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<!DOCTYPE html>
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<head>
<title>Regional Disparities, Aggregation Effects and the Role of Space</title>
<meta charset="utf-8" />
<meta name="author" content="Felipe Santos M1 research student Graduate School of International Development Nagoya University, JAPAN Prof. Carlos Mendez Graduate School of International Development Nagoya University, JAPAN" />
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<textarea id="source">
class: center, middle, inverse, title-slide
# Regional Disparities, Aggregation Effects and the Role of Space
## Evidence from Homicide Rates in Colombia 2010-2018
### Felipe Santos <br />M1 research student<br />Graduate School of International Development<br />Nagoya University, JAPAN <br /> <br /> Prof. Carlos Mendez <br /> Graduate School of International Development<br />Nagoya University, JAPAN <br />
### July 24th 2019
---
## 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.
- Scarce academic literature on inequality (convergence approach) at the municipality level.
## Research Objective:
- Study convergence/divergence of homicide rates across municipalities and departments in Colombia 2010-2018
- Analyze spatial autocorrelation and its robustness at different disaggregate 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)
---
class: middle
# Main Results:
1. **Sigma Convergence** for homicide rates at the state level, **Beta Convergence** at the municipality level
2. Regional disaggretation matters: **Local convergence clusters**
3. **Clustering dynamics**
- State level: 4+? convergence clusters
- Municipality level: 2+? convergence clusters
4. **Spatial Autocorrelation** robust only at the municipality level
---
class: middle
# Outline of this presentation
1. **Data description** Survival rates (not homicide rates)
2. **Global convergence:** Using classical summary measures
- Beta convergence
- Sigma convergence
3. **Regional disaggregation:**
- Distribution dynamics framework
- Distributional convergence
4. **Local convergence clusters**
5. **Global spatial autocorrelation:**
- Disaggreagation effects
5. **Concluding Remarks**
---
class: middle
# Data:
- Total number of homicides in Colombia per year from 2010 until 2018 (data taken from the National police).
- Data is agreggated at the municipality and departament level.
- Population census and estimates for states and municipalitites.
- Raw rates computed `$$Hrate= homicides/population$$`
- Survival rates (non- murder rates) computed
`$$NMR= 10000- raw\ rate * 10000$$`
- **Survival rates** are chosen because positively defined variables are a **standard** in the convergence literature.
---
class: center, middle
# (2) **Global convergence:**
**Using classical summary measures**
Beta convergence
Sigma convergence
---
class: middle,center
## States- Sigma and Beta convergence
`$$\sigma (Standard \ \space deviation)\space\sigma_{2010}= 1.84\space\space\space\space\space \sigma_{2018}=1.26$$`
`$$log{\frac{Y_t}{Y_0}}=\alpha +\beta *logY_0+ \epsilon \space\space\space\space\space\beta=-0.476^{***} \space\space\space\space halflife=8.59\space years$$`
---
class: middle, center
## Municipalities - Beta convergence (only)
`$$log{\frac{Y_t}{Y_0}}=\alpha +\beta *logY_0+ \epsilon \space\space\space\space\space\beta=-0.551^{***} \space\space\space\space halflife=6.92\space years$$`
---
class: center, middle
# (3) **State and Municipality disaggregation:**
Distribution dynamics framework
Distributional convergence
class: middle
# Regional heterogeneity matters
Dynamics of the **entire regional distribution**
**conditional density** estimation
---
class: middle, center
## The distribution dynamics framework
---
class: middle, center
# (4) Local convergence clusters
State level: 4+? convergence clusters
Municipality level: 2+? convergence clusters
---
class: middle, center
# Where are the clusters?
Municipality level **- - - - - - - - - - - - - -** Department Level
Those lines are not regression trends!
---
class: middle, center
# State level: 4+? convergence clusters
Multimodal distribution with sigma convergence
---
class: middle, center
# Municipality level: 2+? convergence clusters
Interesting results; there are fewer clusters but sigma convergence is not present.
---
class: middle
# (4) Spatial Autocorrelation (moran I definition)
##**High Intuition Concept**
##More Formal (less intuitive)
---
class: justify, center, middle
`$$I = \frac{\sum_i\sum_j w_{ij} z_i.z_j}{\sum_i z_i^2} = \frac{\sum_i (z_i \times \sum_j w_{ij} z_j)}{\sum_i z_i^2}.$$`
In the linear regression **y=α+βx**
, the estimate for
**β**
is `\(\sum_i (x_i \times y_i) / \sum_i x_i^2\)`.In the Moran scatter plot shown below, **y** is the spatial lag variable `\(\sum_j w_{ij} z_j\)`
##Differential Moran Scatter Plot ( `\(y_{i,t}−y_{i,t−1}\)` )
Differencing the variable to control for the locational fixed effects: We computate the Moran's I for the variable
`\(y_{i,t}−y_{i,t−1}\)`. If we consider 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. `\(y_{i,t} = y*_{i,t} + \mu_i\)` (Geoda documentation 2019)
---
class: middle, center
# (4) Spatial autocorrelation
**State level**: Moran's I statistic significant from 2012, differntial Moran's I is not significan (**not robust**)
**Municipality level**: Differential Moran's I significant from 2010 (**robust**)
---
# (4) Spatial autocorrelation
## State level (not robust)
- Univatiate Moran's I is significant from 2012.
- But, **The differential moran statistic is not significant**. It is then considered that the significance of Spatial Autocorrelation is **not robust**.
- See plots for 2014 and 2014-2013, similar for other years (standarized variables)
---
# (4) Spatial autocorrelation
## Municipality level (**Robust**)
- The univariate Moran's I is not significant in 2010 and 2011. however, it is significant from 2012 to 2018; reaching a maximum value in 2016.
- Differential Moran's I ( `\(sur_{2018}-sur_{2010}\)` ) is **significant** `\(Moran's\ I = 0.22^{***}\)`
- Subsequent Differential Moran's I `\(sur_{t}-sur_{t-1}\)` **statistically significant at the municipality level**. Except 2014-2013 (not statistically significant) see graphs
---
# (5) Concluding Remarks
## Uplifting results "on average" :
- Differences in overall raw rates at the state level **have decreased** and the means at both levels have increased (survival rate)
- **Global convergence on average at the state level**, while fast beta convergence at the municipality level.
## Beyond classical convergence :
- Regional differences matter in **both disaggreagation 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** are not conlusive and similar to the ones reported by Royuela et al 2015.
---
# (5) Concluding Remarks
# Implications and further research
- Strong spatial autocorrelation suggest the posibility of applying the Getis filtering in order to filter the spatial component of homicide variables.
- Convergence clusters help us to find regions with similar outcomes, coordination among them can be promoted.
- Has crime followed a trajectory? can a speed and direction of contagious patterns be found?
- At the state or department level (including more variables) can a probit model help us to find the determinants for a conditional "jump" to the upper clusters.
---
class: center, middle
# Thank you very much for your attention
If you are interested in our research, please check Prof. Carlos Mendez website
https://carlos-mendez.rbind.io
And the research semminar's website
https://carlos-seminar.rbind.io/
***
Stay tuned for my Felipe's Master's thesis
##Will the SGDs be Achieved in Colombia? A Study of National Convergence and Regional differences.
Gender inequality, Income, Eduacation, Crime... Classical convergence, Distributional Dynamics, Spatial Filtering, Spatial econometrics, long-run Filtering...
</textarea>
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