Regional Convergence, Spatial Scale, and Spatial Dependence:

# 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 Prof. Carlos Mendez Graduate School of International Development Nagoya University, JAPAN 
### Prepared for the 2019 Applied Regional Science Conference, Saga University, Nov 23rd [ Slides available at: <a href="https://quarcs-lab.rbind.io/" class="uri">https://quarcs-lab.rbind.io/</a>]

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## Motivation:

- Beyond GDP, **social 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.
**Among the most unequal countries in the world in terms of the income gini coefficient**.

- **Scarce academic literature on inequality (convergence approach) and crime at the municipality level**. 
  
## Research Objective:
  
- Study convergence/divergence of homicide rates (**NMR**) and personal injury rates (**NPIR**) across municipalities and departments in Colombia 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 autocorrelation (Moran's I and differential Moran's I)

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# Main Results:

1. **Sigma Convergence** and  **Beta Convergence** for both homicide and personal injury rates at the state level. However just **Beta Convergence** for both crimes at the municipal level.

2. Regional disaggretation  matters: **Local convergence clusters**

3. **Clustering dynamics**  different clubs for both crimes and levels
4. **Spatial Autocorrelation** robust only  at the municipality level

# Main Contributions

1.  Study of **classical and distribution convergence** for  two crimes and **contrasting results for two levels**: 32 States and  1120 municipalities.

2.  Spatial autocorrelation is **robust for the higher level**.
3.  Uniform progress of States and municipalitites (NMR). **first robust findings of convergence of NMR** in the literature.

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# 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  
  - CCTs and spatial autocorrelation
  
5. **Concluding Remarks**
  
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# 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 municipalitites.

- Raw rates are computed: `$$raw\space rates = crimes / population$$`

- Non-crime rates are computed:　
   `$$NCR= 10000- raw\ rate * 10000$$`
- **Survival rates** are chosen because positively defined variables are a **standard** in the convergence literature.

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# (2) **Global convergence:**
**Using  the classical convergence framework **

*Beta convergence* (the catch-up effect)

*Sigma convergence*  (the dispersion of the data decreaseses over time )
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#  States- Sigma and Beta convergence (NMR)

`$$\sigma (Standard \ \space deviation)\space\sigma_{2010}= 1.84\space\space\space\space\space \sigma_{2018}=1.26$$`

`$$log{\frac{Y_t}{Y_0}}=\alpha +\beta *logY_0+ \epsilon \space\space\space\space\space\beta=-0.476^{***} \space\space\space\space halflife=8.59\space  years$$`

![](figs/betatrial.png)

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# Municipalities - ONLY Beta convergence   (NMR)

`$$log{\frac{Y_t}{Y_0}}=\alpha +\beta *logY_0+ \epsilon \space\space\space\space\space\beta=-0.551^{***} \space\space\space\space halflife=6.92\space  years$$`
![](figs/beta2.png)

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# Beta and sigma convergence  summary

![](figs/betasum.png)

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# (3) **State and Municipality disaggregation: The distribution dynamics framework**

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# (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

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#NMR at both levels

State level: 4+? convergence clusters (previous studies found 2-3)
 
 <img src="figs/depdyn.png" style="width: 70%" />

Municipality level: 2+? convergence clusters

Interesting results; there are fewer clusters but sigma convergence is not present.

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#NPIR at both levels

State level: 2 convergence clusters
 
 <img src="figs/depdyn2.png" style="width: 70%" />

Municipality level: 2 convergence clusters and "stagnation"

Interesting results; the same number of clusters but stagnation patterns are stronger at the municipal level

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# (4) Spatial Autocorrelation (Theory)

##**High Intuition Concept** 
<img src="figs/moran.png" style="width: 70%" />
##More Formal (less intuitive) 
`$$I = \frac{\sum_i\sum_j w_{ij} z_i.z_j}{\sum_i z_i^2} = \frac{\sum_i (z_i \times \sum_j w_{ij} z_j)}{\sum_i z_i^2}.$$`
##Differential Moran Scatter Plot ( `$y_{i,t}−y_{i,t−1}$` )
 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. `$y_{i,t} = y*_{i,t} + \mu_i$`. Differencing the variable to control for the locational fixed effects
`$y_{i,t}−y_{i,t−1}$`.

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# (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**)

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#(5) Policy discussion

- vertical and horizontal policy coordination, spillovers and borders.

- It could be more appropriate for the formulation of national development plans to have convergence targets at the state level as well as the municipal level

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#(5) Policy discussion - The need for a spatial perspective in current cash transfer programs:

-  Spatial regressions could be used to test determinant hypothesis. Moreover, such research could contribute to the literature by suggesting a case for spatially focused CCTs.

- A research jump **from micro to macro** both in scale and time.

- Ultimately, this type of analysis could serve a as tool **for combating organized crime** in specific locations (Ingram and Marchesini da Costa , 2017).

<img src="figs/rct.png" style="width: 100%" />
 
 Camacho, A., & Mejía, D. (2013).
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# (5) Concluding Remarks

## Uplifting results  "on average" :

- Differences in overall raw rates at the state level **have decreased**. On average less homicides (**inclusive improvement at the state level**) but "more" personal injuries (More research is needed, less dispersion).

-  **fast beta convergence**  at the municipality level.

- **Robust signs of convergence** of homicide and personal injury rates at the state level. The first in the convergence literature about crime in Colombia.

## Beyond classical convergence  :

- Regional differences matter in **both disaggreagation levels**. there are **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**

## Policy, Space and CCTs

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# (5) Concluding Remarks

# Implications and further research

- Strong spatial autocorrelation suggest the posibility of applying spatial filters in order to remove the spatial component of crime variables.

- Convergence clusters help us to find regions with similar outcomes, coordination among them can be promoted.

- Has crime followed a trajectory or are there more spill over patterns? are there local clusters? LISA analysis.

- At the state or department level (including more variables) a probit model may help us to find the determinants for a conditional "jump" to the upper clusters.

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# Thank you very much for your attention

You can find this presentation on my website https://felipe-santos.rbind.io and on our lab's website https://quarcs-lab.rbind.io/

If you are interested in our research, the tools we use and the data we handle; please check our QuaRCS lab website.

**Quantitative Regional and Computational Science Lab**