scinference 0.1.0

Inference methods for synthetic control and related methods

scinference

A Python package for inference methods for synthetic control and related methods.

This is a Python port of the R scinference package by Victor Chernozhukov, Kaspar Wuthrich, and Yinchu Zhu.

Installation

pip install scinference

Validation Against R Package

All results in this README are generated using data from the original R package to demonstrate that Python and R produce identical results.

---

Example 1: Conformal Inference

Conformal inference works with a small number of post-treatment periods and provides valid p-values and confidence intervals.

Data

We use simulated data generated by the R package with set.seed(12345):

• J = 50 control units
• T0 = 50 pre-treatment periods
• T1 = 5 post-treatment periods
• True treatment effect = 2

import numpy as np
from scinference import scinference

# Load data (generated by R for exact comparison)
# Y0: control outcomes (T x J matrix)
# Y1: treated outcome (T x 1 vector)
T0, T1 = 50, 5

Testing a Null Hypothesis

We test the null hypothesis H0: theta = (4, 4, 4, 4, 4)'. Since the true effect is 2, this is a false null and we expect to reject it.

# Synthetic Control with Moving Block permutations
result_sc = scinference(Y1, Y0, T1=T1, T0=T0, theta0=4,
                        estimation_method="sc", permutation_method="mb")

# Difference-in-Differences
result_did = scinference(Y1, Y0, T1=T1, T0=T0, theta0=4,
                         estimation_method="did", permutation_method="mb")

# Constrained Lasso
result_classo = scinference(Y1, Y0, T1=T1, T0=T0, theta0=4,
                            estimation_method="classo", permutation_method="mb")

Results: P-values for H0: theta = 4 (Moving Block Permutations)

Method	Python	R	Match
Synthetic Control	0.018182	0.018182	YES
Difference-in-Diff	0.036364	0.036364	YES
Constrained Lasso	0.036364	0.036364	YES

All three methods reject the false null at the 5% level.

Pointwise Confidence Intervals

Compute 90% pointwise confidence intervals using the synthetic control method:

result_ci = scinference(Y1, Y0, T1=T1, T0=T0,
                        estimation_method="sc",
                        ci=True,
                        ci_grid=np.arange(-2, 8.1, 0.1),
                        alpha=0.1)

print("90% Confidence Intervals:")
for t in range(T1):
    print(f"  Period {t+1}: [{result_ci['lb'][t]:.2f}, {result_ci['ub'][t]:.2f}]")

Results: 90% Pointwise Confidence Intervals

Period	Python LB	R LB	Python UB	R UB	Match
1	0.80	0.80	4.10	4.10	YES
2	1.50	1.50	4.60	4.60	YES
3	0.40	0.40	4.00	4.00	YES
4	1.80	1.80	5.20	5.20	YES
5	-0.50	-0.50	2.60	2.60	YES

The true treatment effect (2) is covered by the confidence intervals in all periods.

---

Example 2: T-test Based Inference

The t-test method requires a larger number of post-treatment periods and provides estimates of the Average Treatment Effect on the Treated (ATT).

Data

Data generated by R with set.seed(12345):

• J = 30 control units
• T0 = 30 pre-treatment periods
• T1 = 30 post-treatment periods
• True ATT = 2

# T-test with K=2 cross-fits
result = scinference(Y1, Y0, T1=T1, T0=T0,
                     inference_method="ttest", K=2, alpha=0.1)

print(f"ATT estimate: {result['att']:.4f}")
print(f"Standard Error: {result['se']:.4f}")
print(f"90% CI: [{result['lb']:.4f}, {result['ub']:.4f}]")

Results: T-test with Synthetic Control (K=2)

Metric	Python	R	Match
ATT	1.488715	1.488715	YES
Standard Error	0.292220	0.292220	YES
90% CI Lower	-0.356287	-0.356287	YES
90% CI Upper	3.333716	3.333716	YES

Results: T-test with Synthetic Control (K=3)

result_K3 = scinference(Y1, Y0, T1=T1, T0=T0,
                        inference_method="ttest", K=3, alpha=0.1)

Metric	Python	R	Match
ATT	1.526818	1.526818	YES
Standard Error	0.194858	0.194858	YES
90% CI Lower	0.957835	0.957835	YES
90% CI Upper	2.095801	2.095801	YES

Results: T-test with Difference-in-Differences (K=2)

result_did = scinference(Y1, Y0, T1=T1, T0=T0,
                         inference_method="ttest",
                         estimation_method="did", K=2, alpha=0.1)

Metric	Python	R	Match
ATT	1.624656	1.624656	YES
Standard Error	0.192063	0.192063	YES
90% CI Lower	0.412019	0.412019	YES
90% CI Upper	2.837293	2.837293	YES

All methods produce estimates close to the true ATT of 2, with the true value covered by the confidence intervals.

---

API Reference

Main Function

scinference(Y1, Y0, T1, T0,
            inference_method="conformal",
            alpha=0.1,
            ci=False,
            theta0=0,
            estimation_method="sc",
            permutation_method="mb",
            ci_grid=None,
            n_perm=5000,
            K=2)

Parameters

Parameter	Type	Default	Description
Y1	array	Required	Outcome for treated unit (T x 1)
Y0	array	Required	Outcomes for control units (T x J)
T1	int	Required	Number of post-treatment periods
T0	int	Required	Number of pre-treatment periods
inference_method	str	"conformal"	"conformal" or "ttest"
alpha	float	0.1	Significance level
ci	bool	False	Compute confidence intervals (conformal)
theta0	float/array	0	Null hypothesis value
estimation_method	str	"sc"	"did", "sc", or "classo"
permutation_method	str	"mb"	"mb" (moving block) or "iid"
ci_grid	array	None	Grid for CI computation
n_perm	int	5000	Permutations for IID method
K	int	2	Number of cross-fits (t-test)

Returns

Conformal inference:

• p_val: p-value for the null hypothesis
• lb: lower bounds of pointwise CIs (if ci=True)
• ub: upper bounds of pointwise CIs (if ci=True)

T-test:

• att: Average Treatment Effect on the Treated
• se: Standard error
• lb: Lower bound of confidence interval
• ub: Upper bound of confidence interval

Estimation Methods

Method	Description
did	Difference-in-differences (simple average of controls)
sc	Synthetic control (Abadie et al.) - constrained weighted average
classo	Constrained lasso - L1-penalized with sum-to-one constraint

---

References

• Chernozhukov, V., Wuthrich, K., & Zhu, Y. (2021). "An Exact and Robust Conformal Inference Method for Counterfactual and Synthetic Controls." Journal of the American Statistical Association. arXiv:1712.09089

• Chernozhukov, V., Wuthrich, K., & Zhu, Y. (2019). "Practical and robust t-test based inference for synthetic control and related methods." arXiv:1812.10820

---

License

GPL-3.0