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Regional income convergence and divergence has been an active field of research for more than 20 years, and research papers in this field are still being produced at a prodigious rate. Despite their importance for the study of dynamics of income distribution, interactive visualization tools revealing spatiotemporal dimensions of the income data have been sparsely developed. This study introduces a visual analytics system for the space–time analysis of income dynamics. We use state‐level US income data from 1929 to 2009 to demonstrate the visual analytics system and its utility for exploring similar data. The system consists of two modules, visualization and analytics. The visualization module, a Web‐based front‐end called Rank‐Path Visualizer (RPV), draws inspiration from the cartographic technique of flow mapping, originally developed by Tobler and embodied in his canonical Flow Mapper application. [ABSTRACT FROM AUTHOR]

Stochastic dominance tests are used to measure whether distributions are directionally‐distinct. Using stochastic dominance measures, an income distribution can be measured to be more favorable for its members at all income levels than another distribution. This contrasts with conventional σ and β‐convergence approaches that compare distributions at a set of predetermined income levels. Given this comprehensiveness, stochastic dominance measures can yield novel insight into the relationship between income distributions, and thus to the relative economic welfare of inhabitants of different societies. However, stochastic dominance measures used in the analysis of regional income convergence have ignored the complications of geography. In this paper we examine the properties of common tests for stochastic dominance using various descriptive models of geographically‐realistic income growth processes. We find that the false positive rate of stochastic dominance tests increases significantly when comparing spatially‐informed income distributions growing over time. Further, this over‐eager rejection rate requires only that one distribution be spatially‐dependent, unlike some other bivariate statistics. We demonstrate that both the parametric and non‐parametric spatial filtering procedures are effective at resolving these issues in restricted circumstances for higher‐order dominance tests. Overall, while providing a novel and useful perspective on income distribution dynamics, stochastic dominance measures are demonstrated to have undesirable properties when used in geographically‐realistic scenarios and they resist one common method to address these issues. Solutions to the concerns expressed here remain open. [ABSTRACT FROM AUTHOR]

Social and interregional inequality patterns across US states from 1929–2012 are analyzed using exploratory space–time methods. The results suggest complex spatial dynamics for both inequality series that were not captured by the stylized model of Alonso. Interpersonal income inequalities of states displayed a U-shaped pattern ending the period at levels that exceeded the alarmingly high patterns that existed in the 1920s. Social inequality is characterized by greater mobility than that found for state per capita incomes. Spatial dependence is also distinct between the two series, with per capita incomes exhibiting strong global spatial autocorrelation, while state interpersonal income inequality does not. Local hot and cold spots are found for the per capita income series, while local spatial outliers are found for state interpersonal inequality. Mobility in both inequality series is found to be influenced by the local spatial context of a state. [ABSTRACT FROM AUTHOR]

Discrete Markov chain models (DMCs) have been widely applied to the study of regional income distribution dynamics and convergence. This popularity reflects the rich body of DMC theory on the one hand and the ability of this framework to provide insights on the internal and external properties of regional income distribution dynamics on the other. In this paper we examine the properties of tests for spatial effects in DMC models of regional distribution dynamics. We do so through a series of Monte Carlo simulations designed to examine the size, power and robustness of tests for spatial heterogeneity and spatial dependence in transitional dynamics. This requires that we specify a data generating process for not only the null, but also alternatives when spatial heterogeneity or spatial dependence is present in the transitional dynamics. We are not aware of any work which has examined these types of data generating processes in the spatial distribution dynamics literature. Results indicate that tests for spatial heterogeneity and spatial dependence display good power for the presence of spatial effects. However, tests for spatial heterogeneity are not robust to the presence of strong spatial dependence, while tests for spatial dependence are sensitive to the spatial configuration of heterogeneity. When the spatial configuration can be considered random, dependence tests are robust to the dynamic spatial heterogeneity, but not so to the process mean heterogeneity when the difference in process means is large relative to the variance of the time series. [ABSTRACT FROM AUTHOR]

In the study of income inequality dynamics, the concept of exchange mobility plays a central role. Applications of classical rank correlation statistics have been used to assess the degree to which individual economies swap positions in the income distribution over time. These classic measures ignore the underlying geographical pattern of rank changes. Rey (2004) introduced a spatial concordance statistic as an extension of Kendall's rank correlation statistic, a commonly employed measure of exchange mobility. This article suggests local forms of the global spatial concordance statistic: local indicators of mobility association (LIMA). The LIMA statistics allow for the decomposition of the global measure into the contributions associated with individual locations. They do so by considering the degree of concordance (stability) or discordance (exchange mobility) reflected within an economy's local spatial context. Different forms of the LIMAs derive from alternative expressions of the neighborhood and neighbor set. Additionally, the additive decomposition of the LIMAs permits the development of a mesolevel analytic to examine whether the overall space–time concordance is driven by either interregional or intraregional concordance. The measures are illustrated in a case study that examines regional income dynamics in Mexico. [ABSTRACT FROM AUTHOR]

In this paper we examine the trajectory of regional income inequality dynamics for two neighboring national systems. Using data on 3038 US counties and 2418 Mexico municipios, from 2000, 2005, and 2010, we employ recent extensions of spatial Markov chains and space-time mobility measures, to consider the following questions: Are regional inequality dynamics fundamentally distinct between Mexico and the United States? Does the role of spatial context influence the distributional dynamics of the two systems? Finally we examine if there is a distinct international border region that displays inequality dynamics different from those of the internal regions of the two national systems. Strong evidence of spatial heterogeneity in regional income mobility is found between the two national systems, with Mexico having higher mobility relative to the US. The international border region is found to have distinct mobility dynamics from either national system, experiencing the strongest mobility. Extensive evidence of spatial contextual effects are found throughout the US-Mexican pooled data set indicating that a region's transitional dynamics are influenced by incomes of neighboring regions. [ABSTRACT FROM AUTHOR]

Markov chains have become a mainstay in the literature on regional income distribution dynamics and convergence. Despite its growing popularity, the Markov framework has some restrictive characteristics associated with the underlying discretization income distributions. This paper introduces several new approaches designed to mitigate some of the issues arising from discretization. Based on the examination of rank distributions, two new Markov-based chains are developed. The first explores the movement of individual economies through the income rank distribution over time. The second provides insight on the movements of ranks over geographical space and time. These also serve as the foundation for two new tests of spatial dynamics or the extent to which movements in the rank distribution are spatially clustered. An illustration of these new methods is included using income data for the lower 48 US states for the years 1929-2009. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Income mobility measures provide convenient and concise ways to reveal the dynamic nature of regional income distributions. Statistical inference about these measures is important especially when it comes to a comparison of two regional income systems. Although the analytical sampling distributions of relevant estimators and test statistics have been asymptotically derived, their properties in small sample settings and in the presence of contemporaneous spatial dependence within a regional income system are underexplored. We approach these issues via a series of Monte Carlo experiments that require the proposal of a novel data generating process capable of generating spatially dependent time series given a transition probability matrix and a specified level of spatial dependence. Results suggest that when sample size is small, the mobility estimator is biased while spatial dependence inflates its asymptotic variance, raising the Type I error rate for a one-sample test. For the two-sample test of the difference in mobility between two regional economic systems, the size tends to become increasingly upward biased with stronger spatial dependence in either income system, which indicates that conclusions about differences in mobility between two different regional systems need to be drawn with caution as the presence of spatial dependence can lead to false positives. In light of this, we suggest adjustments for the critical values of relevant test statistics. [ABSTRACT FROM AUTHOR]