The COVID-19 pandemic has caused unprecedented losses for small businesses in cities across the globe. Policymakers have relied on a wide range of measures to support firms and sustain business continuity. However, significant concerns have been expressed about the degree of equity in the distribution and efficiency of government assistance during the pandemic disruption. Drawing on the case of the Paycheck Protection Program (PPP) and its implementation in inland Southern California, this study examines the spatial distribution of PPP loans at the neighborhood level. Based on spatial regressions and in-depth interviews with small businesses, banks, government agencies, and nonprofit organizations, the study finds that, in terms of their total number and value, the PPP loans have roughly succeeded in reaching their small business targets. However, communities with higher shares of pandemic-vulnerable businesses or higher levels of socioeconomic vulnerability are less likely to have received PPP loans. There have also been spatial spillover effects of community vulnerability when it comes to receiving PPP loans at the neighborhood level. The correlation between fewer PPP loans and community vulnerability also reflects both short-term needs and longstanding challenges facing entrepreneurship and business development in socioeconomically disadvantaged communities. Moreover, small business resilience and community resilience are inseparable, and thus government business assistance must be considered in the context of local communities.

This chapter provides an overview of exploratory approaches to spatial dynamics. The focus is on the application and evidence within social sciences. Spatial dynamics is concerned about the changes in both the spatial and temporal dimensions. Two types of exploratory methods to spatial dynamics are differentiated. The first type extends classic longitudinal methods to interrogate the role of locations in shaping the temporal dynamics, while the second type extends exploratory spatial data analysis methods to investigate its temporal changes. Example methods for each type are illustrated, including spatial explicit Markov methods, a family of spatially explicit rank concordance, and space-time LISA. Though these methods are promising in advancing spatial and spatiotemporal thinking in social sciences, a lack of dynamic cross-fertilization between the field of geographical methodology and social sciences is recognized.

Small businesses have suffered disproportionately from the COVID-19 pandemic. We use near-real-time weekly data from the Small Business Pulse Survey (April 26, 2020 - June 17, 2021) to examine the constantly changing impact of COVID-19 on small businesses across the United States. A set of multilevel models for change are adopted to model the trajectories of the various kinds of impact as perceived by business owners (subjective) and those recorded for business operations (objective), providing insights into regional resilience from a small business perspective. The findings reveal spatially uneven and varied trajectories in both the subjectively and the objectively assessed impact of COVID-19 across the U.S., and the different responses to the pandemic shock can be explained by evolving health situations and public policies, as well as by the economic structure and degree of socioeconomic vulnerability in different areas. This study contributes to scholarship on small businesses and regional resilience, as well as identifying policies and practices that build economic resilience and regional development under conditions of global pandemic disruption.

In this paper we move away from a static view of neighbourhood inequality and investigate the dynamics of neighbourhood economic status, which ties together spatial income inequality at different moments in time. Using census data from three decades (1980–2010) in 294 metropolitan statistical areas, we use a statistical decomposition method to unpack the aggregate spatiotemporal income dynamic into its contributing components: stability, growth and polarisation, providing a new look at the economic fortunes of diverse neighbourhoods. We examine the relative strength of each component in driving the overall pattern, in addition to whether, how, and why these forces wax and wane across space and over time. Our results show that over the long run, growth is a dominant form of change across all metros, but there is a very clear decline in its prominence over time. Further, we find a growing positive relationship between the components of dispersion and growth, in a reversal of prior trends. Looking across metro areas, we find temporal heterogeneity has been driven by different socioeconomic factors over time (such as sectoral growth in certain decades), and that these relationships vary enormously with geography and time. Together these findings suggest a high level of temporal heterogeneity in neighbourhood income dynamics, a phenomenon which remains largely unexplored in the current literature. There is no universal law governing the changing economic status of neighbourhoods in the US over the last 40 years, and our work demonstrates the importance of considering shifting dynamics over multiple spatial and temporal scales.

As spatial statistics are essential to the geographical inquiry, accessible and flexible software offering relevant functionalities is highly desired. Python Spatial Analysis Library (PySAL) represents an endeavor towards this end. It is an open-source python library and ecosystem hosting a wide array of spatial statistical and visualization methods. Since its first public release in 2010, PySAL has been applied to address various research questions, used as teaching materials for pedagogical purposes in regular classes and conference workshops serving a wide audience, and integrated into general GIS software such as ArcGIS and QGIS. This entry first gives an overview of the history and new development with PySAL. This is followed by a discussion of PySAL’s new hierarchical structure, and two different modes of accessing PySAL’s functionalities to perform various spatial statistical tasks, including exploratory spatial data analysis, spatial regression, and geovisualization. Next, a discussion is provided on how to find and utilize useful materials for studying and using spatial statistical functions from PySAL and how to get involved with the PySAL community as a user and prospective developer. The entry ends with a brief discussion of future development with PySAL.

Scale is a fundamental geographic concept, and a substantial literature exists discussing the various roles that scale plays in different geographical contexts. Relatively little work exists, though, that provides a means of measuring the geographic scale over which different processes operate. Here we demonstrate how geographically weighted regression (GWR) can be adapted to provide such measures. GWR explores the potential spatial nonstationarity of relationships and provides a measure of the spatial scale at which processes operate through the determination of an optimal bandwidth. Classical GWR assumes that all of the processes being modeled operate at the same spatial scale, however. The work here relaxes this assumption by allowing different processes to operate at different spatial scales. This is achieved by deriving an optimal bandwidth vector in which each element indicates the spatial scale at which a particular process takes place. This new version of GWR is termed multiscale geographically weighted regression (MGWR), which is similar in intent to Bayesian nonseparable spatially varying coefficients (SVC) models, although potentially providing a more flexible and scalable framework in which to examine multiscale processes. Model calibration and bandwidth vector selection in MGWR are conducted using a back-fitting algorithm. We compare the performance of GWR and MGWR by applying both frameworks to two simulated data sets with known properties and to an empirical data set on Irish famine. Results indicate that MGWR not only is superior in replicating parameter surfaces with different levels of spatial heterogeneity but provides valuable information on the scale at which different processes operate.