regression was applied to identify the core explanatory variable. Based on the spatial weights matrices, a spatial econometric model was constructed using the least squares method. Further, the global Moran’s I was employed to test the spatial correlation, in particular, local indicators of spatial association (LISA) using the queen criterion of contiguity were utilised to determine the dependencies of innovative activity between neighbouring regions. The analysis used panel data from all Russian regions for the period from 2010 to 2019, as well as spatial econometric modelling to identify the side effects of the optimal spatial scale. As a result, the study revealed the presence of spatial correlation in the levels of regional innovative activity, the size of markets, as well as institutional support for enterprises in individual regions. Additionally, the research identified factors positively affecting the scale of innovative activity of the regions and adjacent territories, such as regional domestic income, the number of participants in innovation processes and infrastructure facilities. It has been established that the neighbourhood of regions characterised by the presence of many participants in innovation processes (at least 100 units), as well as innovation infrastructure facilities (at least 810 units) will be seen as the optimal scale of regional cooperation.

Testing Endogeneity of Spatial Weights Matrices in Spatial Dynamic Panel Data Models

Testing Endogeneity of Spatial Weights Matrices in Spatial Dynamic Panel Data Models

Forest Bioelectricity in Brazil: Distribution and Spatial-Time Dependence

This study was to present a methodology for analyzing the distribution and spatial-time dependence of the supply of forest bioelectricity in Brazil, from 2000 to 2019. The data for the granting of forest biomass thermoelectric plants were obtained from the National Electric Energy Agency (in Portuguese Agência Nacional de Energia Elétrica –ANEEL). It used the exploratory analysis of spatial data, and as neighborhood criteria the spatial weighting matrices of k-neighbors closest and based on distance, as well as the global and local Moran indices to detect the presence of spatial dependence. The analysis of the situation, by quartile, showed the states of the central-southern portion of Brazil as the main locations of forest thermals. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{I}_{\mathrm {Moran\_{}Global}}$ </tex-math></inline-formula> highlighted the decrease in spatial autocorrelation between the years 2000 and 2019, associated with the implementation of new thermoelectric plants by the large groups Fibria, Klabin and Suzano Celulose throughout the national territory. The local index ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{I}_{\mathrm {Moran\_{}Local}}$ </tex-math></inline-formula> ) pointed out high-powered clusters, especially in the early years, highlighting: the Bahia, Espírito Santo and Minas Gerais axis, the Paraná thermal plants and Mato Grosso do Sul thermal plants. The local index also pointed outliers, which indicated possibility of associating thermoelectric plants with other activities, such as wood production and industries in the steel and paper and cellulose segment. The knowledge of the spatial pattern of the forest bioelectricity sector presented can help new feasibility studies for the implementation in bioelectricity and/or stimulate the development of public policies, focused on cluster regions and adjacent areas, which results in the growth of forest generation.

Semiparametric spatio‐temporal models with unknown and banded autoregressive coefficient matrices

We consider a new class of semiparametric spatio‐temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a type of sparse structure in order to include as many panels as possible. We apply the local linear method and least squares method for Yule–Walker equation to estimate trend function and spatio‐temporal autoregressive coefficient matrices respectively. We also balance the over‐determined and under‐determined phenomena in part by adjusting the order of extracting sample information. Both the asymptotic normality and convergence rates of the proposed estimators are established. We demonstrate, using both simulation and case studies, that the proposed estimators are stable among different sample sizes, and more efficient than the traditional method with known spatial weight matrices.

Study on the spatial interaction between carbon emission intensity and shadow economy in China

Both high carbon emission intensity (CEI) and large scale of shadow economy in China are the undesirable products of economic development with too fast growth rate. For the rapid and healthy development of the economy in China, the research on the relationship between the two should attract more attention, while the relevant literatures are very few at present. According to the panel data of 30 provinces in China from 2004 to 2016, this paper firstly examines the spatial correlation between CEI and the scale of shadow economic. Then verifies the interaction relationship between them with SPDM (spatial panel Dubin Model). Moreover, the robustness test is conducted with three different spatial weight matrices. As the interaction between CEI and shadow economy has been proved, providing new ideas for carbon emission reduction, environmental protection, and healthy economic development with rapid rate in the future. The specific conclusions are as follows: first, CEI and shadow economy both have significant positive spatial autocorrelation. Second, there is a spatial interaction between CEI and shadow economy, indicating provincial cooperation plays a very important role in both economic growth and environment protection. Third, the impacts from economic development on both CEI and shadow economy satisfy the EKC hypothesis. Also, the development of the tertiary industry plays a positive role in promoting the growth of CEI, while promotes and inhibits the expansion of shadow economic scale at the same time.

Instrumental Variable Quantile Regression of Spatial Dynamic Durbin Panel Data Model with Fixed Effects

This paper studies a quantile regression spatial dynamic Durbin panel data (SDDPD) model with fixed effects. Conventional fixed effects estimators of quantile regression specification are usually biased in the presentation of lagged response variables in spatial and time as regressors. To reduce this bias, we propose the instrumental variable quantile regression (IVQR) estimator with lagged covariates in spatial and time as instruments. Under some regular conditions, the consistency and asymptotic normalityof the estimators are derived. Monte Carlo simulations show that our estimators not only perform well in finite sample cases at different quantiles but also have robustness for different spatial weights matrices and for different disturbance term distributions. The proposed method is used to analyze the influencing factors of international tourism foreign exchange earnings of 31 provinces in China from 2011 to 2017.

Robust space–time modeling of solar photovoltaic deployment

Solar photovoltaic (PV) has established itself as a fairly promising, fast-growing renewable energy source. The main determinants of solar PV deployment are thought to be physical and climatic factors – such as latitude and solar irradiance, not to mention terrain and built environment features – as well as socio-economic drivers — such as population density, household size, and education level. Besides, peer effects and neighborhood effects are found to affect the willingness to adopt solar photovoltaic systems strongly. This study aims to set up robust space–time models, which enable us to investigate the drivers of solar PV deployment using fine-grained spatial and temporal data. We use space–time auto-regressive models (STAR) with several exogenous covariates that are expected to explain the installed solar PV capacity. STAR models require the specification of spatial weight matrices (W). As in regular lattice data, we select causal (lower triangular) W matrices so that the consistency of least-squares (LS) estimators is warranted. We show that they can be extended to robust LS estimators, which are necessary because of strong outlier contamination. Models are tested on the Italian municipal data of residential and industrial PV plants installed under the support schemes in force between 2006 and 2011. Empirical results confirm the important role played by the space–time dynamic components. Significant exogenous predictors are found in the domains of the physical features (elevation and land area), demography (population), built environment (residential buildings), and socio-economic aspects (income, employment rate, commuter workers).

Modelling Representative Population Mobility for COVID-19 Spatial Transmission in South Africa.

The COVID-19 pandemic starting in the first half of 2020 has changed the lives of everyone across the world. Reduced mobility was essential due to it being the largest impact possible against the spread of the little understood SARS-CoV-2 virus. To understand the spread, a comprehension of human mobility patterns is needed. The use of mobility data in modelling is thus essential to capture the intrinsic spread through the population. It is necessary to determine to what extent mobility data sources convey the same message of mobility within a region. This paper compares different mobility data sources by constructing spatial weight matrices at a variety of spatial resolutions and further compares the results through hierarchical clustering. We consider four methods for constructing spatial weight matrices representing mobility between spatial units, taking into account distance between spatial units as well as spatial covariates. This provides insight for the user into which data provides what type of information and in what situations a particular data source is most useful.

Geospatial Least Squares Support Vector Regression Fused with Spatial Weight Matrix

Due to the increasingly complex objects and massive information involved in spatial statistics analysis, least squares support vector regression (LS-SVR) with a good stability and high calculation speed is widely applied in regression problems of geospatial objects. According to Tobler’s First Law of Geography, near things are more related than distant things. However, very few studies have focused on the spatial dependence between geospatial objects via SVR. To comprehensively consider the spatial and attribute characteristics of geospatial objects, a geospatial LS-SVR model for geospatial data regression prediction is proposed in this paper. The 0–1 type and numeric-type spatial weight matrices are introduced as dependence measures between geospatial objects and fused into a single regression function of the LS-SVR model. Comparisons of the results obtained with the proposed and conventional models and other traditional models indicate that fusion of the spatial weight matrix can improve the prediction accuracy. The proposed model is more suitable for geospatial data regression prediction and enhances the ability of geospatial phenomena to explain geospatial data.

Transformation of Regional Budgetary Independence and Security: Spatial Analysis

The issue of increasing budgetary independence and security is relevant for the majority of territorial systems, both at the regional and municipal levels. It was hypothesised that changes in the structure of regional public debt have a negative impact on their budgetary security. According to this hypothesis, an increase in the proportion of bank borrowing and corresponding decrease in the issue of debt securities by the constituent entities of the Russian Federation leads to a greater overall debt burden on the regional budget. In order to study transformation processes affecting budgetary independence and regional security. We developed a methodology to permit a separate assessment of these concepts. According to this approach, we propose to evaluate the budgetary independence of regional systems in terms of: (1) the balance of the budget (ratio of internal tax and non-tax revenues to budget expenditures); (2) financial dependence on transfers and subsidies from budgets at other levels; (3) budget security, taking into account gratuitous and non-gratuitous transfers. Thus, budget ary security can be assessed in accordance with the public debt dynamics, as well as the level of budgetary debt covered by the region’s own tax and non-tax revenues. The novelty of the presented methodological approach consists in its systematic use of Moran’s I for various spatial weight matrices combined with regression analysis methods based on panel data. Testing this methodology demonstrated the spatial heterogeneity of regional fiscal capacity, highlighting the financial dependence of most regions on federal and other gratuitous transfers. Autocorrelation analysis carried out according to Moran’s I using various spatial weight matrices confirmed the increasing tendency of the budgetary debt of Russian regions towards spatial heterogeneity. Future studies will focus on simulating the influence of various factors on regional budgetary security in order to predict the dynamics of its change.

Impact of wind-hydro dynamics on electricity price: A seasonal spatial econometric analysis

Hydro and wind are both commonly deployed renewable sources of electricity. Wind is intermittent and unpredictable to a large degree. Hydro depends on seasonal rainfall patterns, although storage may offer scope to spread the risk associated with dry seasons. We investigate the impact of intermittent wind generation, coupled with a given hydro capacity, on wholesale electricity prices, accounting for both spatial and seasonal effects. Results from a spatial Durbin model provide evidence of significant negative spill-over effects of wind generation on wholesale nodal prices. After robustness analysis with alternative spatial weight matrices, we provide estimates of the seasonal impact of wind generation on nodal prices using a transmission weight matrix. We evaluate seasonal nodal price effects during dry periods and wet periods in New Zealand's hydro-dominated electricity market. Results show that the price reduction associated with a 10% increase in wind penetration varies across seasons, ranging from $0.48 per MWh in winter in 2012 to $3.05 per MWh in spring. The largest price reduction effect of 3.05 is found for the wet season in spring 2012, but the variance change is 3.6 which is less than 5.24 for the dry season in summer 2012. This evidence reveals that increased wind generation reduces nodal prices, as expected, but also increases the variance in nodal prices, particularly during a dry season. Thus, while a wind-hydro system is shown as a favourable low-carbon combination during wet seasons, without backup generation the system remains susceptible to price volatility. We further suggest policy recommendations to ensure the reduction of price volatility and the continuity of electricity supply during dry periods.

Spatial-temporal Patterns of MODIS Active Fire/Hotspots in Chiang Rai, Upper Northern Thailand and the Greater Mekong Subregion Countries During 2003-2015

For the past decade, smoke-haze pollution from forest fires and open burning has been a yearly recurring problem over Chiang Rai and other provinces in Upper Northern Thailand, along with other countries in the Greater Mekong Sub-region. Remote-sensing active fire/ hotspot data are currently used for monitoring the forest fires and open burning in the sub-region. This study aimed to extend the current monitoring work by performing spatial and temporal analysis to examine the patterns, either globally or locally, of MODIS active fires/hotspots during the critical smoke-haze pollution periods from January to April in 2003-2015. Fire radiative power was used as a weight attribute for each active fire/hotspot. Administrative unit maps were used for aggregating data and creating spatial weight matrices. Results indicated that for all the years over the investigated period and based on detected locations, active fires/hotspots were overall clustered spatially across provincial, interprovincial, and international scales. Their density patterns were locally variable for each year, but the high concentrated zones, in terms of both fire counts and fire radiative powers, were consistently bounded in the hilly and mountainous areas, confirming that the forest fires and open burning problem keeps recurring in certain areas. When aggregated by administrative unit, the administrative boundaries with high active fires/hotspots, in terms of both fire counts and fire radiative powers, were spatially clustered, either globally or locally, but there was only an increasing trend of the clustering intensity in fire radiative powers, implying that the forest fires and open burning problem have become more severe in particular areas. These findings could be useful for further reviewing and strengthening current measures and plans of fire and smoke haze pollution management.

Influences of using different spatial weight matrices in analyzing spatial autocorrelation of cardiovascular diseases mortality in China

Objective: To explore the potential influences and applicability of different spatial weight matrices used in analyzing spatial autocorrelation of cardiovascular disease (CVD) mortality in China. Methods: Using data from the National Cause-of-death Reporting System, we used adjacency-based Rook and Queen contiguity and distance-based K nearest neighbors/distance threshold. We then conducted global and local spatial autocorrelation analysis of CVD mortality at the county level in China, 2018. Results: All four categories and 26 types of spatial weight matrices had detected significant global and local spatial autocorrelation of CVD mortality in China. Global Moran's I statistics reached its peak when using first-order Rook (0.406), first-order Queen (0.406), K nearest neighbors including five spatial units (0.409), and distance threshold with 100 kilometers (0.358). Meanwhile, apparent local spatial autocorrelation was found in CVD mortality. Substantial disparities were observed when detecting "High-High clusters", "Low-Low clusters", "High-Low clusters" and "Low-High clusters" of CVD mortality spatial distribution by using different weight matrices. Conclusions: Using different spatial weight matrices in analyzing the spatial autocorrelation of CVD mortality, we could understand the spatial distribution characteristics of CVD mortality in-depth at the county level in China. In this way, adequate supports could also be provided on CVD premature death control and rational medical resource allocation regionally.

A simple closed-form relation between spatial weight matrices with different scalings

Spatial econometric models rely on the weight matrix W to specify dependence. However, formation of W involves scalings of rows and columns. We provide a closed-form for the similarity in results between the common eigenvalue and row-stochastic scalings.

The local-neighborhood effect of green credit on green economy: a spatial econometric investigation.

Green credit is one of the most important financial instruments to promote sustainable development. Taking the provincial panel dataset of China as the research sample, this paper investigates the spatial impacts of green credit on the green economy. The super slack-based measure (Sup-SBM) model with undesirable outputs is employed to calculate the level of green economy within China. On this basis, we establish spatial Durbin models to study the impact of green credit on green economy and its transmission mechanisms. The results show that green credit exhibits a local-neighborhood effect on green economy; that is, the green credit can not only improve the local green economy but also generate spatial spillover effect to promote the development of green economy in surrounding areas. The above conclusion still holds after the robustness test by replacing spatial weight matrices and alternative measurement for the explained variable. Furthermore, enhancing innovation efficiency and optimizing energy structure are important ways for green credit to promote green economy. The findings of this study not only provide a new perspective for understanding the economic consequences of green credit policy but also provide empirical evidence for the important role of green finance in achieving the win-win goals of economic growth and environmental protection.Supplementary InformationThe online version contains supplementary material available at 10.1007/s11356-021-15419-8.

Identification of coexisting dynamics in boundary layer flows through proper orthogonal decomposition with weighting matrices

A different version of the classic proper orthogonal decomposition (POD) procedure introducing spatial and temporal weighting matrices is proposed. Furthermore, a newly defined non-Euclidean (NE) inner product that retain similarities with the POD is introduced in the paper. The aim is to emphasize fluctuation events localized in spatio-temporal regions with low kinetic energy magnitude, which are not highlighted by the classic POD. The different variants proposed in this work are applied to numerical and experimental data, highlighting analogies and differences with respect to the classic and other normalized variants of POD available in the literature. The numerical test case provides a noise-free environment of the strongly organized vortex shedding behind a cylinder. Conversely, experimental data describing transitional boundary layers are used to test the capability of the procedures in strongly not uniform flows. By-pass and separated flow transition processes developing with high free-stream disturbances have been considered. In both cases streaky structures are expected to interact with other vortical structures (i.e. free-stream vortices in the by-pass case and Kelvin–Helmholtz rolls in the separated type) that carry a significant different amount of energy. Modes obtained by the non-Euclidean POD (NE-POD) procedure (where weighted projections are considered) are shown to better extract low energy events sparse in time and space with respect to modes extracted by other variants. Moreover, NE-POD modes are further decomposed as a combination of Fourier transforms of the related temporal coefficients and the normalized data ensemble to isolate the frequency content of each mode.