gmm: Generalised Method of Moment (GMM) estimation of linear...

In gets: General-to-Specific (GETS) Modelling and Indicator Saturation Methods

Generalised Method of Moment (GMM) estimation of linear models

Description

Generalised Method of Moment (GMM) estimation of linear models with either ordinary (homoscedastic error) or robust (heteroscedastic error) coefficient-covariance, see Hayashi (2000) chapter 3.

Usage

gmm(y, x, z, tol = .Machine$double.eps,
  weighting.matrix = c("efficient", "2sls", "identity"),
  vcov.type = c("ordinary", "robust"))

Arguments

y	numeric vector, the regressand
x	numeric matrix, the regressors
z	numeric matrix, the instruments
tol	numeric value. The tolerance for detecting linear dependencies in the columns of the matrices that are inverted, see the solve function
weighting.matrix	a character that determines the weighting matrix to bee used, see "details"
vcov.type	a character that determines the expression for the coefficient-covariance, see "details"

Details

weighting.matrix = "identity" corresponds to the Instrumental Variables (IV) estimator, weighting.matrix = "2sls" corresponds to the 2 Stage Least Squares (2SLS) estimator, whereas weighting.matrix = "efficient" corresponds to the efficient GMM estimator, see chapter 3 in Hayashi(2000).

vcov.type = "ordinary" returns the ordinary expression for the coefficient-covariance, which is valid under conditionally homoscedastic errors. vcov.type = "robust" returns an expression that is also valid under conditional heteroscedasticity, see chapter 3 in Hayashi (2000).

Value

A list with, amongst other, the following items:

n	number of observations
k	number of regressors
df	degrees of freedom, i.e. n-k
coefficients	a vector with the coefficient estimates
fit	a vector with the fitted values
residuals	a vector with the residuals
residuals2	a vector with the squared residuals
rss	the residual sum of squares
sigma2	the regression variance
vcov	the coefficient-covariance matrix
logl	the normal log-likelihood

Author(s)

Genaro Sucarrat, http://www.sucarrat.net/

References

F. Hayashi (2000): 'Econometrics'. Princeton: Princeton University Press

See Also

solve, ols

Examples

##generate data where regressor is correlated with error:
set.seed(123) #for reproducibility
n <- 100
z1 <- rnorm(n) #instrument
eps <- rnorm(n) #ensures cor(z,eps)=0
x1 <- 0.5*z1 + 0.5*eps #ensures cor(x,eps) is strong
y <- 0.4 + 0.8*x1 + eps #the dgp
cor(x1, eps) #check correlatedness of regressor
cor(z1, eps) #check uncorrelatedness of instrument

x <- cbind(1,x1) #regressor matrix
z <- cbind(1,z1) #matrix with instruments

##efficient gmm estimation:
mymod <- gmm(y, x, z)
mymod$coefficients

##ols (for comparison):
mymod <- ols(y,x)
mymod$coefficients

gets documentation built on Sept. 11, 2024, 9:03 p.m.