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Human Capital Constraints, Spatial Dependence, and Regionalization in Bolivia: A Spatial Clustering Approach

QuarRCS-lab
November 13, 2020

Human Capital Constraints, Spatial Dependence, and Regionalization in Bolivia: A Spatial Clustering Approach

Using a novel municipal-level dataset and spatial clustering methods, this article studies the distribution of human capital constraints across 339 municipalities in Bolivia. In particular, the spatial distribution of five human capital constraints are evaluated: chronic malnutrition in children, non-Spanish speaking population, secondary dropout rate of males, secondary dropout rates of females, and the inequality of years of education. Through the lens of both spatial dependence and regionalization frameworks, the municipalities of Bolivia are endogenously classified according to both their level of human capital constraints and their locational similarity. Results from the spatial dependence analysis indicate the location of hotspots (high-value clusters), coldspots (low-value clusters), and spatial outliers for each of the previously listed constraints. Results from the regionalization analysis indicate that Bolivia can be regionalized into six to seven geographical locations that face similar constraints in the accumulation of human capital. The article concludes by highlighting the usefulness of spatial data analysis for designing and monitoring human development goals.

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November 13, 2020
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  1. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Human Capital Constraints, Spatial Dependence,
    and Regionalization in Bolivia:
    A Spatial Clustering Approach
    Carlos Mendez
    Nagoya University, JAPAN
    Erick Gonzales
    United Nations, JAPAN
    https://quarcs-lab.org/
    Quantitative Regional and Computational Science Lab – QuaRCS-lab
    November, 2020
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 1 / 42

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  2. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Summary (1)
    Motivation
    • Human capital is a key element for achieving the 2030 Agenda
    for Sustainable Development
    • Limited evidence on specific regional constraints hindering the
    accumulation of human capital
    • Data-oriented identification of regional clusters can improve
    the effectiveness of public policy
    Research objective
    • Identify contiguous clusters of regions facing similar human
    capital constraints
    Methods
    • Spatial dependence analysis [Anselin, 1995]
    • Spatially constrained clustering [Duque et al., 2012]
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 2 / 42

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  3. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Summary (2)
    Data
    • Municipal Atlas of the Sustainable Development Goals in
    Bolivia [SDSN-Bolivia, 2020]
    • 339 municipalities
    Results
    • Considering constraints to human capital accumulation,
    Bolivia can be divided into six to seven geographical regions
    • Constraints frequently cross current administrative boundaries
    • Human development policies need coordination across multiple
    local governments and support by the national government
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 3 / 42

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  4. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Table of Contents
    1. Motivation
    No one left behind
    Regionalization
    2. Data and methods
    Data
    Methods
    3. Results and discussion
    Results
    Spatial dependence
    Regionalization
    Discussion
    Local Moran vs Max-p
    Univariate vs Multivariate
    Connectivity structures
    4. Conclusion
    Implications
    Further research
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 4 / 42

    View full-size slide

  5. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Table of Contents
    1. Motivation
    No one left behind
    Regionalization
    2. Data and methods
    Data
    Methods
    3. Results and discussion
    Results
    Spatial dependence
    Regionalization
    Discussion
    Local Moran vs Max-p
    Univariate vs Multivariate
    Connectivity structures
    4. Conclusion
    Implications
    Further research
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 5 / 42

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  6. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Leaving no one behind
    Under-performing municipalities that are left behind will affect Bo-
    livia’s capacity to accomplish the 2030 Agenda for Sustainable De-
    velopment.
    • Human capital is central for understanding individual earnings,
    distribution of income, and economic growth [Barro, 2001,
    Becker et al., 1990, Collin and Weil, 2020]
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 6 / 42

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  7. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Leaving no one behind
    Under-performing municipalities that are left behind will affect Bo-
    livia’s capacity to accomplish the 2030 Agenda for Sustainable De-
    velopment.
    • Human capital is central for understanding individual earnings,
    distribution of income, and economic growth [Barro, 2001,
    Becker et al., 1990, Collin and Weil, 2020]
    • For Bolivia, there is less evidence on specific regional
    constraints to human capital accumulation
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 6 / 42

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  8. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Leaving no one behind
    Under-performing municipalities that are left behind will affect Bo-
    livia’s capacity to accomplish the 2030 Agenda for Sustainable De-
    velopment.
    • Human capital is central for understanding individual earnings,
    distribution of income, and economic growth [Barro, 2001,
    Becker et al., 1990, Collin and Weil, 2020]
    • For Bolivia, there is less evidence on specific regional
    constraints to human capital accumulation
    • Novel dataset: Municipal Atlas of the Sustainable
    Development Goals in Bolivia [SDSN-Bolivia, 2020]
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 6 / 42

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  9. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    "Everything is related to everything else, but near things are
    more related than distant things" Waldo Tobler (1970)
    • Identify clusters of regions facing similar attributes (human
    capital constraints) and geographical location
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 7 / 42

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  10. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    "Everything is related to everything else, but near things are
    more related than distant things" Waldo Tobler (1970)
    • Identify clusters of regions facing similar attributes (human
    capital constraints) and geographical location
    • Spatial distribution of five indicators related to constraints to
    human capital development
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 7 / 42

    View full-size slide

  11. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    "Everything is related to everything else, but near things are
    more related than distant things" Waldo Tobler (1970)
    • Identify clusters of regions facing similar attributes (human
    capital constraints) and geographical location
    • Spatial distribution of five indicators related to constraints to
    human capital development
    • Recent advances in geospatial methods
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 7 / 42

    View full-size slide

  12. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    "Everything is related to everything else, but near things are
    more related than distant things" Waldo Tobler (1970)
    • Identify clusters of regions facing similar attributes (human
    capital constraints) and geographical location
    • Spatial distribution of five indicators related to constraints to
    human capital development
    • Recent advances in geospatial methods
    • Classical spatial dependence [Anselin, 1995]
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 7 / 42

    View full-size slide

  13. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    "Everything is related to everything else, but near things are
    more related than distant things" Waldo Tobler (1970)
    • Identify clusters of regions facing similar attributes (human
    capital constraints) and geographical location
    • Spatial distribution of five indicators related to constraints to
    human capital development
    • Recent advances in geospatial methods
    • Classical spatial dependence [Anselin, 1995]
    • Hot and cold spots [Anselin et al., 2007]
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 7 / 42

    View full-size slide

  14. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    "Everything is related to everything else, but near things are
    more related than distant things" Waldo Tobler (1970)
    • Identify clusters of regions facing similar attributes (human
    capital constraints) and geographical location
    • Spatial distribution of five indicators related to constraints to
    human capital development
    • Recent advances in geospatial methods
    • Classical spatial dependence [Anselin, 1995]
    • Hot and cold spots [Anselin et al., 2007]
    • Integer programming [Duque et al., 2012]
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 7 / 42

    View full-size slide

  15. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    "Everything is related to everything else, but near things are
    more related than distant things" Waldo Tobler (1970)
    • Identify clusters of regions facing similar attributes (human
    capital constraints) and geographical location
    • Spatial distribution of five indicators related to constraints to
    human capital development
    • Recent advances in geospatial methods
    • Classical spatial dependence [Anselin, 1995]
    • Hot and cold spots [Anselin et al., 2007]
    • Integer programming [Duque et al., 2012]
    • Municipalities facing similar problems can also benefit from
    increased coordination towards common solutions
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 7 / 42

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  16. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Table of Contents
    1. Motivation
    No one left behind
    Regionalization
    2. Data and methods
    Data
    Methods
    3. Results and discussion
    Results
    Spatial dependence
    Regionalization
    Discussion
    Local Moran vs Max-p
    Univariate vs Multivariate
    Connectivity structures
    4. Conclusion
    Implications
    Further research
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 8 / 42

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  17. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Data
    Municipal Atlas of the Sustainable Development Goals in Bolivia
    • A novel dataset of 339 municipalities [SDSN-Bolivia, 2020]
    • Indicators:
    • Literature and availability
    • Related to SDGs 2, 4, 10 representing constraints to human
    capital development
    • Avoid overlapping
    Statistic Mean St. Dev. Min Pctl(25) Median Pctl(75) Max
    Chronic malnutrition in children (percent, 2016) 24.00 12.00 7.60 14.00 23.00 30.00 53.00
    Non-Spanish speaking population (percent, 2012) 15.00 14.00 0.66 4.90 9.60 20.00 60.00
    Secondary dropout rate (male percent, 2017) 5.00 2.90 0.00 3.20 4.70 6.40 21.00
    Secondary dropout rate (female percent, 2017) 4.10 2.90 0.00 2.40 3.40 5.20 22.00
    GINI coefficient of years of education (2012) 0.39 0.08 0.20 0.33 0.37 0.43 0.64
    Table: Descriptive statistics: Human capital constraints
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 9 / 42

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  18. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Data
    First overview of the spatial distribution: breaks in each choropleth map are optimally
    selected [Fisher, 1958, Jenks, 1977] (1)
    (a) Chronic malnutrition in
    children
    (b) Non-Spanish speaking
    population
    Figure 1: Spatial distribution of human capital constraints
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 10 / 42

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  19. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Data
    First overview of the spatial distribution: breaks in each choropleth map are optimally
    selected [Fisher, 1958, Jenks, 1977] (2)
    (c) Secondary dropout rate
    (males)
    (d) Secondary dropout rate
    (females)
    Figure 1: Spatial distribution of human capital constraints
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 11 / 42

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  20. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Data
    First overview of the spatial distribution: breaks in each choropleth map are optimally
    selected [Fisher, 1958, Jenks, 1977] (3)
    (e) GINI coefficient of years
    of education
    Figure 1: Spatial distribution of human capital constraints
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 12 / 42

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  21. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Data
    −1
    −0.8
    −0.6
    −0.4
    −0.2
    0
    0.2
    0.4
    0.6
    0.8
    1
    (A) Malnutrition
    in children
    (B) Secondary
    dropout rate (males)
    (D) GINI coefficient of
    years of education
    (E) Non-Spanish
    speaking population
    (C) Secondary
    dropout rate (females)
    (A) (B) (C) (D) (E)
    Figure 2: Correlation matrix of human capital constraints
    Notes: Pearson (Spearman) correlations above (below) the diagonal.
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 13 / 42

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  22. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Municipalities tend to have public policies similar to those of their neighbours:
    Direct/indirect learning and/or influencing processes
    • Dealing with spatial autocorrelation to find clusters under two
    conditions
    • Attributes
    • Geographical locations
    • Identify contiguous regions facing similar human capital
    constraints
    • Spatial dependence analysis [Anselin, 1995]
    • Hot-spots
    • Cold-spots
    • Regionalization analysis [Duque et al., 2012]
    • Cluster municipalities
    • More homogeneous regions
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 14 / 42

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  23. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Spatial dependence analysis evaluates the existence of a clustering pattern in the spatial
    distribution of an attribute
    • Null hypothesis:
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 15 / 42

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  24. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Spatial dependence analysis evaluates the existence of a clustering pattern in the spatial
    distribution of an attribute
    • Null hypothesis:
    • All regions are independent from each other
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 15 / 42

    View full-size slide

  25. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Spatial dependence analysis evaluates the existence of a clustering pattern in the spatial
    distribution of an attribute
    • Null hypothesis:
    • All regions are independent from each other
    • Statistical inference:
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 15 / 42

    View full-size slide

  26. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Spatial dependence analysis evaluates the existence of a clustering pattern in the spatial
    distribution of an attribute
    • Null hypothesis:
    • All regions are independent from each other
    • Statistical inference:
    • Computational approach of random permutation and the
    simulation of reference distribution [Anselin, 1995, 2017]
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 15 / 42

    View full-size slide

  27. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Spatial dependence analysis evaluates the existence of a clustering pattern in the spatial
    distribution of an attribute
    • Null hypothesis:
    • All regions are independent from each other
    • Statistical inference:
    • Computational approach of random permutation and the
    simulation of reference distribution [Anselin, 1995, 2017]
    • Moran scatter plot
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 15 / 42

    View full-size slide

  28. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Spatial dependence analysis evaluates the existence of a clustering pattern in the spatial
    distribution of an attribute
    • Null hypothesis:
    • All regions are independent from each other
    • Statistical inference:
    • Computational approach of random permutation and the
    simulation of reference distribution [Anselin, 1995, 2017]
    • Moran scatter plot
    • Local Indicators of Spatial Association (LISA)
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 15 / 42

    View full-size slide

  29. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Spatial dependence analysis evaluates the existence of a clustering pattern in the spatial
    distribution of an attribute
    • Null hypothesis:
    • All regions are independent from each other
    • Statistical inference:
    • Computational approach of random permutation and the
    simulation of reference distribution [Anselin, 1995, 2017]
    • Moran scatter plot
    • Local Indicators of Spatial Association (LISA)
    Moran’s I [Cliff and Ord, 1981]
    I =
    i j
    wij · (xi − µ) · (xj − µ) /
    i
    (xi − µ)2 (1)
    Ii =
    (xi − µ)
    (xi − µ)2
    j
    wij · (xj − µ) (2)
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 15 / 42

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  30. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Regionalization analysis aggregates areas (n) into an unknown maximum number of
    homogeneous regions (p)
    Max-p-regions [Duque et al., 2012]
    Min Z = −
    n
    k=1
    n
    i=1
    xk0
    i
    ∗ 10h +
    i j|j>i
    dij tij , (3)
    • Subject to:
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 16 / 42

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  31. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Regionalization analysis aggregates areas (n) into an unknown maximum number of
    homogeneous regions (p)
    Max-p-regions [Duque et al., 2012]
    Min Z = −
    n
    k=1
    n
    i=1
    xk0
    i
    ∗ 10h +
    i j|j>i
    dij tij , (3)
    • Subject to:
    • An aggregated region should not have more than one core area
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 16 / 42

    View full-size slide

  32. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Regionalization analysis aggregates areas (n) into an unknown maximum number of
    homogeneous regions (p)
    Max-p-regions [Duque et al., 2012]
    Min Z = −
    n
    k=1
    n
    i=1
    xk0
    i
    ∗ 10h +
    i j|j>i
    dij tij , (3)
    • Subject to:
    • An aggregated region should not have more than one core area
    • Area allocated only to one region k and one contiguity order c
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 16 / 42

    View full-size slide

  33. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Regionalization analysis aggregates areas (n) into an unknown maximum number of
    homogeneous regions (p)
    Max-p-regions [Duque et al., 2012]
    Min Z = −
    n
    k=1
    n
    i=1
    xk0
    i
    ∗ 10h +
    i j|j>i
    dij tij , (3)
    • Subject to:
    • An aggregated region should not have more than one core area
    • Area allocated only to one region k and one contiguity order c
    • A municipality i is allocated region k at order c if a
    municipality j is allocated to the same region k in order c1
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 16 / 42

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  34. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Regionalization analysis aggregates areas (n) into an unknown maximum number of
    homogeneous regions (p)
    Max-p-regions [Duque et al., 2012]
    Min Z = −
    n
    k=1
    n
    i=1
    xk0
    i
    ∗ 10h +
    i j|j>i
    dij tij , (3)
    • Subject to:
    • An aggregated region should not have more than one core area
    • Area allocated only to one region k and one contiguity order c
    • A municipality i is allocated region k at order c if a
    municipality j is allocated to the same region k in order c1
    • When a region is created, there is a predefined threshold based
    on a spatially intensive attribute
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 16 / 42

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  35. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Regionalization analysis aggregates areas (n) into an unknown maximum number of
    homogeneous regions (p)
    Max-p-regions [Duque et al., 2012]
    Min Z = −
    n
    k=1
    n
    i=1
    xk0
    i
    ∗ 10h +
    i j|j>i
    dij tij , (3)
    • Subject to:
    • An aggregated region should not have more than one core area
    • Area allocated only to one region k and one contiguity order c
    • A municipality i is allocated region k at order c if a
    municipality j is allocated to the same region k in order c1
    • When a region is created, there is a predefined threshold based
    on a spatially intensive attribute
    • Heterogeneity is calculated from pairwise dissimilarities
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 16 / 42

    View full-size slide

  36. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    Regionalization analysis aggregates areas (n) into an unknown maximum number of
    homogeneous regions (p)
    Max-p-regions [Duque et al., 2012]
    Min Z = −
    n
    k=1
    n
    i=1
    xk0
    i
    ∗ 10h +
    i j|j>i
    dij tij , (3)
    • Subject to:
    • An aggregated region should not have more than one core area
    • Area allocated only to one region k and one contiguity order c
    • A municipality i is allocated region k at order c if a
    municipality j is allocated to the same region k in order c1
    • When a region is created, there is a predefined threshold based
    on a spatially intensive attribute
    • Heterogeneity is calculated from pairwise dissimilarities
    • Variable integrity is preserved
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 16 / 42

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  37. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    n
    i=1
    xk0
    i
    ≤ 1 ∀k = 1, . . . , n (4)
    n
    k=1
    q
    c=0
    xkc
    i
    = 1 ∀i = 1, . . . , n (5)
    xkc
    i

    j∈Ni
    xk(c−1)
    j
    ∀i = 1, . . . , n; ∀k = 1, . . . , n; ∀c = 1, . . . , q (6)
    n
    i=1
    q
    c=0
    xkc
    i
    li ≥ threshold ∗
    n
    i=1
    xk0
    i
    ∀k = 1, . . . , n (7)
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 17 / 42

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  38. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Methods
    tij ≥
    q
    c=0
    xkc
    i
    +
    q
    c=0
    xkc
    j
    − 1 ∀i, j = 1, . . . , n | i < j; ∀k = 1, . . . , n (8)
    xkc
    i
    ∈ {0, 1} ∀i = 1, . . . , n; ∀k = 1, . . . , n; ∀c = 0, . . . , q (9)
    tij ∈ {0, 1} ∀i, j = 1, . . . , n | i < j (10)
    The decision variables are:
    tij
    =
    1, if areas i and j belong to the same region k, with i < j
    0, otherwise
    xkc
    i
    =
    1, if areas i is assigned to region k in order c
    0, otherwise
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 18 / 42

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  39. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Table of Contents
    1. Motivation
    No one left behind
    Regionalization
    2. Data and methods
    Data
    Methods
    3. Results and discussion
    Results
    Spatial dependence
    Regionalization
    Discussion
    Local Moran vs Max-p
    Univariate vs Multivariate
    Connectivity structures
    4. Conclusion
    Implications
    Further research
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 19 / 42

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  40. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Spatial dependence: Chronic malnutrition in the lower center and lower west
    (a) Spatial autocorrelation (b) Hotspots (HH), coldspots (LL),
    and spatial outliers (HL, LH)
    Figure 3: Spatial distribution of malnutrition in children
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 20 / 42

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  41. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Spatial dependence: Non-Spanish speaking populations in lower center
    (a) Spatial autocorrelation
    (b) Hotspots (HH), coldspots (LL),
    and spatial outliers (HL, LH)
    Figure 4: Spatial distribution of non-Spanish speaking population
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 21 / 42

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  42. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Spatial dependence: High secondary dropout for males in the north
    (a) Spatial autocorrelation
    (b) Hotspots (HH), coldspots (LL),
    and spatial outliers (HL, LH)
    Figure 5: Spatial distribution of secondary male dropout of males
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 22 / 42

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  43. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Spatial dependence: High secondary dropout for females in the north
    (a) Spatial autocorrelation
    (b) Hotspots (HH), coldspots (LL),
    and spatial outliers (HL, LH)
    Figure 6: Spatial distribution of secondary dropout of females
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 23 / 42

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  44. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Spatial dependence: High education inequality in the lower center
    (a) Spatial autocorrelation
    (b) Hotspots (HH), coldspots (LL),
    and spatial outliers (HL, LH)
    Figure 7: Spatial distribution of inequality of years of education
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 24 / 42

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  45. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization: While administrative divisions have its uses, the identification of
    new regions can better inform public policy
    • Nine departments based on historic and administrative reasons
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 25 / 42

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  46. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization: While administrative divisions have its uses, the identification of
    new regions can better inform public policy
    • Nine departments based on historic and administrative reasons
    • Some administrative units predate the nation itself
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 25 / 42

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  47. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization: While administrative divisions have its uses, the identification of
    new regions can better inform public policy
    • Nine departments based on historic and administrative reasons
    • Some administrative units predate the nation itself
    • Distinctive economic characteristics
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 25 / 42

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  48. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization: While administrative divisions have its uses, the identification of
    new regions can better inform public policy
    • Nine departments based on historic and administrative reasons
    • Some administrative units predate the nation itself
    • Distinctive economic characteristics
    • Weak integration in terms of transportation
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 25 / 42

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  49. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization: While administrative divisions have its uses, the identification of
    new regions can better inform public policy
    • Nine departments based on historic and administrative reasons
    • Some administrative units predate the nation itself
    • Distinctive economic characteristics
    • Weak integration in terms of transportation
    • Isolated municipalities
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 25 / 42

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  50. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization: While administrative divisions have its uses, the identification of
    new regions can better inform public policy
    • Nine departments based on historic and administrative reasons
    • Some administrative units predate the nation itself
    • Distinctive economic characteristics
    • Weak integration in terms of transportation
    • Isolated municipalities
    • Local elites
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 25 / 42

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  51. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization: While administrative divisions have its uses, the identification of
    new regions can better inform public policy
    • Nine departments based on historic and administrative reasons
    • Some administrative units predate the nation itself
    • Distinctive economic characteristics
    • Weak integration in terms of transportation
    • Isolated municipalities
    • Local elites
    • Geographic diversity can set advantages
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 25 / 42

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  52. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization: While administrative divisions have its uses, the identification of
    new regions can better inform public policy
    • Nine departments based on historic and administrative reasons
    • Some administrative units predate the nation itself
    • Distinctive economic characteristics
    • Weak integration in terms of transportation
    • Isolated municipalities
    • Local elites
    • Geographic diversity can set advantages
    • Spatially, all areas are related, but those closer to each other
    are even more so
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 25 / 42

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  53. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization - Malnutrition
    (a)
    (b)
    Figure 6: Regionalization of chronic malnutrition in children
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 26 / 42

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  54. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization - non-Spanish speaking population
    (a)
    (b)
    Figure 9: Regionalization of non-Spanish speaking population
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 27 / 42

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  55. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization - Secondary dropout rates, males
    (a)
    (b)
    Figure 10: Regionalization of secondary dropout of males
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 28 / 42

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  56. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization - Secondary dropout rates, females
    (a)
    (b)
    Figure 11: Regionalization of secondary dropout of females
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 29 / 42

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  57. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization - Inequality of years of education
    (a)
    (b)
    Figure 12: Regionalization of inequality of years of education
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 30 / 42

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  58. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Regionalization - Human capital constraints
    (a)
    (b)
    Figure 13: Regionalization of integrated human capital constraints
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 31 / 42

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  59. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Local Moran clusters vs Max-p clusters
    (a) Local Moran clusters (b) Max-P clusters
    Figure 14: Local Moran clusters vs Max-P clusters
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 32 / 42

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  60. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Univariate Max-p vs Multivariate Max-p
    (a) Univariate Max-p: 8 clusters (b) Multivariate Max-p: 7 clusters
    Figure 15: Univariate Max-p vs Multivariate Max-p
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 33 / 42

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  61. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Alternative connectivity structures for Max-p clusters (1)
    (a) Queen contiguity: 7 clusters (b) Rook contiguity: 8 clusters
    Figure 16: Max-p clusters based on alternative connectivity structures
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 34 / 42

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  62. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Alternative connectivity structures for Max-p clusters (2)
    (c) Distance band: 8 clusters
    (d) Inverse distance squared: 8
    clusters
    Figure 16: Max-p clusters based on alternative connectivity structures
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 35 / 42

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  63. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Alternative connectivity structures for Max-p clusters (3)
    (e) Six nearest neighbors: 7
    clusters
    (f) Eight nearest neighbors: 7
    clusters
    Figure 16: Max-p clusters based on alternative connectivity structures
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 36 / 42

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  64. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Complementary, integrated, and connectivity analysis
    Complementary
    • Local Moran: extreme cases
    Integrated
    Connectivity
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 37 / 42

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  65. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Complementary, integrated, and connectivity analysis
    Complementary
    • Local Moran: extreme cases
    • Core centers of attraction and spatial outliers
    Integrated
    Connectivity
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 37 / 42

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  66. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Complementary, integrated, and connectivity analysis
    Complementary
    • Local Moran: extreme cases
    • Core centers of attraction and spatial outliers
    • Max-p: classify remaining cases
    Integrated
    Connectivity
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 37 / 42

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  67. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Complementary, integrated, and connectivity analysis
    Complementary
    • Local Moran: extreme cases
    • Core centers of attraction and spatial outliers
    • Max-p: classify remaining cases
    • Create contiguous areas
    Integrated
    Connectivity
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 37 / 42

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  68. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Complementary, integrated, and connectivity analysis
    Complementary
    • Local Moran: extreme cases
    • Core centers of attraction and spatial outliers
    • Max-p: classify remaining cases
    • Create contiguous areas
    Integrated
    • Multivariate approach considers entire variation
    Connectivity
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 37 / 42

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  69. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Complementary, integrated, and connectivity analysis
    Complementary
    • Local Moran: extreme cases
    • Core centers of attraction and spatial outliers
    • Max-p: classify remaining cases
    • Create contiguous areas
    Integrated
    • Multivariate approach considers entire variation
    Connectivity
    • Sensitivity to structures and regional design objectives
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 37 / 42

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  70. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Complementary, integrated, and connectivity analysis
    Complementary
    • Local Moran: extreme cases
    • Core centers of attraction and spatial outliers
    • Max-p: classify remaining cases
    • Create contiguous areas
    Integrated
    • Multivariate approach considers entire variation
    Connectivity
    • Sensitivity to structures and regional design objectives
    • Rock: contiguity and compactness
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 37 / 42

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  71. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Complementary, integrated, and connectivity analysis
    Complementary
    • Local Moran: extreme cases
    • Core centers of attraction and spatial outliers
    • Max-p: classify remaining cases
    • Create contiguous areas
    Integrated
    • Multivariate approach considers entire variation
    Connectivity
    • Sensitivity to structures and regional design objectives
    • Rock: contiguity and compactness
    • K-nearest: compactness and some discontinuity
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 37 / 42

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  72. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Complementary, integrated, and connectivity analysis
    Complementary
    • Local Moran: extreme cases
    • Core centers of attraction and spatial outliers
    • Max-p: classify remaining cases
    • Create contiguous areas
    Integrated
    • Multivariate approach considers entire variation
    Connectivity
    • Sensitivity to structures and regional design objectives
    • Rock: contiguity and compactness
    • K-nearest: compactness and some discontinuity
    • Distance: less suitable for above objectives
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 37 / 42

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  73. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Table of Contents
    1. Motivation
    No one left behind
    Regionalization
    2. Data and methods
    Data
    Methods
    3. Results and discussion
    Results
    Spatial dependence
    Regionalization
    Discussion
    Local Moran vs Max-p
    Univariate vs Multivariate
    Connectivity structures
    4. Conclusion
    Implications
    Further research
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 38 / 42

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  74. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Implications
    Human development policies need coordination across multiple local governments and
    actively supported by the national government
    • Spatial dependence
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 39 / 42

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  75. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Implications
    Human development policies need coordination across multiple local governments and
    actively supported by the national government
    • Spatial dependence
    • Chronic malnutrition mostly in the lower center and lower west
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 39 / 42

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  76. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Implications
    Human development policies need coordination across multiple local governments and
    actively supported by the national government
    • Spatial dependence
    • Chronic malnutrition mostly in the lower center and lower west
    • Non-Spanish speaking populations in the lower center
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 39 / 42

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  77. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Implications
    Human development policies need coordination across multiple local governments and
    actively supported by the national government
    • Spatial dependence
    • Chronic malnutrition mostly in the lower center and lower west
    • Non-Spanish speaking populations in the lower center
    • Secondary dropout rates (both male and female) in the north
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 39 / 42

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  78. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Implications
    Human development policies need coordination across multiple local governments and
    actively supported by the national government
    • Spatial dependence
    • Chronic malnutrition mostly in the lower center and lower west
    • Non-Spanish speaking populations in the lower center
    • Secondary dropout rates (both male and female) in the north
    • High education inequality in the lower center
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 39 / 42

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  79. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Implications
    Human development policies need coordination across multiple local governments and
    actively supported by the national government
    • Spatial dependence
    • Chronic malnutrition mostly in the lower center and lower west
    • Non-Spanish speaking populations in the lower center
    • Secondary dropout rates (both male and female) in the north
    • High education inequality in the lower center
    • Regionalization
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 39 / 42

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  80. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Implications
    Human development policies need coordination across multiple local governments and
    actively supported by the national government
    • Spatial dependence
    • Chronic malnutrition mostly in the lower center and lower west
    • Non-Spanish speaking populations in the lower center
    • Secondary dropout rates (both male and female) in the north
    • High education inequality in the lower center
    • Regionalization
    • Six to seven geographical facing similar constraints in the
    accumulation of human capital
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 39 / 42

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  81. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Implications
    Human development policies need coordination across multiple local governments and
    actively supported by the national government
    • Spatial dependence
    • Chronic malnutrition mostly in the lower center and lower west
    • Non-Spanish speaking populations in the lower center
    • Secondary dropout rates (both male and female) in the north
    • High education inequality in the lower center
    • Regionalization
    • Six to seven geographical facing similar constraints in the
    accumulation of human capital
    • Borders of new regions largely different from those of the
    political map
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 39 / 42

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  82. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Further research
    Robustness and exploration of alternative clustering frameworks
    • Comprehensive robustness analysis of spatial dependence
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 40 / 42

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  83. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Further research
    Robustness and exploration of alternative clustering frameworks
    • Comprehensive robustness analysis of spatial dependence
    • Alternative neighbour structures (spatial weights matrices)
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 40 / 42

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  84. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Further research
    Robustness and exploration of alternative clustering frameworks
    • Comprehensive robustness analysis of spatial dependence
    • Alternative neighbour structures (spatial weights matrices)
    • Distance decay functions
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 40 / 42

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  85. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Further research
    Robustness and exploration of alternative clustering frameworks
    • Comprehensive robustness analysis of spatial dependence
    • Alternative neighbour structures (spatial weights matrices)
    • Distance decay functions
    • Distance thresholds
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 40 / 42

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  86. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Further research
    Robustness and exploration of alternative clustering frameworks
    • Comprehensive robustness analysis of spatial dependence
    • Alternative neighbour structures (spatial weights matrices)
    • Distance decay functions
    • Distance thresholds
    • k-nearest neighbours definitions
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 40 / 42

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  87. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Further research
    Robustness and exploration of alternative clustering frameworks
    • Comprehensive robustness analysis of spatial dependence
    • Alternative neighbour structures (spatial weights matrices)
    • Distance decay functions
    • Distance thresholds
    • k-nearest neighbours definitions
    • Re-evaluate Max-p regionalization algorithm sensitivity
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 40 / 42

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  88. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Further research
    Robustness and exploration of alternative clustering frameworks
    • Comprehensive robustness analysis of spatial dependence
    • Alternative neighbour structures (spatial weights matrices)
    • Distance decay functions
    • Distance thresholds
    • k-nearest neighbours definitions
    • Re-evaluate Max-p regionalization algorithm sensitivity
    • Alternative initialization parameters
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 40 / 42

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  89. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Further research
    Robustness and exploration of alternative clustering frameworks
    • Comprehensive robustness analysis of spatial dependence
    • Alternative neighbour structures (spatial weights matrices)
    • Distance decay functions
    • Distance thresholds
    • k-nearest neighbours definitions
    • Re-evaluate Max-p regionalization algorithm sensitivity
    • Alternative initialization parameters
    • Re-evaluate regionalization of Bolivia using alternative
    clustering frameworks
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 40 / 42

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  90. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Further research
    Robustness and exploration of alternative clustering frameworks
    • Comprehensive robustness analysis of spatial dependence
    • Alternative neighbour structures (spatial weights matrices)
    • Distance decay functions
    • Distance thresholds
    • k-nearest neighbours definitions
    • Re-evaluate Max-p regionalization algorithm sensitivity
    • Alternative initialization parameters
    • Re-evaluate regionalization of Bolivia using alternative
    clustering frameworks
    • Spatially constrained clustering [Assunção et al., 2006]
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 40 / 42

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  91. Motivation
    Data and methods
    Results and discussion
    Conclusion
    QuaRCS-lab
    Further research
    Robustness and exploration of alternative clustering frameworks
    • Comprehensive robustness analysis of spatial dependence
    • Alternative neighbour structures (spatial weights matrices)
    • Distance decay functions
    • Distance thresholds
    • k-nearest neighbours definitions
    • Re-evaluate Max-p regionalization algorithm sensitivity
    • Alternative initialization parameters
    • Re-evaluate regionalization of Bolivia using alternative
    clustering frameworks
    • Spatially constrained clustering [Assunção et al., 2006]
    • Pruning the minimum spanning tree created from the spatial
    weights matrix
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 40 / 42

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  92. References
    QuaRCS-lab
    References (slides) I
    Luc Anselin. Local indicators of spatial association—lisa. Geographical analysis, 27(2):93–115, 1995.
    Luc Anselin. Cluster Analysis (3): Spatially Constrained Clustering Methods, 2017. ISSN 00167363.
    URL https://geodacenter.github.io/workbook/8{_}spatial{_}clusters/lab8.html.
    Luc Anselin, Sanjeev Sridharan, and Susan Gholston. Using exploratory spatial data analysis to leverage
    social indicator databases: the discovery of interesting patterns. Social Indicators Research, 82(2):
    287–309, 2007.
    Renato Martins Assunção, Marcos C Neves, Gilberto Câmara, and Corina Da Costa Frietas. Efficient
    regionalisation techniques for socio-economic geographical units using minimum spanning trees.
    International Journal of Geographical Information Science, 20(7):797–811, 2006. doi:
    10.1080/13658810600665111. URL
    http://mtc-m16c.sid.inpe.br/col/sid.inpe.br/ePrint@80/2006/08.02.19.20/doc/v1.pdf.
    Robert J. Barro. Human Capital and Growth. American Economic Review, 91(2):12–17, 2001.
    Gary S Becker, Kevin M Murphy, and Robert Tamura. Human Capital , Fertility , and Economic
    Growth. Journal of Political Economy, 98(5):12–37, 1990.
    Andrew David Cliff and J Keith Ord. Spatial processes: models & applications. Taylor & Francis, 1981.
    Matthew Collin and David N. Weil. The Effect of Increasing Human Capital Investment on Economic
    Growth and Poverty: A Simulation Exercise. Journal of Human Capital, 14(1):43–83, 2020.
    Juan C. Duque, Luc Anselin, and Sergio J. Rey. The max-p-regions problem. Journal of Regional
    Science, 52(3):397–419, 2012. ISSN 00224146. doi: 10.1111/j.1467-9787.2011.00743.x.
    Walter D. Fisher. On Grouping for Maximum Homogeneity. Journal of the American Statistical
    Association, 53(284):789–798, 1958.
    George F Jenks. Optimal data classification for choropleth maps. Department of Geographiy, University
    of Kansas Occasional Paper, 1977.
    SDSN-Bolivia. Atlas Municipal de los Objetivos de Desarrollo Sostenible en Bolivia, 2020.
    Mendez & Gonzales November, 2020 Human Capital Constraints in Bolivia 41 / 42

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