Description Usage Arguments Details Value Author(s) References
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.
1 2 3 
formula 
A formula of the form 
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 
n.reps 
A positive integer. The number of bootstrap replicates used for the construction of confidence intervals via Bmethod 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 
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 
survey 
The variable name for survey weights. The default is

... 
The arguments passed to other functions. 
For the details of the method implemented by this function, see the references.
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 Bmethod 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 Bmethod 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

Kosuke Imai, Department of Politics, Princeton University [email protected], http://imai.princeton.edu;
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.3758.
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.7784.
HarrisLacewell, 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.
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