How Economists Learn from Data

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# How Economists Learn from Data
## EC 201: Principles of Microeconomics
### Kyle Raze
### Winter 2020

---

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# Prologue

---
# Learning from Data

## Last Time

1. Why bother learning from data?

- Figure out whether policies work or don't work.
    
    - Test theories.

2. Why does correlation .mono[!=] causation?

- Selection bias!

3. When can correlation .mono[==>] causation?

- Randomized contrial trials (experiments).

---
# Learning from Data

## Today

1. Regression analysis.

- The workhorse of data science.
    
2. Natural experiments.

- Sometimes we get lucky.

---
class: inverse, middle

# Regression

---
# Correlation

## Correlation coefficient

.pull-left[

> A measure of the strength of a relationship between two variables, denoted by `$\rho$`.

-1 .mono[<=] `$\rho$` .mono[<] 0 .mono[==>] .pink[negative correlation].

`$\rho$` .mono[=] 0 .mono[==>] .green[no correlation] (unrelated).

0 .mono[<] `$\rho$` .mono[<=] 1 .mono[==>] .purple[positive correlation].

]

.pull-right[

.center[Correlation coefficient .mono[=] -0.56]

]

---
count: false
# Correlation

## Correlation coefficient

.pull-left[

> A measure of the strength of a relationship between two variables, denoted by `$\rho$`.

-1 .mono[<=] `$\rho$` .mono[<] 0 .mono[==>] .pink[negative correlation].

`$\rho$` .mono[=] 0 .mono[==>] .green[no correlation] (unrelated).

0 .mono[<] `$\rho$` .mono[<=] 1 .mono[==>] .purple[positive correlation].

]

.pull-right[

.center[Correlation coefficient .mono[=] -1]

]

---
count: false
# Correlation

## Correlation coefficient

.pull-left[

> A measure of the strength of a relationship between two variables, denoted by `$\rho$`.

-1 .mono[<=] `$\rho$` .mono[<] 0 .mono[==>] .pink[negative correlation].

`$\rho$` .mono[=] 0 .mono[==>] .green[no correlation] (unrelated).

0 .mono[<] `$\rho$` .mono[<=] 1 .mono[==>] .purple[positive correlation].

]

.pull-right[

.center[Correlation coefficient .mono[=] -0.1]

]

---
count: false
# Correlation

## Correlation coefficient

.pull-left[

> A measure of the strength of a relationship between two variables, denoted by `$\rho$`.

-1 .mono[<=] `$\rho$` .mono[<] 0 .mono[==>] .pink[negative correlation].

`$\rho$` .mono[=] 0 .mono[==>] .green[no correlation] (unrelated).

0 .mono[<] `$\rho$` .mono[<=] 1 .mono[==>] .purple[positive correlation].

]

.pull-right[

.center[Correlation coefficient .mono[=] 0.58]

]

---
# Regression

**Goal:** Identify the effect of a treatment variable `$X$` on an outcome variable `$Y$` while .hi[controlling] .pink[for potential confounders].

Economists often rely on regression analysis for statistical comparisons.

- Regression analysis facilitates *other things equal* comparisons by explicitly controlling for certain variables.

- Failure to control for confounding variables leads to .hi[omitted-variable bias], a close cousin of selection bias.

---
# Simple Linear Regression

.more-left[
.center[.purple[Y.sub[*i*] .mono[=] 6.43 .mono[+] 2.64 X.sub[*i*]]]
<img src="10-Data_Learning_files/figure-html/unnamed-chunk-10-1.svg" style="display: block; margin: auto;" />
]

.less-right[

## Model

`$Y_i = \beta_1 + \beta_2 X_i + e_i$`

- `$\beta_1$` .mono[=] intercept

- `$\beta_2$` .mono[=] slope

- `$e_i$` .mono[=] error term

]

---
# Simple Linear Regression

.more-left[
.center[.purple[Crime.sub[*i*] .mono[=] 18.41 .mono[+] 1.76 Police.sub[*i*]]]
<img src="10-Data_Learning_files/figure-html/unnamed-chunk-12-1.svg" style="display: block; margin: auto;" />
]

.less-right[

**Q:** Do 👮 *cause* crime!?

]

---
count: false
# Simple Linear Regression

.more-left[
.center[.purple[Crime.sub[*i*] .mono[=] 18.41 .mono[+] 1.76 Police.sub[*i*]]]
<img src="10-Data_Learning_files/figure-html/unnamed-chunk-14-1.svg" style="display: block; margin: auto;" />
]

.less-right[

**Q:** Do 👮 *cause* crime!?

**A:** .pink[Probably not]
<br> .pink[.mono[-->] Colleges experiencing high crime rates probably respond by hiring more police.]

]

---
# Causality

## Example: Returns to Education

The optimal investment in education by students, parents, and legislators depends in part on the monetary *return to education*.

.hi-purple[Thought experiment:]
- Randomly select an individual.
- Give her an additional year of education.
- How much do her earnings increase?

The change in her earnings describes the .hi-slate[causal effect] of education on earnings.

---
# Causality

## Example: Returns to Education

.more-left[
.center[.purple[Earnings.sub[*i*] .mono[=] 146.95 .mono[+] 60.21 Schooling.sub[*i*]]]
<img src="10-Data_Learning_files/figure-html/unnamed-chunk-16-1.svg" style="display: block; margin: auto;" />
]

.less-right[

**Q:** Does the slope isolate the causal effect of an additional year of education on weekly earnings?

]

---
count: false
# Causality

## Example: Returns to Education

.more-left[
.center[.purple[Earnings.sub[*i*] .mono[=] 146.95 .mono[+] 60.21 Schooling.sub[*i*]]]
<img src="10-Data_Learning_files/figure-html/unnamed-chunk-18-1.svg" style="display: block; margin: auto;" />
]

.less-right[

**Q:** Does the slope isolate the causal effect of an additional year of education on weekly earnings?

**A:** .pink[Probably not] 
<br> .pink[.mono[-->] There could be other variables that influence earnings and schooling.]
]

---
# Omitted Variables

.more-left[
<img src="10-Data_Learning_files/figure-html/venn2-1.svg" style="display: block; margin: auto;" />
]

.less-right[

.pink[**Y**] .mono[=] Outcome

.green[**X**] .mono[=] Treatment

.orange[**W**] .mono[=] Omitted variable

If .orange[**W**] is correlated with both .green[**X**] and .pink[**Y**] .mono[-->] omitted variable bias .mono[-->] regression fails to isolate the causal effect of .green[**X**] on .pink[**Y**].

]

---
count: false
# Omitted Variables

.more-left[
<img src="10-Data_Learning_files/figure-html/unnamed-chunk-19-1.svg" style="display: block; margin: auto;" />
]

.less-right[

.pink[**Y**] .mono[=] Outcome

.green[**X**] .mono[=] Treatment

.orange[**W**] .mono[=] Omitted variable

If .orange[**W**] is correlated with both .green[**X**] and .pink[**Y**] .mono[-->] omitted variable bias .mono[-->] regression fails to isolate the causal effect of .green[**X**] on .pink[**Y**].

]

---
# Controlling for Confounders

Economists can control for a confounder `$W$` by including it in the regression model:

`$$Y_i = \beta_0 + \beta_1 X_i + \beta_2 W_i + e_i$$`

- `$W_i$` is a **control variable**.

- By including `$W_i$`, adjusts the data to account for confounding effects of `$W$`.

- **Note:** The model doesn't care whether a right-hand side variable is a treatment or control variable, but we do.

---
# Controlling for Confounders

.center[![Control](control.gif)]

---
# Controlling for Confounders

## Example: Returns to Education

Two regressions of earnings on schooling. The second regression controls for IQ score, a proxy for ability.

.pull-left[
<table>
<caption>Outcome: Weekly Earnings</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Parameter </th>
   <th style="text-align:center;"> 1 </th>
   <th style="text-align:center;"> 2 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Intercept </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;font-weight: bold;"> 146.95 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> -128.89 </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%;font-weight: bold;"> (77.72) </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (92.18) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Schooling (Years) </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;font-weight: bold;"> 60.21 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 42.06 </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%;font-weight: bold;"> (5.70) </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (6.55) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> IQ Score (Points) </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;font-weight: bold;">  </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 5.14 </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%;font-weight: bold;">  </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;"> (0.96) </td>
  </tr>
</tbody>
</table>
.center[*Standard errors in parentheses.*]
]

.pull-right[

]
---
count: false
# Controlling for Confounders

## Example: Returns to Education

Two regressions of earnings on schooling. The second regression controls for IQ score, a proxy for ability.

.pull-left[
<table>
<caption>Outcome: Weekly Earnings</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Parameter </th>
   <th style="text-align:center;"> 1 </th>
   <th style="text-align:center;"> 2 </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Intercept </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 146.95 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;font-weight: bold;"> -128.89 </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%;"> (77.72) </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (92.18) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Schooling (Years) </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 60.21 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;font-weight: bold;"> 42.06 </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%;"> (5.70) </td>
   <td style="text-align:center;color: #272822 !important;color: #c2bebe !important;line-height: 110%;font-weight: bold;"> (6.55) </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> IQ Score (Points) </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;">  </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;font-weight: bold;"> 5.14 </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%;font-weight: bold;"> (0.96) </td>
  </tr>
</tbody>
</table>
.center[*Standard errors in parentheses.*]
]

.pull-right[
.orange[Bias] from omitting IQ score 
<br> `$\quad$` .mono[=] .pink["short"] .mono[-] .purple["long"]
<br> `$\quad$` .mono[=] .pink[60.21] .mono[-] .purple[42.06]
<br> `$\quad$` .mono[=] .orange[18.15]

The first regression mistakenly attributes some of the influence of intelligence to education.
]
---
class: inverse, middle

# Natural Experiments

---
# Causality

**Q:** Given that selection bias and omitted variables are ubiquitous, how can economists estimate the returns to education and other causal effects of other interventions?

.hi-slate[Option 1:] Run an .hi[experiment].

- Randomly .pink[assign education] (might be difficult/unethical).
- Randomly .pink[encourage education] (might work).
- Randomly .pink[assign programs] that affect education (*e.g.*, mentoring).

.hi-slate[Option 2:] Look for a .hi-purple[natural experiment] (*e.g.,* a policy or accident in society that arbitrarily increased education for one subset of people).

- Admissions .purple[cutoffs].
- .purple[Lottery] enrollment and/or capacity .purple[constraints].

---
# Oregon Medicaid Experiment

## Background

As of 2016, 27 million Americans do not have health insurance.

- Down from 46.5 million in 2010.

- US is the only developed country without universal coverage.

Healthcare spending accounts for a growing share of the economy.

- Almost 18% of GDP or $10,000 per person per year!

- US spends more on healthcare than any other developed country.

---
# Oregon Medicaid Experiment

## Background

**Medicaid:** A social assistance program that provides health insurance to families on welfare, the disabled, other children from low-income families, and low-income pregnant women.

- Federal program run by states.

**Policy Question:** Should we expand Medicaid to cover more of the uninsured?

**Research Questions**

- Would Medicaid expansion reduce costly emergency room visits?

- Would Medicaid expansion improve health?

---
# Oregon Medicaid Experiment

## Natural Experiment

In 2008, Oregon decided to expand its version of Medicaid, called Oregon Health Plan (OHP).

- **Problem:** 75,000 applicants, but only 30,000 spots!

- **Solution:** Ration spots by lottery.

Lottery .mono[=] random assignment!

- .pink[**Treatment group:**] 30,000 lottery winners.

- .purple[**Control group:**] 45,000 people who did not win medicaid lottery.

---
class: clear-slide

.center[**Effect of OHP on Coverage and Healthcare Use**]
<table>
 <thead>
  <tr>
   <th style="text-align:left;"> Outcome </th>
   <th style="text-align:center;"> Control Mean </th>
   <th style="text-align:center;"> Treatment Effect </th>
   <th style="text-align:center;"> Standard Error </th>
   <th style="text-align:center;"> N </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Ever on Medicaid? </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.141 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.256 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.004 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 74922 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Any hospital admissions? </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.067 </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%;"> 0.002 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 74922 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Any emergency room visits? </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.345 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.017 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.006 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 24646 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Emergency room visits </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 1.020 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.101 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.029 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 24646 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Outpatient visits </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 1.910 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.314 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.054 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 23741 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Any prescriptions? </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.637 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.025 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.008 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 23741 </td>
  </tr>
</tbody>
</table>

**Informal Rule:** Estimate of treatment effect more than twice its standard error .mono[==>] effect is statistically distinguishable from zero.

---
class: clear-slide

.center[**Effect of OHP on Health and Personal Finances**]
<table>
 <thead>
  <tr>
   <th style="text-align:left;"> Outcome </th>
   <th style="text-align:center;"> Control Mean </th>
   <th style="text-align:center;"> Treatment Effect </th>
   <th style="text-align:center;"> Standard Error </th>
   <th style="text-align:center;"> N </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Good Health? </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.548 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.039 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.008 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 23741 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Physical health index </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 45.500 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.290 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.210 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 12229 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Mental health index </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 44.400 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.470 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.240 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 12229 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Cholesterol </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 204.000 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.530 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.690 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 12229 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Systolic blood pressure </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 119.000 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> -0.130 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.300 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 12229 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Big medical expenditures? </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.055 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> -0.011 </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%;"> 12229 </td>
  </tr>
  <tr>
   <td style="text-align:left;color: #272822 !important;line-height: 110%;font-style: italic;color: black !important;"> Any medical debt? </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.568 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> -0.032 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 0.010 </td>
   <td style="text-align:center;color: #272822 !important;line-height: 110%;"> 12229 </td>
  </tr>
</tbody>
</table>

**Informal Rule:** Estimate of treatment effect more than twice its standard error .mono[==>] effect is statistically distinguishable from zero.

---
class: inverse, middle

# Differences-in-Differences

---
# Minimum Wage

**Research Question:** Do binding minimum wage laws cause unemployment?

- Theory predicts that binding minimum wage laws reduce employment levels.

- **Q:** How could we test this prediction?

**Idea 1:** Compare employment levels in states with binding minimum wage laws to those without.

- **Q:** Is this a good idea? Would it isolate the causal effect?

- **A:** Probably not. States with binding minimum wages laws are different than those without .mono[-->] selection bias!

---
# Minimum Wage

**Research Question:** Do binding minimum wage laws cause unemployment?

- Theory predicts that binding minimum wage laws reduce employment levels.

- **Q:** How could we test this prediction?

**Idea 2:** Compare employment levels in a state before and after it increases the minimum wage?

- **Q:** Is this a good idea? Would it isolate the causal effect?

- **A:** Probably not. Other things might coincide with the policy change (*e.g.,* a recession) .mono[-->] omitted variable bias!

---
# Minimum Wage

**Research Question:** Do binding minimum wage laws cause unemployment?

- Theory predicts that binding minimum wage laws reduce employment levels.

- **Q:** How could we test this prediction?

**Idea 3:** Two wrongs make a right?

- Compare employment levels in a state that raises its minimum wage with a state that doesn't, before and after the policy change.

- A .pink[difference-in-differences] comparison.

---
# Differences-in-Differences

## Card and Krueger (1994)

Influential study of the impact of minimum wage laws on fast-food workers.

**Natural Experiment:** New Jersey increased its minimum wage in 1992, but neighboring Pennsylvania did not.

- .purple[**Control group:**] Fast food restaurants in Pennsylvania.

- .pink[**Treatment group:**] Fast food restaurants in New Jersey.

---
# Differences-in-Differences

## Card and Krueger (1994)

.center[**Effect of Minimum Wage on Employment**]
<table class="table" style="margin-left: auto; margin-right: auto;">
<caption>Outcome: Number Full-Time Workers</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Group </th>
   <th style="text-align:center;"> After </th>
   <th style="text-align:center;"> Before </th>
   <th style="text-align:center;"> Difference </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;line-height: 110%;"> .pink[Treatment (NJ)] </td>
   <td style="text-align:center;line-height: 110%;"> 21.03 </td>
   <td style="text-align:center;line-height: 110%;"> 20.44 </td>
   <td style="text-align:center;line-height: 110%;">  </td>
  </tr>
  <tr>
   <td style="text-align:left;line-height: 110%;"> .purple[Control (PA)] </td>
   <td style="text-align:center;line-height: 110%;"> 21.17 </td>
   <td style="text-align:center;line-height: 110%;"> 23.33 </td>
   <td style="text-align:center;line-height: 110%;">  </td>
  </tr>
</tbody>
</table>

Difference-in-differences .mono[=]

---
count: false
# Differences-in-Differences

## Card and Krueger (1994)

.center[**Effect of Minimum Wage on Employment**]
<table class="table" style="margin-left: auto; margin-right: auto;">
<caption>Outcome: Number Full-Time Workers</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Group </th>
   <th style="text-align:center;"> After </th>
   <th style="text-align:center;"> Before </th>
   <th style="text-align:center;"> Difference </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;line-height: 110%;"> .pink[Treatment (NJ)] </td>
   <td style="text-align:center;line-height: 110%;"> 21.03 </td>
   <td style="text-align:center;line-height: 110%;"> 20.44 </td>
   <td style="text-align:center;line-height: 110%;"> 0.59 </td>
  </tr>
  <tr>
   <td style="text-align:left;line-height: 110%;"> .purple[Control (PA)] </td>
   <td style="text-align:center;line-height: 110%;"> 21.17 </td>
   <td style="text-align:center;line-height: 110%;"> 23.33 </td>
   <td style="text-align:center;line-height: 110%;"> -2.16 </td>
  </tr>
</tbody>
</table>

Difference-in-differences .mono[=]

---
count: false
# Differences-in-Differences

## Card and Krueger (1994)

.center[**Effect of Minimum Wage on Employment**]
<table class="table" style="margin-left: auto; margin-right: auto;">
<caption>Outcome: Number Full-Time Workers</caption>
 <thead>
  <tr>
   <th style="text-align:left;"> Group </th>
   <th style="text-align:center;"> After </th>
   <th style="text-align:center;"> Before </th>
   <th style="text-align:center;"> Difference </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;line-height: 110%;"> .pink[Treatment (NJ)] </td>
   <td style="text-align:center;line-height: 110%;"> 21.03 </td>
   <td style="text-align:center;line-height: 110%;"> 20.44 </td>
   <td style="text-align:center;line-height: 110%;"> 0.59 </td>
  </tr>
  <tr>
   <td style="text-align:left;line-height: 110%;"> .purple[Control (PA)] </td>
   <td style="text-align:center;line-height: 110%;"> 21.17 </td>
   <td style="text-align:center;line-height: 110%;"> 23.33 </td>
   <td style="text-align:center;line-height: 110%;"> -2.16 </td>
  </tr>
</tbody>
</table>

Difference-in-differences .mono[=] .pink[0.59] .mono[-] .purple[-2.16]
--
<br> `$\quad$` .mono[=] 2.75.

**Result:** Increasing the minimum wage did not reduce employment!

---
# Differences-in-Differences

.more-left[
<img src="10-Data_Learning_files/figure-html/unnamed-chunk-28-1.svg" style="display: block; margin: auto;" />
]

.less-right[
## Internal Validity

**Q:** When should we trust a difference-in-differences comparison?

**A:** When we believe that the comparison groups exhibit .hi-green[parallel trends] in the absence of the policy change.

]

---
class: inverse, middle

# Podcast

---
class: clear-slide

**Podcast Question:** According to Raj Chetty,

> **A.** No social assistance program pays for itself in the long run, on average.

> **B.** All social assistance programs pay for themselves in the long run, on average.

> **C.** Social assistance programs that target adults tend to pay for themselves in the long run, but those targeted toward children do not, on average.

> **D.** Social assistance programs that target children tend to pay for themselves in the long run, but those targeted toward adults do not, on average.

---
count: false
class: clear-slide

**Podcast Question:** According to Raj Chetty,

> **A.** No social assistance program pays for itself in the long run, on average.

> **B.** All social assistance programs pay for themselves in the long run, on average.

> **C.** Social assistance programs that target adults tend to pay for themselves in the long run, but those targeted toward children do not, on average.

> .pink[**D.** Social assistance programs that target children tend to pay for themselves in the long run, but those targeted toward adults do not, on average.]