Spatial Weight Matrices Research Articles

Spatial Panel Data Models Using Stata

xsmle is a new command for spatial analysis using Stata. We consider the quasi-maximum likelihood estimation of a wide set of both fi xed- and random- eff ects spatial models for balanced panel data. Of special note is that xsmle allows to handle unbalanced panels thanks to its full compatibility with the mi suite of commands, to use spatial weight matrices in the form of both Stata matrices and spmat objects, to compute direct, indirect and total e ffects according to the procedure outlined in LeSage and Pace (2009), and to exploit a wide range of postestimation features, extending to the panel data case the predictors proposed by Kelejian and Prucha (2007). This paper describes the command and all its functionalities using both simulated and real data.

Provincial Growth in Turkey: A Spatial Econometric Analysis

This study investigates the conditional income convergence hypotheses among provinces of Turkey over 1991–2009 period using a comprehensive set of spatial econometric models and two alternative definitions of spatial weights matrices. Particular attention is given to the alterations of the political and economic structures in the two sub-periods 1991–2001 and 2002–2009. We first consider non-spatial specification estimated by ordinary least squares and conduct tests to detect the evidence of spatiality in the data. The spatial econometric models are then estimated by maximum likelihood and compared to each other via likelihood ratio tests following a general-to-specific model selection procedure. The results indicate that different political and economic environments may lead not only to distinct convergence dynamics but also to dissimilar spatial relations. Spatial error model is the most appropriate specification for 1991–2009 and 2002–2009 periods whereas spatial cross-regressive model better characterizes the data for 1991–2001. The beta-convergence dynamics are observed in all periods, with noticeably higher rates for the post-2002 period.

Spatial Autoregressive Models for Stand Top and Stand Mean Height Relationship in Mixed Quercus mongolica Broadleaved Natural Stands of Northeast China

The relationship of stand top and stand mean height is important for forest growth and yield modeling, but it has not been explored for natural mixed forests. Observations of stand top and stand mean height can present spatial dependence or autocorrelation, which should be considered in modeling. Simultaneous autoregressive (SAR) models, including spatial lag model (SLM), spatial Durbin model (SDM) and spatial error model (SEM), within nine spatial weight matrices were utilized to model the stand top and stand mean height relationship in the mixed Quercus mongolica Fisch. ex Ledeb. broadleaved natural stands of Northeast China, using ordinary least squares (OLS) as a benchmark model. The results showed that there was a high linear relationship between stand top and stand mean height and that there was a positive spatial autocorrelation pattern in model residuals of OLS. Moreover, SEM and SDM performed better than OLS in terms of reducing the spatial dependence of model residuals and model fitting, regardless of which spatial weight matrix was used. SEM was better than SDM. SLM scarcely reduced the spatial autocorrelation of model residuals. Among nine spatial matrices in SEM, rook contiguous matrix performed best in model fitting, followed by inverse distances raised to the second power (1/d2) and local statistics model matrix (LSM).

The "Political" Geography of Research Networks

The production of scientific and technical knowledge is mostly concentrated in specific locations. Knowledge flows very easily within regions; however, scientific and technical knowledge does flow also between different regions. The aim of this article is to analyze knowledge flows between agglomerations of innovative inputs, and their effects on the innovative performance of regions. We estimate a regional knowledge production function and we test, through appropriate spatial econometric estimation techniques, the effect of both geographical and relational autocorrelation (as measured by participation to joint research networks in the European Union [EU] Sixth Framework Programme [FP6]). We adopt two selection criteria in order to define different relational “geographies” (hence spatial weights matrices), and we model the unobservable structure and link value of knowledge flows within these joint research networks. Our results confirm established evidence that knowledge flows within interregional research networks along a top-down nonsymmetrical and hierarchical structure. However, the EU enlargement - and a modified structure of incentive for collaboration activity of European institutions- changed the direction of knowledge flows toward a top-down dynamics of knowledge diffusion from coordinator to participants for “EASTWARD” research networks (whose coordinator is in the west and most participants in the east); while the contrary (a hierarchical bottom-up dynamic of knowledge transfer) is true for WESTWARD networks (whose coordinator is in the east and most participants in the west). FP6 is therefore a platform for knowledge barter exchange for EU15, while works as a mere one-way channel for knowledge diffusion from EU15 toward Central and Eastern European countries.

On The Eigenvalue Distribution Of Adjacency Matrices For Connected Planar Graphs

Abstract This paper describes the previously unknown statistical distribution of adjacency matrix spectra for planar graphs, also known as spatial weights matrices, in terms of the following three readily available eigenvalue properties: extremes, rank orderings, and sums of powers. This distribution is governed by at most six parameters that, once known, allow accurate approximations of eigenvalues to be computed without resorting to numerical matrix methods applied on a case-by-case basis. Parameter estimates for illustrative real-world examples are obtained using nonlinear least squares regression techniques. Three conjectures are proposed, and graphical and trend results are reported for a diverse set of planar graph-based matrices.

Estimating standard errors in spatial panel models with time varying spatial correlation

AbstractWe connect time varying spatial correlation patterns to examples in the theoretical and empirical literature. Then we use simulation experiments to compare the performance of estimation techniques that use spatial weights matrices (W) and those that do not. The results suggest that the pattern of time varying correlation does impact inference, but not as much as the W misspecification literature suggests. We find choosing the appropriate inferential method is less of a concern if the data generating process follows a hub‐spoke correlation structure. Finally, we confirm earlier results that the cluster robust modifications proposed by Bester et al. (2011) perform well if the group sizes are chosen appropriately.

Power of Moran’s I Test for Spatial Dependence in Panel Data Models with Time Varying Spatial Weights Matrices

AbstractThe spatial weights matrix is usually specified to be time invariant. However, when it are constructed with economic/socioeconomic distance, trade /demographic/climatic characteristics, these characteristics might be changing over time, and then the spatial weights matrix substantially varies over time. This paper focuses on power of Moran’s I test for spatial dependence in panel data models with where spatial weights matrices can be time varying (TV-Moran). Compared with Moran’s I test with time invariant spatial weights matrices (TI-Moran), the empirical power of TV-Moran test for spatial dependence are evaluated. Our extensive Monte Carlo simulation results indicate that Moran’s I test with misspecified time invariant spatial weights matrices is questionable; Instead, TV-Moran test has shown superiority in higher power, especially for cases with negative spatial correlation parameters and the large time dimension.

Convergence: A Story of Quantiles and Spillovers

SummaryIn this paper, we revisit the analysis of cross‐country convergence by combining spatial econometrics and panel quantile regressions to estimate conditional β‐convergence models. Moreover, we use both exogenous and endogenous weight matrices. Our results show that indeed the effects of initial per capita income, investment rate, population growth and human capital on growth rates vary considerably across the estimated quantiles. Convergence is not a generalized phenomenon across the conditional growth distribution. Moreover, while using exogenous spatial weight matrices does not substantially alter the findings found in a‐spatial models, it appears that endogenous weights dramatically affect the estimates of the convergence process.

Value-at-Risk forecasts by a spatiotemporal model in Chinese stock market

This paper generalizes a recently proposed spatial autoregressive model and introduces a spatiotemporal model for forecasting stock returns. We support the view that stock returns are affected not only by the absolute values of factors such as firm size, book-to-market ratio and momentum but also by the relative values of factors like trading volume ranking and market capitalization ranking in each period. This article studies a new method for constructing stocks’ reference groups; the method is called quartile method. Applying the method empirically to the Shanghai Stock Exchange 50 Index, we compare the daily volatility forecasting performance and the out-of-sample forecasting performance of Value-at-Risk (VaR) estimated by different models. The empirical results show that the spatiotemporal model performs surprisingly well in terms of capturing spatial dependences among individual stocks, and it produces more accurate VaR forecasts than the other three models introduced in the previous literature. Moreover, the findings indicate that both allowing for serial correlation in the disturbances and using time-varying spatial weight matrices can greatly improve the predictive accuracy of a spatial autoregressive model.

Quasi Maximum Likelihood Estimation of Spatial Models with Heterogeneous Coefficients

This paper considers spatial autoregressive panel data models and extends their analysis to the case where the spatial coefficients differ across the spatial units. It derives conditions under which the spatial coefficients are identified and develops a quasi maximum likelihood (QML) estimation procedure. Under certain regularity conditions, it is shown that the QML estimators of individual spatial coefficients are consistent and asymptotically normally distributed when both the time and cross section dimensions of the panel are large. It derives the asymptotic covariance matrix of the QML estimators allowing for the possibility of non-Gaussian error processes. Small sample properties of the proposed estimators are investigated by Monte Carlo simulations for Gaussian and non-Gaussian errors, and with spatial weight matrices of differing degree of sparseness. The simulation results are in line with the paper’s key theoretical findings and show that the QML estimators have satisfactory small sample properties for panels with moderate time dimensions and irrespective of the number of cross section units in the panel, under certain sparsity conditions on the spatial weight matrix.

La evolución espacial de los subcentros de empleo en Ciudad Juárez, Chihuahua (1994-2004): un análisis con indicadores de autocorrelación espacial global y local / The Spatial Evolution of Employment Subcenters in Ciudad Juárez, Chihuahua (1994-2004): An Analysis Using Global and Local Spatial Autocorrelation Indicators

El objetivo del artículo es identificar los subcentros de empleo total mediante el uso de indicadores de autocorrelación espacial global y local en Ciudad Juárez, Chihuahua, en el periodo 1994-2004. Esta metodología usa matrices de pesos espaciales e incorpora la noción de unidades vecinas y no está limitada al criterio de contigüidad del método de doble umbral. La variable usada fue la densidad bruta de empleo total (manufactura, comercio y servicio) en los años 1994 y 2004 a nivel de AGEB, obtenida de los Censos Económicos (INEGI, 1994 y 2004). Mediante el uso de dos indicadores de autocorrelación espacial, en específico el I de Moran y los indicadores locales de asociación espacial (LISA por sus siglas en inglés), fue posible identificar varios centros y subcentros de empleo total. Los resultados muestran la presencia de dependencia y heterogeneidad espacial que se manifiestan en la forma de agrupamientos de alta densidad de empleo (alto-alto) tanto en el distrito central de negocios (DCN) como en el subcentro de empleo mixto localizado en el corredor industrial de la avenida Rafael Pérez Serna. Asimismo, existen varios subcentros de empleo manufacturero aislados de alta densidad (alto-alto) localizados sobre las principales vialidades dirigidas a puertos internacionales. En este contexto, se puede concluir que la distribución del empleo fuera del DCN, producto de economías de aglomeración, implica la presencia de una estructura urbana policéntrica.Abstract:The objective of this article is to identify total employment subcenters through the use of global and local spatial autocorrelation indicators in Ciudad Juárez, Chihuahua, during the period from 1994-2004. This methodology uses spatial weights matrices, includes the notion of neighboring units and is not restricted to the contiguity criterion of the double threshold method. The variable used was the gross density of total employment (manufacturing, trade and service) in 1994 and 2004 at the ageb level, obtained from the Economic Census (INEGI, 1994 and 2004). Two spatial autocorrelation indicators, specifically Moran’s I and local indicators of spatial association (LISA) were used to identify several centers and sub-centers of total employment. The results show the presence of dependence and spatial heterogeneity expressed in the form of groups of high density employment (high-high) in both the central business district (CBD) and the mixed employment subcenter located in the industrial corridor of Avenida Rafael Pérez Serna. Likewise, there are several isolated high density manufacturing employment subcenters (high-high) located on the main roads leading to international ports. In this context, one can conclude that employment distribution outside the CBD, resulting from agglomeration economies, implies the presence of a polycentric urban structure.

Large sample properties of the matrix exponential spatial specification with an application to FDI

This paper studies large sample properties of the matrix exponential spatial specification (MESS). We find that the quasi-maximum likelihood estimator (QMLE) for the MESS is consistent under heteroskedasticity, a property not shared by the QMLE of the SAR model. For the general model that has MESS in both the dependent variable and disturbances, labeled MESS(1,1), the QMLE can be consistent under unknown heteroskedasticity when the spatial weights matrices in the two MESS processes are commutative. We also consider the generalized method of moments estimator (GMME). In the homoskedastic case, we derive a best GMME that is as efficient as the maximum likelihood estimator under normality and can be asymptotically more efficient than the QMLE under non-normality. In the heteroskedastic case, an optimal GMME can be more efficient than the QMLE asymptotically. The QML approach for the MESS has the computational advantage over that of a SAR model. The computational simplicity carries over to MESS models with any finite order of spatial matrices. No parameter range needs to be imposed in order for the model to be stable. Results of Monte Carlo experiments for finite sample properties of the estimators are reported. Finally, the MESS(1,1) is applied to Belgium’s outward FDI data and we observe that the dominant motivation of Belgium’s outward FDI lies in finding cheaper factor inputs.

Non-nested testing of spatial correlation

We develop non-nested tests in a general spatial, spatio-temporal or panel data context. The spatial aspect can be interpreted quite generally, in either a geographical sense, or employing notions of economic distance, or when parametric modelling arises in part from a common factor or other structure. In the former case, observations may be regularly-spaced across one or more dimensions, as is typical with much spatio-temporal data, or irregularly-spaced across all dimensions; both isotropic models and non-isotropic models can be considered, and a wide variety of correlation structures. In the second case, models involving spatial weight matrices are covered, such as “spatial autoregressive models”. The setting is sufficiently general to potentially cover other parametric structures such as certain factor models, and vector-valued observations, and here our preliminary asymptotic theory for parameter estimates is of some independent value. The test statistic is based on a Gaussian pseudo-likelihood ratio, and is shown to have an asymptotic standard normal distribution under the null hypothesis that one of the two models is correct; this limit theory rests strongly on a central limit theorem for the Gaussian pseudo-maximum likelihood parameter estimates. A small Monte Carlo study of finite-sample performance is included.

Estimation of spatial panel data models with time varying spatial weights matrices

This paper investigates the quasi-maximum likelihood (QML) estimation of spatial panel data models where spatial weights matrices can be time varying. We show that QML estimate is consistent and asymptotically normal. We also derive the asymptotic distribution of average impact coefficients (direct, indirect, total). Monte Carlo results are reported to investigate the finite sample properties of QML estimates and impact coefficients.

Estimation of partially specified dynamic spatial panel data models with fixed-effects

This paper studies estimation of a partially specified spatial dynamic panel data regression with fixed-effects. Under the assumption of strictly exogenous regressors and strictly exogenous spatial weighting matrix, the model is estimated by 2SLS method aided by the sieve method and through the instrumental variable. Under some sufficient conditions, the proposed estimator for the finite dimensional parameter is shown to be root-N consistent and asymptotically normally distributed. The proposed estimator for the unknown function is shown to be consistent and asymptotically distributed as well, though at a rate slower than root-N. Consistent estimators for the asymptotic variance–covariance matrices of both estimators are provided. The results can be generalized to several spatial weighting matrices and spatial matrix which vary with time. The simulation results suggest that the proposed approach has some practical value.

Quasi Maximum Likelihood Estimation of Spatial Models with Heterogeneous Coefficients

This paper considers spatial autoregressive panel data models and extends their analysis to the case where the spatial coefficients differ across the spatial units. It derives conditions under which the spatial coefficients are identified and develops a quasi maximum likelihood (QML) estimation procedure. Under certain regularity conditions, it is shown that the QML estimators of individual spatial coefficients are consistent and asymptotically normally distributed when both the time and cross section dimensions of the panel are large. It derives the asymptotic covariance matrix of the QML estimators allowing for the possibility of non-Gaussian error processes. Small sample properties of the proposed estimators are investigated by Monte Carlo simulations for Gaussian and non-Gaussian errors, and with spatial weight matrices of differing degree of sparseness. The simulation results are in line with the paper's key theoretical findings and show that the QML estimators have satisfactory small sample properties for panels with moderate time dimensions and irrespective of the number of cross section units in the panel, under certain sparsity conditions on the spatial weight matrix.

Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity

This paper considers a class of GMM estimators for general dynamic panel models, allowing for cross sectional dependence due to spatial lags and due to unspecified common shocks. We significantly expand the scope of the existing literature by allowing for endogenous spatial weight matrices, time-varying interactive effects, as well as weakly exogenous covariates. The model is expected to be useful for empirical work in both macro and microeconomics. An important area of application is in social interaction and network models where our specification can accommodate data dependent network formation. We discuss explicit examples from the recent social interaction literature. Identification of spatial interaction parameters is achieved through a combination of linear and quadratic moment conditions. We develop an orthogonal forward differencing transformation to aid in the estimation of factor components while maintaining orthogonality of moment conditions. This is an important ingredient to a tractable asymptotic distribution of our estimators. In the social interactions example, orthogonal forward differencing amounts to controlling for unobserved correlated effects by combining multiple outcome measures.

Mechanism for Producer Services to Upgrade Value Chain from the Perspective of Spatial Networks

The study aimed to analyze the function mechanism for producer services to upgrade value chain based on spatial networks, with regional domestic Export Sophistication Index for measuring the position of China’s provinces in the global value chain. Using spatial econometrics model, the study set up a variety of spatial weight matrices, to empirically test the spatial networks’ effect as a result of the producer services with changes in the positions of China’s various provinces in the global value chain. Results indicate that: first, the producer services have an obvious spatial networks effect on upgrading of the various parts of China in the global value chain. Second, the estimated results of distance based spatial weights matrix model were contiguity based spatial weights matrix results, implying that space network effect is not limited to the neighboring provinces. Third, the spatial network effect of economic based weights matrix model was stronger than distance based spatial weights matrix model, which shows that today, the changing value chain of Chinese provinces is more inclined to “regional powerful combination”, rather than “regional strength complementary”.

Economic Development And Transfrontier Shipments Of Waste In Poland – Spatio-Temporal Analysis

The aim of the paper is to apply the spatio-temporal Environmental Kuznets Curve (SpEKC) to test the relationship between economic growth and the amount of collected mixed municipal waste. The analysis was conducted at the level of sixty-six Polish sub-regions. The study contained selected environmental indicators. The dependent variable - the amount of municipal waste generated in kilograms per capita characterized the state of the environment. The GDP per capita in constant prices (as an explanatory variable) presented the level of economic development of the sub-regions. In the empirical part of the research there were used spatial panel data models based on EKCs. It determined the levels of economic development, at which the amount of produced wastes has fallen or increased, depending on the wealth of the region. The application of different types of spatial weight matrices was an important element of this modelling. Data obtained the years 2005-2012. Models were estimated in the RCran package.

Modeling spatial patterns of rare species using eigenfunction-based spatial filters: An example of modified delta model for zero-inflated data

Data of rare species usually contain a high percentage of zero observations due to their low abundance. Such data are generally referred as zero-inflated data. Modeling spatial patterns in such data has been challenging, especially when large datasets are involved and intensive computing are required. The eigenfunction-based spatial filtering provides a flexible tool that allows the existing modeling approaches that can handle zero-inflated data such as the delta model to be applied in the presence of spatial dependence. With a real dataset, the longline seabird bycatch data, the present study demonstrated a modification of delta model with the spatial filters to investigate spatial patterns in zero-inflated data for rare species. We explored a total of 108 spatial weighting matrices, and modified the delta model by incorporating the spatial filters generated from the best spatial weighting matrix. We applied the five-fold cross-validation to compare performance of the modified delta model with other three candidate models based on the mean absolute error and the mean bias. The three candidate models included the baseline model without spatial dependence considered, the trend-surface generalized additive model and the random areal effect model. The delta model modified with spatial filters showed superior performance over the other three candidate models in the seabird bycatch example. With the seabird bycatch example, we illustrated a modification of delta model with the eigenfunction-based spatial filters to investigate spatial patterns. This study provides an alternative to incorporate spatial dependence in the existing approaches for modeling spatial patterns in zero-inflated data for rare species.