5.2 — Difference-in-Differences

ECON 480 • Econometrics • Fall 2022

Dr. Ryan Safner
Associate Professor of Economics

safner@hood.edu
ryansafner/metricsF22
metricsF22.classes.ryansafner.com

Difference-in-Differences Models

Example II: “The” Card-Kreuger Minimum Wage Study

Clever Research Designs Identify Causality

Again, this toolkit of research designs to identify causal effects is the economist’s comparative advantage that firms and governments want!

Difference-in-Differences Models

Natural Experiments

Difference-in-Differences Models I

Often, we want to examine the consequences of a change, such as a law or policy intervention

Difference-in-Differences Models I

Often, we want to examine the consequences of a change, such as a law or policy intervention

Example

How do States that implement policy $X$ see changes in $Y$
- Treatment: States that implement $X$
- Control: States that did not implement $X$

If we have panel data with observations for all states before and after the change…
Find the difference between treatment & control groups in their differences before and after the treatment period

Difference-in-Differences Models I

Often, we want to examine the consequences of a change, such as a law or policy intervention

Example

How do States that implement policy $X$ see changes in $Y$
- Treatment: States that implement $X$
- Control: States that did not implement $X$

If we have panel data with observations for all states before and after the change…
Find the difference between treatment & control groups in their differences before and after the treatment period

Difference-in-Differences Models II

The difference-in-differences (aka “diff-in-diff” or “DND”) estimator identifies treatment effect by differencing the difference pre- and post-treatment values of $Y$ between treatment and control groups

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

$\text{Treated}_i= \begin{cases}1 \text{ if } i \text{ is in treatment group}\\ 0 \text{ if } i \text{ is not in treatment group}\end{cases} \quad \text{After}_t= \begin{cases}1 \text{ if } t \text{ is after treatment period}\\ 0 \text{ if } t \text{ is before treatment period}\end{cases}$

	Control	Treatment	Group Diff $(\Delta Y_i)$
Before	$\beta_0$	$\beta_0+\beta_1$	$\beta_1$
After	$\beta_0+\beta_2$	$\beta_0+\beta_1+\beta_2+\beta_3$	$\beta_1+\beta_3$
Time Diff $(\Delta Y_t)$	$\beta_2$	$\beta_2+\beta_3$	$\beta_3$ Diff-in-diff $(\Delta_i \Delta_t)$

Example: Hot Dogs

Is there a discount when you get cheese and chili?

Example: Hot Dogs

Is there a discount when you get cheese and chili?

lm(price ~ cheese + chili + cheese*chili,
   data = hotdogs) %>%
  tidy()

Diff-n-diff is just a model with an interaction term between two dummies!

Visualizing Diff-in-Diff

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

Control group $(\text{Treated}_i = 0)$
$\hat{\beta_0}$: value of $Y$ for control group before treatment
$\hat{\beta_2}$: time difference (for control group)

Visualizing Diff-in-Diff

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

Control group $(\text{Treated}_i = 0)$
$\hat{\beta_0}$: value of $Y$ for control group before treatment
$\hat{\beta_2}$: time difference (for control group)
Treatment group $(\text{Treated}_i = 1)$

Visualizing Diff-in-Diff

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

Control group $(\text{Treated}_i = 0)$
$\hat{\beta_0}$: value of $Y$ for control group before treatment
$\hat{\beta_2}$: time difference (for control group)
Treatment group $(\text{Treated}_i = 1)$
$\hat{\beta_1}$: difference between groups before treatment

Visualizing Diff-in-Diff

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

Control group $(\text{Treated}_i = 0)$
$\hat{\beta_0}$: value of $Y$ for control group before treatment
$\hat{\beta_2}$: time difference (for control group)
Treatment group $(\text{Treated}_i = 1)$
$\hat{\beta_1}$: difference between groups before treatment
$\hat{\beta_3}$: difference-in-differences (treatment effect)

Visualizing Diff-in-Diff II

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

$\bar{Y_i}$ for Control group before: $\hat{\beta_0}$

Visualizing Diff-in-Diff II

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

$\bar{Y_i}$ for Control group before: $\hat{\beta_0}$
$\bar{Y_i}$ for Control group after: $\hat{\beta_0}+\hat{\beta_2}$

Visualizing Diff-in-Diff II

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

$\bar{Y_i}$ for Control group before: $\hat{\beta_0}$
$\bar{Y_i}$ for Control group after: $\hat{\beta_0}+\hat{\beta_2}$
$\bar{Y_i}$ for Treatment group before: $\hat{\beta_0}+\hat{\beta_1}$

Visualizing Diff-in-Diff II

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

$\bar{Y_i}$ for Control group before: $\hat{\beta_0}$
$\bar{Y_i}$ for Control group after: $\hat{\beta_0}+\hat{\beta_2}$
$\bar{Y_i}$ for Treatment group before: $\hat{\beta_0}+\hat{\beta_1}$
$\bar{Y_i}$ for Treatment group after: $\hat{\beta_0}+\hat{\beta_1}+\hat{\beta_2}+\hat{\beta_3}$

Visualizing Diff-in-Diff II

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

$\bar{Y_i}$ for Control group before: $\hat{\beta_0}$
$\bar{Y_i}$ for Control group after: $\hat{\beta_0}+\hat{\beta_2}$
$\bar{Y_i}$ for Treatment group before: $\hat{\beta_0}+\hat{\beta_1}$
$\bar{Y_i}$ for Treatment group after: $\hat{\beta_0}+\hat{\beta_1}+\hat{\beta_2}+\hat{\beta_3}$
Group Difference (before): $\hat{\beta_1}$

Visualizing Diff-in-Diff II

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

$\bar{Y_i}$ for Control group before: $\hat{\beta_0}$
$\bar{Y_i}$ for Control group after: $\hat{\beta_0}+\hat{\beta_2}$
$\bar{Y_i}$ for Treatment group before: $\hat{\beta_0}+\hat{\beta_1}$
$\bar{Y_i}$ for Treatment group after: $\hat{\beta_0}+\hat{\beta_1}+\hat{\beta_2}+\hat{\beta_3}$
Group Difference (before): $\hat{\beta_1}$
Time Difference: $\hat{\beta_2}$

Visualizing Diff-in-Diff II

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

$\bar{Y_i}$ for Control group before: $\hat{\beta_0}$
$\bar{Y_i}$ for Control group after: $\hat{\beta_0}+\hat{\beta_2}$
$\bar{Y_i}$ for Treatment group before: $\hat{\beta_0}+\hat{\beta_1}$
$\bar{Y_i}$ for Treatment group after: $\hat{\beta_0}+\hat{\beta_1}+\hat{\beta_2}+\hat{\beta_3}$
Group Difference (before): $\hat{\beta_1}$
Time Difference: $\hat{\beta_2}$
Difference-in-differences: $\hat{\beta_3}$ (treatment effect)

Comparing Group Means (Again)

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

	Control	Treatment	Group Diff $(\Delta Y_i)$
Before	$\beta_0$	$\beta_0+\beta_1$	$\beta_1$
After	$\beta_0+\beta_2$	$\beta_0+\beta_1+\beta_2+\beta_3$	$\beta_1+\beta_3$
Time Diff $(\Delta Y_t)$	$\beta_2$	$\beta_2+\beta_3$	Diff-in-diff $\Delta_i \Delta_t: \beta_3$

Key Assumption: Counterfactual

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

Key assumption for DND: time trends (for treatment and control) are parallel
Treatment and control groups assumed to be identical over time on average, except for treatment
Counterfactual: if the treatment group had not recieved treatment, it would have changed identically over time as the control group $(\hat{\beta_2})$

Key Assumption: Counterfactual

\[\hat{Y}_{it}=\beta_0+\beta_1 \, \text{Treated}_i +\beta_2 \, \text{After}_{t}+\beta_3 \,(\text{Treated}_i \times \text{After}_{t})+u_{it}\]

If the time-trends would have been different, a biased measure of the treatment effect $(\hat{\beta_3})$!

Example I: HOPE in Georgia

Diff-in-Diff Example I

Example

In 1993 Georgia initiated a HOPE scholarship program to let state residents with at least a B average in high school attend public college in Georgia for free. Did it increase college enrollment?

Micro-level data on 4,291 young individuals

$\text{InCollege}_{it}=\begin{cases}1 \text{ if } i \text{ is in college during year }t\\ 0 \text{ if } i \text{ is not in college during year }t\\ \end{cases}$¹

$\text{Georgia}_i=\begin{cases}1 \text{ if } i \text{ is a Georgia resident}\\ 0 \text{ if } i \text{ is not a Georgia resident}\\ \end{cases}$

$\text{After}_t=\begin{cases}1 \text{ if } t \text{ is after 1992}\\ 0 \text{ if } t \text{ is after 1992}\\ \end{cases}$

Dynarski, Susan, 1999, “Hope for Whom? Financial Aid for the Middle Class and its Impact on College Attendance,” National Tax Journal 53(3): 629-661

Diff-in-Diff Example II

We can use a DND model to measure the effect of HOPE scholarship on enrollments
Georgia and nearby States, if not for HOPE, changes should be the same over time

Treatment period: after 1992

Treatment: Georgia

Difference-in-differences: \[\Delta_i \Delta_t Enrolled = (\text{GA}_{after}-\text{GA}_{before})-(\text{neighbors}_{after}-\text{neighbors}_{before})\]

Regression equation:

\[\widehat{\text{Enrolled}_{it}} = \beta_0+\beta_1 \, \text{Georgia}_{i}+\beta_2 \, \text{After}_{t}+\beta_3 \, (\text{Georgia}_{i} \times \text{After}_{t})\]

Example: Data

hope

Example: Data

Dynarski, Susan, 1999, “Hope for Whom? Financial Aid for the Middle Class and its Impact on College Attendance,” National Tax Journal 53(3): 629-661

Example: Regression

DND_reg <- lm(InCollege ~ Georgia + After + Georgia*After, data = hope)
DND_reg %>% tidy()

\[\widehat{\text{Enrolled}}_{it}=0.406-0.105 \, \text{Georgia}_{i}-0.004 \, \text{After}_{t}+0.089 \, (\text{Georgia}_{i} \times \text{After}_{t})\]

Example: Interpretting the Regression

\[\widehat{\text{Enrolled}}_{it}=0.406-0.105 \, \text{Georgia}_{i}-0.004 \, \text{After}_{t}+0.089 \, (\text{Georgia}_{i} \times \text{After}_{t})\]

$\beta_0$: A non-Georgian before 1992 was 40.6% likely to be a college student

$\beta_1$: Georgians before 1992 were 10.5% less likely to be college students than neighboring states

$\beta_2$: After 1992, non-Georgians are 0.4% less likely to be college students

$\beta_3$: After 1992, Georgians are 8.9% more likely to enroll in colleges than neighboring states
Treatment effect: HOPE increased enrollment likelihood by 8.9%

Example: Comparing Group Means

\[\widehat{\text{Enrolled}}_{it}=0.406-0.105 \, \text{Georgia}_{i}-0.004 \, \text{After}_{t}+0.089 \, (\text{Georgia}_{i} \times \text{After}_{t})\]

A group mean for a dummy $Y$ is $\mathbb{E}[Y=1]$, i.e. the probability a student is enrolled:
Non-Georgian enrollment probability pre-1992: $\beta_0=0.406$

Georgian enrollment probability pre-1992: $\beta_0+\beta_1=0.406-0.105=0.301$

Non-Georgian enrollment probability post-1992: $\beta_0+\beta_2=0.406-0.004=0.402$

Georgian enrollment probability post-1992: $\beta_0+\beta_1+\beta_2+\beta_3=0.406-0.105-0.004+0.089=0.386$

Example: Comparing Group Means in `R`

# group mean for non-Georgian before 1992
hope %>%
  filter(Georgia == 0,
         After == 0) %>%
  summarize(prob = mean(InCollege))

# group mean for non-Georgian AFTER 1992
hope %>%
  filter(Georgia == 0,
         After == 1) %>%
  summarize(prob = mean(InCollege))

Example: Comparing Group Means in `R`

# group mean for Georgian before 1992
hope %>%
  filter(Georgia == 1,
         After == 0) %>%
  summarize(prob = mean(InCollege))

# group mean for Georgian AFTER 1992
hope %>%
  filter(Georgia == 1,
         After == 1) %>%
  summarize(prob = mean(InCollege))

Example: Diff-in-Diff Summary

\[\widehat{\text{Enrolled}}_{it}=0.406-0.105 \, \text{Georgia}_{i}-0.004 \, \text{After}_{t}+0.089 \, (\text{Georgia}_{i} \times \text{After}_{t})\]

	Neighbors	Georgia	Group Diff $(\Delta Y_i)$
Before	$0.406$	$0.301$	$-0.105$
After	$0.402$	$0.386$	$0.016$
Time Diff $(\Delta Y_t)$	$-0.004$	$0.085$	Diff-in-diff: $0.089$

\[\begin{align*} \Delta_i \Delta_t Enrolled &= (\text{GA}_{after}-\text{GA}_{before})-(\text{neighbors}_{after}-\text{neighbors}_{before})\\ &=(0.386-0.301)-(0.402-0.406)\\ &=(0.085)-(-0.004)\\ &=0.089\\ \end{align*}\]

Diff-in-Diff Summary & Data

Dynarski, Susan, 1999, “Hope for Whom? Financial Aid for the Middle Class and its Impact on College Attendance,” National Tax Journal 53(3): 629-661

Example: Diff-in-Diff Graph

Generalizing DND Models

DND can be generalized with a two-way fixed effects model:

\[\hat{Y}_{it}=\beta_1 \, (\text{Treated}_i \times \text{After}_{t})+\alpha_i+\theta_t+\nu_{it}\]

$\alpha_i$: group fixed effects (treatments/control groups)
$\theta_t$: time fixed effects (pre/post treatment)
$\beta_1$: diff-in-diff (interaction effect, $\beta_3$ from before)

Flexibility: many periods (not just before/after), many different treatment(s)/groups, and treatment(s) can occur at different times to different units (so long as some do not get treated)

Can also add control variables that vary within units and over time

\[\hat{Y}_{it}=\beta_1 \, (\text{Treated}_i \times \text{After}_{t})+\beta_2 X_{it}+\cdots + \alpha_i+\theta_t+\nu_{it}\]

Our Example, Generalized I

\[\widehat{\text{Enrolled}_{it}} = \beta_1 \, (\text{Georgia}_{i} \times \text{After}_{t}) + \alpha_i+\theta_t+\]

StateCode is a variable for the State $\implies$ create State fixed effect $(\alpha_i)$
Year is a variable for the year $\implies$ create year fixed effect $(\theta_t)$

Our Example, Generalized II

Using LSDV method:

DND_fe <- lm(InCollege ~ Georgia*After + factor(StateCode) + factor(Year),
           data = hope)
DND_fe %>% tidy()

Our Example, Generalized II

Using fixest

library(fixest)
DND_fe_2 <- feols(InCollege ~ Georgia*After | factor(StateCode) + factor(Year),
           data = hope)
DND_fe_2 %>% tidy()

\[\widehat{\text{InCollege}_{it}}=0.091 \, (\text{Georgia}_i \times \text{After}_{it})+\alpha_i+\theta_t\]

Our Example, Generalized, with Controls II

Using LSDV Method

DND_fe_controls <- lm(InCollege ~ Georgia*After + factor(StateCode) + factor(Year) + Black + LowIncome,
           data = hope)
DND_fe_controls %>% tidy()

Our Example, Generalized, with Controls II

Using fixest

DND_fe_controls_2 <- feols(InCollege ~ Georgia*After + Black + LowIncome | factor(StateCode) + factor(Year),
           data = hope)
DND_fe_controls_2 %>% tidy()

\[\widehat{\text{InCollege}_{it}}=0.023 \, (\text{Georgia}_i \times \text{After}_{it})-0.094 \, \text{Black}_{it}-0.302 \,\text{LowIncome}_{it}\]

Our Example, Generalized, with Controls III

	No FE	TWFE	TWFE
Constant	0.40578***
	(0.01092)
Georgia	−0.10524***
	(0.03778)
After	−0.00446
	(0.01585)
Georgia x After	0.08933*	0.09142***	0.02344
	(0.04889)	(0.00564)	(0.01282)
Black			−0.09399***
			(0.01273)
LowIncome			−0.30172***
			(0.03066)
n	4291	4291	2967
Adj. R²	0.00
SER	0.49	0.49	0.47
* p < 0.1, p < 0.05, * p < 0.01

The Findings

Dynarski, Susan, 1999, “Hope for Whom? Financial Aid for the Middle Class and its Impact on College Attendance,” National Tax Journal 53(3): 629-661

Intuition behind DND

Diff-in-diff models are the quintessential example of exploiting natural experiments
A major change at a point in time (change in law, a natural disaster, political crisis) separates groups where one is affected and another is not—identifies the effect of the change (treatment)
One of the cleanest and clearest causal identification strategies

Example II: “The” Card-Kreuger Minimum Wage Study

Example: ”The” Card-Kreuger Minimum Wage Study I

Example

The controversial minimum wage study, Card & Kreuger (1994) is a quintessential (and clever) diff-in-diff. ]

Card, David, Krueger, Alan B, (1994), “Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania,” American Economic Review 84 (4): 772–793

Card & Kreuger (1994): Background I

Card & Kreuger (1994) compare employment in fast food restaurants on New Jersey and Pennsylvania sides of border between February and November 1992.
Pennsylvania & New Jersey both had a minimum wage of $4.25 before February 1992
In February 1992, New Jersey raised minimum wage from $4.25 to $5.05

Card & Kreuger (1994): Background II

If we look only at New Jersey before & after change:
- Omitted variable bias: macroeconomic variables (there’s a recession!), weather, etc.
  - Including PA as a control will control for these time-varying effects if they are national trends
Surveyed 400 fast food restaurants on each side of the border, before & after min wage increase
- Key assumption: Pennsylvania and New Jersey follow parallel trends,
  - Counterfactual: if not for the minimum wage increase, NJ employment would have changed similar to PA employment

Card & Kreuger (1994): Comparisons

Card & Kreuger (1994): Summary I

Card & Kreuger (1994): Summary II

Card & Kreuger (1994): Model

\[\widehat{\text{Employment}_{i t}}=\beta_0+\beta_1 \, \text{NJ}_{i}+\beta_2 \, \text{After}_{t}+\beta_3 \, (\text{NJ}_i \times After_t)\]

PA Before: $\beta_0$
PA After: $\beta_0+\beta_2$
NJ Before: $\beta_0+\beta_1$
NJ After: $\beta_0+\beta_1+\beta_2+\beta_3$
Diff-in-diff: $(\text{NJ}_{after}-\text{NJ}_{before})-(\text{PA}_{after}-\text{PA}_{before})$

	PA	NJ	Group Diff $(\Delta Y_i)$
Before	$\beta_0$	$\beta_0+\beta_1$	$\beta_1$
After	$\beta_0+\beta_2$	$\beta_0+\beta_1+\beta_2+\beta_3$	$\beta_1+\beta_3$
Time Diff $(\Delta Y_t)$	$\beta_2$	$\beta_2+\beta_3$	Diff-in-diff $\Delta_i \Delta_t: \beta_3$

Card & Kreuger (1994): Results

	Control	Treatment	Group Diff \((\Delta Y_i)\)
Before	\(\beta_0\)	\(\beta_0+\beta_1\)	\(\beta_1\)
After	\(\beta_0+\beta_2\)	\(\beta_0+\beta_1+\beta_2+\beta_3\)	\(\beta_1+\beta_3\)
Time Diff \((\Delta Y_t)\)	\(\beta_2\)	\(\beta_2+\beta_3\)	\(\beta_3\) Diff-in-diff \((\Delta_i \Delta_t)\)

	Control	Treatment	Group Diff \((\Delta Y_i)\)
Before	\(\beta_0\)	\(\beta_0+\beta_1\)	\(\beta_1\)
After	\(\beta_0+\beta_2\)	\(\beta_0+\beta_1+\beta_2+\beta_3\)	\(\beta_1+\beta_3\)
Time Diff \((\Delta Y_t)\)	\(\beta_2\)	\(\beta_2+\beta_3\)	Diff-in-diff \(\Delta_i \Delta_t: \beta_3\)

	Neighbors	Georgia	Group Diff \((\Delta Y_i)\)
Before	\(0.406\)	\(0.301\)	\(-0.105\)
After	\(0.402\)	\(0.386\)	\(0.016\)
Time Diff \((\Delta Y_t)\)	\(-0.004\)	\(0.085\)	Diff-in-diff: \(0.089\)

	PA	NJ	Group Diff \((\Delta Y_i)\)
Before	\(\beta_0\)	\(\beta_0+\beta_1\)	\(\beta_1\)
After	\(\beta_0+\beta_2\)	\(\beta_0+\beta_1+\beta_2+\beta_3\)	\(\beta_1+\beta_3\)
Time Diff \((\Delta Y_t)\)	\(\beta_2\)	\(\beta_2+\beta_3\)	Diff-in-diff \(\Delta_i \Delta_t: \beta_3\)

Contents

Difference-in-Differences Models

Example I: HOPE in Georgia

Generalizing DND Models

Example II: “The” Card-Kreuger Minimum Wage Study

Clever Research Designs Identify Causality

Difference-in-Differences Models

Natural Experiments

Difference-in-Differences Models I

Difference-in-Differences Models I

Difference-in-Differences Models I

Difference-in-Differences Models II

Example: Hot Dogs

Example: Hot Dogs

Visualizing Diff-in-Diff

Visualizing Diff-in-Diff

Visualizing Diff-in-Diff

Visualizing Diff-in-Diff

Visualizing Diff-in-Diff II

Visualizing Diff-in-Diff II

Visualizing Diff-in-Diff II

Visualizing Diff-in-Diff II

Visualizing Diff-in-Diff II

Visualizing Diff-in-Diff II

Visualizing Diff-in-Diff II

Comparing Group Means (Again)

Key Assumption: Counterfactual

Key Assumption: Counterfactual

Example I: HOPE in Georgia

Diff-in-Diff Example I

Diff-in-Diff Example II

Example: Data

Example: Data

Example: Regression

Example: Interpretting the Regression

Example: Comparing Group Means

Example: Comparing Group Means in R

Example: Comparing Group Means in R

Example: Diff-in-Diff Summary

Diff-in-Diff Summary & Data

Example: Diff-in-Diff Graph

Example: Diff-in-Diff Graph

Generalizing DND Models

Generalizing DND Models

Our Example, Generalized I

Our Example, Generalized II

Our Example, Generalized II

Our Example, Generalized, with Controls II

Our Example, Generalized, with Controls II

Our Example, Generalized, with Controls III

The Findings

Intuition behind DND

Example II: “The” Card-Kreuger Minimum Wage Study

Example: ”The” Card-Kreuger Minimum Wage Study I

Card & Kreuger (1994): Background I

Card & Kreuger (1994): Background II

Card & Kreuger (1994): Comparisons

Card & Kreuger (1994): Summary I

Card & Kreuger (1994): Summary II

Card & Kreuger (1994): Model

Card & Kreuger (1994): Results

Example: Comparing Group Means in `R`

Example: Comparing Group Means in `R`