Generalised Method of Moment (GMM) estimation of linear models

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

References

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

Author

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

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
#> [1] 0.7109826
cor(z1, eps) #check uncorrelatedness of instrument
#> [1] -0.04953215

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

##efficient gmm estimation:
mymod <- gmm(y, x, z)
mymod$coefficients
#> [1] 0.2915040 0.6892453

##ols (for comparison):
mymod <- ols(y,x)
mymod$coefficients
#>                  x1 
#> 0.3015429 1.8605825