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Inference for Income Mobility Measures in the Presence of Spatial Dependence

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  • Wei Kang
  • Sergio J. Rey

Abstract

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.

Suggested Citation

  • Wei Kang & Sergio J. Rey, 2020. "Inference for Income Mobility Measures in the Presence of Spatial Dependence," International Regional Science Review, , vol. 43(1-2), pages 10-39, January.
    • Handle: RePEc:sae:inrsre:v:43:y:2020:i:1-2:p:10-39
    DOI: 10.1177/0160017619826291
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    References listed on IDEAS

    as
    1. Trede Mark, 1999. "Statistical Inference for Measures of Income Mobility / Statistische Inferenz zur Messung der Einkommensmobilität," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 218(3-4), pages 473-490, June.
    2. Sergio J. Rey & Wei Kang & Levi Wolf, 2016. "The properties of tests for spatial effects in discrete Markov chain models of regional income distribution dynamics," Journal of Geographical Systems, Springer, vol. 18(4), pages 377-398, October.
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