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Regional Convergence, Spatial Scale, and Spatial Dependence: Evidence from Homicides and Personal Injuries in Colombia 2010-2018

Regional Convergence, Spatial Scale, and Spatial Dependence: Evidence from Homicides and Personal Injuries in Colombia 2010-2018

QuarRCS-lab

July 27, 2020
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  1. Regional Convergence, Spatial Scale, and Spatial
    Regional Convergence, Spatial Scale, and Spatial
    Dependence:
    Dependence:
    Evidence from Homicides and Personal Injuries in Colombia 2010-2018
    Evidence from Homicides and Personal Injuries in Colombia 2010-2018
    Felipe Santos-Marquez
    Felipe Santos-Marquez
    Master’s student
    Master’s student
    Graduate School of International Development
    Graduate School of International Development
    Nagoya University, JAPAN
    Nagoya University, JAPAN
    Carlos Mendez
    Carlos Mendez
    Graduate School of International Development
    Graduate School of International Development
    Nagoya University, JAPAN
    Nagoya University, JAPAN
    Prepared for the 2020 Bolivian Conference on Development Economics July 27th
    Prepared for the 2020 Bolivian Conference on Development Economics July 27th
    [ Working paper available at:
    [ Working paper available at: https://felipe-santos.rbind.io/
    https://felipe-santos.rbind.io/]
    ]

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  2. Motivation:
    Motivation:
    Beyond GDP, socio-economic variables and their convergence are relevant for
    Beyond GDP, socio-economic variables and their convergence are relevant for
    development studies (Royuela et al 2015)
    development studies (Royuela et al 2015)
    Persistent income di erences, di erences in health indicators and in "general"
    Persistent income di erences, di erences in health indicators and in "general"
    regional inequality in Colombia.
    regional inequality in Colombia.
    Scarce academic literature on convergence at the municipal level.
    Scarce academic literature on convergence at the municipal level.
    Research Objective:
    Research Objective:
    Study convergence/divergence of homicide rates (
    Study convergence/divergence of homicide rates (NMR
    NMR) and personal injury rates
    ) and personal injury rates
    (
    (NPIR
    NPIR) across municipalities and departments in Colombia over 2010-2018.
    ) across municipalities and departments in Colombia over 2010-2018.
    Analyze spatial autocorrelation and its robustness at di erent disaggregation levels.
    Analyze spatial autocorrelation and its robustness at di erent disaggregation levels.
    Methods:
    Methods:
    Classical convergence framework (Barro and Sala-i-Martin 1992)
    Classical convergence framework (Barro and Sala-i-Martin 1992)
    Distributional convergence framework (Quah 1996; Hyndman et. al 1996)
    Distributional convergence framework (Quah 1996; Hyndman et. al 1996)
    Spatial convergence (spatial lag and spatial error models)
    Spatial convergence (spatial lag and spatial error models)
    Spatial autocorrelation (Moran's I and di erential Moran's I)
    Spatial autocorrelation (Moran's I and di erential Moran's I)
    2 / 20
    2 / 20

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  3. Main Results:
    Main Results:
    1. Sigma Convergence
    Sigma Convergence for both homicide and personal injury rates at the state level,
    for both homicide and personal injury rates at the state level,
    Beta Convergence
    Beta Convergence for both levels and rates.
    for both levels and rates.
    2. Clustering dynamics
    Clustering dynamics
    NMR State level: 4+? convergence clusters
    NMR State level: 4+? convergence clusters
    NMR Municipal level: 2+? convergence clusters
    NMR Municipal level: 2+? convergence clusters
    NPIR State level: 2 convergence clubs
    NPIR State level: 2 convergence clubs
    NPIR Municipal level: stagnation and 2 convergence clubs
    NPIR Municipal level: stagnation and 2 convergence clubs
    3. Spatial Autocorrelation
    Spatial Autocorrelation robust only
    robust only at the municipality level
    at the municipality level
    3 / 20
    3 / 20

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  4. Outline of this presentation
    Outline of this presentation
    1. Data description
    Data description Non crime rates
    Non crime rates
    2. Global convergence:
    Global convergence: Using classical summary measures
    Using classical summary measures
    Beta convergence
    Beta convergence
    Sigma convergence
    Sigma convergence
    3. Regional disaggregation:
    Regional disaggregation:
    Distribution dynamics framework
    Distribution dynamics framework
    Distributional convergence
    Distributional convergence
    4. Global spatial autocorrelation:
    Global spatial autocorrelation:
    Disaggreagation e ects
    Disaggreagation e ects
    5. Policy discussion
    Policy discussion
    The Colombian National Development Plan 2018-22
    The Colombian National Development Plan 2018-22
    6. Concluding Remarks
    Concluding Remarks
    4 / 20
    4 / 20

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  5. (1) Data:
    (1) Data:
    Total number of
    Total number of homicides
    homicides and
    and personal injuries
    personal injuries in Colombia per year from 2010 until
    in Colombia per year from 2010 until
    2018 (data taken from the national police).
    2018 (data taken from the national police).
    Data is agreggated at the municipal
    Data is agreggated at the municipal and departmental levels.
    and departmental levels.
    Population census and estimates for states and municipalities (data from the National
    Population census and estimates for states and municipalities (data from the National
    Bureau of Statistics).
    Bureau of Statistics).
    Raw rates computed
    Raw rates computed
    Non crime rates
    Non crime rates computed
    computed
    Survival rates
    Survival rates are chosen because positively de ned variables are a
    are chosen because positively de ned variables are a standard
    standard in the
    in the
    convergence literature.
    convergence literature.
    r
    ra
    aw
    w r
    ra
    at
    te
    es
    s =
    = c
    cr
    ri
    im
    me
    es
    s/
    /p
    po
    op
    pu
    ul
    la
    at
    ti
    io
    on
    n
    N
    N C
    CR
    R =
    = 10000
    10000 −
    − r
    ra
    aw
    w r
    ra
    at
    te
    e ∗
    ∗ 10000
    10000
    5 / 20
    5 / 20

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  6. Non-crime variables over time
    Non-crime variables over time
    6 / 20
    6 / 20

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  7. (2)
    (2) Global convergence:
    Global convergence:
    Beta convergence
    Beta convergence (catch-up process)
    (catch-up process)
    Spatial Beta models
    Spatial Beta models
    Spatial lag Model:
    Spatial lag Model:
    Spatial Error Model:
    Spatial Error Model:
    Sigma convergence
    Sigma convergence (the dispersion of the data decreases over time)
    (the dispersion of the data decreases over time)
    l
    lo
    og
    g =
    = α
    α +
    + β
    β ⋅
    ⋅ l
    lo
    og
    g(
    (Y
    Y
    i
    i0
    0
    )
    ) +
    + ϵ
    ϵ
    Y
    Y
    i
    iT
    T
    Y
    Yi
    i0
    0
    log
    log =
    = α
    α +
    + β
    β ⋅
    ⋅ log
    log(
    (Y
    Yi
    i0
    0
    )
    ) +
    + ρ
    ρW
    W log
    log +
    + ε
    εt
    t
    Y
    Yi
    iT
    T
    Y
    Yi
    i0
    0
    Y
    Yi
    iT
    T
    Y
    Yi
    i0
    0
    log
    log =
    = α
    α +
    + β
    β ⋅
    ⋅ log
    log(
    (Y
    Yi
    i0
    0
    )
    ) +
    + λ
    λW
    W ε
    εt
    t
    +
    + u
    ut
    t
    Y
    Y
    i
    iT
    T
    Y
    Yi
    i0
    0
    7 / 20
    7 / 20

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  8. States- Sigma and Beta convergence
    States- Sigma and Beta convergence Municipalities - ONLY Beta convergence
    Municipalities - ONLY Beta convergence
    Classical Convergence results (NMR)
    Classical Convergence results (NMR)
    Sigma convergence results
    Sigma convergence results
    8 / 20
    8 / 20

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  9. Beta and sigma
    Beta and sigma convergence summary
    convergence summary
    Lagrange multiplier tests
    Lagrange multiplier tests also indicate that the SEM is the best tting model.
    also indicate that the SEM is the best tting model.
    Royuela and García (2015) also reported that the
    Royuela and García (2015) also reported that the and
    and coe cients
    coe cients were
    were NOT
    NOT
    signi cant at the state level
    signi cant at the state level over the period 1990 to 2005.
    over the period 1990 to 2005.
    The authors reported half-lives of
    The authors reported half-lives of 15.3, 11.5 and 15.8 years
    15.3, 11.5 and 15.8 years.
    .
    ρ
    ρ λ
    λ
    9 / 20
    9 / 20

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  10. (3)
    (3) State and Municipality disaggregation:
    State and Municipality disaggregation:
    The distribution dynamics framework
    The distribution dynamics framework
    10 / 20
    10 / 20

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  11. The distribution dynamics framework
    The distribution dynamics framework
    Convergence, divergence and stagnation
    Convergence, divergence and stagnation
    11 / 20
    11 / 20

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  12. (3) Local convergence clusters
    (3) Local convergence clusters
    NMR State level
    NMR State level: 4+? convergence clusters
    : 4+? convergence clusters
    NMR Municipal level
    NMR Municipal level: 2+? convergence clusters
    : 2+? convergence clusters
    NPIR State level
    NPIR State level : 2 convergence clubs
    : 2 convergence clubs
    NPIR Municipal level
    NPIR Municipal level : stagnation and 2 convergence clubs
    : stagnation and 2 convergence clubs
    12 / 20
    12 / 20

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  13. NMR at both levels
    NMR at both levels
    State level: 4+? convergence clusters
    State level: 4+? convergence clusters
    Municipal level: 2+? convergence clusters
    Municipal level: 2+? convergence clusters
    At the municipal level there are fewer clusters but no signs of sigma convergence
    At the municipal level there are fewer clusters but no signs of sigma convergence
    13 / 20
    13 / 20

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  14. NPIR at both levels
    NPIR at both levels
    State level: 2 convergence clusters
    State level: 2 convergence clusters
    Municipal level: 2 convergence clusters and stagnation
    Municipal level: 2 convergence clusters and stagnation
    the same number of clusters but stagnation patterns are strong at the municipal level.
    the same number of clusters but stagnation patterns are strong at the municipal level.
    14 / 20
    14 / 20

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  15. (4) Spatial Autocorrelation (Theory)
    (4) Spatial Autocorrelation (Theory)
    High Intuition Concept
    High Intuition Concept
    More Formal (less intuitive)
    More Formal (less intuitive)
    Differential Moran's I (
    Differential Moran's I ( )
    )
    We compute the Moran's I
    We compute the Moran's I for the
    for the variable
    variable .
    .
    If there is a
    If there is a xed e ect
    xed e ect related to location
    related to location , it is possible to present the value at each
    , it is possible to present the value at each
    location for time
    location for time as the sum of some intrinsic value and the xed e ect.
    as the sum of some intrinsic value and the xed e ect.
    I
    I =
    = =
    = .
    .


    i
    i


    j
    j
    w
    wi
    ij
    j
    y
    yi
    i
    .
    . y
    yj
    j


    i
    i
    y
    y
    2
    2
    i
    i


    i
    i
    (
    (y
    yi
    i
    ×
    × ∑

    j
    j
    w
    wi
    ij
    j
    y
    yj
    j
    )
    )


    i
    i
    y
    y
    2
    2
    i
    i
    y
    y
    i
    i,
    ,t
    t

    − y
    y
    i
    i,
    ,t
    t−
    −1
    1
    y
    yi
    i,
    ,t
    t

    − y
    yi
    i,
    ,t
    t−
    −1
    1
    μ
    μi
    i
    i
    i
    t
    t y
    yi
    i,
    ,t
    t
    =
    = y
    y ∗
    ∗i
    i,
    ,t
    t
    +

    μi
    i
    15 / 20
    15 / 20

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  16. (4) Spatial autocorrelation
    (4) Spatial autocorrelation (Results)
    (Results)
    State level
    State level: Moran's I statistic is signi cant, di erential Moran's I is not signi cant (
    : Moran's I statistic is signi cant, di erential Moran's I is not signi cant (not
    not
    robust
    robust)
    )
    Municipal level
    Municipal level: Standard and Di erential Moran's I signi cant
    : Standard and Di erential Moran's I signi cant (
    (robust
    robust)
    )
    Space matters at the Municipal level
    Space matters at the Municipal level
    16 / 20
    16 / 20

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  17. (5) Policy discussion
    (5) Policy discussion
    Vertical and horizontal policy coordination, spillovers and borders.
    Vertical and horizontal policy coordination, spillovers and borders.
    Spatial spillovers from neighbors can have
    Spatial spillovers from neighbors can have both positive and negative e ects
    both positive and negative e ects on the
    on the
    convergence path of a region.
    convergence path of a region.
    It could be more appropriate for the formulation of national development plans to
    It could be more appropriate for the formulation of national development plans to
    have targets at the state level
    have targets at the state level
    17 / 20
    17 / 20

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  18. (5) Concluding Remarks
    (5) Concluding Remarks
    Uplifting results "on average" :
    Uplifting results "on average" :
    The dispersion of non-crime (crime) rates at the state level
    The dispersion of non-crime (crime) rates at the state level has decreased
    has decreased. On average
    . On average
    less homicides but more personal injuries.
    less homicides but more personal injuries.
    Global convergence on average at the state level
    Global convergence on average at the state level, while fast beta convergence at the
    , while fast beta convergence at the
    municipality level.
    municipality level.
    Beyond classical convergence
    Beyond classical convergence :
    :
    Regional di erences matter in
    Regional di erences matter in both disaggregation levels
    both disaggregation levels.
    .
    Multiple local convergence clubs
    Multiple local convergence clubs; with more clubs at the state level.
    ; with more clubs at the state level.
    The Role of Space
    The Role of Space
    Subsequent Di erential Moran's I are robust and signi cant at the
    Subsequent Di erential Moran's I are robust and signi cant at the municipality level
    municipality level
    only
    only
    Results at the
    Results at the state level
    state level for NMR are not conclusive and similar to the ones reported
    for NMR are not conclusive and similar to the ones reported
    by Royuela et al 2015.
    by Royuela et al 2015.
    18 / 20
    18 / 20

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  19. (5) Concluding Remarks
    (5) Concluding Remarks
    Implications and further research
    Implications and further research
    Convergence clusters help us to nd regions with similar outcomes, coordination
    Convergence clusters help us to nd regions with similar outcomes, coordination
    among them can be promoted.
    among them can be promoted.
    Strong spatial autocorrelation suggest the possibility of applying spatial lters in order
    Strong spatial autocorrelation suggest the possibility of applying spatial lters in order
    to remove the spatial component of crime variables.
    to remove the spatial component of crime variables.
    At the state level (including more variables) a probit model may help us to nd the
    At the state level (including more variables) a probit model may help us to nd the
    determinants for a conditional "jump" to the upper clusters.
    determinants for a conditional "jump" to the upper clusters.
    As many municipalities have small population, crime rates have high
    As many municipalities have small population, crime rates have high variance
    variance
    instability. Empirical Bayes methods can be used.
    instability. Empirical Bayes methods can be used.
    19 / 20
    19 / 20

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  20. Thank you very much for your attention
    Thank you very much for your attention
    You can nd the working paper on my website
    You can nd the working paper on my website https://felipe-santos.rbind.io
    https://felipe-santos.rbind.io
    If you are interested in our research please check our QuaRCS lab website
    If you are interested in our research please check our QuaRCS lab website
    https://quarcs-lab.rbind.io/
    https://quarcs-lab.rbind.io/
    Quantitative Regional and Computational Science Lab
    Quantitative Regional and Computational Science Lab
    20 / 20
    20 / 20

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