LIML: Limited Information Maximum Likelihood Ratio (LIML) Estimator

Description Usage Arguments Details Value Author(s) See Also Examples

View source: R/LIML.r

Description

LIML computes the LIML estimate for the ivmodel object.

Usage

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

Arguments

ivmodel

ivmodel object.

beta0

Null value β_0 for testing null hypothesis H_0: β = β_0 in ivmodel. Default is 0.

alpha

The significance level for hypothesis testing. Default is 0.05.

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.

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: β = β_0 in ivmodel along with a 1-α confidence interval.

Value

LIML returns a list containing the following components

k

The k value for LIML.

point.est

Point estimate of β.

std.err

Standard error of the estimate.

test.stat

The value of the test statistic for testing the null hypothesis H_0: β = β_0 in ivmodel.

p.value

The p value of the test under the null hypothesis H_0: β = β_0 in ivmodel.

ci

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

Author(s)

Yang Jiang, Hyunseung Kang, Dylan Small

See Also

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

Examples

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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)

ivmodel documentation built on Nov. 17, 2017, 4:09 a.m.