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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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 

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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