POL90: Statistics

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# POL90: Statistics
## Introduction to Natural Experiments
### Prof. Wasow, Politics</br>Pomona College
### 2022-04-26

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# Announcements

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- Assignments
  - PS10 due Tuesday
  - Report 3

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

]

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# 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;color: black !important;background-color: yellow !important;"> 15 </td>
   <td style="text-align:left;color: black !important;background-color: yellow !important;"> Apr 25 </td>
   <td style="text-align:left;color: black !important;background-color: yellow !important;"> Mon </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;"> Handout </td>
  </tr>
  <tr>
   <td style="text-align:right;"> 15 </td>
   <td style="text-align:left;"> Apr 27 </td>
   <td style="text-align:left;"> Wed </td>
   <td style="text-align:left;"> Causal inference: Natural Experiments </td>
   <td style="text-align:right;"> 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>

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## Assignment schedule

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# Natural Experiments

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## Is Covid-19 transmitted by large droplets and/or aerosols?

.footnote[https://wwwnc.cdc.gov/eid/article/26/7/20-0764_article]

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## Case: Outbreak in a restaurant in Guangzhou

.footnote[Source: Lu, Gu, Li, Xu, Su, Lai, Zhou, Yu, Xu & Yang  
https://wwwnc.cdc.gov/eid/article/26/7/20-0764_article]

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## Case: Outbreak in a restaurant in Guangzhou

.footnote[Source: Lu, Gu, Li, Xu, Su, Lai, Zhou, Yu, Xu & Yang  
https://wwwnc.cdc.gov/eid/article/26/7/20-0764_article]

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## Case: Outbreak in a restaurant in Guangzhou

> On January 24, a total of 91 persons (83 customers, 8 staff members) were in the restaurant. Of these, a total of 83 had eaten lunch at 15 tables on the third floor. Among the 83 customers, 10 became ill with COVID-19; the other 73 were identified as close contacts and quarantined for 14 days.

> <mark>From our examination of the potential routes of transmission, we concluded that the most likely cause of this outbreak was droplet transmission.</mark>

> Virus transmission in this outbreak cannot be explained by droplet transmission alone.… However, <mark>strong airflow from the air conditioner could have propagated droplets from table C to table A, then to table B, and then back to table C</mark> (Figure).

> Potential aerosol transmission of severe acute respiratory syndrome and Middle East respiratory syndrome viruses has been reported (5,6). However, <mark>none of the staff or other diners in restaurant X were infected.</mark>

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<img src="images/dunning_cover_medres_color.jpg" width="57%" style="display: block; margin: auto;" />
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<br>
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>John Snow, an anesthesiologist who lived through the devastating cholera epidemics in nineteenth-century London (Richardson [1887] 1936: xxxiv), believed that cholera was a waste- or waterborne infectious disease-contradicting the then-prevalent theory of "bad air" (miasma) that was used to explain cholera's transmission. 
]

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<br>
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>Snow noted that epidemics seemed to follow the "great tracks of human intercourse" (Snow [1855] 1965: 2); moreover, sailors who arrived in a cholera-infested port did not become infected until they disembarked, which provided evidence against the miasma theory. During London's cholera outbreak of 1853-54, Snow drew a map showing addresses of deceased victims; these clustered around the Broad Street water pump in London's Soho district, leading Snow to argue that contaminated water supply from this pump contributed to the cholera outbreak.
]

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<br>
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>Snow's strongest piece of evidence, however, came from a natural experiment that he studied during the epidemic of 1853-54 (Freedman 1991, 1999). Large areas of London were served by two water companies, the Lambeth company and the Southwark & Vauxhall company. In 1852, the Lambeth company had moved its intake pipe further upstream on the Thames, thereby "obtaining a supply of water quite free from the sewage of London," while Southwark & Vauxhall left its intake pipe in place (Snow 1855 1965: 68). Snow obtained records on cholera deaths in households throughout London, as well as information on the company that provided water to each household and the total number of houses served by each company. He then compiled a simple cross-tabulation showing the cholera death rate by source of water supply.

]

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## Natural Experiments in the Social Science
<br><br>
<img src="images/dunning_table_1_1.png" width="90%" style="display: block; margin: auto;" />

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<br><br>

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>The mixing of the (water) supply is of the most intimate kind. The pipes of each Company go down all the streets, and into nearly all the courts and alleys. A few houses are supplied by one Company and a few by the other, according to the decision of the owner or occupier at that time when the Water Companies were in active competition. In many cases a single house has a supply different from that on either side. Each company supplies both rich and poor, both large houses and small; there is no difference either in the condition or occupation of the persons receiving the water of the different Companies ... It is obvious that no experiment could have been devised which would more thoroughly test the effect of water supply on the progress of cholera than this. (Snow 1855) 1965: 74-75)

]

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## Natural Experiments Growing in Social Science
<br><br>
<img src="images/dunning_fig_1_1.png" width="90%" style="display: block; margin: auto;" />

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## Randomized Controlled Experiments

<br>

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1. The response of experimental subjects assigned to receive a treatment is compared to the response of subjects assigned to a control group

2. The assignment of subjects to treatment and control groups is done at random, through a randomizing device such as a coin flip

3. The manipulation of the treatment — also known as the intervention — is under the control of an experimental researcher
]

.footnote[Source: Freedman, Pisani, and Purves (2007), Dunning (2012)]

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## Natural Experiments

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- 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

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.footnote[Source: Dunning (2012)]

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## Types of Natural Experiments

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- "Standard" natural experiments

- Instrumental-variables designs

- Regression-discontinuity designs

]

.footnote[Source: Dunning (2012)]

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# "Standard Natural" Experiments

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## Does Coal & Oil Pollution Harm Babies?

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<img src="images/coal_birth_01_title.png" width="100%" style="display: block; margin: auto;" />
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