Package 'sccic'

Title: Synthetic Control Changes-in-Changes Estimator
Description: Implements the Changes-in-Changes (CIC) estimator of Athey and Imbens (2006) <doi:10.1111/j.1468-0262.2006.00668.x> combined with synthetic control methods. Provides nonparametric estimation of the entire counterfactual distribution of outcomes for a treated group, allowing evaluation of average, quantile, and distributional treatment effects. Synthetic control weights are constructed via elastic net regularization to handle settings with many potential control units.
Authors: Neil Hwang [aut, cre]
Maintainer: Neil Hwang <[email protected]>
License: GPL (>= 3)
Version: 0.1.0
Built: 2026-05-10 06:24:30 UTC
Source: https://github.com/neilhwang/sccic

Help Index

Validate CIC Input Data

Description

Checks for common data issues and issues informative warnings. Called internally by cic when input is potentially problematic. Also available for manual use.

Usage

check_data(y_00, y_01, y_10, y_11)

Arguments

y_00, y_01, y_10, y_11

Numeric vectors of outcomes.

Value

Invisible TRUE. Produces warnings for potential issues.

Check Support Condition

Description

Warns if the treated unit's pre-treatment outcomes fall outside the range of the synthetic control's pre-treatment outcomes, which can cause the CIC distributional transport to extrapolate.

Usage

check_support(x)

Arguments

x

An object of class "sc_cic".

Value

Logical. TRUE if support condition is satisfied.

Changes-in-Changes Estimator

Description

Implements the Changes-in-Changes (CIC) estimator of Athey and Imbens (2006) for the average treatment effect on the treated in a two-group, two-period difference-in-differences setting.

Usage

cic(
  y_00,
  y_01,
  y_10,
  y_11,
  se = TRUE,
  boot = FALSE,
  boot_iters = 500L,
  seed = NULL
)

Arguments

y_00

Numeric vector. Outcomes for the control group in the pre-treatment period.
y_01

Numeric vector. Outcomes for the control group in the post-treatment period.
y_10

Numeric vector. Outcomes for the treated group in the pre-treatment period.
y_11

Numeric vector. Outcomes for the treated group in the post-treatment period.
se

Logical. If TRUE (default), compute analytic standard errors using the asymptotic variance from Theorem 5.1 of Athey and Imbens (2006).
boot

Logical. If TRUE, also compute bootstrap standard errors. Default is FALSE.
boot_iters

Integer. Number of bootstrap iterations. Default 500.
seed

Integer or NULL. Random seed for bootstrap.

Details

The CIC estimator constructs a counterfactual distribution for the treated group in the post-treatment period by applying the transformation:

Y11N,CIC=FY,01−1(FY,00(Y10))Y^{N,CIC}_{11} = F^{-1}_{Y,01}(F_{Y,00}(Y_{10}))

The average treatment effect is then:

τ^CIC=1N11∑Y11,i−1N10∑FY,01−1(FY,00(Y10,i))\hat{\tau}^{CIC} = \frac{1}{N_{11}} \sum Y_{11,i} - \frac{1}{N_{10}} \sum F^{-1}_{Y,01}(F_{Y,00}(Y_{10,i}))

The analytic variance follows Theorem 5.1 of Athey and Imbens (2006):

Var(Nτ^CIC)=Vp/α00+Vq/α01+Vr/α10+Vs/α11Var(\sqrt{N} \hat{\tau}^{CIC}) = V^p/\alpha_{00} + V^q/\alpha_{01} + V^r/\alpha_{10} + V^s/\alpha_{11}

Value

An object of class "cic" containing:

tau

The CIC average treatment effect estimate.
se

Analytic standard error (if se = TRUE).
z

z-statistic.
pval

Two-sided p-value.
counterfactual_mean

Mean of the counterfactual distribution.
tau_did

The standard DID estimate for comparison.
N

Total sample size.
n

Named vector of group sample sizes.
boot_se

Bootstrap standard error (if boot = TRUE).
ecdfs

List of empirical CDF objects for each group.

References

Athey, S. and Imbens, G. W. (2006). Identification and Inference in Nonlinear Difference-in-Differences Models. Econometrica, 74(2), 431–497. doi:10.1111/j.1468-0262.2006.00668.x

Examples

# Workers' compensation example (Meyer, Viscusi, and Durbin 1995)
if (requireNamespace("wooldridge", quietly = TRUE)) {
  data("injury", package = "wooldridge")
  result <- cic(
    y_00 = injury$ldurat[injury$highearn == 0 & injury$afchnge == 0],
    y_01 = injury$ldurat[injury$highearn == 0 & injury$afchnge == 1],
    y_10 = injury$ldurat[injury$highearn == 1 & injury$afchnge == 0],
    y_11 = injury$ldurat[injury$highearn == 1 & injury$afchnge == 1]
  )
  print(result)
}

Leave-One-Out Donor Analysis

Description

Re-estimates SC-CIC dropping one donor at a time to assess sensitivity to individual donors.

Usage

loo_donors(y_treated, y_donors, treatment_period, alpha = 1, seed = 42)

Arguments

y_treated

Numeric vector. Treated unit outcomes.
y_donors

Numeric matrix. Donor unit outcomes.
treatment_period

Integer. First treatment period index.
alpha

Elastic net mixing parameter.
seed

Integer or NULL. Random seed.

Value

A data frame with one row per donor, showing the SC-CIC estimate when that donor is excluded.

Plot Counterfactual Distribution

Description

Plots the empirical CDFs of the four group-period cells used in the CIC estimator, illustrating the distributional transport.

Usage

plot_distributions(x, ...)

Arguments

x

An object of class "cic" or "sc_cic".
...

Additional arguments (currently unused).

Value

Invisible. Called for its side effect of producing a plot.

Q-Q Plot of Treated vs Synthetic Control (Pre-treatment)

Description

Produces a quantile-quantile plot comparing the pre-treatment distributions of the treated unit and the synthetic control. This assesses whether the synthetic control tracks the treated unit's distributional dynamics, not just its mean—a necessary condition for CIC validity. Points on the 45-degree line indicate identical distributions.

Usage

plot_qq(x, ...)

Arguments

x

An object of class "sc_cic" or "cic".
...

Additional arguments passed to plot.

Value

Invisible. Called for its side effect of producing a plot.

Plot Quantile Treatment Effects

Description

Plot Quantile Treatment Effects

Usage

plot_qte(x, probs = seq(0.05, 0.95, 0.05), ...)

Arguments

x

An object of class "cic" or "sc_cic".
probs

Numeric vector of quantiles.
...

Additional arguments passed to plot.

Value

Invisible. Called for its side effect of producing a plot.

Plot Pre-treatment Fit for SC-CIC

Description

Plots the treated unit against the synthetic control over time, with a vertical line at the treatment period.

Usage

## S3 method for class 'sc_cic'
plot(x, ...)

Arguments

x

An object of class "sc_cic".
...

Additional arguments passed to plot.

Details

The plot shows the treated unit (solid line) and synthetic control (dashed line) over all time periods, with a vertical dashed line marking the start of treatment. Good pre-treatment fit is a necessary (but not sufficient) condition for valid SC-CIC inference.

Value

Invisible. Called for its side effect of producing a plot.

Compute Quantile Treatment Effects

Description

Estimates quantile treatment effects from a CIC fit by comparing quantiles of the actual post-treatment treated distribution with quantiles of the counterfactual distribution.

Usage

quantile_te(x, probs = seq(0.05, 0.95, 0.05))

Arguments

x

An object of class "cic" or "sc_cic".
probs

Numeric vector of quantiles at which to compute effects. Default is seq(0.05, 0.95, 0.05).

Details

The quantile treatment effect at quantile qq is:

τ^q=F^YI,11−1(q)−F^YN,11−1(q)\hat{\tau}_q = \hat{F}^{-1}_{Y^I,11}(q) - \hat{F}^{-1}_{Y^N,11}(q)

where F^YN,11−1\hat{F}^{-1}_{Y^N,11} is the CIC counterfactual distribution.

Value

A data frame with columns quantile, actual, counterfactual, and qte (quantile treatment effect).

Synthetic Control Changes-in-Changes Estimator

Description

Combines synthetic control methods with the Changes-in-Changes estimator. First constructs a synthetic control unit from donor units using elastic net regularization, then applies the CIC estimator using the synthetic control as the comparison group.

Usage

sc_cic(
  y_treated,
  y_donors,
  treatment_period,
  alpha = 1,
  boot = TRUE,
  boot_iters = 500L,
  seed = NULL
)

Arguments

y_treated

Numeric vector. Outcome for the treated unit across all time periods (pre and post).
y_donors

Numeric matrix. Outcomes for donor units, with rows as time periods (matching y_treated) and columns as donor units.
treatment_period

Integer. The index (row number) of the first treatment period. Periods 1 to treatment_period - 1 are pre-treatment.
alpha

Elastic net mixing parameter. alpha = 1 (default) is lasso; alpha = 0 is ridge.
boot

Logical. Compute bootstrap standard errors. Default TRUE. The bootstrap re-estimates the elastic net weights in every iteration to account for first-stage estimation uncertainty.
boot_iters

Integer. Number of bootstrap iterations. Default 500.
seed

Integer or NULL. Random seed for reproducibility.

Details

The procedure works in two steps:

Step 1: Synthetic Control Construction. In the pre-treatment period, the treated unit's outcome is regressed on the donor units' outcomes using elastic net (via cv.glmnet). This yields a sparse set of weights that construct a synthetic control unit as a weighted combination of donors.

Step 2: CIC Estimation. The CIC estimator is applied with the synthetic control as the "control group" and the treated unit as the "treatment group."

Inference. Because the synthetic control is an estimated object, the analytic asymptotic variance of Athey and Imbens (2006) does not directly apply. Instead, sc_cic provides bootstrap standard errors that re-estimate the elastic net weights in each bootstrap iteration, thereby accounting for first-stage estimation uncertainty. The bootstrap resamples time periods (with replacement) within the pre-treatment and post-treatment windows separately, preserving the panel structure.

Value

An object of class "sc_cic" inheriting from "cic", with components:

tau

The SC-CIC average treatment effect estimate.
se

Bootstrap standard error (if boot = TRUE). Note: analytic standard errors from Athey and Imbens (2006) Theorem 5.1 are not provided for sc_cic, because they do not account for first-stage synthetic control estimation uncertainty. Use cic directly if analytic SEs are needed for a pre-specified control group.
z

z-statistic (bootstrap-based).
pval

Two-sided p-value (bootstrap-based).
boot_se

Same as se (for compatibility with cic).
tau_did

The SC-DID estimate for comparison.
sc_weights

Named vector of synthetic control weights (including intercept).
sc_fitted

Synthetic control outcome across all time periods.
donors_selected

Names of donor units with nonzero weights.
pre_fit_rmse

Root mean squared error of pre-treatment fit.

References

Athey, S. and Imbens, G. W. (2006). Identification and Inference in Nonlinear Difference-in-Differences Models. Econometrica, 74(2), 431–497.

Abadie, A., Diamond, A., and Hainmueller, J. (2010). Synthetic Control Methods for Comparative Case Studies. Journal of the American Statistical Association, 105(490), 493–505.

Examples

# Basque Country example
if (requireNamespace("Synth", quietly = TRUE)) {
  data("basque", package = "Synth")
  gdp <- reshape(basque[, c("regionno", "year", "gdpcap")],
                 idvar = "year", timevar = "regionno", direction = "wide")
  y_treated <- gdp[, "gdpcap.17"]
  donors <- as.matrix(gdp[, grep("gdpcap\\.", names(gdp))])
  donors <- donors[, !colnames(donors) %in% c("gdpcap.17", "gdpcap.1")]
  valid <- complete.cases(y_treated, donors)
  result <- sc_cic(y_treated[valid], donors[valid, ],
                   treatment_period = 16, seed = 42)
  print(result)
}

Extract Synthetic Control Weights

Description

Returns a data frame of donor weights from an SC-CIC fit, sorted by absolute weight. Useful for inspecting which donors contribute to the synthetic control.

Usage

sc_weights(x, nonzero_only = TRUE)

Arguments

x

An object of class "sc_cic".
nonzero_only

Logical. If TRUE (default), only return donors with nonzero weights.

Value

A data frame with columns donor and weight.

Sensitivity Analysis for SC-CIC

Description

Re-estimates the SC-CIC treatment effect over a grid of elastic net penalty parameters, showing sensitivity to the regularization choice.

Usage

sensitivity_alpha(
  y_treated,
  y_donors,
  treatment_period,
  alphas = seq(0, 1, 0.2),
  seed = 42
)

Arguments

y_treated

Numeric vector. Treated unit outcomes.
y_donors

Numeric matrix. Donor unit outcomes.
treatment_period

Integer. First treatment period index.
alphas

Numeric vector. Grid of alpha values to evaluate. Default is seq(0, 1, 0.2).
seed

Integer or NULL. Random seed.

Value

A data frame with columns alpha, tau_cic, tau_did, n_donors, and pre_rmse.

Simulation Study for SC-CIC

Description

Generates data under controlled DGPs and evaluates SC-CIC performance.

Usage

simulate_sccic(
  n_sims = 500,
  T_pre = 25,
  T_post = 15,
  J = 15,
  tau_true = 1,
  dgp = c("linear", "nonlinear", "sc_good", "sc_bad"),
  alpha = 1,
  boot_iters = 200,
  seed = 42,
  verbose = TRUE
)

Arguments

n_sims

Integer. Number of simulation replications.
T_pre

Integer. Number of pre-treatment periods.
T_post

Integer. Number of post-treatment periods.
J

Integer. Number of donor units.
tau_true

Numeric. True average treatment effect.
dgp

Character. Data generating process. See Details.
alpha

Elastic net mixing parameter for SC construction.
boot_iters

Integer. Bootstrap iterations per simulation.
seed

Integer. Random seed.
verbose

Logical. Print progress.

Details

Four DGPs are available, designed to test different aspects of SC-CIC:

DGP 1: "linear" — Baseline. Outcomes are linear in a common factor and unit-specific loadings. DID is correctly specified. CIC matches DID. SC fits well. Purpose: verify the method works in the easy case.

DGP 2: "nonlinear" — CIC advantage. Cross-sectional DGP (not SC). N observations per cell. Control and treated have different distributions of unobservables. The production function is nonlinear and changes over time. DID is biased due to the nonlinear distributional shift; CIC is correct. Purpose: demonstrate the advantage of CIC over DID. Note: this tests cic(), not sc_cic().

DGP 3: "sc_good" — SC with good distributional fit. The treated unit is a true sparse combination of donors plus noise. SC recovers the weights well; the distributional dynamics are similar. Purpose: show SC-CIC works when SC fit is good.

DGP 4: "sc_bad" — SC with mean-only fit. The SC matches the treated mean, but donors have much lower variance than the treated unit. The distributional transport is wrong. Purpose: show SC-CIC fails when distributional assumptions are violated.

Value

A data frame with simulation results.

Examples

## Not run: 
r <- simulate_sccic(n_sims = 200, dgp = "nonlinear", tau_true = 1)
summarize_simulation(r, tau_true = 1)

## End(Not run)

Summarize simulation results

Description

Summarize simulation results

Usage

summarize_simulation(results, tau_true)

Arguments

results

Data frame from simulate_sccic.
tau_true

True treatment effect.

Value

Prints summary statistics and returns them invisibly.