Data and Causation

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# Data and Causation
## EC 350: Labor Economics
### <a href="https://kyleraze.com">Kyle Raze</a>
### Winter 2022

---

# Data and Causation

1. The rise of empirical evidence
2. Making *other-things-equal* comparisons
3. Causal identification
    - Average treatment effects
    - Selection bias
4. Randomized control trials
5. *Thinking Fast and Slow*, Chicago edition

---
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# The rise of empirical evidence

---
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.center[**The fading *American dream***]
<img src="03-Data_Causation_files/figure-html/unnamed-chunk-1-1.svg" style="display: block; margin: auto;" />

.footnote[*Source:* Raj Chetty et al. (2017), [The fading American dream: Trends in absolute income mobility since 1940](https://science.sciencemag.org/content/356/6336/398.abstract), *Science*.]

---
# Why is the *American dream* fading?

**Policy Question:** Why is a child's chance of climbing the income ladder decreasing in the United States?

- What can we do to reverse this trend?

Difficult to answer with historical data on macroeconomic trends.

- **That other things change over time makes it difficult** to separately identify the roles of alternative explanations

---
# Theoretical social science

Historically, the social sciences had **limited data** to study policy questions.

**The result?** Social sciences were .pink[theoretical] fields

- Some researchers developed .pink[mathematical models]
- Some developed .pink[qualitative theories]
- Both used their theories to make policy recommendations (*e.g.,* to improve upward mobility)

**The problem?** Without data, even falsifiable theories are never tested!

- Five researchers could have five different answers to the same question
- Can lead to a politicization of questions that, in principle, have scientific answers (*e.g.,* do minimum wage laws reduce employment?)

---
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.center[**Economics is becoming more data-driven** <br>.slate[Empirical articles in the top three economics journals over time]]
<img src="03-Data_Causation_files/figure-html/unnamed-chunk-2-1.svg" style="display: block; margin: auto;" />

.footnote[*Source:* Daniel S. Hamermesh (2013), [Six Decades of Top Economics Publishing: Who and How?](https://www.aeaweb.org/articles?id=10.1257/jel.51.1.162) *Journal of Economic Literature*.]

---
# The rise of empirical evidence

Today, the social sciences are increasingly **empirical** thanks to the growing availability of data and computational power.

- Gives us **the ability to test** existing theories
- Gives us **the ability to refine** theory to (i) better explain decision making and (ii) better fit real-world data

The social sciences have caught up to the natural sciences in terms of scientific rigor, arguably surpassing the natural sciences in sophistication.

- Given the complexity of human decision making, inability to experiment in controlled environments, *etc.*?

---
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# Making *other-things-equal* comparisons

---
# *Other-things-equal* comparisons

**The policy?** In 2017, the University of Oregon started requiring first-year students to live on campus.

**The rationale?** First-year students who live on campus outperform those who live off campus.

- Average 2.super[nd]-year retention rate _5 percentage points higher_
- _80 percent more likely to graduate_ in four years
- GPA _0.13 points higher_

**Q:** Do these comparisons suggest that the policy will improve student outcomes?

**Q:** Do they describe the effect of living on campus?

**Q:** Do they describe *something else?*

---
# *Other-things-equal* comparisons

**Healthy skepticism** should leave us questioning the UO's interpretation.

- The **decision** to live on campus is likely related to family wealth and interest in school.
- Family wealth and interest in school are also related to academic achievement.

**The difference in outcomes** between those on and off campus **does not offer an *other-things-equal* comparison**.

- Without further evidence, one should not attribute the difference in outcomes to living on campus.
    - Not without considering those things that both (i) correlate with living on campus (*e.g.,* family wealth) and (ii) correlate with outcomes (*e.g.,* graduation)

---
# *Other-things-equal* comparisons

Statistical comparisons can only identify causal relationships between variables **when all other factors are "held constant."**

- *Causal* relationship .mono[=] How a change in one variable *induces* a change in another

Economists have developed a *comparative advantage*.super[.hi-pink[<span>&#8224;</span>]] in understanding where **other-things-equal** comparisons can (and cannot) be made.

.footnote[.super[.hi-pink[<span>&#8224;</span>]] *Comparative advantage* .mono[=] Ability of an individual or group to perform an activity at lower cost relative to another individual or group.]

- Anyone can retort "_correlation doesn't imply causation!_"
--

- Understanding why it doesn't? The conditions under which it actually does imply causality?
    - Difficult, but necessary for learning from data!

---
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# Causal identification

---
# Causal identification

## The objective

Identify the effect of a .hi[treatment] on an .hi[outcome].

## The ideal comparison

Ideally, we could calculate the **treatment effect** *for each individual* as

`$$Y_{1,i} - Y_{0,i}$$`

- `$Y_{1,i}$` is the outcome for person `$i$` when `$i$` receives the treatment
- `$Y_{0,i}$` is the outcome for person `$i$` when `$i$` does not receive the treatment
- Known as **potential outcomes**

---
# Causal identification

The **ideal data** for 10 people

.pull-left[

```
#>     i treat Y_1i Y_0i
#> 1   1     1 5.01 4.56
#> 2   2     1 8.85 4.53
#> 3   3     1 6.31 4.67
#> 4   4     1 5.97 4.79
#> 5   5     1 7.61 6.34
#> 6   6     0 7.63 4.15
#> 7   7     0 4.75 0.56
#> 8   8     0 5.77 3.52
#> 9   9     0 7.47 4.49
#> 10 10     0 7.79 1.40
```
]

.pull-right[
We could calculate the treatment effect for each individual `$i$`,
$$
`\begin{align}
  \tau_i = Y_{1,i} -  Y_{0,i}~,
\end{align}`
$$
and we would be inclined to think of it as the causal effect.
]

---
count: false
# Causal identification

The **ideal data** for 10 people

.pull-left[

```
#>     i treat Y_1i Y_0i effect_i
#> 1   1     1 5.01 4.56     0.45
#> 2   2     1 8.85 4.53     4.32
#> 3   3     1 6.31 4.67     1.64
#> 4   4     1 5.97 4.79     1.18
#> 5   5     1 7.61 6.34     1.27
#> 6   6     0 7.63 4.15     3.48
#> 7   7     0 4.75 0.56     4.19
#> 8   8     0 5.77 3.52     2.25
#> 9   9     0 7.47 4.49     2.98
#> 10 10     0 7.79 1.40     6.39
```
]

---
count: false
# Causal identification

The **ideal data** for 10 people

.pull-left[

]

The mean of these individual treatment effects .mono[=] 2.82

- We call this the .hi-green[average treatment effect] (ATE)

---
# Causal identification

## The fundamental problem of causal inference

While the ideal comparison is
$$
`\begin{align}
  \tau_i = \color{#e64173}{Y_{1,i}} &- \color{#9370DB}{Y_{0,i}}~,
\end{align}`
$$
this comparison is fundamentally challenged!

- If we observe `$\color{#e64173}{Y_{1}}$` for `$i$`, then we cannot observe `$\color{#9370DB}{Y_{0}}$` for `$i$`
- If we observe `$\color{#9370DB}{Y_{0}}$` for `$i$`, then we cannot observe `$\color{#e64173}{Y_{1}}$` for `$i$`
- We only observe what *actually* happened&mdash;we cannot observe the **counterfactual**

**The implication?** .hi-pink[ALL] .pink[causal inference is] .hi-pink[by assumption!]

---
# Causal identification

The data we *actually* see for these 10 people?
.pull-left[

```
#>     i treat Y_1i Y_0i
#> 1   1     1 5.01   NA
#> 2   2     1 8.85   NA
#> 3   3     1 6.31   NA
#> 4   4     1 5.97   NA
#> 5   5     1 7.61   NA
#> 6   6     0   NA 4.15
#> 7   7     0   NA 0.56
#> 8   8     0   NA 3.52
#> 9   9     0   NA 4.49
#> 10 10     0   NA 1.40
```
]

.pull-right[
We only observe `$\color{#e64173}{Y_{1}}$` for `$i \in \{1, ..., 5\}$`

We only observe `$\color{#9370DB}{Y_{0}}$` for `$i \in \{6, ..., 10\}$`
 
We do not observe both `$\color{#e64173}{Y_{1,i}}$` and `$\color{#9370DB}{Y_{0,i}}$` for anyone

]

**Q:** How can we estimate the average treatment effect when we cannot observe individual treatment effects?

---
# Causal identification

Can we **compare the mean outcomes** of each group?

- Take the average of `$\color{#e64173}{Y_{1}}$` for those who received the treatment (*i.e.,* the .pink[treatment-group mean])
- Take the average of `$\color{#9370DB}{Y_{0}}$` for those who didn't receive the treatment (*i.e.,* the .purple[control-group mean])

**Q:** Does .pink[treatment-group mean] .mono[-] .purple[control-group mean] isolate the causal effect of the treatment?

---
# Causal identification

.pull-left[

.pull-right[
.pink[Treatment group mean] .mono[=] 6.75

.purple[Control group mean] .mono[=] 2.82

Difference-in-means .mono[=] 3.93
]

Difference-in-means .mono[=] .hi-green[average treatment effect] .mono[+] .hi-orange[selection bias]
--
<br> `$\quad$` .mono[=] .green[2.82] .mono[+] .orange[(3.93 .mono[-] 2.82)]
--
 .mono[=] .green[2.82] .mono[+] .orange[1.11]

.orange[Selection bias] .mono[!=] 0 .mono[==>] people who "select into" treatment are different

---
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# Randomized control trials

---
# Randomized control trials

## Overcoming selection bias

**The problem?** The existence of selection bias precludes making *other-things-equal* comparisons.

- To make valid comparisons that identify causal effects, we need to shut down the bias coming from selection.

**The solution?** Conduct an experiment!

- How? Assign treatment .hi-pink[randomly]
- Hence the name, .hi-pink[*randomized* control trial] (RCT)

---
# Randomized control trials

## Example: Effect of de-worming on attendance

**Motivation:** Intestinal worms are common among children in less-developed countries. The symptoms of these parasites can keep school-aged children at home, disrupting human capital accumulation.

**Policy question:** Do school-based de-worming interventions provide a cost-effective way to increase school attendance?

---
# Randomized control trials

## Example: Effect of de-worming on attendance

**Research question:** How much do de-worming interventions increase school attendance?

**Q:** **Could we simply compare average attendance** among children with and without access to de-worming medication?

- **A:** If we're after the causal effect, probably not. (Why not?)

**Selection bias:** Families with access to de-worming medication probably have healthier children for other reasons, too (wealth, access to clean drinking water, *etc.*).

- **We can't make an *all-else-equal* comparison** .mono[-->] in expectation, observed differences will deviate *systematically* from the ATE!

---
# Randomized control trials

## Example: Effect of de-worming on attendance

**Solution:** Run an experiment.

Imagine an RCT where we have two groups:

- .hi-slate[Treatment:] Villages where children get de-worming medication in school.
- .hi-slate[Control:] Villages where children don't get de-worming medication in school (status quo).

By randomizing villages into .hi-slate[treatment] or .hi-slate[control], we will, on average, include all kinds of villages (poor _vs._ less poor, access to clean water _vs._ contaminated water, hospital _vs._ no hospital, *etc.*) in both groups.

*All else equal*!

---
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.hi-slate[72 villages] 
<img src="03-Data_Causation_files/figure-html/plot1-1.svg" style="display: block; margin: auto;" />
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.hi-slate[72 villages] .hi[of varying levels of development]
<img src="03-Data_Causation_files/figure-html/plot2-1.svg" style="display: block; margin: auto;" />
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.hi-slate[72 villages] .hi[of varying levels of development] .mono[+] .hi-orange[randomly assigned treatment]
<img src="03-Data_Causation_files/figure-html/plot3_1-1.svg" style="display: block; margin: auto;" />
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.hi-slate[72 villages] .hi[of varying levels of development] .mono[+] .hi-orange[randomly assigned treatment]
<img src="03-Data_Causation_files/figure-html/plot3_2-1.svg" style="display: block; margin: auto;" />
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.hi-slate[72 villages] .hi[of varying levels of development] .mono[+] .hi-orange[randomly assigned treatment]
<img src="03-Data_Causation_files/figure-html/plot3_3-1.svg" style="display: block; margin: auto;" />
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.hi-slate[72 villages] .hi[of varying levels of development] .mono[+] .hi-orange[randomly assigned treatment]
<img src="03-Data_Causation_files/figure-html/plot3_4-1.svg" style="display: block; margin: auto;" />
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.hi-slate[72 villages] .hi[of varying levels of development] .mono[+] .hi-orange[randomly assigned treatment]
<img src="03-Data_Causation_files/figure-html/plot3_5-1.svg" style="display: block; margin: auto;" />
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.hi-slate[72 villages] .hi[of varying levels of development] .mono[+] .hi-orange[randomly assigned treatment]
<img src="03-Data_Causation_files/figure-html/plot3_6-1.svg" style="display: block; margin: auto;" />
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.hi-slate[72 villages] .hi[of varying levels of development] .mono[+] .hi-orange[randomly assigned treatment]
<img src="03-Data_Causation_files/figure-html/plot3_7-1.svg" style="display: block; margin: auto;" />
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.hi-slate[72 villages] .hi[of varying levels of development] .mono[+] .hi-orange[randomly assigned treatment]
<img src="03-Data_Causation_files/figure-html/plot3_8-1.svg" style="display: block; margin: auto;" />
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.hi-slate[72 villages] .hi[of varying levels of development] .mono[+] .hi-orange[randomly assigned treatment]
<img src="03-Data_Causation_files/figure-html/plot3_9-1.svg" style="display: block; margin: auto;" />
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.hi-slate[72 villages] .hi[of varying levels of development] .mono[+] .hi-orange[randomly assigned treatment]
<img src="03-Data_Causation_files/figure-html/plot3_10-1.svg" style="display: block; margin: auto;" />
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.hi-slate[72 villages] .hi[of varying levels of development] .mono[+] .hi-orange[randomly assigned treatment]
<img src="03-Data_Causation_files/figure-html/plot3_11-1.svg" style="display: block; margin: auto;" />
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---
# Randomized control trials

## Example: Effect of de-worming on attendance

We can estimate the **causal effect** of de-worming on school attendance by **comparing the average attendance rates** in the .hi-pink[treatment group] (💊) with those in the .hi-purple[control group] (no 💊):

.center[.hi-pink[Treatment group attendance rate] .mono[-] .hi-purple[Control group attendance rate]]

**Result:** This was done in Kenya, where [attendance increased](https://www.povertyactionlab.org/case-study/deworming-schools-improves-attendance-and-benefits-communities-over-long-term) with the random assignment of treatment.

- 25-percent decrease in absenteeism at a cost of $0.60 per child
- Long term cost effectiveness: Additional 11.91 years of schooling per $100 spent on de-worming

.footnote[*Source:* [Deworming to increase school attendance](https://www.povertyactionlab.org/case-study/deworming-increase-school-attendance), *Abdul Latif Jameel Poverty Action Lab*.]

---
# Randomized control trials

## Example: Effect of de-worming on attendance

.center[.hi-pink[Treatment group attendance rate] .mono[-] .hi-purple[Control group attendance rate]]

**Q:** Should we trust the results of the comparison?

**A:** Even with healthy skepticism, we probably should? On average, randomly assigning treatment balances the treatment and control groups across other dimensions that could explain school attendance.

---
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Balance ***on average*** .mono[!=] Balance ***every time***
<img src="03-Data_Causation_files/figure-html/fertilizer_plot3_bad-1.svg" style="display: block; margin: auto;" />

---
# Interpreting results

## Internal validity

Addresses the question, ***should we believe the study?***

A study has high **internal validity** if, within the context of the study, we are confident that one variable has a **causal** influence on the outcome of interest (*e.g.,*  there's **no selection bias**).

## External validity

Addresses the question, ***how far can we generalize the results of the study?***

A study has high **external validity** to the extent that the results **apply to other contexts** (not just the local environment that generated the results).

---
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# *Thinking Fast and Slow*, Chicago edition

---
# *Thinking Fast and Slow*, Chicago edition

## Background

**Policy question:** How can we reduce violent crime among young men?

**Research agenda:** What factors influence an individual's proclivity toward violent crime?

- Self control? Social skills? Grit?
- Economic hardship?
- Police presesnce?
- Early chilhood education?
- Something else?

---
# *Thinking Fast and Slow*, Chicago edition

**Research question:** Can cognitive-behavioral therapy keep young men in school and out of trouble?

- Proposed mechanism: Automaticity.

.footnote[*Source:* Sara B Heller et al. (2017), [Thinking, Fast and Slow? Some Field Experiments to Reduce Crime and Dropout in Chicago](https://academic.oup.com/qje/article-abstract/132/1/1/2724542?redirectedFrom=fulltext), *The Quarterly Journal of Economics*.]

**Experiment:** *Becoming a Man*

4804 young men in Chicago Public Schools randomly assigned to one of two groups:

- .hi-pink[Treatment group:] Group cognitive-behavioral therapy program during school (once per week for 1-2 school years)
- .hi-purple[Control group:] No intervention

A similar experiment was also conducted in the Cook County Juvenile Temporary Detention Center.

---
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.center[***Becoming a Man*: Experimental results**]
<table class="table table-hover" style="font-size: 20.5px; margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;"> Outcome </th>
   <th style="text-align:center;"> Control mean </th>
   <th style="text-align:center;"> Treatment mean </th>
   <th style="text-align:center;"> Effect of treatment assignment </th>
   <th style="text-align:center;"> Effect of participation </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> School engagement index </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.04 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.04 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.088 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.016) </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.034) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Total arrests per youth per year </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.603 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.53 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> -0.073 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> -0.161 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.031) </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.068) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;">     Violent </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.136 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.109 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> -0.027 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> -0.06 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.011) </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.024) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;">     Property </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.069 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.072 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.003 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.006 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.008) </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.018) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;">     Drug </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.132 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.127 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> -0.005 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> -0.011 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.012) </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.027) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;">     Other </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.266 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.222 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> -0.044 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> -0.097 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;color: #c2bebe !important;line-height: 110%;font-style: italic;color: black !important;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.019) </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.040) </td>
  </tr>
</tbody>
</table>
.smallest[*Notes:* 4804 observations. Standard errors in parentheses.]