AR.power: Power of the Anderson-Rubin (1949) Test

In ivmodel: Statistical Inference and Sensitivity Analysis for Instrumental Variables Model

Power of the Anderson-Rubin (1949) Test

Description

AR.power computes the power of Anderson-Rubin (1949) test based on the given values of parameters.

Usage

AR.power(n, k, l, beta, gamma, Zadj_sq, 
         sigmau, sigmav, rho, alpha = 0.05)

Arguments

n	Sample size.
k	Number of exogenous variables.
l	Number of instrumental variables.
beta	True causal effect minus null hypothesis causal effect.
gamma	Regression coefficient for effect of instruments on treatment.
Zadj_sq	Variance of instruments after regressed on the observed variables.
sigmau	Standard deviation of potential outcome under control. (structural error for y)
sigmav	Standard deviation of error from regressing treatment on instruments.
rho	Correlation between u (potential outcome under control) and v (error from regressing treatment on instrument).
alpha	Significance level.

Value

Power of the Anderson-Rubin test based on the given values of parameters.

Author(s)

Yang Jiang, Hyunseung Kang, and Dylan Small

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.

See Also

See also ivmodel for details on the instrumental variables model.

Examples

# Assume we calculate the power of AR test in a study with one IV (l=1) 
# and the only one exogenous variable is the intercept (k=1). 

# Suppose the difference between the null hypothesis and true causal 
# effect is 1 (beta=1).
# The sample size is 250 (n=250), the IV variance is .25 (Zadj_sq =.25).
# The standard deviation of potential outcome is 1(sigmau= 1). 
# The coefficient of regressing IV upon exposure is .5 (gamma= .5).
# The correlation between u and v is assumed to be .5 (rho=.5). 
# The standard deviation of first stage error is .4 (sigmav=.4). 
# The significance level for the study is alpha = .05.

# power of Anderson-Rubin test:
AR.power(n=250, k=1, l=1, beta=1, gamma=.5, Zadj_sq=.25, 
         sigmau=1, sigmav=.4, rho=.5, alpha = 0.05)

ivmodel documentation built on April 9, 2023, 5:08 p.m.