LIML: Limited Information Maximum Likelihood Ratio (LIML) Estimator

In ivmodel: Statistical Inference and Sensitivity Analysis for Instrumental Variables Model

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)

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.

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.

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.

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

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 April 9, 2023, 5:08 p.m.