# Mean Difference in Differences

### Description

`MDiD`

is a Difference in Differences type method for
computing the QTET.

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. |

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

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

`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

A `QTE`

object

### References

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

Thuysbaert, Bram. “Distributional Comparisons in Difference in Differences Models.” Working Paper, 2007.

### Examples

1 2 3 4 5 6 7 8 9 10 | ```
## load the data
data(lalonde)
## Run the Mean Difference in Differences method conditioning on
## age, education, black, hispanic, married, and nodegree
md1 <- MDiD(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(md1)
``` |