Author: Neil Hwang
Date: 2026-04-09

# Introduction to sccic

#### Neil Hwang

#### 2026-04-09

## Overview

The sccic package implements the Changes-in-Changes (CIC) estimator of Athey and Imbens (2006), combined with synthetic control methods for causal inference. It provides two main functions:

- `cic()`: Standard CIC for two-group, two-period settings
- `sc_cic()`: Synthetic control + CIC for single-treated-unit settings

## Example 1: Standard CIC

We demonstrate `cic()` on the workers’ compensation data from Meyer, Viscusi, and Durbin (1995), the dataset used in the supplementary application of Athey and Imbens (2006). Injury duration is measured in integer weeks, so both the continuous estimator (the default) and the discrete estimator (`discrete = TRUE`) are relevant.

    library(sccic)

    # Load workers' comp data
    if (requireNamespace("wooldridge", quietly = TRUE)) {
      data("injury", package = "wooldridge")

      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]

      # Continuous CIC (Theorem 3.1)
      result <- cic(y_00, y_01, y_10, y_11)
      print(result)

      # Discrete CIC (Theorem 4.1) — matches Athey and Imbens (2006)
      result_d <- cic(y_00, y_01, y_10, y_11, discrete = TRUE, boot = FALSE)
      print(result_d)
    }
    #>
    #> Changes-in-Changes Estimator
    #> ----------------------------------------
    #>   Estimator: continuous (Theorem 3.1)
    #>   tau^CIC  = 0.0687
    #>   tau^DID  = 0.1883
    #>   SE       = 0.4044
    #>   z-stat   = 0.1699
    #>   p-value  = 0.8651
    #>   N        = 7150 (2294/2004/1472/1380)
    #> Analytic standard errors (Theorem 5.1) assume a continuous outcome distribution and are not valid when discrete = TRUE. Use boot = TRUE for inference.
    #>
    #> Changes-in-Changes Estimator
    #> ----------------------------------------
    #>   Estimator: discrete (Theorem 4.1)
    #>   tau^CIC  = 0.1842
    #>   tau^DID  = 0.1883
    #>   N        = 7150 (2294/2004/1472/1380)

C:14bb47d8d33a8-intro.R

The discrete CIC estimate (0.184) closely matches the value reported by Athey and Imbens (2006) (0.18 on a subsample of N = 5,624), confirming the correctness of the implementation. The continuous CIC estimate (0.069) treats log-transformed duration as approximately continuous.

## Example 2: SC-CIC

For settings with a single treated unit and multiple donors, `sc_cic()` combines synthetic control construction with CIC estimation. We demonstrate on the Basque Country terrorism dataset.

    if (requireNamespace("Synth", quietly = TRUE)) {
      data("basque", package = "Synth")

      # Reshape to wide format
      gdp <- reshape(basque[, c("regionno", "year", "gdpcap")],
                     idvar = "year", timevar = "regionno", direction = "wide")

      y_treated <- gdp[, "gdpcap.17"]  # Basque Country
      donor_cols <- grep("gdpcap\\.", names(gdp), value = TRUE)
      donor_cols <- donor_cols[!donor_cols %in% c("gdpcap.17", "gdpcap.1")]
      donors <- as.matrix(gdp[, donor_cols])

      valid <- complete.cases(y_treated, donors)
      result2 <- sc_cic(y_treated[valid], donors[valid, ],
                        treatment_period = 16, seed = 42)
      print(result2)
    }
    #>
    #> Synthetic Control + Changes-in-Changes Estimator
    #> --------------------------------------------------
    #> SC donors selected: 4
    #> Pre-treatment RMSE: 0.0493
    #> Pre-treatment KS p: 0.938 [OK]
    #> --------------------------------------------------
    #>   tau^CIC  = -0.7943
    #>   tau^DID  = -0.7346
    #>   boot SE  = 0.3229
    #>   z-stat   = -2.4596
    #>   p-value  = 0.01391
    #>   N        = 86 (15/28/15/28)

C:14bb47d8d33a8-intro.R

## Bootstrap standard errors

Both functions support bootstrap inference via the `boot` argument:

    result <- cic(y_00, y_01, y_10, y_11, boot = TRUE, boot_iters = 500, seed = 42)

C:14bb47d8d33a8-intro.R

## References

- Athey, S. and Imbens, G. W. (2006). Identification and Inference in Nonlinear Difference-in-Differences Models. Econometrica, 74(2), 431-497.
- Abadie, A. and Gardeazabal, J. (2003). The Economic Costs of Conflict: A Case Study of the Basque Country. American Economic Review, 93(1), 113-132.
- Meyer, B. D., Viscusi, W. K., and Durbin, D. L. (1995). Workers’ Compensation and Injury Duration. American Economic Review, 85(3), 322-340.