POL90: Statistics

class: center, middle, inverse, title-slide

# POL90: Statistics
## Natural Experiments
### Prof. Wasow, Politics</br>Pomona College
### 2022-04-27

---

.regression12 table {
  font-size: 12px;     
}

.regression14 table {
  font-size: 14px;     
}

</style>

# Announcements

.large[

- Assignments
  - PS10 due Wednesday (today)
  - Report 3 due Monday
  - Final is on Sakai

- Reading:
  - Dunning *Natural Experiments in the Social Sciences*: 
    - Chapter 1 (on Sakai -> Lessons)

]

---
# Schedule

<table>
 <thead>
  <tr>
   <th style="text-align:right;"> Week </th>
   <th style="text-align:left;"> Date </th>
   <th style="text-align:left;"> Day </th>
   <th style="text-align:left;"> Title </th>
   <th style="text-align:right;"> Chapter </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:right;"> 11 </td>
   <td style="text-align:left;"> Mar 30 </td>
   <td style="text-align:left;"> Wed </td>
   <td style="text-align:left;"> Interaction terms </td>
   <td style="text-align:right;"> 9 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 12 </td>
   <td style="text-align:left;"> Apr 4 </td>
   <td style="text-align:left;"> Mon </td>
   <td style="text-align:left;"> Logistic regression </td>
   <td style="text-align:right;"> 20 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 12 </td>
   <td style="text-align:left;"> Apr 6 </td>
   <td style="text-align:left;"> Wed </td>
   <td style="text-align:left;"> Logistic regression </td>
   <td style="text-align:right;"> 20 </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 13 </td>
   <td style="text-align:left;"> Apr 11 </td>
   <td style="text-align:left;"> Mon </td>
   <td style="text-align:left;"> Missing Data </td>
   <td style="text-align:right;"> Handout </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 13 </td>
   <td style="text-align:left;"> Apr 13 </td>
   <td style="text-align:left;"> Wed </td>
   <td style="text-align:left;"> Panel Data </td>
   <td style="text-align:right;"> Handout </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 14 </td>
   <td style="text-align:left;"> Apr 18 </td>
   <td style="text-align:left;"> Mon </td>
   <td style="text-align:left;"> Matching </td>
   <td style="text-align:right;"> Handout </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 14 </td>
   <td style="text-align:left;"> Apr 20 </td>
   <td style="text-align:left;"> Wed </td>
   <td style="text-align:left;"> Matching </td>
   <td style="text-align:right;"> Handout </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 15 </td>
   <td style="text-align:left;"> Apr 25 </td>
   <td style="text-align:left;"> Mon </td>
   <td style="text-align:left;"> Causal inference: Natural Experiments </td>
   <td style="text-align:right;"> Handout </td>
  </tr>
  <tr>
   <td style="text-align:right;color: black !important;background-color: yellow !important;"> 15 </td>
   <td style="text-align:left;color: black !important;background-color: yellow !important;"> Apr 27 </td>
   <td style="text-align:left;color: black !important;background-color: yellow !important;"> Wed </td>
   <td style="text-align:left;color: black !important;background-color: yellow !important;"> Causal inference: Natural Experiments </td>
   <td style="text-align:right;color: black !important;background-color: yellow !important;"> Dunning </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 16 </td>
   <td style="text-align:left;"> May 2 </td>
   <td style="text-align:left;"> Mon </td>
   <td style="text-align:left;"> Causal inference: RDD </td>
   <td style="text-align:right;"> NA </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 16 </td>
   <td style="text-align:left;"> May 4 </td>
   <td style="text-align:left;"> Wed </td>
   <td style="text-align:left;"> Review </td>
   <td style="text-align:right;"> NA </td>
  </tr>
</tbody>
</table>

---
## Assignment schedule

---
class: center, middle

# Natural Experiments

---

.center[
<img src="images/dunning_cover_medres_color.jpg" width="57%" style="display: block; margin: auto;" />
]

---
## Natural Experiments

.large[

- Share attribute (1) of true experiments --- comparison of outcomes across treatment and control conditions

- At least partially share (2), since assignment is random or "as if" random

- Assignment *not* under control of researcher

]

.footnote[Source: Dunning (2012)]

---
## Types of Natural Experiments

.large[
- "Standard" natural experiments

- Instrumental-variables designs

- Regression-discontinuity designs

]

.footnote[Source: Dunning (2012)]

---
## Overview of natural experiments
</br>
.center[
<img src="images/dunning_p12_balance_mimics_random_process.png" width="100%" style="display: block; margin: auto;" />
]

.footnote[Source: Dunning (2012)]

---
## Natural Experiments Growing in Social Science

.vertical-center[
<img src="images/dunning_fig_1_1.png" width="90%" style="display: block; margin: auto;" />
]

---
## Examples of Natural Experiments in Social Science

---
## Examples of Natural Experiments in Social Science

---
## Examples of Natural Experiments in Social Science

---
class: center, middle

# Do Police Reduce Crime?

---
## Do Police Reduce Crime?

---
## Do Police Reduce Crime?

---
## Do Police Reduce Crime?

---
## Do Police Reduce Crime?

---
## Do Police Reduce Crime?

---
class: center, middle

# Revisiting Instrumental Variables

---

## Another way to think about IV designs

.vertical-center[
<img src="images/blackwell_instrumental_variable_diagram1.png" width="70%" style="display: block; margin: auto;" />
]

---
## What if unobserved variable is driving both *x* and *y*?

.vertical-center[
<img src="images/blackwell_instrumental_variable_diagram2.png" width="70%" style="display: block; margin: auto;" />
]

---
## Maybe a variable *z* that influences *x*?

.vertical-center[
<img src="images/blackwell_instrumental_variable_diagram3.png" width="70%" style="display: block; margin: auto;" />
]

---
## Maybe a variable *z* that influences *x* but not *y*?

.vertical-center[
<img src="images/blackwell_instrumental_variable_diagram4.png" width="70%" style="display: block; margin: auto;" />
]

---
class: middle, center

# Did media influence health behavior?

---
## Did media influence health behavior?

.footnote[Source: Bursztyn, Rao, Roth & Yanagizawa-Drott  
https://bfi.uchicago.edu/wp-content/uploads/BFI_WP_202044.pdf
]

---
## Did media influence health behavior?

.footnote[Source: Bursztyn, Rao, Roth & Yanagizawa-Drott  
https://bfi.uchicago.edu/wp-content/uploads/BFI_WP_202044.pdf
]

---
## Did media influence health behavior?

.footnote[Source: Bursztyn, Rao, Roth & Yanagizawa-Drott  
https://bfi.uchicago.edu/wp-content/uploads/BFI_WP_202044.pdf
]

---
## Did media influence health behavior?

.footnote[Source: Bursztyn, Rao, Roth & Yanagizawa-Drott  
https://bfi.uchicago.edu/wp-content/uploads/BFI_WP_202044.pdf
]

---
## Did media influence health behavior?

> The two most widely-viewed cable news shows in the United States — Hannity and Tucker Carlson Tonight, both on Fox News – originally took very different stances on the risks associated with the novel coronavirus. While Hannity downplayed the threat during the initial period of the virus’ spread in the United States, Tucker Carlson Tonight warned its viewers that the virus posed a serious threat from early February. In this paper, we show that differential exposure to these two shows affected behavior and downstream health outcomes.

> Using both OLS regressions with a rich set of controls and an instrumental variable strategy exploiting variation in the timing of TV consumption, we then document that <mark>greater exposure to Hannity relative to Tucker Carlson Tonight increased the number of total cases and deaths in the initial stages of the coronavirus pandemic.</mark> Moreover, the effects on cases start declining in mid-March, consistent with the convergence in coronavirus coverage between the two shows.

---
class: center, middle

# Other Designs: Syntethetic Controls

---

## Synthetic Control Method

.center[
<img src="images/synthetic_control_method1.png" width="70%" style="display: block; margin: auto;" />
]
.footnote[Source: Abadie, Diamond, & Hainmuller (2010)]

---
## Trends in Per-capita Cigarette Sales

.center[
<img src="images/synthetic_control_method_fig1.png" width="70%" style="display: block; margin: auto;" />
]

---
## Cigarette Sales Predictor Means

.center[

]
.footnote[Source: Abadie, Diamond, & Hainmuller (2010)]

---
## State Weights in the Synthetic California

.center[ 
<img src="images/synthetic_control_method_table2.png" width="50%" style="display: block; margin: auto;" />
]
.footnote[Source: Abadie, Diamond, & Hainmuller (2010)]
---
## Trends in Per-capita Cigarette Sales

.center[ 
<img src="images/synthetic_control_method_fig2.png" width="70%" style="display: block; margin: auto;" />
]

---
## Trends in Per-capita Cigarette Sales

.center[ 
<img src="images/synthetic_control_method_fig3.png" width="70%" style="display: block; margin: auto;" />
]

---
## Trends in Per-capita Cigarette Sales

.center[ 
<img src="images/synthetic_control_method_fig4.png" width="100%" style="display: block; margin: auto;" />
]
.footnote[Source: Abadie, Diamond, & Hainmuller (2010)]

---
class: center, middle

# Questions?

---
class: center, middle

# Appendix

---
class: center, middle

# Does Car Pollution Harm Babies?

---

## Does Car Pollution Harm Babies?

.center[
<img src="images/currie_reed_ezpass1.png" width="75%" style="display: block; margin: auto;" />
]

.footnote[Currie & Reed (2011), http://faculty.haas.berkeley.edu/rwalker/research/CurrieWalker_EZPass_2011.pdf]