Does crime relocate?

class: center, middle, inverse, title-slide

# Does crime relocate?
## Estimating the (side)-effects of local police interventions on violence
### Marcelino Guerra
### March 12, 2021

---

# Motivation and Background

* Based on Becker's model, most of the crime economics literature focuses on the estimation of the "deterrent effect"
  * e.g., Levitt (AER 1997,2002), Di Tella and Schargrodsky (AER 2004), Klick and Tabarrok (J. Law. Econ. 2005), Draca, Machin, and Witt (AER 2011)
  
  * It is already painful to properly establish the causal effect of police on crime due to simultaneity, and displacement of criminal activities is often ignored
  
  * Those "more cops, less crime" studies have no words on what precisely extra cops would do on the streets

* **This study** seeks to evaluate one of the most common policing strategies in Brazil: the allocation of blitzes
 
  * Well defined place-based intervention with the precise policing assignment 
  
  * Given the level of geographic and temporal disaggregation, it is possible to estimate crime displacement

*  The novelty comes from the complete assessment of the impacts of a large-scale police operation and the identification of suitable displacement areas

---
# Data and Context I

.pull-left[

1. Police blitzes

* 2004 identified blitzes over the weeks of 2012
  * 450 census tracts treated (out of 3020) in 52 weeks 
  * Information provided by the Public Security State Department

2. Crime data

* Only violent crimes in 2012 so far - robbery, homicide, and bodily injury
   * Information provided by the Public Security State Department

3. Socioeconomic profile of Fortaleza, Brazil

* Brazilian Census 2010
  * Population density, income level, favelas, etc.

]

.pull-right[![](figs/fortal2.png) 
**Note**: Fortaleza has around 2.6 million inhabitants and is divided in 3020 census tracts that have, on average, 0.104 `\(km^{2}\)`

]

---
# Data and Context II

.pull-left[

* A blitz interrupts the flow of vehicles and people through a physical, visual, and audible warning. Police officers proceed with checks and inspections in selected targets
  * This sudden increase in policing (5-10 policemen) in a street segment usually lasts between 3 and 6 hours
  * With precise coordinates of each blitz, it is possible to locate each police intervention inside of those 3020 census tracts

* The Bureau of Operations meets every Friday and decides where to allocate the blitzes in the subsequent week
  * It is not determined by crime. Instead, the command considers the past allocation to create the optimal deterrence effect (initial plus residual)
 
]

.pull-right[ * One important feature of the strategy's design is that the treatment varies in time and intensity

<br/>

![](figs/blitz.png)
**Note**: An example of a "fixed blitz". ]

---

# Allocation of Blitzes in 2012

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# Violent Crimes in 2012

---

# Research Design I

.panelset[
.panel[ .panel-name[Identification]

* As mentioned before, it is challenging to disentangle the effect of police on crime. I deal with the simultaneity using police crackdowns that essentially **[tried to surprise drivers both temporal and geographically](https://guerramarcelino.shinyapps.io/weekblitz/)** and do not depend on shocks to crime levels

* The reduced-form model that captures the direct effect of the increase in policing on crime:

`\begin{align}
\text{VCrate}_{it} = \delta Blitz_{it}+ c_{i}+ \lambda_{t} +  \varepsilon_{it} & & (1)
\end{align}`

* Conditional on time and census tracts fixed effects, the allocation of blitzes in a small area `\((0.1 km^{2})\)` at a given week is treated as good as random and used to identify the causal effect of local police interventions on crime. For robustness, neighborhood week trends are included in most specifications

* The reduced-form model that captures the total effects of the increase in policing on crime (SLX model):

`\begin{align}
\text{VCrate}_{it} = \delta Blitz_{it}+ \theta WBlitz_{it} + c_{i}+ \lambda_{t} +  \varepsilon_{it} & & (2)
\end{align}`

* `\(WBlitz_{it}\)` is the weighted average of blitzes in the surrounding area of sector `\(i\)` at week `\(t\)`

]

.panel[.panel-name[Blitz Allocation]

<table>
 <thead>
   <tr>
   <td style="text-align:center;" colspan="3"> <b> Dependent variable: Number of blitzes </b> </td>
   </tr>
  <tr>
   <th height="10" style="text-align:left;">   </th>
   <th height="10" style="text-align:center;"> (1) </th>
   <th height="10" style="text-align:center;"> (2) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> \(VCrate_{t-1}\)</td>
   <td style="text-align:center;"> -0.000087 (0.000146)  </td>
   <td style="text-align:center;"> -0.000015 (0.000072) </td>

</tr>
   <tr>
   <td style="text-align:left;"> \(VCrate_{t-2}\) </td>
   <td style="text-align:center;"> -0.000079 (0.000145)  </td>
   <td style="text-align:center;"> -0.000032 (0.000069) </td>

</tr>

<tr>
   <td style="text-align:left;"> \(Blitz_{t-1}\) </td>
   <td style="text-align:center;">   </td>
   <td style="text-align:center;"> 0.310247*** (0.040682)  </td>

</tr>
  
  <tr>
   <td style="text-align:left;">\(Blitz_{t-2}\)  </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;"> 0.160942*** (0.020222) </td>

</tr>
  
   <tr>
   <td style="text-align:left;">\(Blitz_{t-3}\)  </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;"> 0.075374*** (0.014051) </td>

</tr>
  
   <tr>
   <td style="text-align:left;">\(Blitz_{t-4}\)  </td>
   <td style="text-align:center;">  </td>
   <td style="text-align:center;"> 0.012015 (0.012769)</td>

</tr>
  
  
 
  <tr>
   <td style="text-align:left;"> <b>Observations</b> </td>
   <td style="text-align:center;"> 151,000 </td>
   <td style="text-align:center;"> 144,960 </td>
  </tr>

<tfoot><tr><td colspan="3">Standard-errors in parentheses and clustered at the Census tract level. Regressions include week and census tract Fixed Effects. </td></tr></tfoot>
    <tfoot><tr><td colspan="3"> <b>Note:</b> ***: 0.01, **: 0.05, *: 0.1 </td></tr></tfoot>
</tbody>
</table>

]

---

# Research Design II

.pull-left[
 
* The main neighborhood specification considers a parameterized spatial weight matrix `\((W)\)` that is based on the inverse distance of the blocks' centroids. Distance cutoffs set the "areas of influence" of the police intervention

* The weights of the `\(W\)` matrix are defined as `\(w_{ij}=\cfrac{1}{d_{ij}^{\gamma}}\)`, where `\(d_{ij}\)` is the distance between census tracts `\(i\)` and `\(j\)`, and `\(\gamma\)` is a distance decay parameter to be estimated

* The estimated `\(\gamma\)` (ranges from 0.01 to 10) is the one that minimizes the SSR of the equation (2)

* In some specifications, I add temporal lags of Blitz to equation (2)

]

.pull-right[
<iframe src="maps/indirect.html"  style="width: 600px; height: 500px; border: 5px" alt="">
]

---

# Results and Discussion I

.pull-left2[

* The first two columns of the table show the estimated direct effects using equation (1). One additional blitz reduces the violent crime rate (per 1,000), on average, by 10.4-12.5%

* Columns three and four show the results of the basic TWFE model when the census tracts are restricted by treated and their identical blocks in pretreatment covariates

]

.pull-right2[

<table>
 <thead>
   <tr>
   <td style="text-align:center;" colspan="5"> <b> Dependent variable: Violent Crime Rate (per 1,000) </b> </td>
   </tr>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:center;"> (1) </th>
   <th style="text-align:center;"> (2) </th>
   <th style="text-align:center;"> (3) </th>
   <th style="text-align:center;"> (4) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Blitz </td>
   <td style="text-align:left;"> -0.0715***  </td>
   <td style="text-align:left;"> -0.0592***  </td>
   <td style="text-align:left;"> -0.074***  </td>
   <td style="text-align:left;"> -0.0669***  </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> (0.0232)</td>
   <td style="text-align:left;">(0.0221) </td>
   <td style="text-align:left;">(0.0238) </td>
   <td style="text-align:left;"> (0.0218) </td>
 
  </tr>
  
  <tr>
   <td style="text-align:left;"> <b>Fixed-Effects:</b> </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> </td>
   <td style="text-align:left;">  </td>
  </tr>
  
  <tr>
   <td style="text-align:left;"> Census tract </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Week </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Neighborhood x Week </td>
   <td style="text-align:left;"> No </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> No </td>
   <td style="text-align:left;"> Yes </td>
  </tr>
  <tr>
   <td style="text-align:left;"> <b>Mean of Outcome</b> </td>
   <td style="text-align:center;" colspan="2"> 0.57  </td>
   <td style="text-align:center;" colspan="2"> 0.89 </td>

</tr>
  <tr>
   <td style="text-align:left;"> <b>Observations</b> </td>
   <td style="text-align:left;"> 157,040 </td>
   <td style="text-align:left;"> 157,040 </td>
   <td style="text-align:left;"> 46,800 </td>
   <td style="text-align:left;"> 46,800 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Adjusted \(R^2\) </td>
   <td style="text-align:left;"> 0.61415 </td>
   <td style="text-align:left;"> 0.62962 </td>
   <td style="text-align:left;"> 0.75866 </td>
   <td style="text-align:left;"> 0.7778 </td>
  </tr>
   <tfoot><tr><td colspan="5">Standard-errors in parentheses and clustered at the Census tract level.</td></tr></tfoot>
    <tfoot><tr><td colspan="5"> <b>Note:</b> ***: 0.01, **: 0.05, *: 0.1 </td></tr></tfoot>
</tbody>
</table>

]

---

# Results and Discussion II

.pull-left2[

*  The table shows the extent to which there is crime displacement or diffusion of benefits coming from police interventions in small geographic areas

* There is no evidence that an increase in the number of blitzes in neighboring blocks causes more crime in a typical census tract. Indeed, diffusion of benefits is more likely, but one needs to be cautious about the interpretation of the `\(\hat{\theta}\)`

* Including Neighborhood x Week trends, the spatial lag of Blitz is no longer significant

]

.pull-right2[
<table>
 <thead>
    <tr>
   <td style="text-align:center;" colspan="5"> <b> Dependent variable: Violent Crime Rate (per 1,000) </b> </td>
   </tr>
  <tr>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:center;"> Queen </th>
   <th style="text-align:center;"> 20-NN </th>
   <th style="text-align:center;"> I.D. (2 km, \(\gamma=.42\)) </th>
   <th style="text-align:center;"> I.D. (\(\gamma=.85\)) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Blitz </td>
   <td style="text-align:left;"> -0.0709***  </td>
   <td style="text-align:left;"> -0.07***  </td>
   <td style="text-align:center;"> -0.0694***  </td>
   <td style="text-align:center;"> -0.0707***  </td>
  </tr>
  
   <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> (0.0232) </td>
   <td style="text-align:left;"> (0.0232) </td>
   <td style="text-align:center;"> (0.0232) </td>
   <td style="text-align:center;"> (0.0233) </td>
  </tr>
  
  <tr>
   <td style="text-align:left;"> Spatial Lag Blitz </td>
   <td style="text-align:left;"> -0.0374  </td>
   <td style="text-align:left;"> -0.258**  </td>
   <td style="text-align:center;"> -1.90***  </td>
   <td style="text-align:center;"> -4.73***  </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> (0.0282)  </td>
   <td style="text-align:left;"> (0.108) </td>
   <td style="text-align:center;"> (0.560) </td>
   <td style="text-align:center;"> (1.225) </td>
  </tr>
 
 <tr>
   <td style="text-align:left;"> <b>Fixed-Effects:</b> </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> </td>
   <td style="text-align:left;">  </td>
  </tr>
 <tr>
   <td style="text-align:left;"> Census tract </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Week </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
  </tr>
 
  <tr>
   <td style="text-align:left;"> <b>Mean of Outcome</b> </td>
   <td style="text-align:center;" colspan="4"> 0.57  </td>
  </tr>
 
  <tr>
   <td style="text-align:left;"> <b> Observations </b> </td>
   <td style="text-align:left;"> 157,040 </td>
   <td style="text-align:left;"> 157,040 </td>
   <td style="text-align:left;"> 157,040 </td>
   <td style="text-align:left;"> 157,040 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Adjusted \(R^2\) </td>
   <td style="text-align:left;"> 0.61415 </td>
   <td style="text-align:left;"> 0.61415 </td>
   <td style="text-align:left;"> 0.61417 </td>
   <td style="text-align:left;"> 0.61416 </td>
  </tr>
<tfoot><tr><td colspan="5">Standard-errors in parentheses and clustered at the Census tract level.</td></tr></tfoot>
    <tfoot><tr><td colspan="5"> <b>Note:</b> ***: 0.01, **: 0.05, *: 0.1 </td></tr></tfoot>
</tbody>
</table>
]

---
# Results and Discussion III

<table>
 <thead>
    <tr>
   <td style="text-align:center;" colspan="4"> <b> Dependent variable: Violent Crime Rate (per 1,000) </b> </td>
   </tr>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:left;"> I.D. (1.5 km, \(\gamma=.31\)) </th>
   <th style="text-align:left;"> I.D. (2 km, \(\gamma=.42\)) </th>
   <th style="text-align:left;"> I.D. (2.5 km, \(\gamma=.69\)) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> Blitz </td>
   <td style="text-align:left;"> -0.0551** (0.0227) </td>
   <td style="text-align:left;"> -0.0551** (0.0227) </td>
   <td style="text-align:left;"> -0.055** (0.0227) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Spatial Lag </td>
   <td style="text-align:left;"> -1.36*** (0.398) </td>
   <td style="text-align:left;"> -1.82*** (0.606) </td>
   <td style="text-align:left;"> -1.97*** (0.698) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> \(Blitz_{t-1}\) </td>
   <td style="text-align:left;"> -0.00612 (0.0258) </td>
   <td style="text-align:left;"> -0.00566 (0.0258) </td>
   <td style="text-align:left;"> -0.00557 (0.0258) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> \(Blitz_{t-2}\) </td>
   <td style="text-align:left;"> -0.013 (0.0256) </td>
   <td style="text-align:left;"> -0.0129 (0.0256) </td>
   <td style="text-align:left;"> -0.0128 (0.0256) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> \(Blitz_{t-3}\) </td>
   <td style="text-align:left;"> 0.028 (0.0223) </td>
   <td style="text-align:left;"> 0.0283 (0.0223) </td>
   <td style="text-align:left;"> 0.0282 (0.0223) </td>
  </tr>
  <tr>
   <td style="text-align:left;"> <b>Fixed-Effects:</b> </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> </td>
  </tr>
 <tr>
   <td style="text-align:left;"> Census tract </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Week </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
   <td style="text-align:left;"> Yes </td>
  </tr>
 
  <tr>
   <td style="text-align:left;"> <b>Mean of Outcome</b> </td>
   <td style="text-align:center;" colspan="4"> 0.573  </td>
  </tr>
   <td style="text-align:left;"> Observations </td>
   <td style="text-align:left;"> 147,980 </td>
   <td style="text-align:left;"> 147,980 </td>
   <td style="text-align:left;"> 147,980 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Adjusted \(R^2\) </td>
   <td style="text-align:left;"> 0.6201 </td>
   <td style="text-align:left;"> 0.6201 </td>
   <td style="text-align:left;"> 0.6201 </td>
  </tr>
 <tfoot><tr><td colspan="4"> <b>Note:</b> ***: 0.01, **: 0.05, *: 0.1. Standard-errors in parentheses and clustered at the Census tract level. </td></tr></tfoot>
</tbody>
</table>