# ARsensitivity.ci: ARsensitivity.ci In ivpack: Instrumental Variable Estimation.

## Description

Calculates the confidence interval for the effect of a treatment (endogenous) variable using an instrumental variable, which is based on an extension of Anderson-Rubin test and allows IV be possibly invalid within a certain range.

## Usage

 `1` ```ARsensitivity.ci(ivmodel, Delta=NULL, conflevel=.95) ```

## Arguments

 `ivmodel` Instrumental variable (IV) model fit using ivreg. Make sure to use the option x=TRUE when fitting the ivreg model. `Delta` The allowance of sensitivity parameter for possibly invalid IV. If Delta=NULL, the ARsensitivity.ci function will calculate the confidence interval for a standard Anderson-Rubin test with valid IV. `conflevel` Confidence level for confidence interval.

## Value

 `confidence.interval` Confidence interval for effect of treatment. If it's a 2*2 matrix, the confidence interval is consisted of two disjoint intervals, each row of the matrix is one interval. `printinfo` Report the confidence interval in one printing sentence. `ci.type` If ci.type=1, the confidence interval is finite. If ci.type=2, the confidence interval is infinite. If ci.type=3, the confidence interval is an empty set.

Yang Jiang

## References

Anderson, T.W. and Rubin, H. (1949), Estimation of the parameters of a single equation in a complete system of stochastic equations, Annals of Mathematical Statistics, 20, 46-63.
Jiang, Y., Zhang, N. and Small, D. (2013), Sensitivity analysis and power for instrumental variable studies, Working paper.

`ivreg`
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```### a simulated data set z = rnorm(100) d = z+rnorm(100) y = d+0.1*z+rnorm(100) ivmodel = ivreg(y~d|z, x=TRUE) ### calculate confidence interval, given the allowance of sensitivity is (-0.1, 0.1) ARsensitivity.ci(ivmodel, Delta=c(-0.1, 0.1)) ### calculate confidence interval, assuming that IV is valid ARsensitivity.ci(ivmodel) ```