class: center, middle, inverse, title-slide # Regional Convergence, Spatial Scale, and Spatial Dependence: ## Evidence from Homicides and Personal Injuries in Colombia 2010-2018 ### Felipe Santos-Marquez
Master’s student
Graduate School of International Development
Nagoya University, JAPAN
Carlos Mendez
Graduate School of International Development
Nagoya University, JAPAN
### Prepared for the 2020 Bolivian Conference on Development Economics July 27th
[ Working paper available at:
https://felipe-santos.rbind.io/
] --- ## Motivation: - Beyond GDP, socio-economic variables and their convergence are relevant for development studies (Royuela et al 2015) - Persistent income differences, differences in health indicators and in "general" regional inequality in Colombia. - Scarce academic literature on convergence at the municipal level. ## Research Objective: - Study convergence/divergence of homicide rates (**NMR**) and personal injury rates (**NPIR**) across municipalities and departments in Colombia over 2010-2018. - Analyze spatial autocorrelation and its robustness at different disaggregation levels. ## Methods: - Classical convergence framework (Barro and Sala-i-Martin 1992) - Distributional convergence framework (Quah 1996; Hyndman et. al 1996) - Spatial convergence (spatial lag and spatial error models) - Spatial autocorrelation (Moran's I and differential Moran's I) --- class: middle # Main Results: 1. **Sigma Convergence** for both homicide and personal injury rates at the state level, **Beta Convergence** for both levels and rates. 3. **Clustering dynamics** - NMR State level: 4+? convergence clusters - NMR Municipal level: 2+? convergence clusters - NPIR State level: 2 convergence clubs - NPIR Municipal level: stagnation and 2 convergence clubs 4. **Spatial Autocorrelation** robust only at the municipality level --- class: middle # Outline of this presentation 1. **Data description** Non crime rates 2. **Global convergence:** Using classical summary measures - Beta convergence - Sigma convergence 3. **Regional disaggregation:** - Distribution dynamics framework - Distributional convergence 4. **Global spatial autocorrelation:** - Disaggreagation effects 5. **Policy discussion** - The Colombian National Development Plan 2018-22 5. **Concluding Remarks** --- class: middle # (1) Data: - Total number of **homicides** and **personal injuries** in Colombia per year from 2010 until 2018 (data taken from the national police). - Data is agreggated at the municipal and departmental levels. - Population census and estimates for states and municipalities (data from the National Bureau of Statistics). - Raw rates computed `$$raw\space rates = crimes / population$$` - Non crime rates computed `$$NCR= 10000- raw\ rate * 10000$$` - **Survival rates** are chosen because positively defined variables are a **standard** in the convergence literature. --- class: middle,center ## Non-crime variables over time <img src="figs/mun_quantile.png" style="width: 100%" /> <img src="figs/dep_quantile.png" style="width: 100%" /> --- class: center, middle # (2) **Global convergence:** **Beta convergence** (catch-up process) `\(log{\frac{Y_{iT}}{Y_{i0}}}=\alpha +\beta \cdot log(Y_{i0})+ \epsilon\)` <img src="figs/betaexpl.png" style="width: 40%" /> **Spatial Beta models** *Spatial lag Model:* `\(\log \frac{Y_{i T}}{Y_{i 0}}=\alpha+\beta \cdot \log \left(Y_{i 0}\right)+\rho W \log \frac{Y_{i T}}{Y_{i 0}}+\varepsilon_{t}\)` *Spatial Error Model:* `\(\log \frac{Y_{i T}}{Y_{i 0}}=\alpha+\beta \cdot \log \left(Y_{i 0}\right)+\lambda W \varepsilon_{t}+u_{t}\)` **Sigma convergence** (the dispersion of the data decreases over time) --- class: middle, center # Classical Convergence results (NMR) .pull-left[ ##States- Sigma and Beta convergence ![](figs/beta1.png) ] .pull-right[ ## Municipalities - ONLY Beta convergence ![](figs/beta2.png) ] **Sigma convergence results** <img src="figs/sigma_table.png" style="width: 40%" /> --- class: justify ## Beta and sigma convergence summary <img src="figs/reg_table2.png" style="width: 100%" /> - **Lagrange multiplier tests** also indicate that the SEM is the best fitting model. - Royuela and García (2015) also reported that the `\(\rho\)` and `\(\lambda\)` coefficients were **NOT significant at the state level** over the period 1990 to 2005. - The authors reported half-lives of **15.3, 11.5 and 15.8 years**. --- class: center, middle # (3) **State and Municipality disaggregation:** ## The distribution dynamics framework <img src="figs/dynt.png" style="width: 70%" /> --- class: center, middle ## The distribution dynamics framework ## Convergence, divergence and stagnation <img src="figs/dyn3.png" style="width: 70%" /> --- class: middle, center # (3) Local convergence clusters **NMR State level**: 4+? convergence clusters **NMR Municipal level**: 2+? convergence clusters **NPIR State level **: 2 convergence clubs **NPIR Municipal level **: stagnation and 2 convergence clubs --- class: middle, center ##NMR at both levels State level: 4+? convergence clusters <img src="figs/depdyn.png" style="width: 70%" /> Municipal level: 2+? convergence clusters <img src="figs/mundyn.png" style="width: 70%" /> ## At the municipal level there are fewer clusters but no signs of sigma convergence --- class: middle, center ##NPIR at both levels State level: 2 convergence clusters <img src="figs/depdyn2.png" style="width: 70%" /> Municipal level: 2 convergence clusters and stagnation <img src="figs/mundyn2.png" style="width: 70%" /> ## the same number of clusters but stagnation patterns are strong at the municipal level. --- class: middle, center # (4) Spatial Autocorrelation (Theory) ##**High Intuition Concept** <img src="figs/moran4.png" style="width: 70%" /> ## More Formal (less intuitive) `$$I = \frac{\sum_i\sum_j w_{ij} y_i.y_j}{\sum_i y_i^2} = \frac{\sum_i (y_i \times \sum_j w_{ij} y_j)}{\sum_i y_i^2}.$$` ##Differential Moran's I ( `\(y_{i,t}−y_{i,t−1}\)` ) We compute the Moran's I for the variable `\(y_{i,t}−y_{i,t−1}\)`. If there is a fixed effect `\(\mu_i\)` related to location `\(i\)`, it is possible to present the value at each location for time `\(t\)` as the sum of some intrinsic value and the fixed effect. `\(y_{i,t} = y*_{i,t} + \mu_i\)` --- class: justify # (4) Spatial autocorrelation (Results) - **State level**: Moran's I statistic is significant, differential Moran's I is not significant (**not robust**) - **Municipal level**: Standard and Differential Moran's I significant (**robust**) - **Space matters at the Municipal level** <br /> <img src="figs/moranall3.png" style="width: 140%" /> --- #(5) Policy discussion - Vertical and horizontal policy coordination, spillovers and borders. - Spatial spillovers from neighbors can have **both positive and negative effects** on the convergence path of a region. - It could be more appropriate for the formulation of national development plans to have targets at the state level <img src="figs/pol4.png" style="width: 90%" /> --- # (5) Concluding Remarks ## Uplifting results "on average" : - The dispersion of non-crime (crime) rates at the state level **has decreased**. On average less homicides but more personal injuries. - **Global convergence on average at the state level**, while fast beta convergence at the municipality level. ## Beyond classical convergence : - Regional differences matter in **both disaggregation levels**. - **Multiple local convergence clubs**; with more clubs at the state level. ## The Role of Space - Subsequent Differential Moran's I are robust and significant at the **municipality level only** - Results at the **state level** for NMR are not conclusive and similar to the ones reported by Royuela et al 2015. --- # (5) Concluding Remarks # Implications and further research - Convergence clusters help us to find regions with similar outcomes, coordination among them can be promoted. - Strong spatial autocorrelation suggest the possibility of applying spatial filters in order to remove the spatial component of crime variables. - At the state level (including more variables) a probit model may help us to find the determinants for a conditional "jump" to the upper clusters. - As many municipalities have small population, crime rates have high variance instability. Empirical Bayes methods can be used. --- class: center, middle # Thank you very much for your attention You can find the working paper on my website https://felipe-santos.rbind.io If you are interested in our research please check our QuaRCS lab website <br /> https://quarcs-lab.rbind.io/ <img src="figs/logo2.png" style="width: 30%" /> **Quantitative Regional and Computational Science Lab**