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Spatiotemporal methods for analysis of urban system dynamics: an application to Chile

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Abstract

This paper presents a methodological procedure to evaluate the influence of spatial proximity on evolution of cities to detect regional differences in their spatiotemporal dynamics. The six-step method based on a set of statistical methods can be computed with a new R package: estdaR. The first step consists of the usual characterization of the cross-sectional distribution of the urban areas by means of nonparametric estimations of density functions for a set of significant years. In the second and third steps, the growth process is modeled as a first-order stationary Markov chain to evaluate the effect of global and local spatial autocorrelation on the transition probabilities with a set of indices based on the spatial version of the standard Markov chain. The fourth, fifth, and sixth steps perform in-depth analysis to detect the existence and interaction of spatial regimes in the movement direction and ranking mobility of urban distribution. We apply this novel strategy for the period 1930–2002 to analyze the entire Chilean urban system—not only the Central Zone, in which most of the population and economic activities are concentrated, but also other urban zones in the country.

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Notes

  1. This phenomenon is also common in other Latin American countries with highly centralized governments exerting greater control over resources (Willis et al. 1999).

  2. estdaR must be installed in the R console: devtools::install_github("amvallone/estdaR").

  3. Throughout this paper, the terms “movement” and “mobility” refer to movements across the population distribution, as is common in the social inequality literature (Kang and Rey 2019). In this context, population mobility could thus be viewed as a re-ranking phenomenon in which cities switch population positions. Mobility could also be viewed as occurring, however, whenever cities move away from their previous city size levels. The former is termed absolute mobility and the latter relative mobility.

  4. Spatial autocorrelation and spatial dependence are used as interchangeable terms, though in strong sense, the first is a specific type of the second.

  5. Spatial Markov chains have also been applied in other contexts, such as employment of disabled people (Agovino 2014), pro-environmental behavior (Agovino et al. 2016) and quality of life (Delmelle et al. 2016).

  6. A rose diagram is a circular chart to display data that contain direction and magnitude variables. They normally comprises of 8 or 16 radiating spokes, which represent degrees of a circle or compass points North, East, South, West and their intermediate directions. Each direction axis has values increasing outwards and similar to pie charts, the data are divided into proportional slices or sectors. The arc length of each slice is proportional to the quantity it represents.

  7. Rey (2016) presents the full mathematical decomposition of this index.

  8. Despite the existence of previous censuses, we choose 1930 as the first period of analysis because the Southern city of Aysen was founded in 1928. We include Aysen in the sample because cities are scarce and sparsely disseminated in the far South of Chile. We excluded information from the 2012 Chilean census due to significant methodological problems. The new 2017 census data on entities are not yet available. For more information, see Instituto Nacional de Estadísticas (2014).

  9. The Republic of Chile is politically divided into regions, provinces, “comunas” (municipalities) and censal districts. Each municipality contains different “entities”: cities, towns, villages, and hamlets, among others.

  10. There are 10 cities registered in the 2002 Census but not in the 1930 Census: Alto Hospicio (Region I), Estación Zaldivar (Region II), El Salvador (Region III), El Quisco (Region V), Quirihue (Region VIII), Padre de las Casas and Labranza (Region IX), Panguipulli and Los Muermos (Region X), and Padre Hurtado (Metropolitan Region). To homogenize the panel database, we added the population of these new cities to their corresponding originals. For example, since Alto Hospicio became independent of Iquique before the 2002 Census, the population of the former was added to that of the latter.

  11. As a robustness check, similar results were obtained with other spatial weight specifications, such as driving distance and other neighborhood measures. Complete computations are available from the authors upon request.

  12. In this paper, p values are computed with a 1000-replication process.

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Funding

The funding was provided by Ministerio de Economía, Industria y Competitividad, Gobierno de España (Grand No. ECO2015-65758-P).

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Correspondence to Coro Chasco.

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Appendices

Appendix 1

See Table 6.

Table 6 List of the Chilean cities and labor market areas (LMAs) used in this paper

Appendix 2

See Fig. 6.

Fig. 6
figure 6figure 6

Spatial regimes of urban subsystems in Chile

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Vallone, A., Chasco, C. Spatiotemporal methods for analysis of urban system dynamics: an application to Chile. Ann Reg Sci 64, 421–454 (2020). https://doi.org/10.1007/s00168-019-00960-9

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