---
title: "Introduction to sccic"
author: "Neil Hwang"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Introduction to sccic}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

## 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.

```{r cic-example}
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)
}
```

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.

```{r sccic-example, warning=FALSE}
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)
}
```

## Bootstrap standard errors

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

```{r boot-example, eval = FALSE}
result <- cic(y_00, y_01, y_10, y_11, boot = TRUE, boot_iters = 500, seed = 42)
```

## 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.
