Confidence intervals for GMM or GEL

Description

It produces confidence intervals for the coefficients from gel or gmm estimation.

Usage

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## S3 method for class 'gel'
confint(object, parm, level = 0.95, lambda = FALSE,
                        type = c("Wald", "invLR", "invLM", "invJ"),
                        fact = 3, corr = NULL, ...)
## S3 method for class 'gmm'
confint(object, parm, level = 0.95, ...)
## S3 method for class 'confint'
print(x, digits = 5, ...)

Arguments

object

An object of class gel or gmm returned by the function gel or gmm

parm

A specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.

level

The confidence level

lambda

If set to TRUE, the confidence intervals for the Lagrange multipliers are produced.

type

'Wald' is the usual symetric confidence interval. The thee others are based on the inversion of the LR, LM, and J tests.

fact

This parameter control the span of search for the inversion of the test. By default we search within plus or minus 3 times the standard error of the coefficient estimate.

corr

This numeric scalar is meant to apply a correction to the critical value, such as a Bartlett correction. This value depends on the model (See Owen; 2001)

x

An object of class confint produced by confint.gel and confint.gmm

digits

The number of digits to be printed

...

Other arguments when confint is applied to another classe object

Value

It returns a matrix with the first column being the lower bound and the second the upper bound.

References

Hansen, L.P. (1982), Large Sample Properties of Generalized Method of Moments Estimators. Econometrica, 50, 1029-1054, Hansen, L.P. and Heaton, J. and Yaron, A.(1996), Finit-Sample Properties of Some Alternative GMM Estimators. Journal of Business and Economic Statistics, 14 262-280. Owen, A.B. (2001), Empirical Likelihood. Monographs on Statistics and Applied Probability 92, Chapman and Hall/CRC

Examples

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#################
n = 500
phi<-c(.2,.7)
thet <- 0
sd <- .2
x <- matrix(arima.sim(n = n, list(order = c(2,0,1), ar = phi, ma = thet, sd = sd)), ncol = 1)
y <- x[7:n]
ym1 <- x[6:(n-1)]
ym2 <- x[5:(n-2)]

H <- cbind(x[4:(n-3)], x[3:(n-4)], x[2:(n-5)], x[1:(n-6)])
g <- y ~ ym1 + ym2
x <- H
t0 <- c(0,.5,.5)

resGel <- gel(g, x, t0)

confint(resGel)
confint(resGel, level = 0.90)
confint(resGel, lambda = TRUE)

########################

resGmm <- gmm(g, x)

confint(resGmm)
confint(resGmm, level = 0.90)

## Confidence interval with inversion of the LR, LM or J test.
##############################################################

set.seed(112233)
x <- rt(40, 3)
y <- x+rt(40,3)
# Simple interval on the mean
res <- gel(x~1, ~1, method="Brent", lower=-4, upper=4)
confint(res, type = "invLR")
confint(res)
# Using a Bartlett correction
k <- mean((x-mean(x))^4)/sd(x)^4
s <- mean((x-mean(x))^3)/sd(x)^3
a <- k/2-s^2/3
corr <- 1+a/40
confint(res, type = "invLR", corr=corr)

# Interval on the slope
res <- gel(y~x, ~x)
confint(res, "x", type="invLR")
confint(res, "x")