ivmodel (version 1.9.1)

LIML: Limited Information Maximum Likelihood Ratio (LIML) Estimator

Description

LIML computes the LIML estimate for the ivmodel object.

Usage

LIML(ivmodel,
     beta0 = 0, alpha = 0.05,
     manyweakSE = FALSE, heteroSE = FALSE,clusterID = NULL)

Value

LIML returns a list containing the following components

k

The k value for LIML.

point.est

Point estimate of \(\beta\).

std.err

Standard error of the estimate.

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 one row by two columns specifying the confidence interval associated with the Fuller estimator.

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.

manyweakSE

Should many weak instrument (and heteroscedastic-robust) asymptotics in Hansen, Hausman and Newey (2008) be used to compute standard errors?

heteroSE

Should heteroscedastic-robust standard errors be used? Default is FALSE.

clusterID

If cluster-robust standard errors are desired, provide a vector of length that's identical to the sample size. For example, if n = 6 and clusterID = c(1,1,1,2,2,2), there would be two clusters where the first cluster is formed by the first three observations and the second cluster is formed by the last three observations. clusterID can be numeric, character, or factor.

Author

Yang Jiang, Hyunseung Kang, Dylan Small

Details

LIML computes the LIML estimate for the instrumental variables model in ivmodel, specifically for the parameter \(beta\). The computation uses KClass with the value of \(k = k_{LIML}\), which is the smallest root of the equation $$det(L^T L - k L^T R_Z L) = 0$$ where \(L\) is a matrix of two columns, the first column consisting of the outcome vector, \(Y\), and the second column consisting of the endogenous variable, \(D\), and \(R_Z = I - Z (Z^T Z)^{-1} Z^T\) with \(Z\) being the matrix of instruments. LIML generates a point estimate, a standard error associated with the point estimate, a test statistic and a p value under the null hypothesis \(H_0: \beta = \beta_0\) in ivmodel along with a \(1-\alpha\) confidence interval.

See Also

See also ivmodel for details on the instrumental variables model. See also KClass for more information about the k-Class estimator.

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)
LIML(card.model2IV,alpha=0.01)