Space–Time Patterns of Rank Concordance: Local Indicators of Mobility Association with Application to Spatial Income Inequality Dynamics

Abstract

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.

在研究所得不均的动态中, 交换能动性的概念扮演了核心角色。古典的等级相关统计, 长期以来被用来评估个人经济在所得分布中, 随着时间交换位置的程度。这些古典方法, 忽略了等级改变的根本地理模式。瑟吉欧༎瑞 (Rey 2004) 引进了空间一致性统计, 作为肯德尔(Kendall) 的等级相关统计的延伸, 该方法广泛运用于交换能动性之中。本文主张全球空间一致性统计的在地形式 : 能动性关联 (LIMA) 的在地指标。 LIMA 统计能将全球测量方法分解成与个人区位有关的贡献。它们透过考量一个经济体的在地空间脉络所反映的一致性 (稳定) 或不一致性(交换能动性) 的程度进行上述工作。不同形式的 LIMAs, 从邻里和邻近集合的其它表现中衍生而出。此外, LIMAs 的进一步分解, 让中等层级的分析发展, 能够检视总体的时空一致性是否是由跨区域或区域内的一致性所驱动。该方法在一个检视墨西哥区域所得动态的案例研究中进行说明。

En el estudio de la dinámica de desigualdad del ingreso, el concepto de movilidad del intercambio juega un papel central. Las aplicaciones de estadísticas clásicas de la correlación de rangos han sido usadas para evaluar el grado con el que las economías individuales intercambian posiciones en la distribución del ingreso conforme pasa el tiempo. Estas medidas clásicas ignoran el patrón geográfico subyacente de los cambios de rango. Rey (2004) introdujo una estadística de concordancia espacial como extensión de la estadística de correlación de rangos de Kendall, una medida de movilidad de intercambio comúnmente empleada. Este artículo sugiere formas locales de la estadística de concordancia espacial global: los indicadores locales de asociación de la movilidad (LIMA, por su acrónimo en inglés). Las estadísticas LIMA permiten la descomposición de la medida global en las contribuciones asociadas con localizaciones individuales. Hacen eso considerando el grado de concordancia (estabilidad) o de discordancia (movilidad de intercambio) reflejadas dentro del contexto espacial local de una economía. Formas diferentes de las LIMAs provienen de expresiones alternativas del vecindario y del escenario del vecino. Adicionalmente, la descomposición añadida de las LIMAs permite el desarrollo de una herramienta de análisis de nivel intermedio para examinar si la concordancia espacio-tiempo en general es controlada por concordancia interregional o intrarregional. Las medidas se ilustran por medio de un estudio de caso que examina la dinámica regional del ingreso en México.

Key Words:

• autocorrelation
• concordance
• inequality
• space–time

关键词：:

• 自相关, 一致性, 不均, 时空。

Palabras clave:

• autocorrelación, concordancia, desigualdad, espacio-tiempo

Acknowledgments

Comments and suggestions by Dani Arribes-Bel, Janet Franklin, Wei Kang, Julia Koschinsky, Trisalyn Nelson, Myrna Sastre Gutiérrez, Levi Wolf, three anonymous referees, and the editor are greatly appreciated. Any remaining errors are mine alone.

Supplemental Material

The code and data to reproduce the results of this article are available at: http://github.com/sjsrey/limaaag

Funding

This research was supported in part by National Science Foundation Grant SES-1421935.

Notes

1. The focus in this article is on new methods for the analysis of regional income inequality dynamics. The literatures on inequality in personal income distributions, where the observational unit is an individual, and regional income inequality, where the observational unit is a regional economy, are largely separate ones. For a recent examination of the potential linkages between these two literatures, see Rey (2016).

2. Figure 6A contains a map of the Mexican states.

3. Spatial autocorrelation is measured with Moran's and a row-standardized Queen contiguity matrix using the PySAL library (Rey and Anselin 2007).

4. I thank the anonymous referees for these suggestions.

Additional information

Notes on contributors

Sergio J. Rey

SERGIO J. REY is a Professor in the School of Geographical Sciences and Urban Planning at Arizona State University, Tempe, AZ 85287. E-mail: [email protected]. His research interests include spatiotemporal data analysis, geocomputation, geovisualization, regional inequality dynamics, open science, and regional science.