Explanation of Common Terminology in Causal Studies in (Urban) Economics

class: center, middle, inverse, title-slide

.title[
# Explanation of Common Terminology in Causal Studies in (Urban) Economics
]
.subtitle[
## Common Terminology in Causal Studies
]
.author[
### Hussain Hadah (he/him)
]
.date[
### 18 February 2025
]

---

layout: true
<div style="position: absolute;left:20px;bottom:5px;color:black;font-size: 12px;">Hussain Hadah (he/him) (Tulane) | Common Terminology in Causal Studies | 18 February 2025</div>

---
class: title-slide
background-image: url("assets/TulaneLogo-white.svg"), url("assets/title-image1.jpg")
background-position: 10% 90%, 100% 50%
background-size: 160px, 50% 100%
background-color: #0148A4

.remark-slide table{
        width: auto !important; /* Adjusts table width */
    }

/* Change the background color to white for shaded rows (even rows) */

.remark-slide thead, .remark-slide tr:nth-child(2n) {
        background-color: white;
    }
    .remark-slide thead, .remark-slide tr:nth-child(n) {
        background-color: white;
    }
</style>
# .text-shadow[.white[Outline for Today]]

<ol>
    <li><h4 class="white">Introduce Endogeneity <br> ("Chicken or the Egg") Issue in Crime Econ</h4></li>
    <li><h4 class="white">Exogeneity vs. Endogeneity</h4></li>
    <li><h4 class="white">Bias in Causal Inference</h4></li>
</ol>

---
class: segue-yellow
background-image: url("assets/TulaneLogo.svg")
background-size: 20%
background-position: 95% 95%

# Issues in Causal Inference: Endogeneity

---
## Endogeneity in Crime Econ <svg viewBox="0 0 384 512" style="height:1em;display:inline-block;position:fixed;top:10;right:10;" xmlns="http://www.w3.org/2000/svg">  <path d="M202.021 0C122.202 0 70.503 32.703 29.914 91.026c-7.363 10.58-5.093 25.086 5.178 32.874l43.138 32.709c10.373 7.865 25.132 6.026 33.253-4.148 25.049-31.381 43.63-49.449 82.757-49.449 30.764 0 68.816 19.799 68.816 49.631 0 22.552-18.617 34.134-48.993 51.164-35.423 19.86-82.299 44.576-82.299 106.405V320c0 13.255 10.745 24 24 24h72.471c13.255 0 24-10.745 24-24v-5.773c0-42.86 125.268-44.645 125.268-160.627C377.504 66.256 286.902 0 202.021 0zM192 373.459c-38.196 0-69.271 31.075-69.271 69.271 0 38.195 31.075 69.27 69.271 69.27s69.271-31.075 69.271-69.271-31.075-69.27-69.271-69.27z"></path></svg>

.pull-left[
- Suppose you were to compare areas/cities with more police officers to areas/cities with fewer officers to see how crime differs. 
- Do the areas/cities with more officers have less crime?
- But the number of police officers is endogenous to crime.
- Endogenous since crime affects the number of police officers, but police officers affect crime.
- E.g., police officers allocated to high crime areas.
- Increases in crime prompt the hiring of additional officers.
]

.pull-right[
<img src="causal-term_files/figure-html/unnamed-chunk-3-1.png" width="100%" style="display: block; margin: auto;" />

]

.pull-left[
- Suppose you were to do this comparison anyways…

- Suppose you were to compare areas/cities with more police officers to areas/cities with fewer officers to see how crime differs. 
- Do the areas/cities with more officers have less crime?
- Do you think that by doing this comparison you would overestimate or underestimate the effect of police on reducing crime?
]

.pull-right[
<img src="causal-term_files/figure-html/unnamed-chunk-4-1.png" width="100%" style="display: block; margin: auto;" />

]

.pull-left[
- Suppose you were to compare areas/cities with more police officers to areas/cities with fewer officers to see how crime differs.
- This would probably underestimate the effect of police on crime, perhaps showing incorrectly that they increase crime, or that their effect on crime reduction is smaller than it actually is.
- Estimates would be negatively biased.
- Why?
]

.pull-right[
<img src="causal-term_files/figure-html/unnamed-chunk-5-1.png" width="100%" style="display: block; margin: auto;" />

]

.pull-left[
- Estimates would be negatively biased.
- Why?
- Since police are allocated to places with higher crime rates, or more police are deployed when crime increases, there is going to be a positive correlation between the two.
- Mistaking that for a causal relationship will bias the estimate.
- We have to break this endogeneity loop!
]

.pull-right[
<img src="causal-term_files/figure-html/unnamed-chunk-6-1.png" width="100%" style="display: block; margin: auto;" />

]

---
class: segue-yellow
background-image: url("assets/TulaneLogo.svg")
background-size: 20%
background-position: 95% 95%

# How to Break the Endogeneity Loop?

---
## Solving the Egg and Chicken Problem: DALL-E

---
## Randomization

- We covered how Differece-in-Difference (DiD) can help us break the endogeneity loop.
- The ideal way to investigate the effect of police on crime would be to randomly allocate areas/cities with more/fewer police officers.
- Likely not possible…
- Is there a way that police are allocated that is “quasi-random”?
- Is there a natural experiment?
- Or, phrased another way, is there a way that police were allocated that was independent from the crime level (i.e. Is there a case where police officers were not allocated based on crime levels?)

---
## Empirical Studies on How Police Affect Crime

- In this course we will cover some neat empirical research articles that investigate how police affect crime using different experimental or “quasi-experimental” methods.
- These are the readings for the Jigsaw activity
- **Levitt, Steven D.** 1997. “Using Electoral Cycles in Police Hiring to Estimate the Effect of Police on
Crime.” American Economic Review, 87(3): 270–290.
- **Sullivan, Christopher M, and Zachary P. O’Keeffe.** 2017. “Evidence that curtailing proactive
policing can reduce major crime.” Nature Human Behaviour, 1(10): 730–737.
- **Di Tella, Rafael, and Ernesto Schargrodsky.** 2004. “Do Police Reduce Crime? Estimate Using the
Allocation of Police Forces after a Terrorist Attack.” American Economic Review, 94(1): 115–133.
- **Dur, Robert, and Ben Vollaard. 2019.** “Salience of law enforcement: A field experiment.” Journal
of Environmental Economics and Management, 93: 208–220.
- **Cheng, Cheng, and Wei Long. 2018.** “Improving police services: Evidence from the French quarter
task force.” Journal of Public Economics, 164: 1–18.

---
class: segue-yellow
background-image: url("assets/TulaneLogo.svg")
background-size: 20%
background-position: 95% 95%

# Terminology

---
## Some Terms that are Helpful to Know

- These terms will come up in the practice questions you’ll do today, in the course, and in economics in general.
1. Treatment variation
1. Exogenous
1. Endogenous
1. External validity

---
## Treatment Variation

- This term often comes up in empirical research that estimates causal effects.
- Treatment variation refers to the variation in X that you are using to identify the causal effect of X on Y.
- E.g., the variation in the timing and location of MDPs (as in GHM).
- E.g., the increase in police officer hiring that occurs before elections (this is the variation used in Levitt, 1997).
- E.g., the randomly-assigned change in police enforcement by location (as in Dur and Voolaard, 2019).

---
## Exogenous

- If a variation is exogenous, then it is not a function of other factors.
- It is not a function of other variable in the economic/statistical model.
- If something is exogenous, you can think of it being random.
- We ideally want to use treatment variation that is exogenous. 
- The gold standard would be randomization `\(\rightarrow\)` randomized treatment (e.g., randomizing police) would be strictly exogenous since treatment status does not depend on anything.

---
## Endogenous

- The opposite of exogenous.
- More specifically, if something is endogenous, it means it is a function of (it depends on, it is endogenous to) something else.
- E.g., police allocation is endogenous to crime (unless we find some random or quasi-random variation to use).
- E.g., state adoption of tax incentives for the film industry may be endogenous to the size of the existing film industry (larger existing film industry = more likely to adopt an incentive)

---
## Endogenous vs. Exogenous

- The key question is how exogenous/endogenous the treatment variation is. 
- It’s not black and white where it is always clearly one or the other.
- Most treatment variation outside of an experiment lies on a spectrum between fully exogenous and strongly endogenous.
- There is no way to know or to test of treatment variation is endogenous.
- Determining how endogenous it is requires thinking critically about the factors that affect the treatment variation.
- For example, is there something non-random about the change in policing that is used in the paper? Could this non-randomness cause bias by creating a feedback loop (like the crime `\(\leftrightarrow\)` police feedback loop shown earlier)?