AR.power: 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)

Value

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

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.

Author

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.

Examples

Run this code

# 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)

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