Examining the spatial and non-spatial linkages between suburban housing markets

Purpose The purpose of this paper is on developing and implementing a model which provides a fuller and more comprehensive reflection of the interaction of house prices at the suburb level. Design/methodology/approach The authors examine how changes in housing prices evolve across space within the suburban context. In doing so, the authors developed a model which allows for suburbs to be connected both because of their geographic proximity but also by non-spatial factors, such as similarities in socioeconomic or demographic characteristics. This approach is applied to modelling home price dynamics in Melbourne, Australia, from 2007 to 2018. Findings The authors found that including both spatial and non-spatial linkages between suburbs provides a better representation of the data. It also provides new insights into the way spatial shocks are transmitted around the city and how suburban housing markets are clustered. Originality/value The authors have generalized the widely used SAR model and advocated building a spatial weights matrix that allows for both geographic and socioeconomic linkages between suburbs within the HOSAR framework. As the authors outlined, such a model can be easily estimated using maximum likelihood. The benefits of such a model are that it yields an improved fit to the data and more accurate spatial spill-over estimates.

Spatial Models in Econometric Research

Since the late 1990s, spatial models have become a growing addition to econometric research. They are characterized by attention paid to the location of observations (i.e., ordered spatial locations) and the interaction among them. Specifically, spatial models formally express spatial interaction by including variables observed at other locations into the regression specification. This can take different forms, mostly based on an averaging of values at neighboring locations through a so-called spatially lagged variable, or spatial lag. The spatial lag can be applied to the dependent variable, to explanatory variables, and/or to the error terms. This yields a range of specifications for cross-sectional dependence, as well as for static and dynamic spatial panels. A critical element in the spatially lagged variable is the definition of neighbor relations in a so-called spatial weights matrix. Historically, the spatial weights matrix has been taken to be given and exogenous, but this has evolved into research focused on estimating the weights from the data and on accounting for potential endogeneity in the weights. Due to the uneven spacing of observations and the complex way in which asymptotic properties are obtained, results from time series analysis are not applicable, and specialized laws of large numbers and central limit theorems need to be developed. This requirement has yielded an active body of research into the asymptotics of spatial models.

Bias from Network Misspecification Under Spatial Dependence

The prespecification of the network is one of the biggest hurdles for applied researchers in undertaking spatial analysis. In this letter, we demonstrate two results. First, we derive bounds for the bias in nonspatial models with omitted spatially-lagged predictors or outcomes. These bias expressions can be obtained without prior knowledge of the network, and are more informative than familiar omitted variable bias formulas. Second, we derive bounds for the bias in spatial econometric models with nondifferential error in the specification of the weights matrix. Under these conditions, we demonstrate that an omitted spatial input is the limit condition of including a misspecificed spatial weights matrix. Simulated experiments further demonstrate that spatial models with a misspecified weights matrix weakly dominate nonspatial models. Our results imply that, where cross-sectional dependence is presumed, researchers should pursue spatial analysis even with limited information on network ties.

Determinants of Per Capita Personal Income in the US: Spatial Fixed Effects Panel Data Modeling

Over the last decades, the Per Capita Personal Income (PCPI) variable was a common measure of the effectiveness of economic development policy. Therefore, this paper is an attempt to investigate the determinants of personal income by using spatial panel data models for 48 U.S. states during the period from 2009 to 2017. We utilize the three following models: spatial autoregressive (SAR) model, Spatial Error (SEM) Model, and Spatial Autoregressive Combined (SAC) model, with individual (or spatial) fixe deffects according to three different known methods for constructing spatial weights matrices: binary contiguity, inverse distance, and Gaussian transformation spatial weights matrix. Additionally, we pay attention for direct and indirect effects estimates of the explanatory variables for SAR, SEM, and SAC models. The second objective of this paper is to show how to select the appropriate model to fit our data. The results indicate that the three used spatial weights matrices provide the same result based on goodness of fit criteria, and the SAC model is the most appropriate model among the models presented. However, the SAC model with spatial weights matrix based on inverse distance is better compared to other used models. Also, the results indicate that percentage of individuals with graduate or professional degree, real Gross Domestic Product (GDP) per capita,and number of nonfarm jobs have a positive impact on the PCPI, while the percentage of individuals without degree or bachelor’s degree have a negative impact on the PCPI.

A New Approach to Identifying Crash Hotspot Intersections (CHIs) Using Spatial Weights Matrices

In this paper we develop a new approach to directly detect crash hotspot intersections (CHIs) using two customized spatial weights matrices, which are the inverse network distance-band spatial weights matrix of intersections (INDSWMI) and the k-nearest distance-band spatial weights matrix between crash and intersection (KDSWMCI). This new approach has three major steps. The first step is to build the INDSWMI by forming the road network, extracting the intersections from road junctions, and constructing the INDSWMI with road network constraints. The second step is to build the KDSWMCI by obtaining the adjacency crashes for each intersection. The third step is to perform intersection hotspot analysis (IHA) by using the Getis–Ord Gi* statistic with the INDSWMI and KDSWMCI to identify CHIs and test the Intersection Prediction Accuracy Index (IPAI). This approach is validated by comparison of the IPAI obtained using open street map (OSM) roads and intersection-related crashes (2008–2017) from Spencer city, Iowa, USA. The findings of the comparison show that higher prediction accuracy is achieved by using the proposed approach in identifying CHIs.

Bias from network misspecification under spatial dependence

The pre-specification of the network is one of the biggest hurdles for applied researchers in undertaking spatial analysis. In this letter, we demonstrate two results. First, we derive bounds for the bias in non-spatial models with omitted spatially-lagged predictors or outcomes. These bias expressions can be obtained without prior knowledge of the network, and are more informative than familiar omitted variable bias formulas. Second, we derive bounds for the bias in spatial econometric models with non-differential error in the specification of the weights matrix. Under these conditions, we demonstrate that an omitted spatial input is the limit condition of including a misspecificed spatial weights matrix. Simulated experiments further demonstrate that spatial models with a misspecified weights matrix weakly dominate non-spatial models. Our results imply that, where cross-sectional dependence is presumed, researchers should pursue spatial analysis even with limited information on network ties.

Measurement Error and the Specification of the Weights Matrix in Spatial Regression Models

While the spatial weights matrix $\boldsymbol{W}$ is at the core of spatial regression models, there is a scarcity of techniques for validating a given specification of $\boldsymbol{W}$. I approach this problem from a measurement error perspective. When $\boldsymbol{W}$ is inflated by a constant, a predictable form of endogeneity occurs that is not problematic in other regression contexts. I use this insight to construct a theoretically appealing test and control for the validity of $\boldsymbol{W}$ that is tractable in panel data, which I call the K test. I demonstrate the utility of the test using Monte Carlo simulations.