Staggered DID: TWFE Bias and New Estimators (CS/SA/BJS)

Article Structure

Principles: Why TWFE is biased under staggered treatment
Intuition: An intuitive understanding of the negative weighting problem
Code: A comparative implementation of CS/SA/BJS estimators in Stata

Layer 1: Principles

Why is TWFE biased?

Under the standard staggered treatment setting, the TWFE estimator is:

Y_{it} = \alpha_i + \lambda_t + \tau \cdot D_{it} + \varepsilon_{it}

where $D_{it} = \mathbf{1}[t \geq G_i]$ , and $G_i$ is the time when unit $i$ first receives treatment.

The Problem: TWFE's $\hat{\tau}$ is a weighted average of all $2 \times 2$ DID estimators, but the weights can be negative!

\hat{\tau}_{TWFE} = \sum_g \sum_t w_{g,t} \cdot \tau_{g,t}

When $w_{g,t} < 0$ , even if all $\tau_{g,t} > 0$ , $\hat{\tau}_{TWFE}$ can be negative or severely deviate from the true ATT.

Three New Estimators

Estimator	Core Idea	Control Group Definition
Callaway & Sant'Anna (2021)	Estimate separately by cohort-time, then aggregate	Never-treated + not-yet-treated
Sun & Abraham (2021)	Interaction-weighted estimator	Never-treated
Borusyak, Jaravel & Spiess (2024)	Imputation method, first estimate $Y(0)$ , then take differences	Never-treated + not-yet-treated

Layer 2: Intuition

An Intuitive Understanding of Negative Weights

Imagine three states implementing a policy in 2010, 2012, and 2014, respectively. When TWFE estimates the effect for the 2012 state, it uses the states already treated in 2010 as the "control group"—but these states have already received treatment!

If the effects for early-treated states are growing over time, using them as "controls" will underestimate the effects for later-treated groups, potentially even producing negative weights.

Layer 3: Stata Code

// ═══════════════════════════════════════════════
// Staggered DID: TWFE vs CS vs SA
// ═══════════════════════════════════════════════
 
clear all
set seed 11111
 
// Simulate staggered treatment data
local N = 300
local T = 15
set obs `=`N'*`T''
gen id = ceil(_n/`T')
bysort id: gen t = _n + 2005
 
gen treat_time = .
replace treat_time = 2010 if id <= 100
replace treat_time = 2012 if id > 100 & id <= 200
 
gen treated = (t >= treat_time) if treat_time != .
replace treated = 0 if treat_time == .
 
// Heterogeneous treatment effects
gen tau = 0
replace tau = 2 if treated == 1 & treat_time == 2010
replace tau = 4 if treated == 1 & treat_time == 2012
gen y = 1 + 0.5*t + tau + rnormal(0, 1)
 
// ═══ TWFE (biased) ═══════════════════════════
reghdfe y treated, absorb(id t) cluster(id)
 
// ═══ Callaway & Sant'Anna ═══════════════════
gen gvar = treat_time
replace gvar = 0 if treat_time == .
csdid y, ivar(id) time(t) gvar(gvar) agg(simple)
csdid y, ivar(id) time(t) gvar(gvar) agg(event)
csdid_plot

The complete code file can be downloaded from the code library.

References

Callaway, B., & Sant'Anna, P. H. C. (2021). Difference-in-Differences with Multiple Time Periods. Journal of Econometrics, 225(2), 200-230.
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: Robust and Efficient Estimation. Review of Economic Studies.
de Chaisemartin, C., & D'Haultfœuille, X. (2020). Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects. AER, 110(9), 2964-2996.