Event Study: Dynamic Effect Estimation and Coefficient Plots

Structure of This Article

Principles: Model specification of the event study
Intuition: The economic meaning of dynamic effects
Code: Complete Stata implementation and standard coefficient plots

Layer 1: Principles

The Event Study Model

Y_{it} = \alpha_i + \lambda_t + \sum_{k=-K}^{L} \beta_k \cdot D_{i,t-k} + X_{it}'\gamma + \varepsilon_{it}

$D_{i,t-k}$ : Leads and lags of the treatment indicator
$\beta_k$ : Dynamic treatment effect at period $k$
The base period (typically $k = -1$ ) is omitted, with $\beta_{-1} = 0$

Interpreting the Coefficients

$k < 0$ (leads/pre-treatment): Should be close to zero (parallel trends)
$k = 0$ : Immediate effect
$k > 0$ (lags/post-treatment): Lagged effects

Layer 2: Intuition

The event study method answers the question: Do treatment effects vary over time?

In policy evaluation, this is crucial:

Minimum wage policies may have no short-run effects but reduce employment in the long run
Environmental regulations may immediately raise costs but gradually generate innovation benefits

The coefficient plot is the standard visualization tool for presenting this dynamic process.

Layer 3: Stata Code

// ═══════════════════════════════════════════════
// Complete Event Study Implementation
// ═══════════════════════════════════════════════
 
clear all
set seed 98765
 
local N = 200
local T = 20
local treat_time = 10
 
set obs `=`N'*`T''
gen id = ceil(_n/`T')
bysort id: gen t = _n
gen treat = (id > `=`N'/2')
 
// Dynamic treatment effects
gen tau = 0
replace tau = 0.5*(t - `treat_time' + 1) if treat & t >= `treat_time'
gen y = 2 + 0.1*t + tau + rnormal(0, 1)
 
// Event time
gen rel_time = t - `treat_time'
 
// Generate dummy variables
tab rel_time if treat, gen(D)
// Omit the base period rel_time = -1
 
reghdfe y D*, absorb(id t) cluster(id)
 
coefplot, vertical drop(_cons) ///
    yline(0) xline(9.5, lpattern(dash) lcolor(red)) ///
    title("Event Study: Dynamic Treatment Effects") ///
    xtitle("Relative Period") ytitle("Coefficient Estimate")

References

Sun, L., & Abraham, S. (2021). Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects. Journal of Econometrics, 225(2), 175-199.
Borusyak, K., Jaravel, X., & Spiess, J. (2024). Revisiting Event-Study Designs. Review of Economic Studies.