AR.size {ivmodel}

Sample Size Calculator for the Power of the Anderson-Rubin (1949) Test

Description

AR.size computes the minimum sample size required for achieving certain power of Anderson-Rubin (1949) test for giving value of parameters.

Usage

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

Arguments

power

The desired power over a constant.

k

Number of exogenous variables.

l

Number of instrumental variables.

beta

True causal effect minus null hypothesis causal effect.

gamma

Regression coefficient for the effect of instrument 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

Minimum sample size required for achieving certain power of Anderson-Rubin (1949) test.

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 performed an AR test in a study with one IV (l=1) and the 
# only one exogenous variable is the intercept (k=1). We want to know 
# the minimum sample size for this test to have an at least 0.8 power.

# Suppose the difference between the null hypothesis and true causal 
# effect is 1 (beta=1).
# 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.

# minimum sample size required for Anderson-Rubin test:
AR.size(power=0.8, k=1, l=1, beta=1, gamma=.5, Zadj_sq=.25, 
        sigmau=1, sigmav=.4, rho=.5, alpha = 0.05)