The Annals of Regional Science

, Volume 61, Issue 1, pp 73–93 | Cite as

Conditional and joint tests for spatial effects in discrete Markov chain models of regional income distribution dynamics

  • Wei KangEmail author
  • Sergio J. Rey
Original Paper


Spatial effects have been recognized to play an important role in transitional dynamics of regional incomes. Detection and evaluation of both spatial heterogeneity and spatial dependence in discrete Markov chain models, which have been widely applied to the study of regional income distribution dynamics and convergence, are vital, but under-explored issues. Indeed, in this spatiotemporal setting, spatial effects can take much more complex forms than that in a pure cross-sectional setting. In this paper, we address two test frameworks. The first is a conditional spatial Markov chains test framework, which can be used to detect spatial heterogeneity and temporally lagged spatial dependence; the second is a joint spatial Markov chains test framework, which tests for contemporaneous spatial dependence. A series of Monte Carlo experiments are designed to examine size, power and robustness properties of these tests for a range of sample sizes (spatial \(\times \) temporal dimensions), for different levels of discretization granularity and for different number of regimes. Results indicate that all tests display good size property except when sample size is fairly small. All tests for spatial dependence are similar in almost all aspects—size, power and robustness. Conditional spatial Markov tests for spatial heterogeneity have highest power for detecting spatial heterogeneity. Granularity of discretization has a major impact on the size properties of the tests when sample size is fairly small.

JEL Classification

C12 O47 R11 



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

Supplementary material

168_2017_859_MOESM1_ESM.pdf (77 kb)
Supplementary material 1 (pdf 77 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Geographical Sciences and Urban PlanningArizona State UniversityTempeUSA
  2. 2.Center for Geospatial Sciences, School of Public PolicyUniversity of California, RiversideRiversideUSA

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