gmm (version 0.1-0)

gmm: Generalized method of moment estimation

Description

Function to estimate a vector of parameters based on moment conditions using the GMM method of Hansen(82). It is a preliminary version. It has been tested with monte carlo experiment but it may have bugs. Comments are welcome.

Usage

gmm(g,t0,x,grad=NULL,type=c("twoStep","cue","iterative"),kernel=c("Quadratic Spectral", 
    "Truncated", "Bartlett", "Parzen", "Tukey-Hanning"),iid=FALSE,crit=10e-7,
     itermax=100,algo=c("Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN"), vcov=HAC, ...)

Arguments

g

A function of the form $g(\theta,x)$ and which returns a $n \times q$ matrix of time series. This series is than used to build the q sample moment conditions.

t0

A $k \times 1$ vector of starting values

x

The matrix or vector of data from which the function $g(\theta,x)$ is computed

grad

A function of the form $G(\theta,x)$ which returns a $q\times k$ matrix of derivatives of $\bar{g}(\theta)$. By default, the numerical algorithm numericDeriv is used.

type

The GMM method: "twostep" is the two step GMM proposed by Hansen(1982) and the cue and iterative are respectively the continuous updated and the iterative GMM proposed by Hansen, Eaton et Yaron (1996)

kernel

type of kernel used to compute the covariance matrix of the vector of moment conditions. See HAC for more details

iid

Hypothesis on the properties of x. By default, x is a weakly dependant time series

crit

The level of precision required for the iterative GMM

itermax

The maximum number of iterations for the iterative GMM

algo

The numerical algorithm for the optimization problem. See optim for more details.

vcov

The method used to compute de covariance matrix. By default it is the HAC. For now it is the only option. But in a futur version, more choices will be available.

...

More option to give to the HAC procedure.

Value

• 'gmm' returns an object of 'class' '"gmm"'

  The functions 'summary' is used to obtain and print a summary of the results. It also compute the J-test of overidentying restriction The object of class "gmm" is a list containing:

  par: $k\times 1$ vector of parameters

  vcov: the covariance matrix

  objective: the value of the objective function $\bar{g}'var(\bar{g})^{-1}\bar{g}$

Details

weightsAndrews2 and bwAndrews2 are simply modified version of weightsAndrews and bwAndrews from the package sandwich. The modifications have been made so that the argument x can be a matrix instead of an object of class lm or glm. The details on how is works can be found on the sandwich manual.

References

Zeileis A (2006), Object-oriented Computation of Sandwich Estimators. Journal of Statistical Software, 16(9), 1--16. URL http://www.jstatsoft.org/v16/i09/.

Andrews DWK (1991), Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation. Econometrica, 59, 817--858.

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.

Examples

g <- function(tet,x)
	{
	n <- nrow(x)
	u <- (x[7:n] - tet[1] - tet[2]*x[6:(n-1)] - tet[3]*x[5:(n-2)])
	f <- cbind(u,u*x[5:(n-2)],u*x[4:(n-3)],u*x[3:(n-4)])
	return(f)
	}

Dg <- function(tet,x)
	{
	n <- nrow(x)
	xx <- cbind(rep(1,(n-6)),x[6:(n-1)],x[5:(n-2)])
        H  <- cbind(rep(1,(n-6)),x[5:(n-2)],x[4:(n-3)],x[3:(n-4)])
	f <- -crossprod(H,xx)/(n-6)
	return(f)
	}
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)
resgmm <- gmm(g,c(0,.3,.6),x,grad=Dg)