Week 09 - Regression

# Week 09 - Regression
## Regression Discontinuity Design
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### Danilo Freire
### 18th March 2019

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# Regression Discontinuity Design (RDD)

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* As we have discussed before, sometimes it is unfeasible to conduct an experiment to evaluate a question of interest. E.g.:

- Education and income
  - Incumbency and reelection rates
  - Gun laws and homicides
  - Drunk driving and accidents
  
* Observations tend to have _systematic differences_

* .orange[However:] some candidates might be suitable for comparison
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# Regression Discontinuity Design (RDD)

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* RDD's basic setup: treatment is assigned according to a **precise rule** based on another variable

- Test scores, voting percentage, legislation timing, drinking age

* Useful for analysis in a "rule-based" world (administrative programs, elections, etc.)

* People who barely passed and who barely failed are comparable in many dimensions

* RDDs are a _quasi-experimental_ method at the cutoff (_and only at the cutoff_!)
]
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# Basic RDD Setup

# Basic RDD Setup

# RDD Assumptions

- If graphs show _no other discontinuities_, the design is more credible
  
* Individuals _cannot choose_ if they are in the treatment or control group (_no sorting_)

* If treatment is not deterministic (fuzzy RDD), statistical adjustements are necessary
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# Effect of Scholarship

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* [Thistlethwaite and Campbell (1960)](https://obsstudies.org/wp-content/uploads/2017/01/regression_discontinuity_all_comments-1.pdf) study the effects of collegescholarships on later students’ achievements

* Observation: scholarship winners have different attitudes

* Are scholarship winners more likely to pursue further education or become teachers?

* Spoiler: yes!
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# Effect of Scholarship

# More examples

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* David E. Broockman (2009). [Do Congressional Candidates Have Reverse Coattails? Evidence from a Regression Discontinuity Design](http://web.stanford.edu/~dbroock/published%20paper%20PDFs/broockman%20rdd%20reverse%20coattails.pdf)
]

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# Concealed Carry Ban and Homicides

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* Rodrigo Schneider (2019). [Crime and political effects of a concealed carry ban in Brazil](https://drive.google.com/file/d/0B1QCQasYG8iHaWJVZ0Z3VDJ2eEE/view)

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# Concealed Carry Ban and Homicides

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* Testing the assumption that the law has caused the decline in homicide rates
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.center[![:scale 70%](brazil02.png)]
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# Let's Estimate Our Own Model

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* _Question:_ does minimum legal drinking age (MLDA) have an effect on mortality? Let's find out

```r
library(foreign) # load dta files
library(rdd)     # run RDD model
df <- read.dta("http://masteringmetrics.com/wp-content/uploads/2015/01/AEJfigs.dta")
rdd1 <- RDestimate(all ~ agecell, data = df, cutpoint = 21)
rdd1
```

```
## 
## Call:
## RDestimate(formula = all ~ agecell, data = df, cutpoint = 21)
## 
## Coefficients:
##      LATE    Half-BW  Double-BW  
##     9.001      9.579      7.953
```
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# MLDA and Mortality

```r
plot(rdd1)
title(main = "All Causes of Death",
      xlab = "Age", ylab = "Mortality rate from all causes (per 100,000)")
abline(v = 21, lwd = 2, lty = "dashed", col = "red")
```

<img src="week09a_files/figure-html/mm02-1.png" style="display: block; margin: auto;" />
]
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# Motor Vehicle Accidents

```r
rdd2 <- RDestimate(mva ~ agecell, data =  df, cutpoint = 21)
plot(rdd2)
title(main = "Motor Vehicle Accidents Death",
      xlab = "Age", ylab = "Mortality rate per 100,000")
abline(v = 21, lwd = 2, lty = "dashed", col = "red")
```

<img src="week09a_files/figure-html/mm03-1.png" style="display: block; margin: auto;" />
]
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# Other Causes of Death

```r
rdd3 <- RDestimate(internal ~ agecell, data =  df, cutpoint = 21)
plot(rdd3)
title(main = "Other Causes of Death",
      xlab = "Age", ylab = "Mortality rate per 100,000")
abline(v = 21, lwd = 2, lty = "dashed", col = "red")
```

<img src="week09a_files/figure-html/mm04-1.png" style="display: block; margin: auto;" />
]
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# Questions?

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# See you on Wednesday!