The Spatial Dependence of Judicial Data


This article examines the significance of spatial dependence in judicial activity rates using aggregated geographical data of 60 Mexican metropolitan areas. It begins with a theoretical discussion on spatial variation, spatial dependence, and spatial heterogeneity. Later, spatial statistics demonstrate a strong clustering of judicial activity in northern Mexico. In terms of social correlates, judicial activity is found to significantly increase with better public institutions and to decrease with better urban infrastructure conditions. Spatial models accounted for the spatial autocorrelation in the residuals, telling that the spatial variation in judicial activity is not independent of the aggregate social characteristics of the population. These results support the functional versus the local contextual hypothesis of spatial variation. However, additional research is needed to evaluate the impact of future institutional and urban infrastructure developments. A crucial implication of the results is that future legal empirical research must incorporate spatial effects into their models.

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  1. 1.

    If there is negative spatial autocorrelation (i.e. dispersion), the effect is right the opposite: sampling variance is overestimated.

  2. 2.

    The latest year for which data is available.

  3. 3.

    The total number of metropolitan areas is 60 encompassing 226 municipalities. Theft suspects rates were calculated for each metropolitan area.

  4. 4.


  5. 5.

    A statistically significant result, in this case, a statistically significant geographical unit, is that which differs by 1.96 standard errors or more from the rest. For our study, a significant spatial cluster, or outlier, is that metropolitan area which shows to have a judicial activity rate above or below 1.96 standard error times from its neighboring areas arithmetic mean. This latter result suggesting that we are dealing with a statistically distinctive metropolitan area.

  6. 6.

    Remember that regional variation is due to a regionalization process (categorization) which is intrinsically subjective, whereas spatial variation is necessarily objective since it is constrained to physical (often linear) distance.

  7. 7.

    Although the yearly rates for the data set (n = 60) were normally distributed, not all regional distributions were normally distributed. Neither regional variances were homogeneous; this table is not included. As a result, I applied the non-parametric alternative for k > 2 groups test of difference (i.e. the Kruskal-Wallis test).

  8. 8.

    This is the result of a Mann-Whitney’s two independent samples test.

  9. 9.

    CIDE stands for Centro de Investigacion y Docencia Economicas.

  10. 10.

    The CIDE index was specifically developed to provide a measure of competitiveness for these 60 metropolitan areas.

  11. 11.

    r = .238, p = 0.066

  12. 12.

    Remember that institutional capacity was unrelated to urban infrastructure capacity.

  13. 13.

    In Spanish “cifra negra” It is considered black for its opaque black-box qualities.

  14. 14.

    Black figures are high when victims do not go to the police to make a warrant.

  15. 15.

    Notice the absence of evidence regarding a statistical linear correlation between institutional and urban metropolitan capacities.


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Correspondence to Carlos J. Vilalta.

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I would like to thank Professor Jeff Gill from the Center for Applied Statistics at Washington University in St. Louis (WUSTL) for providing excellent research facilities and an energizing intellectual atmosphere. I would also like to thank professors James Monogan and Itai Sened for their interest in my work.

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Vilalta, C.J. The Spatial Dependence of Judicial Data. Appl. Spatial Analysis 5, 273–289 (2012).

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  • Theft crimes
  • Judicial data
  • Spatial dependence
  • Spatial statistics
  • Mexico