# Change in Changes

### Description

`CiC`

computes the Quantile Treatment Effect on the
Treated (QTET) using the method of Athey and Imbens (2006). `CiC`

is a Difference in Differences type method. It requires
having two periods of data that can be either repeated cross sections
or panel data.

The method can accommodate conditioning on covariates though it does so in a restrictive way: It specifies a linear model for outcomes conditional on group-time dummies and covariates. Then, after residualizing (see details in Athey and Imbens (2006)), it computes the Change in Changes model based on these quasi-residuals.

### Usage

1 2 3 4 |

### Arguments

`formla` |
The formula y ~ d where y is the outcome and d is the treatment indicator (d should be binary) |

`t` |
The 3rd time period in the sample (this is the name of the column) |

`tmin1` |
The 2nd time period in the sample (this is the name of the column) |

`tname` |
The name of the column containing the time periods |

`x` |
A vector of covariates (the name of the columns) |

`data` |
The name of the data.frame that contains the data |

`dropalwaystreated` |
How to handle always treated observations in panel data case (not currently used) |

`panel` |
Binary variable indicating whether or not the dataset is panel. This is used for computing bootstrap standard errors correctly. |

`plot` |
Boolean whether or not the estimated QTET should be plotted |

`se` |
Boolean whether or not to compute standard errors |

`idname` |
The individual (cross-sectional unit) id name |

`uniqueid` |
Not sure if this is used anymore |

`alp` |
The significance level used for constructing bootstrap confidence intervals |

`probs` |
A vector of values between 0 and 1 to compute the QTET at |

`iters` |
The number of iterations to compute bootstrap standard errors. This is only used if se=TRUE |

`seedvec` |
Optional value to set random seed; can possibly be used in conjunction with bootstrapping standard errors. |

`printIter` |
Boolean only used for debugging |

### Value

QTE Object

### References

Athey, Susan and Guido Imbens. “Identification and Inference in Nonlinear Difference-in-Differences Models.” Econometrica 74.2, pp. 431-497, 2006.

### Examples

1 2 3 4 5 6 7 8 9 10 | ```
## load the data
data(lalonde)
## Run the Change in Changes model conditioning on age, education,
## black, hispanic, married, and nodegree
c1 <- CiC(re ~ treat, t=1978, tmin1=1975, tname="year",
x=c("age","education","black","hispanic","married","nodegree"),
data=lalonde.psid.panel, idname="id", se=FALSE,
probs=seq(0.05, 0.95, 0.05))
summary(c1)
``` |