ATEbounds {experiment}

Bounding the Average Treatment Effect when some of the Outcome Data are Missing

Description

This function computes the sharp bounds on the average treatment effect when some of the outcome data are missing. The confidence intervals for the bounds are also computed.

Usage

ATEbounds(
  formula,
  data = parent.frame(),
  maxY = NULL,
  minY = NULL,
  alpha = 0.05,
  n.reps = 0,
  strata = NULL,
  ratio = NULL,
  survey = NULL,
  ...
)

Arguments

formula

A formula of the form Y ~ X where Y is the name of the outcome variable and X is the name of the (randomized) treatment variable. X should be a factor variable but its value can take more than two levels. The missing values for Y should be coded as NA.

data

A data frame containing the relevant variables.

maxY

A scalar. The maximum value of the outcome variable. The default is the maximum sample value.

minY

A scalar. The minimum value of the outcome variable. The default is the minimum sample value.

alpha

A positive scalar that is less than or equal to 0.5. This will determine the (1-alpha) level of confidence intervals. The default is 0.05.

n.reps

A positive integer. The number of bootstrap replicates used for the construction of confidence intervals via B-method of Berran (1988). If it equals zero, the confidence intervals will not be constructed.

strata

The variable name indicating strata. If this is specified, the quantities of interest will be first calculated within each strata and then aggregated. The default is NULL.

ratio

A J \times M matrix of probabilities where J is the number of strata and M is the number of treatment and control groups. Each element of the matrix specifies the probability of a unit falling into that category. The default is NULL in which case the sample estimates of these probabilities are used for computation.

survey

The variable name for survey weights. The default is NULL.

...

The arguments passed to other functions.

Details

For the details of the method implemented by this function, see the references.

Value

A list of class ATEbounds which contains the following items:

call

The matched call.

Y

The outcome variable.

D

The treatment variable.

bounds

The point estimates of the sharp bounds on the average treatment effect.

bounds.Y

The point estimates of the sharp bounds on the outcome variable within each treatment/control group.

bmethod.ci

The B-method confidence interval of the bounds on the average treatment effect.

bonf.ci

The Bonferroni confidence interval of the bounds on the average treatment effect.

bonf.ci.Y

The Bonferroni confidence interval of the bounds on the outcome variable within each treatment/control group.

bmethod.ci.Y

The B-method confidence interval of the bounds on the outcome variable within each treatment/control group.

maxY

The maximum value of the outcome variable used in the computation.

minY

The minimum value of the outcome variable used in the computation.

nobs

The number of observations.

nobs.Y

The number of observations within each treatment/control group.

ratio

The probability of treatment assignment (within each strata if strata is specified) used in the computation.

Author(s)

Kosuke Imai, Department of Government and Department of Statistics, Harvard University [e-mail], https://imai.fas.harvard.edu;

References

Horowitz, Joel L. and Charles F. Manski. (1998). “Censoring of Outcomes and Regressors due to Survey Nonresponse: Identification and Estimation Using Weights and Imputations.” Journal of Econometrics, Vol. 84, pp.37-58.

Horowitz, Joel L. and Charles F. Manski. (2000). “Nonparametric Analysis of Randomized Experiments With Missing Covariate and Outcome Data.” Journal of the Americal Statistical Association, Vol. 95, No. 449, pp.77-84.

Harris-Lacewell, Melissa, Kosuke Imai, and Teppei Yamamoto. (2007). “Racial Gaps in the Responses to Hurricane Katrina: An Experimental Study”, Technical Report. Department of Politics, Princeton University.