Difference-in-Differences (DiD): Simulated Example
difference-in-differences.Rmd📊 Difference-in-Differences (DiD)
DiD is a popular method to estimate causal effects using panel or repeated cross-sectional data before and after a treatment is applied to one group but not another.
1. ✨ Simulate DiD Setup
set.seed(123)
n <- 1000
group <- rep(c("control", "treatment"), each = n/2)
time <- rep(c("pre", "post"), times = n/2)
treated <- ifelse(group == "treatment" & time == "post", 1, 0)
baseline <- rnorm(n)
Y <- 2 * treated + 0.5 * as.numeric(group == "treatment") +
0.3 * as.numeric(time == "post") + baseline + rnorm(n, 0, 0.5)
df <- data.frame(group, time, treated, Y)
head(df)## group time treated Y
## 1 control pre 0 -1.0583750
## 2 control post 0 -0.4501550
## 3 control pre 0 1.5497182
## 4 control post 0 0.3044208
## 5 control pre 0 -1.1453837
## 6 control post 0 2.53535172. 📈 Visualize Group-Time Means
df_summary <- df %>%
group_by(group, time) %>%
summarise(mean_Y = mean(Y), .groups = "drop")
ggplot(df_summary, aes(x = time, y = mean_Y, group = group, color = group))
geom_line(size = 1.2)## geom_line: na.rm = FALSE, orientation = NA
## stat_identity: na.rm = FALSE
## position_identity
geom_point(size = 2)## geom_point: na.rm = FALSE
## stat_identity: na.rm = FALSE
## position_identity
labs(title = "Group-Time Averages", y = "Mean Outcome", x = "Time")## $y
## [1] "Mean Outcome"
##
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## [1] "Time"
##
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## - attr(*, "validate")= logi TRUE3. 🧮 Estimate DiD Effect
df$time_num <- ifelse(df$time == "post", 1, 0)
df$group_num <- ifelse(df$group == "treatment", 1, 0)
did_model <- lm(Y ~ group_num * time_num, data = df)
summary(did_model)##
## Call:
## lm(formula = Y ~ group_num * time_num, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9273 -0.7774 0.0005 0.7100 3.7544
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.11072 0.07285 1.520 0.1288
## group_num 0.43432 0.10302 4.216 2.71e-05 ***
## time_num 0.17393 0.10302 1.688 0.0917 .
## group_num:time_num 2.09004 0.14569 14.346 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.152 on 996 degrees of freedom
## Multiple R-squared: 0.4742, Adjusted R-squared: 0.4726
## F-statistic: 299.4 on 3 and 996 DF, p-value: < 2.2e-16The coefficient on group_num:time_num is the DiD
estimate.