confint function

Confidence intervals for GMM or GEL

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

## 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 'ategel'
confint(object, parm, level = 0.95, lambda = FALSE,
                            type = c("Wald", "invLR", "invLM", "invJ"), fact = 3,
                            corr = NULL, robToMiss=TRUE, ...)
## 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
• robToMiss: If TRUE, the confidence interval is based on the standard errors that are robust to misspecification
• ...: Other arguments when confint is applied to another classe object

Returns

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

#################
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")