mad-sdid 0.1.0

Synthetic Difference in Differences (Arkhangelsky et al.)

SDID — Synthetic Difference in Differences

⚠️ Pre-release — This implementation is not fully tested against the paper's full simulation suite. The API and numerical defaults are subject to breaking changes without notice. Use at your own risk.

Python implementation of the synthetic difference-in-differences estimator from Arkhangelsky, Athey, Hirshberg, Imbens & Wager (2021).

Quick start (cloned repo with test data)

import pandas as pd
from mad_sdid import synthdid_estimate, panel_matrices

panel = pd.read_csv("tests/data/california_prop99.csv", sep=";")
setup = panel_matrices(panel, unit="State", time="Year",
                       outcome="PacksPerCapita", treatment="treated")
result = synthdid_estimate(setup["Y"], setup["N0"], setup["T0"])
print(f"tau_hat = {result.estimate:.2f}")

# Jackknife standard error
import numpy as np
from mad_sdid.inference import vcov_synthdid
se = np.sqrt(vcov_synthdid(result, method="jackknife"))
print(f"SE = {se:.2f}")

Installation

pip install mad-sdid

Dev extras (cvxpy reference solver):

pip install "mad-sdid[dev]"

Using with your own data

Your panel must be a balanced CSV with the following columns:

• unit: unit identifier
• time: time period
• outcome: outcome variable
• treatment: binary indicator (0 = control, 1 = treated)

All treated units must share the same treatment onset time.

import pandas as pd
import numpy as np
from mad_sdid import synthdid_estimate, panel_matrices
from mad_sdid.inference import vcov_synthdid

panel = pd.read_csv("my_data.csv")
setup = panel_matrices(panel, unit="unit", time="time",
                       outcome="outcome", treatment="treatment")

result = synthdid_estimate(setup["Y"], setup["N0"], setup["T0"])
se = np.sqrt(vcov_synthdid(result, method="jackknife"))

print(f"tau_hat = {result.estimate:.2f}")
print(f"SE = {se:.2f}")
print(f"95% CI = ({result.estimate - 1.96 * se:.2f}, {result.estimate + 1.96 * se:.2f})")

Input format

unit	time	outcome	treatment
Alabama	1970	89.8	0
California	1970	123.0	0
...	...	...	...
California	1989	76.5	1

The first N0 rows of the outcome matrix are control units, and the first T0 columns are pre-treatment periods — done automatically by panel_matrices().

Reference

Arkhangelsky, D., Athey, S., Hirshberg, D. A., Imbens, G. W., & Wager, S. "Synthetic Difference in Differences." American Economic Review, 2021. arXiv:1812.09970