Event Study LP

MacroEconometricModels.jl provides two LP-based event study estimators for causal inference in panel settings: the Event Study LP (Jorda 2005; Acemoglu, Naidu, Restrepo & Robinson 2019) and the LP-DiD estimator (Dube, Girardi, Jorda & Taylor 2025) with clean control samples, switching indicator treatment, and time-only fixed effects. The package achieves full parity with Stata lpdid v1.0.2.

• Event Study LP: Horizon-by-horizon local projections with switching indicator treatment and time-only FE
• LP-DiD: Clean control sample restrictions (absorbing/non-absorbing/one-off), pre-mean differencing, IPW reweighting, pooled estimates
• DDCG dataset: Built-in Acemoglu et al. (2019) democracy-GDP panel (184 countries, 1960–2010)
• Panel utilities: panel_lag, panel_lead, panel_diff for within-group transformations
• Diagnostics: Pre-trend tests and HonestDiD sensitivity analysis

using MacroEconometricModels, Random, DataFrames
Random.seed!(42)

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Quick Start

Recipe 1: Standard Event Study LP

N, T_per = 50, 20
df = DataFrame(
    group = repeat(1:N, inner=T_per),
    time = repeat(1:T_per, outer=N),
    outcome = randn(N * T_per) .+ [i <= 25 && t >= 10 ? 1.0 : 0.0
        for i in 1:N for t in 1:T_per],
    treat = Float64.([i <= 25 ? 10 : 0 for i in 1:N for _ in 1:T_per])
)
pd = xtset(df, :group, :time)
eslp = estimate_event_study_lp(pd, :outcome, :treat, 5; leads=3, lags=2)
report(eslp)

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Recipe 2: LP-DiD with absorbing treatment

N, T_per = 50, 20
df = DataFrame(
    group = repeat(1:N, inner=T_per),
    time = repeat(1:T_per, outer=N),
    outcome = randn(N * T_per) .+ [i <= 25 && t >= 10 ? 1.0 : 0.0
        for i in 1:N for t in 1:T_per],
    treat = Float64.([i <= 25 ? 10 : 0 for i in 1:N for _ in 1:T_per])
)
pd = xtset(df, :group, :time)

r = estimate_lp_did(pd, :outcome, :treat, 5; pre_window=3, ylags=2)
report(r)

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Recipe 3: LP-DiD on DDCG dataset

# Democracy and GDP: Acemoglu et al. (2019)
ddcg = load_example(:ddcg)
r = estimate_lp_did(ddcg, :y, :dem, 10; pre_window=5, ylags=1)
report(r)

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plot_result(r; title="Democracy -> GDP (DDCG)")

Recipe 4: LP-DiD with PMD and IPW reweighting

ddcg = load_example(:ddcg)

# Pre-mean differencing + inverse probability weighting
r_pmd = estimate_lp_did(ddcg, :y, :dem, 10; pre_window=5, pmd=:max, reweight=true)
report(r_pmd)

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Recipe 5: Pooled estimates

ddcg = load_example(:ddcg)

r = estimate_lp_did(ddcg, :y, :dem, 10;
    post_pooled=(0, 5),   # Average effect over h=0,...,5
    pre_pooled=(1, 5)     # Pre-treatment placebo over h=-5,...,-1
)
report(r)

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Model Specification

Both estimators run separate regressions for each event-time horizon $h \in \{-K, \ldots, -1, 0, 1, \ldots, H\}$:

\[Y_{i,t+h} - Y_{i,t-1} = \gamma_t^h + \beta_h \, \Delta D_{it} + \mathbf{X}_{it}'\boldsymbol{\delta}^h + \varepsilon_{i,t+h}\]

where:

• $Y_{i,t+h} - Y_{i,t-1}$ is the long-differenced outcome (absorbs unit fixed effects)
• $\Delta D_{it} = D_{it} - D_{i,t-1}$ is the switching indicator (equals 1 only at treatment onset)
• $\gamma_t^h$ is a time fixed effect (absorbed by within-time demeaning)
• $\mathbf{X}_{it}$ includes lagged outcomes $L_1.Y, \ldots, L_k.Y$, differenced lags $\Delta Y_{t-l}$, and optional covariates
• $\beta_h$ is the dynamic treatment effect at horizon $h$

The reference period $h = -1$ is normalized to zero.

Event Study LP

The standard estimator uses all switching ($\Delta D = 1$) and control ($D = 0$) observations at each horizon:

N, T_per = 50, 20
df = DataFrame(
    group = repeat(1:N, inner=T_per),
    time = repeat(1:T_per, outer=N),
    outcome = randn(N * T_per) .+ [i <= 25 && t >= 10 ? 1.0 : 0.0
        for i in 1:N for t in 1:T_per],
    treat = Float64.([i <= 25 ? 10 : 0 for i in 1:N for _ in 1:T_per])
)
pd = xtset(df, :group, :time)

eslp = estimate_event_study_lp(pd, :outcome, :treat, 5;
    leads=3,             # Pre-treatment horizons K
    lags=2,              # Lagged outcome controls
    cluster=:unit,       # :unit, :time, or :twoway
    conf_level=0.95
)
report(eslp)

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plot_result(eslp)

The estimate_event_study_lp function runs $K + H + 1$ separate OLS regressions (one per event-time horizon), each with cluster-robust standard errors. The resulting coefficients $\beta_h$ trace out the dynamic treatment effect path.

Keyword Arguments

Return Value (EventStudyLP{T})

LP-DiD (Dube et al. 2025)

The LP-DiD estimator adds clean control sample (CCS) restrictions. At each horizon $h$, the control group contains only units whose treatment status does not change between $t$ and $t + h$. This prevents already-treated units from contaminating the control group under heterogeneous treatment effects.

Clean Control Samples

Three CCS specifications match the Stata lpdid package:

Absorbing treatment (default): A $(i, t)$ pair belongs to CCS at horizon $h$ if the unit is switching ($\Delta D_{it} = 1$) or treatment status remains at zero through $t + h$:

ddcg = load_example(:ddcg)
r = estimate_lp_did(ddcg, :y, :dem, 10)  # Absorbing is default
report(r)

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Non-absorbing treatment: Treatment may reverse. A pair belongs to CCS if no switches occurred in the stabilization window of $L$ periods before $t$:

r = estimate_lp_did(ddcg, :y, :dem, 10; nonabsorbing=5)
nothing # hide

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One-off treatment: Treatment lasts exactly one period. Requires nonabsorbing:

r = estimate_lp_did(ddcg, :y, :dem, 10; nonabsorbing=3, oneoff=true)
nothing # hide

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Pre-Mean Differencing (PMD)

Instead of long differencing $Y_{t+h} - Y_{t-1}$, PMD uses the average of pre-treatment outcomes as baseline. This reduces noise from a single pre-treatment period:

\[Y_{i,t+h} - \bar{Y}_{i,\text{pre}} = \gamma_t^h + \beta_h \, \Delta D_{it} + \mathbf{X}_{it}'\boldsymbol{\delta}^h + \varepsilon_{i,t+h}\]

where:

• $\bar{Y}_{i,\text{pre}}$ is the average of $Y_{i,t-1}, Y_{i,t-2}, \ldots$ over a window of pre-treatment periods

ddcg = load_example(:ddcg)

# Use cumulative pre-treatment mean
r = estimate_lp_did(ddcg, :y, :dem, 10; pmd=:max)

# Use moving average of k pre-treatment periods
r = estimate_lp_did(ddcg, :y, :dem, 10; pmd=3)
nothing # hide

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IPW Reweighting

Inverse probability weights ensure equally weighted ATE across time periods, correcting for compositional changes in the treatment-control balance:

ddcg = load_example(:ddcg)
r = estimate_lp_did(ddcg, :y, :dem, 10; reweight=true)
nothing # hide

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Pooled Estimates

Pooled regressions average the left-hand side over a window of horizons, producing a single average treatment effect:

ddcg = load_example(:ddcg)
r = estimate_lp_did(ddcg, :y, :dem, 10;
    post_pooled=(0, 5),   # Average effect over h=0,...,5
    pre_pooled=(1, 3)     # Pre-treatment placebo over h=-3,...,-1
)
report(r)

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The pooled estimates are stored in r.pooled_post and r.pooled_pre as named tuples with fields coef, se, ci_lower, ci_upper, and nobs.

Full Keyword Arguments

Return Value (LPDiDResult{T})

DDCG Dataset

The built-in DDCG dataset contains 184 countries from 1960–2010 with log GDP per capita and a binary democracy indicator from Acemoglu, Naidu, Restrepo & Robinson (2019):

ddcg = load_example(:ddcg)

r = estimate_lp_did(ddcg, :y, :dem, 25;
    pre_window=5, ylags=1, post_pooled=(0, 25))
report(r)

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The dataset is organized as a balanced panel with country-year observations. The dem variable records democratic transitions (0 to 1) and reversals (1 to 0), making this a non-absorbing treatment setting suitable for nonabsorbing CCS.

Panel Utilities

Within-group lag, lead, and difference operations for PanelData:

ddcg = load_example(:ddcg)

# Compute lag/lead/diff vectors
l1 = panel_lag(ddcg, :y, 1)     # L1.y
f1 = panel_lead(ddcg, :y, 1)    # F1.y
dy = panel_diff(ddcg, :y)       # delta y = y - L1.y

# Add as new columns (returns new PanelData)
ddcg2 = add_panel_lag(ddcg, :y, 1)    # adds "lag1_y"
ddcg3 = add_panel_lead(ddcg, :y, 1)   # adds "lead1_y"
ddcg4 = add_panel_diff(ddcg, :y)      # adds "d_y"
nothing # hide

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These functions respect panel group boundaries –- lags, leads, and differences do not cross from one unit to another.

Clustering

Both estimators support three clustering options for standard error computation:

• :unit (default) –- accounts for serial correlation within units
• :time –- accounts for cross-sectional correlation within periods
• :twoway –- two-way clustering (Cameron, Gelbach & Miller 2011): $V_{\text{twoway}} = V_{\text{unit}} + V_{\text{time}} - V_{\text{het}}$

ddcg = load_example(:ddcg)
r = estimate_lp_did(ddcg, :y, :dem, 10; cluster=:twoway)
report(r)

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Two-way clustering is recommended when both serial correlation (within units) and cross-sectional correlation (across units within periods) are present, as in macroeconomic panels where common shocks affect all countries simultaneously.

Diagnostics

Pre-Trend Test

Joint Wald test that all pre-treatment coefficients are zero:

\[H_0: \beta_{-K} = \beta_{-K+1} = \cdots = \beta_{-2} = 0\]

where:

• $\beta_k$ is the LP coefficient at event-time $k$

N, T_per = 50, 20
df = DataFrame(
    group = repeat(1:N, inner=T_per),
    time = repeat(1:T_per, outer=N),
    outcome = randn(N * T_per) .+ [i <= 25 && t >= 10 ? 1.0 : 0.0
        for i in 1:N for t in 1:T_per],
    treat = Float64.([i <= 25 ? 10 : 0 for i in 1:N for _ in 1:T_per])
)
pd = xtset(df, :group, :time)
eslp = estimate_event_study_lp(pd, :outcome, :treat, 5; leads=3, lags=2)

pt = pretrend_test(eslp)

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A high p-value indicates no evidence against parallel trends at the given sample size.

HonestDiD Sensitivity Analysis

Rambachan & Roth (2023) robust confidence intervals under bounded violations of parallel trends:

h = honest_did(eslp; Mbar=1.0)
nothing # hide

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plot_result(h)

The breakdown value $\bar{M}^*$ reports the smallest violation magnitude at which the robust confidence interval includes zero. See Difference-in-Differences for detailed documentation of bacon_decomposition, negative_weight_check, and HonestDiD methodology.

Visualization

plot_result produces interactive D3.js event study plots for both EventStudyLP and LPDiDResult:

N, T_per = 50, 20
df = DataFrame(
    group = repeat(1:N, inner=T_per),
    time = repeat(1:T_per, outer=N),
    outcome = randn(N * T_per) .+ [i <= 25 && t >= 10 ? 1.0 : 0.0
        for i in 1:N for t in 1:T_per],
    treat = Float64.([i <= 25 ? 10 : 0 for i in 1:N for _ in 1:T_per])
)
pd = xtset(df, :group, :time)
eslp = estimate_event_study_lp(pd, :outcome, :treat, 5; leads=3, lags=2)
nothing # hide

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p = plot_result(eslp)
save_plot(p, "event_study.html")

Complete Example

# Load DDCG democracy-GDP dataset (Acemoglu et al. 2019)
ddcg = load_example(:ddcg)

# LP-DiD: effect of democracy on log GDP per capita
r = estimate_lp_did(ddcg, :y, :dem, 25;
    pre_window=5,
    ylags=1,
    post_pooled=(0, 25),
    pre_pooled=(1, 5)
)
report(r)

# Robustness: PMD + reweighting
r_pmd = estimate_lp_did(ddcg, :y, :dem, 25;
    pre_window=5, ylags=1, pmd=:max, reweight=true)
report(r_pmd)

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plot_result(r; title="Democracy -> GDP (LP-DiD, DDCG)")

The baseline LP-DiD specification estimates the causal effect of democratic transitions on log GDP per capita using a switching indicator and clean control samples. The pooled post-treatment estimate averages the dynamic treatment effect over horizons 0 through 25, providing a single summary measure of democracy's long-run GDP impact. The pre-treatment pooled estimate serves as a placebo –- a value near zero supports the parallel trends assumption. The PMD + IPW robustness check uses pre-mean differencing to reduce noise from a single baseline period and inverse probability weighting to ensure equal representation across time periods, confirming that the baseline result is not driven by compositional changes in the sample.

Common Pitfalls

1. Treatment column format: estimate_lp_did auto-detects binary (0/1) vs timing (year values). Mixing formats (e.g., 0, 1, 2019) causes misclassification. Ensure the treatment column is consistently encoded.

2. Small effective samples at long horizons: CCS restrictions reduce the sample at each horizon as more units switch treatment status. Monitor r.nobs_per_horizon and reduce $H$ if counts drop below approximately 30 observations.

3. Combining notyet and nevertreated: These are mutually exclusive. notyet uses units not yet treated at $t+h$ as controls; nevertreated uses only units with $G_i = 0$. Specifying both raises an error.

4. oneoff requires nonabsorbing: One-off treatment is a special case of non-absorbing treatment where the treatment indicator lasts exactly one period. Calling oneoff=true without setting nonabsorbing raises an error.

5. PMD with short pre-treatment windows: pmd=:max uses all available pre-treatment data. With few pre-treatment periods, the average baseline may be noisy. Consider pmd=k with a small $k$ to use a fixed window.

References

• Acemoglu, Daron, Suresh Naidu, Pascual Restrepo, and James A. Robinson. 2019. "Democracy Does Cause Growth." Journal of Political Economy 127 (1): 47–100. DOI

• Cameron, A. Colin, Jonah B. Gelbach, and Douglas L. Miller. 2011. "Robust Inference with Multiway Clustering." Journal of Business & Economic Statistics 29 (2): 238–249. DOI

• Dube, Arindrajit, Daniele Girardi, Oscar Jorda, and Alan M. Taylor. 2025. "A Local Projections Approach to Difference-in-Differences." Journal of Applied Econometrics. DOI

• Jorda, Oscar. 2005. "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review 95 (1): 161–182. DOI

• Rambachan, Ashesh, and Jonathan Roth. 2023. "A More Credible Approach to Parallel Trends." Review of Economic Studies 90 (5): 2555–2591. DOI