Nothing
Panel Event Studies: A Guide Following Miller (2023)
In EventStudy: Event Study Analysis
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
Introduction
Panel event studies---also known as difference-in-differences (DiD) event
studies---are among the most widely used research designs in applied economics,
public policy, and health research. When units (firms, states, individuals)
receive a treatment at known times and are observed over multiple periods, the
panel event study framework lets us estimate treatment effects while controlling
for both time-invariant unit characteristics and common time shocks.
This vignette follows the practical guide laid out in
Miller (2023), "An Introductory Guide to Event Study Models,"
Journal of Economic Perspectives, 37(2), 203--230.
Miller's paper provides a unified framework covering data structure, the
estimating equation, reference-period normalization, endpoint binning,
heterogeneous treatment effects with staggered adoption, pre-trend testing, and
inference. We map each concept to the EventStudy package's panel module.
library(EventStudy)
library(dplyr)
library(ggplot2)
Data Structure (Miller Section I)
Miller classifies panel event study settings along two dimensions:
- Single vs. staggered event dates --- Do all treated units receive
treatment in the same period, or do different cohorts adopt at different
times?
- Never-treated units present or not --- Is there a set of units that
remain untreated throughout the sample?
These distinctions matter because staggered adoption, combined with
heterogeneous treatment effects, can bias conventional two-way fixed effects
(TWFE) estimators---a point we return to in Section 8.
Dataset A: Single-Cohort Design
Thirty units observed over 20 periods. Fifteen units are treated at period 10;
fifteen are never treated.
set.seed(42)
n_units <- 30
n_periods <- 20
treat_period <- 10
true_effect <- 2.0
dataset_a <- tibble(
unit_id = rep(1:n_units, each = n_periods),
time_id = rep(1:n_periods, n_units)
) %>%
mutate(
# First 15 units are treated at period 10
treatment_time = ifelse(unit_id <= 15, treat_period, NA_integer_),
treated = ifelse(!is.na(treatment_time) & time_id >= treatment_time, 1, 0),
# Unit and time fixed effects + treatment effect + noise
unit_fe = rep(rnorm(n_units, 0, 1), each = n_periods),
time_fe = rep(rnorm(n_periods, 0, 0.5), n_units),
outcome = unit_fe + time_fe + true_effect * treated + rnorm(n() , 0, 1)
)
Dataset B: Staggered Multi-Cohort Design
Fifty units over 20 periods. Three treatment cohorts adopt at periods 8, 12,
and 16; a fourth group is never treated.
set.seed(123)
n_units_b <- 50
n_periods_b <- 20
dataset_b <- tibble(
unit_id = rep(1:n_units_b, each = n_periods_b),
time_id = rep(1:n_periods_b, n_units_b)
) %>%
mutate(
# Assign cohorts: units 1-12 at t=8, 13-25 at t=12, 26-37 at t=16, rest never
treatment_time = case_when(
unit_id <= 12 ~ 8L,
unit_id > 12 & unit_id <= 25 ~ 12L,
unit_id > 25 & unit_id <= 37 ~ 16L,
TRUE ~ NA_integer_
),
treated = ifelse(!is.na(treatment_time) & time_id >= treatment_time, 1, 0),
# Heterogeneous effects: early adopters have larger effects
true_te = case_when(
treatment_time == 8 ~ 3.0,
treatment_time == 12 ~ 2.0,
treatment_time == 16 ~ 1.0,
TRUE ~ 0
),
unit_fe = rep(rnorm(n_units_b, 0, 1), each = n_periods_b),
time_fe = rep(rnorm(n_periods_b, 0, 0.5), n_units_b),
outcome = unit_fe + time_fe + true_te * treated + rnorm(n(), 0, 1)
)
Creating Tasks
Each dataset is wrapped in a PanelEventStudyTask:
task_a <- PanelEventStudyTask$new(
dataset_a,
unit_id = "unit_id",
time_id = "time_id",
outcome = "outcome",
treatment = "treated",
treatment_time = "treatment_time"
)
task_a
#> PanelEventStudyTask
#> Units: 30
#> Periods: 20
#> Treated: 1 cohort(s)
#> Outcome: outcome
#> Estimated: FALSE
task_b <- PanelEventStudyTask$new(
dataset_b,
unit_id = "unit_id",
time_id = "time_id",
outcome = "outcome",
treatment = "treated",
treatment_time = "treatment_time"
)
The Estimating Equation (Miller Section II)
Miller presents a general dynamic specification for panel event studies:
$$Y_{it} = \alpha_i + \gamma_t + \sum_{j \neq j^*} \delta_j \cdot D_{it}^j + \varepsilon_{it}$$
where:
- $\alpha_i$ are unit fixed effects, absorbing time-invariant differences
across units;
- $\gamma_t$ are time fixed effects, absorbing common shocks that affect all
units in a given period;
- $D_{it}^j$ is an event-time indicator equal to 1 when unit $i$ is exactly
$j$ periods from its treatment date at time $t$;
- $j^*$ is the omitted reference period (normalized to zero); and
- $\delta_j$ is the treatment effect at event time $j$, measured relative to
the reference period.
The EventStudy package implements this equation in
estimate_panel_event_study(). The method argument selects the variant, while
leads, lags, and base_period control the event-time window and
normalization.
Static TWFE: The Single-Coefficient Model (Miller Section II.A)
The simplest panel event study specification restricts all post-treatment
effects to a single coefficient $\beta$:
$$Y_{it} = \alpha_i + \gamma_t + \beta \cdot D_{it} + \varepsilon_{it}$$
Here $D_{it} = 1$ if unit $i$ has been treated by time $t$ (post-treatment),
and 0 otherwise. The coefficient $\beta$ is the average treatment effect on
the treated (ATT) under the assumption that the treatment effect is constant
across all post-treatment periods and cohorts.
task_a <- estimate_panel_event_study(task_a, method = "static_twfe")
task_a$results$coefficients
#> term estimate std.error statistic p.value
#> ATT 2.01 0.15 13.4 <0.001
The static model is a good starting point, but it assumes homogeneous
effects. If the treatment effect varies over time (e.g., growing or fading),
this assumption can be misleading. The dynamic specification relaxes it.
Dynamic TWFE: Event-Time Coefficients (Miller Section II.B)
The dynamic specification estimates a separate coefficient $\delta_j$ for each
event-time period, allowing us to trace out the treatment effect path:
task_a <- estimate_panel_event_study(
task_a,
method = "dynamic_twfe",
leads = 5,
lags = 5,
base_period = -1
)
task_a$results$coefficients
#> relative_time estimate std.error statistic p.value
#> -5 0.02 0.30 0.07 0.95
#> -4 -0.10 0.28 -0.36 0.72
#> ...
#> -1 0.00 0.00 NA NA
#> 0 1.95 0.22 8.86 <0.001
#> 1 2.03 0.23 8.83 <0.001
#> ...
The pre-treatment coefficients ($j < 0$) should be close to zero under the
parallel trends assumption, while the post-treatment coefficients ($j \geq 0$)
capture the treatment effect dynamics.
plot_panel_event_study(task_a, title = "Dynamic TWFE - Single Cohort")
The plot shows point estimates and confidence intervals at each event time, with
a vertical dashed line separating the pre- and post-treatment periods.
Reference Period and Normalization (Miller Section III)
One event-time indicator must be omitted to avoid perfect collinearity with the
unit and time fixed effects. This is the reference period $j^*$, and all
coefficients $\delta_j$ are interpreted relative to it.
Miller emphasizes that the choice of reference period is not merely a
mechanical necessity---it has substantive implications. The default
base_period = -1 normalizes to the period immediately before treatment, so
that $\delta_0$ captures the immediate treatment effect. Alternative choices
include:
# Normalize to two periods before treatment
task_a <- estimate_panel_event_study(
task_a,
method = "dynamic_twfe",
leads = 5,
lags = 5,
base_period = -2
)
With base_period = -2, the coefficient at $j = -1$ becomes interpretable as
a test for anticipation effects: if units begin reacting before treatment, this
coefficient will be non-zero.
Miller also discusses extended reference periods where multiple pre-treatment
periods are pooled as the reference group. While the package normalizes a single
period, you can approximate this by checking that all pre-treatment coefficients
are jointly close to zero (see Section 9 on pre-trend testing).
Endpoint Binning (Miller Section IV)
In practice, event time extends beyond the window we estimate. Miller discusses
endpoint binning: grouping all event times below $-K$ (or above $K$) into
a single bin. This prevents observations far from the treatment date from being
dropped and captures the cumulative effect of treatment at long horizons.
The package automatically bins at the leads/lags boundaries. The coefficient
at relative time $-\text{leads}$ captures the average effect for all event times
$\leq -\text{leads}$, and similarly for $+\text{lags}$.
# Narrow window: leads = 3, lags = 3
task_a_narrow <- estimate_panel_event_study(
task_a,
method = "dynamic_twfe",
leads = 3,
lags = 3
)
task_a_narrow$results$coefficients
# Wider window: leads = 8, lags = 8
task_a_wide <- estimate_panel_event_study(
task_a,
method = "dynamic_twfe",
leads = 8,
lags = 8
)
task_a_wide$results$coefficients
With the narrow window, the endpoint bins absorb more observations, and the
binned coefficients may differ from the interior ones. With a wider window, each
coefficient captures a more specific event time but with potentially fewer
observations.
Miller recommends reporting results for multiple window widths as a robustness
check, and being transparent about which observations are binned at the
endpoints.
Staggered Treatment and Heterogeneous Effects (Miller Section V)
The TWFE Problem
When treatment is staggered and treatment effects are heterogeneous across
cohorts or over time, the standard TWFE estimator can produce misleading
results. The core issue is that TWFE uses all untreated and
already-treated units as comparisons. When already-treated units serve as
controls for newly-treated units---what Miller calls "forbidden comparisons"---
the resulting weights on cohort-specific treatment effects can be negative.
This means the TWFE estimate can be an inconsistent estimate of the ATT,
potentially even with the wrong sign, when:
- Treatment is staggered (different cohorts adopt at different times), and
- Treatment effects are heterogeneous (differ by cohort or evolve over time).
Sun & Abraham (2021) Interaction-Weighted Estimator
Sun & Abraham (2021) propose an interaction-weighted (IW) estimator that
avoids forbidden comparisons. The idea is to estimate cohort-specific effects by
interacting event-time indicators with cohort indicators, then aggregate using
cohort-size weights.
The EventStudy package implements this as method = "sun_abraham":
task_b <- estimate_panel_event_study(
task_b,
method = "sun_abraham",
leads = 5,
lags = 5
)
task_b$results$coefficients
Comparing TWFE and Sun & Abraham
To see the difference, we can estimate both on the staggered dataset and
compare:
# TWFE on staggered data (potentially biased)
task_b_twfe <- PanelEventStudyTask$new(
dataset_b,
unit_id = "unit_id", time_id = "time_id",
outcome = "outcome", treatment = "treated",
treatment_time = "treatment_time"
)
task_b_twfe <- estimate_panel_event_study(
task_b_twfe,
method = "dynamic_twfe",
leads = 5, lags = 5
)
# Sun & Abraham on the same data
task_b_sa <- PanelEventStudyTask$new(
dataset_b,
unit_id = "unit_id", time_id = "time_id",
outcome = "outcome", treatment = "treated",
treatment_time = "treatment_time"
)
task_b_sa <- estimate_panel_event_study(
task_b_sa,
method = "sun_abraham",
leads = 5, lags = 5
)
# Side-by-side comparison
coefs_comparison <- bind_rows(
task_b_twfe$results$coefficients %>% mutate(method = "Dynamic TWFE"),
task_b_sa$results$coefficients %>% mutate(method = "Sun & Abraham")
)
ggplot(coefs_comparison, aes(x = relative_time, y = estimate, color = method)) +
geom_hline(yintercept = 0, linetype = "dashed", color = "grey40") +
geom_vline(xintercept = -0.5, linetype = "dotted", color = "red", alpha = 0.6) +
geom_point(position = position_dodge(width = 0.3), size = 2) +
geom_line(position = position_dodge(width = 0.3), linewidth = 0.8) +
labs(
title = "TWFE vs Sun & Abraham: Staggered Adoption",
x = "Relative Time to Treatment",
y = "Estimate",
color = "Method"
) +
theme_minimal()
When treatment effects are homogeneous, the two estimators will agree. When
effects are heterogeneous---as in Dataset B where early adopters have larger
effects---the Sun & Abraham estimates correctly recover the cohort-weighted
ATT, while TWFE may be attenuated or distorted.
Pre-trend Testing (Miller Section VI)
The validity of the panel event study hinges on the parallel trends
assumption: in the absence of treatment, treated and control units would have
followed the same outcome trajectory. While this assumption is fundamentally
untestable, we can look for indirect evidence.
Visual Inspection
The pre-treatment coefficients $\delta_j$ for $j < 0$ should be close to zero.
The event study plot provides a visual check---if the pre-treatment coefficients
trend systematically away from zero, the parallel trends assumption is suspect.
Joint Test for Pre-trends
A more formal approach is a joint F-test of the null hypothesis that all
pre-treatment coefficients equal zero:
coefs <- task_a$results$coefficients
pre_treatment <- coefs %>%
filter(relative_time < 0, relative_time != -1) # exclude base period
if (nrow(pre_treatment) > 0) {
f_stat <- sum(pre_treatment$estimate^2 / pre_treatment$std.error^2) /
nrow(pre_treatment)
p_value <- pf(f_stat, df1 = nrow(pre_treatment),
df2 = task_a$results$model$df.residual,
lower.tail = FALSE)
cat("Joint pre-trend F-stat:", round(f_stat, 3), "\n")
cat("p-value: ", round(p_value, 4), "\n")
}
Miller's Caution
Miller warns that absence of evidence is not evidence of absence. A
non-significant pre-trend test does not prove parallel trends---it may simply
reflect low statistical power. Conversely, small but statistically significant
pre-treatment coefficients may be substantively unimportant. Researchers should:
- Report the pre-treatment coefficients and their confidence intervals.
- Contextualize the magnitude of any pre-trends relative to the estimated
treatment effects.
- Consider sensitivity analyses (e.g., Rambachan & Roth, 2023) for how
violations of parallel trends would affect the conclusions.
Reporting and Counterfactuals (Miller Section VII)
Miller recommends reporting not just the treatment effect estimates, but also
the counterfactual outcomes---what the treated units' outcomes would have
been absent treatment. This helps readers assess both the magnitude and
plausibility of the estimates.
From the dynamic model, the counterfactual for a treated unit at event time $j$
is the observed outcome minus the estimated effect:
# Construct counterfactual for treated units
coef_lookup <- task_a$results$coefficients %>%
select(relative_time, estimate) %>%
deframe()
counterfactual <- dataset_a %>%
filter(!is.na(treatment_time)) %>%
mutate(
rel_time = time_id - treatment_time,
delta_hat = coef_lookup[as.character(rel_time)],
delta_hat = ifelse(is.na(delta_hat), 0, delta_hat),
outcome_counterfactual = outcome - delta_hat
)
# Plot observed vs counterfactual
counterfactual_summary <- counterfactual %>%
group_by(time_id) %>%
summarise(
observed = mean(outcome),
counterfactual = mean(outcome_counterfactual),
.groups = "drop"
)
ggplot(counterfactual_summary, aes(x = time_id)) +
geom_line(aes(y = observed, color = "Observed"), linewidth = 0.8) +
geom_line(aes(y = counterfactual, color = "Counterfactual"),
linetype = "dashed", linewidth = 0.8) +
geom_vline(xintercept = 10, linetype = "dotted", color = "red") +
labs(
title = "Observed vs Counterfactual Outcomes (Treated Units)",
x = "Time Period",
y = "Mean Outcome",
color = NULL
) +
theme_minimal()
The gap between the observed and counterfactual lines after the treatment date
visualizes the estimated treatment effect.
Statistical Inference (Miller Section VIII)
Clustered Standard Errors
Panel event studies typically require clustering standard errors at the unit
level to account for serial correlation within units. When the sandwich
package is installed, estimate_panel_event_study() automatically computes
cluster-robust standard errors via sandwich::vcovCL(). The cluster
parameter controls the clustering variable and defaults to the unit ID:
# Cluster-robust SEs at the unit level (the default)
task_a <- estimate_panel_event_study(
task_a,
method = "dynamic_twfe",
leads = 5,
lags = 5,
cluster = "unit_id"
)
# Cluster at a different level (e.g., state)
task_a <- estimate_panel_event_study(
task_a,
method = "dynamic_twfe",
leads = 5,
lags = 5,
cluster = "state_id"
)
If sandwich is not installed, the function falls back to OLS standard errors
with an informative message. Install it with install.packages("sandwich").
How Many Clusters Are Enough?
Miller discusses the well-known problem that clustered standard errors are
unreliable when the number of clusters is small. His rule of thumb, drawing on
the simulation evidence in the literature: you need approximately 42--50 or
more clusters for cluster-robust inference to be reliable.
When the number of clusters is small, alternatives include:
- Wild cluster bootstrap (Cameron, Gelbach, & Miller, 2008) --- available
via the
fwildclusterboot package
- Randomization inference (Fisher, 1935)
Practical Checklist
Drawing on Miller (2023), here is a checklist for panel event study research:
- Classify your setting. Single cohort or staggered? Never-treated controls
available?
- Start with the dynamic specification. Plot the event-time coefficients
before collapsing to a static estimate.
- Inspect pre-trends. Report pre-treatment coefficients visually and with a
joint test.
- Choose the reference period deliberately.
base_period = -1 is standard;
consider whether anticipation effects warrant an earlier reference.
- Report endpoint binning. Be transparent about which event times are binned
and test sensitivity to different window widths.
- Use appropriate estimators for staggered designs. If treatment timing
varies and effects may be heterogeneous, use Sun & Abraham or similar
heterogeneity-robust estimators instead of TWFE.
- Report counterfactual outcomes. Show what would have happened absent
treatment.
- Cluster standard errors appropriately. Cluster at the unit level and
ensure you have enough clusters (42--50+) for reliable inference.
- Test robustness. Vary the window width, reference period, and estimator.
Report results for multiple specifications.
References
-
Miller, D. L. (2023). An Introductory Guide to Event Study Models.
Journal of Economic Perspectives, 37(2), 203--230.
doi:10.1257/jep.37.2.203
-
Sun, L., & Abraham, S. (2021). Estimating Dynamic Treatment Effects in
Event Studies with Heterogeneous Treatment Effects.
Journal of Econometrics, 225(2), 175--199.
doi:10.1016/j.jeconom.2020.09.006
-
MacKinlay, A. C. (1997). Event Studies in Economics and Finance.
Journal of Economic Literature, 35(1), 13--39.
-
Cameron, A. C., Gelbach, J. B., & Miller, D. L. (2008). Bootstrap-Based
Improvements for Inference with Clustered Errors.
Review of Economics and Statistics, 90(3), 414--427.
-
Rambachan, A., & Roth, J. (2023). A More Credible Approach to Parallel
Trends. Review of Economic Studies, 90(5), 2555--2591.
Try the EventStudy package in your browser
Any scripts or data that you put into this service are public.
EventStudy documentation built on Oct. 31, 2026, 1:07 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
Introduction
Panel event studies---also known as difference-in-differences (DiD) event studies---are among the most widely used research designs in applied economics, public policy, and health research. When units (firms, states, individuals) receive a treatment at known times and are observed over multiple periods, the panel event study framework lets us estimate treatment effects while controlling for both time-invariant unit characteristics and common time shocks.
This vignette follows the practical guide laid out in Miller (2023), "An Introductory Guide to Event Study Models," Journal of Economic Perspectives, 37(2), 203--230. Miller's paper provides a unified framework covering data structure, the estimating equation, reference-period normalization, endpoint binning, heterogeneous treatment effects with staggered adoption, pre-trend testing, and inference. We map each concept to the EventStudy package's panel module.
library(EventStudy) library(dplyr) library(ggplot2)
Data Structure (Miller Section I)
Miller classifies panel event study settings along two dimensions:
- Single vs. staggered event dates --- Do all treated units receive treatment in the same period, or do different cohorts adopt at different times?
- Never-treated units present or not --- Is there a set of units that remain untreated throughout the sample?
These distinctions matter because staggered adoption, combined with heterogeneous treatment effects, can bias conventional two-way fixed effects (TWFE) estimators---a point we return to in Section 8.
Dataset A: Single-Cohort Design
Thirty units observed over 20 periods. Fifteen units are treated at period 10; fifteen are never treated.
set.seed(42) n_units <- 30 n_periods <- 20 treat_period <- 10 true_effect <- 2.0 dataset_a <- tibble( unit_id = rep(1:n_units, each = n_periods), time_id = rep(1:n_periods, n_units) ) %>% mutate( # First 15 units are treated at period 10 treatment_time = ifelse(unit_id <= 15, treat_period, NA_integer_), treated = ifelse(!is.na(treatment_time) & time_id >= treatment_time, 1, 0), # Unit and time fixed effects + treatment effect + noise unit_fe = rep(rnorm(n_units, 0, 1), each = n_periods), time_fe = rep(rnorm(n_periods, 0, 0.5), n_units), outcome = unit_fe + time_fe + true_effect * treated + rnorm(n() , 0, 1) )
Dataset B: Staggered Multi-Cohort Design
Fifty units over 20 periods. Three treatment cohorts adopt at periods 8, 12, and 16; a fourth group is never treated.
set.seed(123) n_units_b <- 50 n_periods_b <- 20 dataset_b <- tibble( unit_id = rep(1:n_units_b, each = n_periods_b), time_id = rep(1:n_periods_b, n_units_b) ) %>% mutate( # Assign cohorts: units 1-12 at t=8, 13-25 at t=12, 26-37 at t=16, rest never treatment_time = case_when( unit_id <= 12 ~ 8L, unit_id > 12 & unit_id <= 25 ~ 12L, unit_id > 25 & unit_id <= 37 ~ 16L, TRUE ~ NA_integer_ ), treated = ifelse(!is.na(treatment_time) & time_id >= treatment_time, 1, 0), # Heterogeneous effects: early adopters have larger effects true_te = case_when( treatment_time == 8 ~ 3.0, treatment_time == 12 ~ 2.0, treatment_time == 16 ~ 1.0, TRUE ~ 0 ), unit_fe = rep(rnorm(n_units_b, 0, 1), each = n_periods_b), time_fe = rep(rnorm(n_periods_b, 0, 0.5), n_units_b), outcome = unit_fe + time_fe + true_te * treated + rnorm(n(), 0, 1) )
Creating Tasks
Each dataset is wrapped in a PanelEventStudyTask:
task_a <- PanelEventStudyTask$new( dataset_a, unit_id = "unit_id", time_id = "time_id", outcome = "outcome", treatment = "treated", treatment_time = "treatment_time" ) task_a #> PanelEventStudyTask #> Units: 30 #> Periods: 20 #> Treated: 1 cohort(s) #> Outcome: outcome #> Estimated: FALSE task_b <- PanelEventStudyTask$new( dataset_b, unit_id = "unit_id", time_id = "time_id", outcome = "outcome", treatment = "treated", treatment_time = "treatment_time" )
The Estimating Equation (Miller Section II)
Miller presents a general dynamic specification for panel event studies:
$$Y_{it} = \alpha_i + \gamma_t + \sum_{j \neq j^*} \delta_j \cdot D_{it}^j + \varepsilon_{it}$$
where:
- $\alpha_i$ are unit fixed effects, absorbing time-invariant differences across units;
- $\gamma_t$ are time fixed effects, absorbing common shocks that affect all units in a given period;
- $D_{it}^j$ is an event-time indicator equal to 1 when unit $i$ is exactly $j$ periods from its treatment date at time $t$;
- $j^*$ is the omitted reference period (normalized to zero); and
- $\delta_j$ is the treatment effect at event time $j$, measured relative to the reference period.
The EventStudy package implements this equation in
estimate_panel_event_study(). The method argument selects the variant, while
leads, lags, and base_period control the event-time window and
normalization.
Static TWFE: The Single-Coefficient Model (Miller Section II.A)
The simplest panel event study specification restricts all post-treatment effects to a single coefficient $\beta$:
$$Y_{it} = \alpha_i + \gamma_t + \beta \cdot D_{it} + \varepsilon_{it}$$
Here $D_{it} = 1$ if unit $i$ has been treated by time $t$ (post-treatment), and 0 otherwise. The coefficient $\beta$ is the average treatment effect on the treated (ATT) under the assumption that the treatment effect is constant across all post-treatment periods and cohorts.
task_a <- estimate_panel_event_study(task_a, method = "static_twfe") task_a$results$coefficients #> term estimate std.error statistic p.value #> ATT 2.01 0.15 13.4 <0.001
The static model is a good starting point, but it assumes homogeneous effects. If the treatment effect varies over time (e.g., growing or fading), this assumption can be misleading. The dynamic specification relaxes it.
Dynamic TWFE: Event-Time Coefficients (Miller Section II.B)
The dynamic specification estimates a separate coefficient $\delta_j$ for each event-time period, allowing us to trace out the treatment effect path:
task_a <- estimate_panel_event_study( task_a, method = "dynamic_twfe", leads = 5, lags = 5, base_period = -1 ) task_a$results$coefficients #> relative_time estimate std.error statistic p.value #> -5 0.02 0.30 0.07 0.95 #> -4 -0.10 0.28 -0.36 0.72 #> ... #> -1 0.00 0.00 NA NA #> 0 1.95 0.22 8.86 <0.001 #> 1 2.03 0.23 8.83 <0.001 #> ...
The pre-treatment coefficients ($j < 0$) should be close to zero under the parallel trends assumption, while the post-treatment coefficients ($j \geq 0$) capture the treatment effect dynamics.
plot_panel_event_study(task_a, title = "Dynamic TWFE - Single Cohort")
The plot shows point estimates and confidence intervals at each event time, with a vertical dashed line separating the pre- and post-treatment periods.
Reference Period and Normalization (Miller Section III)
One event-time indicator must be omitted to avoid perfect collinearity with the unit and time fixed effects. This is the reference period $j^*$, and all coefficients $\delta_j$ are interpreted relative to it.
Miller emphasizes that the choice of reference period is not merely a
mechanical necessity---it has substantive implications. The default
base_period = -1 normalizes to the period immediately before treatment, so
that $\delta_0$ captures the immediate treatment effect. Alternative choices
include:
# Normalize to two periods before treatment task_a <- estimate_panel_event_study( task_a, method = "dynamic_twfe", leads = 5, lags = 5, base_period = -2 )
With base_period = -2, the coefficient at $j = -1$ becomes interpretable as
a test for anticipation effects: if units begin reacting before treatment, this
coefficient will be non-zero.
Miller also discusses extended reference periods where multiple pre-treatment periods are pooled as the reference group. While the package normalizes a single period, you can approximate this by checking that all pre-treatment coefficients are jointly close to zero (see Section 9 on pre-trend testing).
Endpoint Binning (Miller Section IV)
In practice, event time extends beyond the window we estimate. Miller discusses endpoint binning: grouping all event times below $-K$ (or above $K$) into a single bin. This prevents observations far from the treatment date from being dropped and captures the cumulative effect of treatment at long horizons.
The package automatically bins at the leads/lags boundaries. The coefficient
at relative time $-\text{leads}$ captures the average effect for all event times
$\leq -\text{leads}$, and similarly for $+\text{lags}$.
# Narrow window: leads = 3, lags = 3 task_a_narrow <- estimate_panel_event_study( task_a, method = "dynamic_twfe", leads = 3, lags = 3 ) task_a_narrow$results$coefficients # Wider window: leads = 8, lags = 8 task_a_wide <- estimate_panel_event_study( task_a, method = "dynamic_twfe", leads = 8, lags = 8 ) task_a_wide$results$coefficients
With the narrow window, the endpoint bins absorb more observations, and the binned coefficients may differ from the interior ones. With a wider window, each coefficient captures a more specific event time but with potentially fewer observations.
Miller recommends reporting results for multiple window widths as a robustness check, and being transparent about which observations are binned at the endpoints.
Staggered Treatment and Heterogeneous Effects (Miller Section V)
The TWFE Problem
When treatment is staggered and treatment effects are heterogeneous across cohorts or over time, the standard TWFE estimator can produce misleading results. The core issue is that TWFE uses all untreated and already-treated units as comparisons. When already-treated units serve as controls for newly-treated units---what Miller calls "forbidden comparisons"--- the resulting weights on cohort-specific treatment effects can be negative.
This means the TWFE estimate can be an inconsistent estimate of the ATT, potentially even with the wrong sign, when:
- Treatment is staggered (different cohorts adopt at different times), and
- Treatment effects are heterogeneous (differ by cohort or evolve over time).
Sun & Abraham (2021) Interaction-Weighted Estimator
Sun & Abraham (2021) propose an interaction-weighted (IW) estimator that avoids forbidden comparisons. The idea is to estimate cohort-specific effects by interacting event-time indicators with cohort indicators, then aggregate using cohort-size weights.
The EventStudy package implements this as method = "sun_abraham":
task_b <- estimate_panel_event_study( task_b, method = "sun_abraham", leads = 5, lags = 5 ) task_b$results$coefficients
Comparing TWFE and Sun & Abraham
To see the difference, we can estimate both on the staggered dataset and compare:
# TWFE on staggered data (potentially biased) task_b_twfe <- PanelEventStudyTask$new( dataset_b, unit_id = "unit_id", time_id = "time_id", outcome = "outcome", treatment = "treated", treatment_time = "treatment_time" ) task_b_twfe <- estimate_panel_event_study( task_b_twfe, method = "dynamic_twfe", leads = 5, lags = 5 ) # Sun & Abraham on the same data task_b_sa <- PanelEventStudyTask$new( dataset_b, unit_id = "unit_id", time_id = "time_id", outcome = "outcome", treatment = "treated", treatment_time = "treatment_time" ) task_b_sa <- estimate_panel_event_study( task_b_sa, method = "sun_abraham", leads = 5, lags = 5 ) # Side-by-side comparison coefs_comparison <- bind_rows( task_b_twfe$results$coefficients %>% mutate(method = "Dynamic TWFE"), task_b_sa$results$coefficients %>% mutate(method = "Sun & Abraham") ) ggplot(coefs_comparison, aes(x = relative_time, y = estimate, color = method)) + geom_hline(yintercept = 0, linetype = "dashed", color = "grey40") + geom_vline(xintercept = -0.5, linetype = "dotted", color = "red", alpha = 0.6) + geom_point(position = position_dodge(width = 0.3), size = 2) + geom_line(position = position_dodge(width = 0.3), linewidth = 0.8) + labs( title = "TWFE vs Sun & Abraham: Staggered Adoption", x = "Relative Time to Treatment", y = "Estimate", color = "Method" ) + theme_minimal()
When treatment effects are homogeneous, the two estimators will agree. When effects are heterogeneous---as in Dataset B where early adopters have larger effects---the Sun & Abraham estimates correctly recover the cohort-weighted ATT, while TWFE may be attenuated or distorted.
Pre-trend Testing (Miller Section VI)
The validity of the panel event study hinges on the parallel trends assumption: in the absence of treatment, treated and control units would have followed the same outcome trajectory. While this assumption is fundamentally untestable, we can look for indirect evidence.
Visual Inspection
The pre-treatment coefficients $\delta_j$ for $j < 0$ should be close to zero. The event study plot provides a visual check---if the pre-treatment coefficients trend systematically away from zero, the parallel trends assumption is suspect.
Joint Test for Pre-trends
A more formal approach is a joint F-test of the null hypothesis that all pre-treatment coefficients equal zero:
coefs <- task_a$results$coefficients pre_treatment <- coefs %>% filter(relative_time < 0, relative_time != -1) # exclude base period if (nrow(pre_treatment) > 0) { f_stat <- sum(pre_treatment$estimate^2 / pre_treatment$std.error^2) / nrow(pre_treatment) p_value <- pf(f_stat, df1 = nrow(pre_treatment), df2 = task_a$results$model$df.residual, lower.tail = FALSE) cat("Joint pre-trend F-stat:", round(f_stat, 3), "\n") cat("p-value: ", round(p_value, 4), "\n") }
Miller's Caution
Miller warns that absence of evidence is not evidence of absence. A non-significant pre-trend test does not prove parallel trends---it may simply reflect low statistical power. Conversely, small but statistically significant pre-treatment coefficients may be substantively unimportant. Researchers should:
- Report the pre-treatment coefficients and their confidence intervals.
- Contextualize the magnitude of any pre-trends relative to the estimated treatment effects.
- Consider sensitivity analyses (e.g., Rambachan & Roth, 2023) for how violations of parallel trends would affect the conclusions.
Reporting and Counterfactuals (Miller Section VII)
Miller recommends reporting not just the treatment effect estimates, but also the counterfactual outcomes---what the treated units' outcomes would have been absent treatment. This helps readers assess both the magnitude and plausibility of the estimates.
From the dynamic model, the counterfactual for a treated unit at event time $j$ is the observed outcome minus the estimated effect:
# Construct counterfactual for treated units coef_lookup <- task_a$results$coefficients %>% select(relative_time, estimate) %>% deframe() counterfactual <- dataset_a %>% filter(!is.na(treatment_time)) %>% mutate( rel_time = time_id - treatment_time, delta_hat = coef_lookup[as.character(rel_time)], delta_hat = ifelse(is.na(delta_hat), 0, delta_hat), outcome_counterfactual = outcome - delta_hat ) # Plot observed vs counterfactual counterfactual_summary <- counterfactual %>% group_by(time_id) %>% summarise( observed = mean(outcome), counterfactual = mean(outcome_counterfactual), .groups = "drop" ) ggplot(counterfactual_summary, aes(x = time_id)) + geom_line(aes(y = observed, color = "Observed"), linewidth = 0.8) + geom_line(aes(y = counterfactual, color = "Counterfactual"), linetype = "dashed", linewidth = 0.8) + geom_vline(xintercept = 10, linetype = "dotted", color = "red") + labs( title = "Observed vs Counterfactual Outcomes (Treated Units)", x = "Time Period", y = "Mean Outcome", color = NULL ) + theme_minimal()
The gap between the observed and counterfactual lines after the treatment date visualizes the estimated treatment effect.
Statistical Inference (Miller Section VIII)
Clustered Standard Errors
Panel event studies typically require clustering standard errors at the unit
level to account for serial correlation within units. When the sandwich
package is installed, estimate_panel_event_study() automatically computes
cluster-robust standard errors via sandwich::vcovCL(). The cluster
parameter controls the clustering variable and defaults to the unit ID:
# Cluster-robust SEs at the unit level (the default) task_a <- estimate_panel_event_study( task_a, method = "dynamic_twfe", leads = 5, lags = 5, cluster = "unit_id" ) # Cluster at a different level (e.g., state) task_a <- estimate_panel_event_study( task_a, method = "dynamic_twfe", leads = 5, lags = 5, cluster = "state_id" )
If sandwich is not installed, the function falls back to OLS standard errors
with an informative message. Install it with install.packages("sandwich").
How Many Clusters Are Enough?
Miller discusses the well-known problem that clustered standard errors are unreliable when the number of clusters is small. His rule of thumb, drawing on the simulation evidence in the literature: you need approximately 42--50 or more clusters for cluster-robust inference to be reliable.
When the number of clusters is small, alternatives include:
- Wild cluster bootstrap (Cameron, Gelbach, & Miller, 2008) --- available
via the
fwildclusterbootpackage - Randomization inference (Fisher, 1935)
Practical Checklist
Drawing on Miller (2023), here is a checklist for panel event study research:
- Classify your setting. Single cohort or staggered? Never-treated controls available?
- Start with the dynamic specification. Plot the event-time coefficients before collapsing to a static estimate.
- Inspect pre-trends. Report pre-treatment coefficients visually and with a joint test.
- Choose the reference period deliberately.
base_period = -1is standard; consider whether anticipation effects warrant an earlier reference. - Report endpoint binning. Be transparent about which event times are binned and test sensitivity to different window widths.
- Use appropriate estimators for staggered designs. If treatment timing varies and effects may be heterogeneous, use Sun & Abraham or similar heterogeneity-robust estimators instead of TWFE.
- Report counterfactual outcomes. Show what would have happened absent treatment.
- Cluster standard errors appropriately. Cluster at the unit level and ensure you have enough clusters (42--50+) for reliable inference.
- Test robustness. Vary the window width, reference period, and estimator. Report results for multiple specifications.
References
-
Miller, D. L. (2023). An Introductory Guide to Event Study Models. Journal of Economic Perspectives, 37(2), 203--230. doi:10.1257/jep.37.2.203
-
Sun, L., & Abraham, S. (2021). Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects. Journal of Econometrics, 225(2), 175--199. doi:10.1016/j.jeconom.2020.09.006
-
MacKinlay, A. C. (1997). Event Studies in Economics and Finance. Journal of Economic Literature, 35(1), 13--39.
-
Cameron, A. C., Gelbach, J. B., & Miller, D. L. (2008). Bootstrap-Based Improvements for Inference with Clustered Errors. Review of Economics and Statistics, 90(3), 414--427.
-
Rambachan, A., & Roth, J. (2023). A More Credible Approach to Parallel Trends. Review of Economic Studies, 90(5), 2555--2591.
Try the EventStudy package in your browser
Any scripts or data that you put into this service are public.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.