ivmodel (version 1.9.1)

CLR: Conditional Likelihood Ratio Test

Description

CLR computes the conditional likelihood ratio test (Moreira, 2003) for the ivmodel object as well as the associated confidence interval.

Usage

CLR(ivmodel, beta0 = 0, alpha = 0.05)

Value

CLR returns a list containing the following components

test.stat

The value of the test statistic for testing the null hypothesis \(H_0: \beta = \beta_0\) in ivmodel

p.value

The p value of the test under the null hypothesis \(H_0: \beta = \beta_0\) in ivmodel

ci

A matrix of two columns, each row contains an interval associated with the confidence interval

ci.info

A human-readable string describing the confidence interval

Arguments

ivmodel

ivmodel object

beta0

Null value \(\beta_0\) for testing null hypothesis \(H_0: \beta = \beta_0\) in ivmodel. Default is 0

alpha

The significance level for hypothesis testing. Default is 0.05

Author

Yang Jiang, Hyunseung Kang, and Dylan Small

Details

CLR.test computes the conditional likelihood ratio test for the instrumental variables model in ivmodel object, specifically for the parameter \(\beta\). It also computes the \(1 -\alpha\) confidence interval associated with it by inverting the test. The test is fully robust to weak instruments (Moreira 2003). We use the approximation suggested in Andrews et al. (2006) to evaluate the p value and the confidence interval.

References

Andrews, D. W. K., Moreira, M. J., and Stock, J. H. (2006). Optimal two-side invariant similar tests for instrumental variables regression. Econometrica 74, 715-752.
Moreira, M. J. (2003). A conditional likelihood ratio test for structural models. Econometrica 71, 1027-1048.

See Also

See also ivmodel for details on the instrumental variables model.

Examples

data(card.data)
Y=card.data[,"lwage"]
D=card.data[,"educ"]
Z=card.data[,c("nearc4","nearc2")]
Xname=c("exper", "expersq", "black", "south", "smsa", "reg661", 
        "reg662", "reg663", "reg664", "reg665", "reg666", "reg667", 
		"reg668", "smsa66")
X=card.data[,Xname]
card.model2IV = ivmodel(Y=Y,D=D,Z=Z,X=X)
CLR(card.model2IV,alpha=0.01)