Difference-in-differences I & II

# Diff-in-diff I & II

**Sessions 8–9**

]

---

# Plan for today

.box-6.medium.sp-after-half[Quasi-experiments]

.box-2.medium.sp-after-half[Interactions & regression]

.box-5.medium.sp-after-half[Two wrongs make a right]

.box-3.medium.sp-after-half[Diff-in-diff assumptions]

---

name: quasi-experiments
class: center middle section-title section-title-6 animated fadeIn

# Quasi-experiments

---

&nbsp;

.box-6.large.sp-after[RCTs are great!]

.box-6.large[Super impractical to do all the time though!]

---

---

# Quasi-experiments

.box-inv-6.medium[You can't always randomly assign people to do things]

.box-inv-6.medium[So let other people (or the government, or nature, or something else) do it for you]

---

# Quasi-experiments

.box-inv-6.medium.sp-after[**Quasi-experiment** A situation where you, as researcher, did not assign people to treatment/control]

.center.float-left.sp-after[
.box-6[External validity 👍]&ensp;.box-6[Selection 👎]
]

.box-inv-6.medium[Assignment to treatment is "as if" random]

???

Good bc of external validity; bad bc of selection

---

# Quasi-experiments vs. DAG adjustment

.box-inv-6.sp-after[DAGs can work for any kind of observational data, even without a quasi-experimentalish situation]

.box-6[Quasi-experiments are a little different: the **context** isolates pathway between treatment and outcome]

.box-6.smaller[They're wildly popular in social sciences (especially economics!), maybe more credible (?) there than just making DAG adjustments]

.box-6.smaller[You can still draw a DAG for a quasi-experiment though!]

---

# Analyzing quasi-experiments

.box-inv-6.medium[Difference-in-differences]

.box-6.small.sp-after[DiD; DD; diff-in-diff]

.box-inv-6.medium[Regression discontinuity]

.box-6.small.sp-after[RD; RDD]

.box-inv-6.medium[Instrumental variables]

.box-6.small[IV]
 
---

layout: false
name: interactions-regression
class: center middle section-title section-title-2 animated fadeIn

# Interactions & regression

---

---

# Sliders and switches

.center[
<figure>
 <img src="img/02/slider-switch-annotated-80.jpg" alt="Switch and slider" title="Switch and slider" width="100%">
</figure>
]

---

.smaller[
$$
\widehat{\text{Happiness}} = \beta_0 + \beta_1 \text{Life expectancy} + \beta_2 \text{Latin America} + \varepsilon
$$
]

```r
model1 <- lm(happiness_score ~ life_expectancy + latin_america, 
 data = world_happiness)
tidy(model1)
```

```
## # A tibble: 3 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -2.08 0.537 -3.87 1.61e- 4
## 2 life_expectancy 0.102 0.00745 13.7 1.95e-28
## 3 latin_americaLatin America 0.623 0.173 3.61 4.17e- 4
```
]

.box-2.smaller["For every 1-year increase in life expectancy, happiness is associated with a β1 increase"]
]

.box-2.smaller["Being in Latin America is associated with a β2 increase in happiness"]
]

---

# Indicators and interactions

.box-inv-2.medium[Indicators .tiny[(dummies)]]

.box-2.sp-after[Change in intercept for specific group]

---

---

.box-2.small[World slope = 0.102]

---

.box-2.small[Latin America intercept shifted up 0.62; line has same slope as world (0.102)]

---

.smaller[
$$
`\begin{aligned}
\widehat{\text{Happiness}} = &\beta_0 + \beta_1 \text{Life expectancy} + \beta_2 \text{Latin America} + \\
&\beta_3 (\text{Life expectancy} \times \text{Latin America}) + \varepsilon
\end{aligned}`
$$
]

```r
model2 <- lm(happiness_score ~ life_expectancy + latin_america + 
 (life_expectancy * latin_america), data = world_happiness)
tidy(model2)
```

```
## # A tibble: 4 × 5
## term estimate std.error stati…¹ p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -2.02 0.545 -3.70 2.98e- 4
## 2 life_expectancy 0.102 0.00757 13.4 1.65e-27
## 3 latin_americaLatin America -1.52 3.36 -0.450 6.53e- 1
## 4 life_expectancy:latin_americaLatin America 0.0288 0.0453 0.637 5.25e- 1
## # … with abbreviated variable name ¹statistic
```
]

.box-2.small["In Latin America, for every 1-year increase in life expectancy, happiness is associated with a β1 + β3 increase *and* the intercept is β2 lower"]

---

# Indicators and interactions

.box-inv-2.medium[Indicators .tiny[(dummies)]]

.box-2.sp-after[Change in intercept for specific group]

.box-inv-2.medium.sp-before[Interactions]

---

.box-2.small[Latin America slope is 0.029 + 0.102 = 0.13; different from rest of the world]

---

# Interactions

```r
model3 <- lm(happiness_score ~ (life_expectancy * latin_america), 
 data = world_happiness)
```
]

.box-2.small[**It still works!** Both terms have to be in the model; R will add them for you if you leave them out]

---

# Interactions

```r
model4 <- lm(happiness_score ~ life_expectancy * region, # region has multiple categories
 data = world_happiness)
```
]

```
## # A tibble: 14 × 5
## term estim…¹ std.e…² stati…³ p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -2.81 2.05 -1.37 1.73e-1
## 2 life_expectancy 0.112 0.0271 4.12 6.33e-5
## 3 regionEurope & Central Asia -2.78 2.76 -1.01 3.16e-1
## 4 regionLatin America & Caribbean -0.724 3.72 -0.195 8.46e-1
## 5 regionMiddle East & North Africa -3.13 3.14 -0.997 3.21e-1
## 6 regionNorth America 2.88 23.2 0.124 9.01e-1
## 7 regionSouth Asia 4.98 5.54 0.898 3.71e-1
## 8 regionSub-Saharan Africa 6.33 2.48 2.55 1.18e-2
## 9 life_expectancy:regionEurope & Central Asia 0.0367 0.0361 1.02 3.11e-1
## 10 life_expectancy:regionLatin America & Caribb… 0.0187 0.0497 0.376 7.07e-1
## 11 life_expectancy:regionMiddle East & North Af… 0.0410 0.0419 0.978 3.30e-1
## 12 life_expectancy:regionNorth America -0.0221 0.288 -0.0767 9.39e-1
## 13 life_expectancy:regionSouth Asia -0.0768 0.0790 -0.972 3.33e-1
## 14 life_expectancy:regionSub-Saharan Africa -0.101 0.0354 -2.84 5.12e-3
## # … with abbreviated variable names ¹estimate, ²std.error, ³statistic
```
]
]

---

# General idea of interactions

.box-inv-2.medium[The *additional* change that happens when combining two explanatory variables]

---

&nbsp;

.pull-right.center[
<figure>
 <img src="img/08/hotdogs.jpg" alt="Hot dog prices" title="Hot dog prices" width="90%">
</figure>
]

???

- Cheese effect: 0.35
- Chili effect: 0.35
- Chili × cheese effect: 0

https://twitter.com/kevin_stange/status/1186056025897684992

---

layout: false
name: two-wrongs
class: center middle section-title section-title-5 animated fadeIn

# Two wrongs make a right

---

???

https://twitter.com/causalinf/status/1021392181209255938

---

---

# Raising the minimum wage

.box-inv-5.medium.sp-after-half[What happens if you raise the minimum wage?]

.box-5.sp-after[Economic theory says there should be fewer jobs]

.box-inv-5.medium[New Jersey in 1992]

.box-inv-5.medium[$4.25 → $5.05]

---

# Before vs. after

.box-inv-5.medium.sp-after-half[Average # of jobs per fast food restaurant in NJ]

.box-5.sp-after[∆ = 0.59]

.box-inv-5.medium[Is this the causal effect?]

???

No! Not possible because maybe other things happened in NJ to cause that – there's no control state to compare with NJ

---

# Treatment vs. control

.box-inv-5.medium.sp-after-half[Average # of jobs per fast food restaurant]

.box-5.sp-after[∆ = −0.14]

.box-inv-5.medium[Is this the causal effect?]

???

No! There's no pre-level to compare with. Maybe both states went up, maybe both went down. Can't tell.

---

# Problems

.box-inv-5.medium[Comparing only before/after]

.box-5.small[You're only looking at the treatment group!]

.box-5.small.sp-after[Impossible to know if change happened because of treatment or just naturally]

.box-inv-5.medium.sp-before[Comparing only treatment/control]

.box-5.small[You're only looking at post-treatment values]

.box-5.small[Impossible to know if change happened because of natural growth]

---

---

<table style="margin-left: auto; margin-right: auto;">
 <thead>
 <tr>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Pre mean </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Post mean </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> ∆ (post − pre) </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:center;background-color: #FFFFFF !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Control </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> A (never treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> B (never treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;background-color: #DDDDDD !important;color: #FFFFFF !important;background-color: #FFFFFF !important;"> B − A </td>
 </tr>
 <tr>
 <td style="text-align:center;background-color: #FFFFFF !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Treatment </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> C (not yet treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> D (treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;background-color: #DDDDDD !important;color: #FFFFFF !important;background-color: #FFFFFF !important;"> D − C </td>
 </tr>
 <tr>
 <td style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;color: #FFFFFF !important;background-color: #FFFFFF !important;"> ∆ (treatment − control) </td>
 <td style="text-align:center;color: #FFFFFF !important;background-color: #FFFFFF !important;"> C − A </td>
 <td style="text-align:center;color: #FFFFFF !important;background-color: #FFFFFF !important;"> D − B </td>
 <td style="text-align:center;background-color: #DDDDDD !important;color: #FFFFFF !important;background-color: #FFFFFF !important;color: #FFFFFF !important;background-color: #FFFFFF !important;"> (B − A) − (D − C) or (B − D) − (A − C) </td>
 </tr>
</tbody>
</table>

---

<table style="margin-left: auto; margin-right: auto;">
 <thead>
 <tr>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Pre mean </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Post mean </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> ∆ (post − pre) </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:center;background-color: #FFFFFF !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Control </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> A (never treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> B (never treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;background-color: #DDDDDD !important;"> B − A </td>
 </tr>
 <tr>
 <td style="text-align:center;background-color: #FFFFFF !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Treatment </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> C (not yet treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> D (treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;background-color: #DDDDDD !important;"> D − C </td>
 </tr>
 <tr>
 <td style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;color: #FFFFFF !important;background-color: #FFFFFF !important;"> ∆ (treatment − control) </td>
 <td style="text-align:center;color: #FFFFFF !important;background-color: #FFFFFF !important;"> A − C </td>
 <td style="text-align:center;color: #FFFFFF !important;background-color: #FFFFFF !important;"> B − D </td>
 <td style="text-align:center;background-color: #DDDDDD !important;color: #FFFFFF !important;background-color: #FFFFFF !important;"> (B − A) − (D − C) or (B − D) − (A − C) </td>
 </tr>
</tbody>
</table>

---

<table style="margin-left: auto; margin-right: auto;">
 <thead>
 <tr>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Pre mean </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Post mean </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> ∆ (post − pre) </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:center;background-color: #FFFFFF !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Control </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> A (never treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> B (never treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;color: #FFFFFF !important;background-color: #FFFFFF !important;"> B − A </td>
 </tr>
 <tr>
 <td style="text-align:center;background-color: #FFFFFF !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Treatment </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> C (not yet treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> D (treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;color: #FFFFFF !important;background-color: #FFFFFF !important;"> D − C </td>
 </tr>
 <tr>
 <td style="text-align:center;background-color: #DDDDDD !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> ∆ (treatment − control) </td>
 <td style="text-align:center;background-color: #DDDDDD !important;"> C − A </td>
 <td style="text-align:center;background-color: #DDDDDD !important;"> D − B </td>
 <td style="text-align:center;background-color: #DDDDDD !important;color: #FFFFFF !important;background-color: #FFFFFF !important;"> (B − A) − (D − C) or (B − D) − (A − C) </td>
 </tr>
</tbody>
</table>

---

<table style="margin-left: auto; margin-right: auto;">
 <thead>
 <tr>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Pre mean </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Post mean </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> ∆ (post − pre) </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:center;background-color: #FFFFFF !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Control </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> A (never treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> B (never treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;background-color: #DDDDDD !important;"> B − A </td>
 </tr>
 <tr>
 <td style="text-align:center;background-color: #FFFFFF !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Treatment </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> C (not yet treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> D (treated) 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;background-color: #DDDDDD !important;"> D − C </td>
 </tr>
 <tr>
 <td style="text-align:center;background-color: #DDDDDD !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> ∆ (treatment − control) </td>
 <td style="text-align:center;background-color: #DDDDDD !important;"> C − A </td>
 <td style="text-align:center;background-color: #DDDDDD !important;"> D − B </td>
 <td style="text-align:center;background-color: #DDDDDD !important;background-color: #DDDDDD !important;"> (D − C) − (B − A) or (D − B) − (C − A) </td>
 </tr>
</tbody>
</table>

---

.medium[
`$$\begin{aligned}
\text{DD}\ =\ &(\bar{x}_\text{treatment, post} - \bar{x}_\text{treatment, pre}) \\
&- (\bar{x}_\text{control, post} - \bar{x}_\text{control, pre})
\end{aligned}$$`
]

---

<table style="margin-left: auto; margin-right: auto;">
 <thead>
 <tr>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Pre mean </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Post mean </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> ∆ (post − pre) </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:center;background-color: #FFFFFF !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Pennsylvania </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> 23.33 A 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> 21.17 B 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;background-color: #DDDDDD !important;"> -2.16 B − A 
</td>
 </tr>
 <tr>
 <td style="text-align:center;background-color: #FFFFFF !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> New Jersey </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> 20.44 C 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> 21.03 D 
</td>
 <td style="text-align:center;background-color: #FFFFFF !important;background-color: #DDDDDD !important;"> 0.59 D − C 
</td>
 </tr>
 <tr>
 <td style="text-align:center;background-color: #DDDDDD !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> ∆ (NJ − PA) </td>
 <td style="text-align:center;background-color: #DDDDDD !important;"> -2.89 C − A 
</td>
 <td style="text-align:center;background-color: #DDDDDD !important;"> -0.14 D − B 
</td>
 <td style="text-align:center;background-color: #DDDDDD !important;background-color: #DDDDDD !important;"> (0.59) − (−2.16) = 2.76 </td>
 </tr>
</tbody>
</table>

---

---

# An easier way?

.box-inv-5.medium[Finding all the group means is tedious!]

.box-inv-5.medium.sp-after[What if there are other backdoors to worry about?]

.box-5.medium[Regression to the rescue!]

---

![](08-slides_files/figure-html/min-wage-dag-1.png)

---

`$$\begin{aligned}
\color{#2ECC40}{Y_{it}}\ =\ &\alpha + \beta\ \color{#0074D9}{\text{Group}_i} + \gamma\ \color{#39CCCC}{\text{Time}_t} + \\
&\delta\ \color{#FF4136}{(\text{Group}_i \times \text{Time}_t)} + \varepsilon_{it}
\end{aligned}$$`

.center.sp-after[

<code class ='r hljs remark-code'>model <- lm(outcome ~ group + time + (group * time))</code>
]

&nbsp;

Group = 1 or TRUE if treatment

Time = 1 or TRUE if after

---

`$$\begin{aligned}
\color{#2ECC40}{Y_{it}}\ =\ &\color{#666666}{\alpha} + \color{#0074D9}{\beta\ \text{Group}_i} + \color{#39CCCC}{\gamma\ \text{Time}_t} + \\
&\color{#FF4136}{\delta\ (\text{Group}_i \times \text{Time}_t)} + \varepsilon_{it}
\end{aligned}$$`

.center.sp-after[

α = Mean of control, pre-treatment

β = Increase in outcome across groups

γ = Increase in outcome over time within units

δ = Difference in differences!

---

<table style="margin-left: auto; margin-right: auto;">
 <thead>
 <tr>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;">  Pre mean  </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;">  Post mean  </th>
 <th style="text-align:center;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;">  ∆ (post − pre)  </th>
 </tr>
 </thead>
<tbody>
 <tr>
 <td style="text-align:center;background-color: #FFFFFF !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Control </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> α </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> α + γ </td>
 <td style="text-align:center;background-color: #FFFFFF !important;background-color: #EEEEEE !important;"> γ </td>
 </tr>
 <tr>
 <td style="text-align:center;background-color: #FFFFFF !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;"> Treatment </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> α + β </td>
 <td style="text-align:center;background-color: #FFFFFF !important;"> α + β + γ + δ </td>
 <td style="text-align:center;background-color: #FFFFFF !important;background-color: #EEEEEE !important;"> γ + δ </td>
 </tr>
 <tr>
 <td style="text-align:center;background-color: #EEEEEE !important;font-weight: bold;color: #CF4446 !important;background-color: #FFC6C6 !important;">  ∆ (trtmt − ctrl)  </td>
 <td style="text-align:center;background-color: #EEEEEE !important;"> β </td>
 <td style="text-align:center;background-color: #EEEEEE !important;"> β + δ </td>
 <td style="text-align:center;background-color: #EEEEEE !important;background-color: #EEEEEE !important;"> δ </td>
 </tr>
</tbody>
</table>

---

.center[
<figure>
 <img src="img/08/hotdogs-small.jpg" alt="Hot dog prices" title="Hot dog prices" width="50%">
</figure>
]

```r
hotdogs
```

```
## # A tibble: 4 × 3
## price cheese chili
## <dbl> <lgl> <lgl>
## 1 2 FALSE FALSE
## 2 2.35 TRUE FALSE
## 3 2.35 FALSE TRUE 
## 4 2.7 TRUE TRUE
```
]
]

.pull-right.small-code[

```r
model_hotdogs <- 
 lm(price ~ cheese + chili + 
 cheese * chili, 
 data = hotdogs)
```

```r
tidy(model_hotdogs)
```

```
## # A tibble: 4 × 2
## term estimate
## <chr> <dbl>
## 1 (Intercept) 2 
## 2 cheeseTRUE 0.35
## 3 chiliTRUE 0.35
## 4 cheeseTRUE:chiliTRUE 0
```
]

---

???

https://doi.org/10.1136/bmj.i6270

---

???

https://doi.org/10.1136/bmj.i6270

---

???

https://doi.org/10.1136/bmj.i6270

---

layout: false
name: diff-diff-assumptions
class: center middle section-title section-title-3 animated fadeIn

# Diff-in-diff assumptions

---

# Assumptions

.box-inv-3.medium[Parallel trends]

.box-3[Treatment and control groups might have different values at first, but we assume that the treatment group would have changed like the control group in the absence of treatment]

---

---

---

---

# Assumptions

.box-inv-3.medium[Parallel trends]

.box-3[Check by pretending the treatment happened earlier; if there's an effect, there's likely an underlying trend]

---

---

---

---

# Assumptions

.box-inv-3.medium[Treatment timing]

---

---

---

# Assumptions

.center[
<figure>
 <img src="img/08/goodman-bacon.png" alt="Goodman-Bacon paper" title="Goodman-Bacon paper" width="45%">
</figure>
]

???

https://www.nber.org/papers/w25018.pdf