Lab: Event Studies from Scratch

Overview#

Event studies extend the DiD framework by estimating separate treatment effects for each time period relative to treatment. Instead of a single "before vs. after" estimate, you trace out how the treatment effect evolves over time. The pre-treatment coefficients serve as a diagnostic for the parallel trends assumption.

What you will learn:

• How to construct event-time (relative time) indicators
• How to estimate a dynamic treatment effects regression
• How to create and interpret the classic event study plot
• How to test for pre-trends
• Why you typically need to omit one reference period (and which one to choose)
• What can go wrong with event study specifications

Prerequisites: DiD (see the DiD lab), Fixed Effects.

Step 1: The Setting#

Imagine a corporate governance reform that is adopted by different firms at different times. We want to estimate (a) the dynamic path of the treatment effect and (b) whether there were pre-existing trends that might invalidate the design.

Step 2: Simulate Panel Data with Staggered Treatment#

1# First-time setup: install.packages(c("fixest", "ggplot2"))
2library(fixest)
3library(ggplot2)
4
5set.seed(2024)
6n_firms <- 200
7n_periods <- 20
8
9# Treatment timing
10treatment_year <- rep(Inf, n_firms)
11treated_firms <- sample(n_firms, 100)
12for (i in treated_firms) {
13treatment_year[i] <- sample(2005:2014, 1)
14}
15
16# Build panel
17df <- data.frame()
18for (i in 1:n_firms) {
19firm_fe <- rnorm(1, 0, 2)
20for (t in 0:(n_periods - 1)) {
21  year <- 2000 + t
22  year_fe <- 0.3 * t
23
24  if (treatment_year[i] < Inf) {
25    event_time <- year - treatment_year[i]
26    treated <- 1
27    post <- as.integer(year >= treatment_year[i])
28    te <- ifelse(post, 1.0 + 0.5 * pmin(event_time, 5), 0)
29  } else {
30    event_time <- NA
31    treated <- 0
32    post <- 0
33    te <- 0
34  }
35
36  y <- 10 + firm_fe + year_fe + te + rnorm(1, 0, 1.5)
37  df <- rbind(df, data.frame(
38    firm_id = i, year = year, treated = treated, post = post,
39    event_time = event_time, performance = y,
40    treatment_year = ifelse(treatment_year[i] < Inf,
41                             treatment_year[i], NA)
42  ))
43}
44}
45
46cat("Panel:", nrow(df), "observations\n")
47cat("Treated firms:", sum(treatment_year < Inf), "\n")

Expected output:

Summary statistics:

Step 3: Create Event-Time Indicators#

The event study regression requires dummy variables for each period relative to treatment. We normalize to one period before treatment ($k = -1$) as the reference category.

1# Create event-time indicators
2# fixest makes this easy with the i() function
3# Clip event time to [-5, 5]
4df$event_time_clipped <- pmin(pmax(df$event_time, -5), 5)
5
6# For the manual approach, create dummies
7event_times <- c(-5, -4, -3, -2, 0, 1, 2, 3, 4, 5)
8
9for (k in event_times) {
10col_name <- paste0("et_", ifelse(k < 0, "m", ""), abs(k))
11df[[col_name]] <- as.integer(df$event_time_clipped == k & df$treated == 1)
12}
13
14cat("Event-time dummies created. Reference period: k = -1\n")

Expected output:

Step 4: Estimate the Event Study Regression#

1# Event study using fixest (the easiest approach)
2# i(event_time_clipped, ref = -1) creates all dummies with -1 as reference
3m_es <- feols(performance ~ i(event_time_clipped, treated, ref = -1) |
4            firm_id + year,
5            data = df[!is.na(df$event_time) | df$treated == 0, ],
6            vcov = ~firm_id)
7
8summary(m_es)
9
10# The coefficients are the event study estimates

Expected output:

The pre-treatment coefficients (k = -5 to -2) are all close to zero and statistically insignificant, consistent with parallel trends. The post-treatment coefficients grow over time, matching the true DGP of 1.0 + 0.5 * min(k, 5).

Step 5: Create the Event Study Plot#

The coefficient plot is the signature visualization of the event study design.

1# Event study plot using fixest
2iplot(m_es,
3    main = "Event Study: Governance Reform and Firm Performance",
4    xlab = "Event Time (Years Relative to Treatment)",
5    ylab = "Coefficient (Relative to k = -1)")
6
7# Add reference line at treatment onset
8abline(v = -0.5, lty = 2, col = "red")

Step 6: Interpreting the Post-Treatment Dynamics#

The post-treatment coefficients tell a story about how the treatment effect evolves over time.

1# Extract and interpret post-treatment coefficients
2coefs <- coeftable(m_es)
3cat("Post-Treatment Dynamics:\n")
4cat("The effect grows over time as the governance reform takes hold.\n\n")
5
6# True effects for comparison
7for (k in 0:5) {
8true_te <- 1.0 + 0.5 * min(k, 5)
9cat(sprintf("  k = %+d: True = %+.3f\n", k, true_te))
10}

Expected output:

The gradually building pattern reflects a reform that takes time to produce its full impact. The DGP generates this pattern with the formula: treatment effect = 1.0 + 0.5 * min(k, 5).

Step 7: What Can Go Wrong#

Pre-trend Violation#

1# Simulate pre-trend violation (similar to Python code)
2# When you see an upward slope in pre-treatment coefficients,
3# parallel trends is violated.
4# The post-treatment coefficients mix the true effect
5# with the pre-existing differential trend.
6
7cat("If pre-treatment coefficients slope upward, this indicates\n")
8cat("a violation of parallel trends. The post-treatment estimates\n")
9cat("are contaminated by the pre-existing trend.\n")

Step 8: Advanced Considerations#

Binning Endpoint Periods#

In most settings, bin distant event times to avoid sparse cells. For example, group all $k \leq -5$ into a single "$k \leq -5$" dummy and all $k \geq 5$ into "$k \geq 5$".

Joint Test for Pre-Trends#

Instead of eyeballing individual pre-trend coefficients, formally test whether they are jointly zero.

# Joint test for pre-trends using fixest
# wald() function tests if specified coefficients are jointly zero
wald(m_es, "event_time_clipped::-[2-5]")

cat("p > 0.05: Cannot reject that pre-trends are jointly zero\n")

Expected output:

The joint F-test confirms what the event study plot shows visually: the pre-treatment coefficients are not distinguishable from zero, consistent with the parallel trends assumption.

Aggregating Post-Treatment Effects#

Sometimes you want a single summary treatment effect rather than period-by-period estimates.

# Simple summary DiD estimate
df$treat_post <- df$treated * df$post
m_did <- feols(performance ~ treat_post | firm_id + year,
             data = df, vcov = ~firm_id)
cat("Summary DiD estimate:", coef(m_did)["treat_post"], "\n")

Expected output:

The average of the true DGP treatment effects across k = 0 to 5 is (1.0 + 1.5 + 2.0 + 2.5 + 3.0 + 3.5) / 6 = 2.25.

Step 9: Exercises#

1. Change the reference period. Re-estimate with $k = -2$ as the reference period. How do the coefficients and plot change? Which reference period makes more sense for your setting?

2. Test for anticipation effects. What if firms change behavior before the formal treatment date? Allow the treatment effect to begin one period before the official date and re-estimate.

3. Staggered DiD concerns. With staggered treatment timing and heterogeneous treatment effects, the standard TWFE event study can be biased (Sun & Abraham, 2021). Read about this issue and think about when it matters.

4. Placebo test. For the never-treated firms, assign a random "fake" treatment year and estimate the event study. All coefficients should be near zero.

Summary#

In this lab you learned:

• Event studies estimate separate treatment effects for each period relative to treatment
• You typically need to omit one reference period (typically $k = -1$) to avoid multicollinearity
• Flat pre-treatment coefficients are consistent with parallel trends but do not prove it
• The post-treatment pattern reveals dynamic treatment effects (growing, stable, or fading)
• In most settings, include firm and year fixed effects and cluster standard errors appropriately
• Bin endpoint event times to avoid sparse cells
• Use a joint F-test for pre-trends rather than eyeballing individual coefficients
• Pre-trend violations are a fundamental threat — "detrending" is not a reliable fix
• With staggered treatment, be aware of potential biases in standard TWFE event studies