Event Study Cars

Event Study: Cumulative Abnormal Returns (CARs)

A complete methodology reference for computing publication-quality CARs with robust test statistics, matching the rigor of Kaspereit's eventstudy2 (v3.2b) for Stata. This skill is generic — applicable to any market, asset class, or event type.

Use the shipped engine first (do not rewrite it)

scripts/eventstudy.py is a complete, runnable Python replication of eventstudy2, validated against the Stata package to floating-point precision (AR ~1e-8, CAR ~6e-8, CAAR and the implemented test statistics ~1e-7) on a generic CRSP sample across all four models (FM, COMEAN, MA, RAW). It is generic — all column names, the model, windows, thin-trading, and log handling are CLI flags. When a user wants CARs computed, run this engine; do not author a new pipeline.

python scripts/eventstudy.py --selftest          # synthetic self-check, no inputs
python scripts/eventstudy.py \
    --returns returns.csv --market market.csv --events events.csv \
    --id-col permno --ret-col ret --event-date-col event_date --mkt-col vwretd \
    --model FM --car-windows "-1,1;-5,5;-10,10" \
    --eswlb -250 --eswub -30 --evwlb -10 --evwub 10 --out-dir out/

Inputs are CSV/Parquet: returns (id, date, ret), market/factors (date, mkt[, factors]), events (id, event_date). Outputs: ar_panel.csv, car_panel.csv, test_statistics.csv. Requires numpy/pandas/scipy. Run --help for all flags (--factor-cols smb,hml, --model MA, --no-thin-trading, ...). The sections below document the methodology the engine implements; read them to audit, extend, or port it.

Methodology Overview: The 8-Step Pipeline

Step 1: Build Trading Calendar (Dateline)

Construct a master list of valid trading dates from the security returns file.

1. Collect all unique dates on which at least one security has a non-missing return (or, if using a factor model, dates where market/factor returns exist).
2. Count the number of securities with valid returns on each date.
3. Optionally drop weekends (delweekend).
4. Apply dateline_threshold: drop dates where the count of return observations falls below threshold × mean(daily_count). A threshold of 0.2 works well for international samples with heterogeneous holidays.
5. The resulting date vector is the dateline — all downstream windows are defined in dateline time (relative trading days), not calendar time.

Step 2: Map Event Dates to Nearest Valid Trading Day

For each event:

1. Find the nearest dateline date on or after the event date.
2. If the shift exceeds max_shift calendar days (default: 3), exclude the event entirely — do not silently map it to a distant trading day.
3. Events with missing dates, or dates outside the dateline range, are also excluded and logged with the reason.

Step 3: Construct Estimation and Event Windows

For each firm-event pair, define windows in relative trading time (offsets from the event day on the dateline):

• Estimation window: [esw_lb, esw_ub] — default [-250, -30].
• Event window: [evw_lb, evw_ub] — determined by the widest CAR window requested.
• Enforce a gap between the estimation and event windows to prevent event contamination of the benchmark model.

Exclusion checks (per firm-event):

• Insufficient estimation-window observations (fewer than min_esw_obs, default 120).
• Insufficient event-window observations.
• IPO/delisting guard: if the stock's first observed return date falls after evw_lb or last observed return date falls before evw_ub, exclude the firm-event. These are survivorship-biased observations.

Step 4: Apply Thin-Trading Adjustment

For markets with non-trivially thin trading (most markets outside US mega-caps), apply the Maynes-Rumsey (1993) trade-to-trade transformation by default.

Read references/thin_trading.md for the complete transformation, including the cum_periods construction, the regression specification with nocons, and the boundary contamination guard.

Summary: Non-trading days accumulate into the next trading day's return. All variables (returns, factors, intercept) are divided by sqrt(cum_periods). OLS is run with nocons because the intercept regressor 1/sqrt(d) replaces the standard constant. This is a GLS correction for the heteroscedasticity introduced by multi-period returns.

Step 5: Run OLS and Compute STDF

For each firm-event pair, estimate the benchmark model over the estimation window and compute the standard deviation of forecast (STDF) for every observation (estimation + event window).

Read references/estimation_models.md for model specifications (RAW, COMEAN, MA, FM, BHAR).

STDF (Theil 1971 prediction error correction):

For each observation t, the forecast standard deviation is:

STDF_it = sigma_hat_i * sqrt(1 + x'_t (X'X)^{-1} x_t)

where x_t is the regressor vector at time t, X is the estimation-window design matrix, and sigma_hat_i = sqrt(SSR / (T_i - 2 - df)) is the OLS residual standard deviation. df is the number of additional factors beyond the market (0 for market model, 2 for FF3, etc.).

The STDF accounts for both the inherent noise in returns (sigma) and the estimation uncertainty in the model coefficients (which grows when event-window factor values are far from estimation-window means).

Python: after numpy.linalg.lstsq, compute the hat matrix H = X @ inv(X'X) @ X' and h_t = x'_t @ inv(X'X) @ x_t for each event-window observation. Then STDF_t = sigma_hat * sqrt(1 + h_t).

Step 6: Compute Abnormal Returns

AR_it = R_it - predicted_it

where predicted_it comes from the estimated benchmark model applied to event-window factor values.

Critical rule: do NOT zero-fill missing event-window returns. A missing return means the stock did not trade — setting it to zero biases CARs toward zero for illiquid stocks. Leave it as NaN and let the accumulation step handle the count of valid ARs.

Step 7: Accumulate CARs

For each requested CAR window [lb, ub] and each firm-event:

CAR_i = sum of AR_it for t in [lb, ub] where AR_it is not NaN

Boundary contamination guard (from eventstudy2):

• If the first day of the CAR window has cum_periods > 1, the return on that day spans back before the window start. Set CAR = NaN.
• If the last day of the CAR window has a missing AR, the firm-event lacks coverage at the window boundary. Set CAR = NaN.
• For AAR (day-by-day) output: any day with cum_periods > 1 has its AR set to NaN (the multi-period return cannot be attributed to a single day).

Track n_valid_ar per CAR: the count of non-NaN ARs in the window. A valid CAR should have n_valid_ar == window_length. CARs with fewer valid days should be flagged or excluded depending on the analysis.

Step 8: Compute Test Statistics

Compute at minimum: Patell (1976), BMP (Boehmer et al. 1991), Kolari-Pynnonen adjusted BMP, and the generalized sign test (Cowan 1992). For maximum rigor, compute all 13 tests.

Read references/test_statistics.md for exact formulas, null hypotheses, distributions, and Python implementation notes for all 13 tests.

Read references/kolari_pynnonen.md for the cross-correlation adjustment procedure (ADJ factor) and the GRANK-T test.

Test statistics are reported at two levels:

• AAR level: one test statistic per event day (tests whether the average AR across firms is significantly different from zero on that day).
• CAAR level: one test statistic per CAR window (tests whether the cumulative average AR is significantly different from zero over the window).

Model Selection

Read references/estimation_models.md for full mathematical specifications.

Default: FM with market model (1 factor) for short-window studies.

Critical Rules

1. NEVER replace missing event-window returns with zero. This biases CARs toward zero for illiquid stocks. The only exception is BHAR models, which assume continuous holding.

2. NEVER compute CARs when the stock's first/last trading date falls inside the event window (IPO/delisting bias).

3. NEVER sum CARs when a boundary day has cum_periods > 1 — the return spans outside the intended window.

4. NEVER run OLS with a standard constant when using the trade-to-trade transformation. Use nocons with 1/sqrt(cum_periods) as the intercept regressor.

5. NEVER report CARs without at least one parametric and one non-parametric test statistic.

6. NEVER mix log and simple returns between the LHS and RHS of the market model. If stock returns are in logs, factor returns must also be in logs (or convert both via ln(1+R) before estimation). Jensen's inequality creates bias otherwise.

Output Contract

A valid CAR output dataset must contain:

Identifiers (column names vary by project):

• firm_id, event_id, event_date

Estimation diagnostics (per firm-event, per model):

• alpha, beta (per factor), nobs, r2, sigma_hat

Per CAR window per model:

• car_value — NaN if invalid
• n_valid_ar — count of non-NaN ARs in the window

Exclusion reason (per firm-event):

• insufficient_est_obs, insufficient_evt_obs, ipo_in_window, delisting_in_window, event_off_dateline, boundary_contamination

Test statistics (separate output):

• AAR-level and CAAR-level tests, each with test statistic value and p-value
• Minimum: Patell, BMP, Kolari-Pynnonen adjusted BMP, generalized sign test

Sensible Defaults

These can be overridden by the user:

Reference Files

Read these for detailed formulas and implementation guidance:

Validation Script

After computing CARs, run scripts/validate_cars.py to check output integrity:

python scripts/validate_cars.py --car-file output.parquet \
    --firm-col firm_id --event-col event_id \
    --car-cols CAR_m1_p1,CAR_m5_p5 \
    --exclusion-col exclusion_reason \
    --nar-cols n_ar_m1_p1,n_ar_m5_p5 \
    --window-lengths 3,11

The script checks: no CARs where exclusion reasons exist, valid AR counts match window lengths, required columns are present, and test statistic files exist alongside the CAR panel.