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

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1. Regional Convergence, Spatial Scale, and Spatial Regional Convergence, Spatial Scale, and Spatial Dependence: Dependence: Evidence from Homicides and Personal Injuries in Colombia 2010-2018 Evidence from Homicides and Personal Injuries in Colombia 2010-2018 Felipe Santos-Marquez Felipe Santos-Marquez Master’s student Master’s student Graduate School of International Development Graduate School of International Development Nagoya University, JAPAN Nagoya University, JAPAN Carlos Mendez Carlos Mendez Graduate School of International Development Graduate School of International Development Nagoya University, JAPAN Nagoya University, JAPAN Prepared for the 2020 Bolivian Conference on Development Economics July 27th Prepared for the 2020 Bolivian Conference on Development Economics July 27th [ Working paper available at: [ Working paper available at: https://felipe-santos.rbind.io/ https://felipe-santos.rbind.io/] ]
2. Motivation: Motivation: Beyond GDP, socio-economic variables and their convergence are relevant for Beyond GDP, socio-economic variables and their convergence are relevant for development studies (Royuela et al 2015) development studies (Royuela et al 2015) Persistent income di erences, di erences in health indicators and in "general" Persistent income di erences, di erences in health indicators and in "general" regional inequality in Colombia. regional inequality in Colombia. Scarce academic literature on convergence at the municipal level. Scarce academic literature on convergence at the municipal level. Research Objective: Research Objective: Study convergence/divergence of homicide rates ( Study convergence/divergence of homicide rates (NMR NMR) and personal injury rates ) and personal injury rates ( (NPIR NPIR) across municipalities and departments in Colombia over 2010-2018. ) across municipalities and departments in Colombia over 2010-2018. Analyze spatial autocorrelation and its robustness at di erent disaggregation levels. Analyze spatial autocorrelation and its robustness at di erent disaggregation levels. Methods: Methods: Classical convergence framework (Barro and Sala-i-Martin 1992) Classical convergence framework (Barro and Sala-i-Martin 1992) Distributional convergence framework (Quah 1996; Hyndman et. al 1996) Distributional convergence framework (Quah 1996; Hyndman et. al 1996) Spatial convergence (spatial lag and spatial error models) Spatial convergence (spatial lag and spatial error models) Spatial autocorrelation (Moran's I and di erential Moran's I) Spatial autocorrelation (Moran's I and di erential Moran's I) 2 / 20 2 / 20
3. Main Results: Main Results: 1. Sigma Convergence Sigma Convergence for both homicide and personal injury rates at the state level, for both homicide and personal injury rates at the state level, Beta Convergence Beta Convergence for both levels and rates. for both levels and rates. 2. Clustering dynamics Clustering dynamics NMR State level: 4+? convergence clusters NMR State level: 4+? convergence clusters NMR Municipal level: 2+? convergence clusters NMR Municipal level: 2+? convergence clusters NPIR State level: 2 convergence clubs NPIR State level: 2 convergence clubs NPIR Municipal level: stagnation and 2 convergence clubs NPIR Municipal level: stagnation and 2 convergence clubs 3. Spatial Autocorrelation Spatial Autocorrelation robust only robust only at the municipality level at the municipality level 3 / 20 3 / 20
4. Outline of this presentation Outline of this presentation 1. Data description Data description Non crime rates Non crime rates 2. Global convergence: Global convergence: Using classical summary measures Using classical summary measures Beta convergence Beta convergence Sigma convergence Sigma convergence 3. Regional disaggregation: Regional disaggregation: Distribution dynamics framework Distribution dynamics framework Distributional convergence Distributional convergence 4. Global spatial autocorrelation: Global spatial autocorrelation: Disaggreagation e ects Disaggreagation e ects 5. Policy discussion Policy discussion The Colombian National Development Plan 2018-22 The Colombian National Development Plan 2018-22 6. Concluding Remarks Concluding Remarks 4 / 20 4 / 20
5. (1) Data: (1) Data: Total number of Total number of homicides homicides and and personal injuries personal injuries in Colombia per year from 2010 until in Colombia per year from 2010 until 2018 (data taken from the national police). 2018 (data taken from the national police). Data is agreggated at the municipal Data is agreggated at the municipal and departmental levels. and departmental levels. Population census and estimates for states and municipalities (data from the National Population census and estimates for states and municipalities (data from the National Bureau of Statistics). Bureau of Statistics). Raw rates computed Raw rates computed Non crime rates Non crime rates computed computed Survival rates Survival rates are chosen because positively de ned variables are a are chosen because positively de ned variables are a standard standard in the in the convergence literature. convergence literature. r ra aw w r ra at te es s = = c cr ri im me es s/ /p po op pu ul la at ti io on n N N C CR R = = 10000 10000 − − r ra aw w r ra at te e ∗ ∗ 10000 10000 5 / 20 5 / 20
6. Non-crime variables over time Non-crime variables over time 6 / 20 6 / 20
7. (2) (2) Global convergence: Global convergence: Beta convergence Beta convergence (catch-up process) (catch-up process) Spatial Beta models Spatial Beta models Spatial lag Model: Spatial lag Model: Spatial Error Model: Spatial Error Model: Sigma convergence Sigma convergence (the dispersion of the data decreases over time) (the dispersion of the data decreases over time) l lo og g = = α α + + β β ⋅ ⋅ l lo og g( (Y Y i i0 0 ) ) + + ϵ ϵ Y Y i iT T Y Yi i0 0 log log = = α α + + β β ⋅ ⋅ log log( (Y Yi i0 0 ) ) + + ρ ρW W log log + + ε εt t Y Yi iT T Y Yi i0 0 Y Yi iT T Y Yi i0 0 log log = = α α + + β β ⋅ ⋅ log log( (Y Yi i0 0 ) ) + + λ λW W ε εt t + + u ut t Y Y i iT T Y Yi i0 0 7 / 20 7 / 20
8. States- Sigma and Beta convergence States- Sigma and Beta convergence Municipalities - ONLY Beta convergence Municipalities - ONLY Beta convergence Classical Convergence results (NMR) Classical Convergence results (NMR) Sigma convergence results Sigma convergence results 8 / 20 8 / 20
9. Beta and sigma Beta and sigma convergence summary convergence summary Lagrange multiplier tests Lagrange multiplier tests also indicate that the SEM is the best tting model. also indicate that the SEM is the best tting model. Royuela and García (2015) also reported that the Royuela and García (2015) also reported that the and and coe cients coe cients were were NOT NOT signi cant at the state level signi cant at the state level over the period 1990 to 2005. over the period 1990 to 2005. The authors reported half-lives of The authors reported half-lives of 15.3, 11.5 and 15.8 years 15.3, 11.5 and 15.8 years. . ρ ρ λ λ 9 / 20 9 / 20
10. (3) (3) State and Municipality disaggregation: State and Municipality disaggregation: The distribution dynamics framework The distribution dynamics framework 10 / 20 10 / 20
11. The distribution dynamics framework The distribution dynamics framework Convergence, divergence and stagnation Convergence, divergence and stagnation 11 / 20 11 / 20
12. (3) Local convergence clusters (3) Local convergence clusters NMR State level NMR State level: 4+? convergence clusters : 4+? convergence clusters NMR Municipal level NMR Municipal level: 2+? convergence clusters : 2+? convergence clusters NPIR State level NPIR State level : 2 convergence clubs : 2 convergence clubs NPIR Municipal level NPIR Municipal level : stagnation and 2 convergence clubs : stagnation and 2 convergence clubs 12 / 20 12 / 20
13. NMR at both levels NMR at both levels State level: 4+? convergence clusters State level: 4+? convergence clusters Municipal level: 2+? convergence clusters Municipal level: 2+? convergence clusters At the municipal level there are fewer clusters but no signs of sigma convergence At the municipal level there are fewer clusters but no signs of sigma convergence 13 / 20 13 / 20
14. NPIR at both levels NPIR at both levels State level: 2 convergence clusters State level: 2 convergence clusters Municipal level: 2 convergence clusters and stagnation Municipal level: 2 convergence clusters and stagnation the same number of clusters but stagnation patterns are strong at the municipal level. the same number of clusters but stagnation patterns are strong at the municipal level. 14 / 20 14 / 20
15. (4) Spatial Autocorrelation (Theory) (4) Spatial Autocorrelation (Theory) High Intuition Concept High Intuition Concept More Formal (less intuitive) More Formal (less intuitive) Differential Moran's I ( Differential Moran's I ( ) ) We compute the Moran's I We compute the Moran's I for the for the variable variable . . If there is a If there is a xed e ect xed e ect related to location related to location , it is possible to present the value at each , it is possible to present the value at each location for time location for time as the sum of some intrinsic value and the xed e ect. as the sum of some intrinsic value and the xed e ect. I I = = = = . . ∑ ∑ i i ∑ ∑ j j w wi ij j y yi i . . y yj j ∑ ∑ i i y y 2 2 i i ∑ ∑ i i ( (y yi i × × ∑ ∑ j j w wi ij j y yj j ) ) ∑ ∑ i i y y 2 2 i i y y i i, ,t t − − y y i i, ,t t− −1 1 y yi i, ,t t − − y yi i, ,t t− −1 1 μ μi i i i t t y yi i, ,t t = = y y ∗ ∗i i, ,t t + +μ μi i 15 / 20 15 / 20
16. (4) Spatial autocorrelation (4) Spatial autocorrelation (Results) (Results) State level State level: Moran's I statistic is signi cant, di erential Moran's I is not signi cant ( : Moran's I statistic is signi cant, di erential Moran's I is not signi cant (not not robust robust) ) Municipal level Municipal level: Standard and Di erential Moran's I signi cant : Standard and Di erential Moran's I signi cant ( (robust robust) ) Space matters at the Municipal level Space matters at the Municipal level 16 / 20 16 / 20
17. (5) Policy discussion (5) Policy discussion Vertical and horizontal policy coordination, spillovers and borders. Vertical and horizontal policy coordination, spillovers and borders. Spatial spillovers from neighbors can have Spatial spillovers from neighbors can have both positive and negative e ects both positive and negative e ects on the on the convergence path of a region. convergence path of a region. It could be more appropriate for the formulation of national development plans to It could be more appropriate for the formulation of national development plans to have targets at the state level have targets at the state level 17 / 20 17 / 20
18. (5) Concluding Remarks (5) Concluding Remarks Uplifting results "on average" : Uplifting results "on average" : The dispersion of non-crime (crime) rates at the state level The dispersion of non-crime (crime) rates at the state level has decreased has decreased. On average . On average less homicides but more personal injuries. less homicides but more personal injuries. Global convergence on average at the state level Global convergence on average at the state level, while fast beta convergence at the , while fast beta convergence at the municipality level. municipality level. Beyond classical convergence Beyond classical convergence : : Regional di erences matter in Regional di erences matter in both disaggregation levels both disaggregation levels. . Multiple local convergence clubs Multiple local convergence clubs; with more clubs at the state level. ; with more clubs at the state level. The Role of Space The Role of Space Subsequent Di erential Moran's I are robust and signi cant at the Subsequent Di erential Moran's I are robust and signi cant at the municipality level municipality level only only Results at the Results at the state level state level for NMR are not conclusive and similar to the ones reported for NMR are not conclusive and similar to the ones reported by Royuela et al 2015. by Royuela et al 2015. 18 / 20 18 / 20
19. (5) Concluding Remarks (5) Concluding Remarks Implications and further research Implications and further research Convergence clusters help us to nd regions with similar outcomes, coordination Convergence clusters help us to nd regions with similar outcomes, coordination among them can be promoted. among them can be promoted. Strong spatial autocorrelation suggest the possibility of applying spatial lters in order Strong spatial autocorrelation suggest the possibility of applying spatial lters in order to remove the spatial component of crime variables. to remove the spatial component of crime variables. At the state level (including more variables) a probit model may help us to nd the At the state level (including more variables) a probit model may help us to nd the determinants for a conditional "jump" to the upper clusters. determinants for a conditional "jump" to the upper clusters. As many municipalities have small population, crime rates have high As many municipalities have small population, crime rates have high variance variance instability. Empirical Bayes methods can be used. instability. Empirical Bayes methods can be used. 19 / 20 19 / 20
20. Thank you very much for your attention Thank you very much for your attention You can nd the working paper on my website You can nd the working paper on my website https://felipe-santos.rbind.io https://felipe-santos.rbind.io If you are interested in our research please check our QuaRCS lab website If you are interested in our research please check our QuaRCS lab website https://quarcs-lab.rbind.io/ https://quarcs-lab.rbind.io/ Quantitative Regional and Computational Science Lab Quantitative Regional and Computational Science Lab 20 / 20 20 / 20