gmm4 {momentfit}

GMM estimation

Description

The main functions and methods to fit any model with GMM. As opposed to gmmFit, models don't need to be created. It is all done by the functions. It is meant to be more user friendly. This document needs to changed. It is just a copy and paste from the gmm package

Usage

gmm4(g, x, theta0 = NULL, grad = NULL, 
     type = c("twostep", "iter", "cue", "onestep"),
     vcov = c("iid", "HAC", "MDS", "TrueFixed", "CL"),
     initW = c("ident", "tsls", "EbyE"), weights = "optimal", 
     itermaxit = 50, cstLHS=NULL, cstRHS=NULL,
     vcovOptions=list(), survOptions=list(),
     itertol = 1e-07, centeredVcov = TRUE,
     data = parent.frame(), ...)

## S4 method for signature 'formula'
tsls(model, x, vcov = c("iid", "HAC", "MDS", "CL"),
         vcovOptions=list(), survOptions=list(), centeredVcov = TRUE,
         data = parent.frame())

## S4 method for signature 'list'
tsls(model, x=NULL, vcov = c("iid", "HAC", "MDS",
          "CL"), vcovOptions=list(), survOptions=list(),
          centeredVcov = TRUE, data = parent.frame())

## S4 method for signature 'list'
ThreeSLS(model, x=NULL, vcov = c("iid", "HAC", "MDS",
          "CL"), vcovOptions=list(), survOptions=list(),
          centeredVcov = TRUE, data = parent.frame())

Arguments

model

A formula or a list of formulas.

g

A function of the form g(\theta,x) and which returns a n \times q matrix with typical element g_i(\theta,x_t) for i=1,...q and t=1,...,n. This matrix is then used to build the q sample moment conditions. It can also be a formula if the model is linear or nonlinear, or a list of formulas for systems of equations.

x

The matrix or vector of data from which the function g(\theta,x) is computed. If "g" is a formula, it is an n \times Nh matrix of instruments or a formula (see details below).

theta0

A k \times 1 vector of starting values. It is required only when "g" is a function or a nonlinear equation defined by a formula, in which case, it must be a named vector

grad

A function of the form G(\theta,x) which returns a q\times k matrix of derivatives of \bar{g}(\theta) with respect to \theta. By default, the numerical algorithm numericDeriv is used. It is of course strongly suggested to provide this function when it is possible. This gradient is used to compute the asymptotic covariance matrix of \hat{\theta} and to obtain the analytical gradient of the objective function if the method is set to "CG" or "BFGS" in optim and if "type" is not set to "cue". If "g" is a formula, the gradiant is not required (see the details below).

type

What GMM methods should we use? for type=="onestep", if "weights" is not a matrix, the model will be estimated with the weights equals to the identity matrix

vcov

Assumption on the properties of the random vector x. By default, x is a weakly dependant process. The "iid" option will avoid using the HAC matrix which will accelerate the estimation if one is ready to make that assumption. The option "TrueFixed" is used only when the matrix of weights is provided and it is the optimal one. For type CL, clustered covariance matrix is computed. The options are then included in vcovOptions (see meatCL).

initW

How should be compute the initial coefficient vector in the first. It only makes a difference for linear models for which the choice is GMM with identity matrix or two-stage least quares.

weights

What weighting matrix to use? The choices are "optimal", in which case it is the inverse of the moment vovariance matrix, "ident" for the identity matrix, or a fixed matrix.

itermaxit

Maximum iterations for iterative GMM

itertol

Tolance for the stopping rule in iterative GMM

centeredVcov

Should the moment function be centered when computing its covariance matrix. Doing so may improve inference.

data

A data.frame or a matrix with column names (Optional).

cstLHS

The left hand side of the constraints to impose on the coefficients. See restModel for more details.

cstRHS

The right hand side of the constraints to impose on the coefficients. See restModel for more details.

vcovOptions

A list of options for the covariance matrix of the moment conditions. See vcovHAC for the default values.

survOptions

If needed, a list with the type of survey weights and the weights as a numeric vector, data.frame or formula. The type is either "sampling" or "fequency".

...

Arguments to pass to optim when the model is nonlinear.

Value

It returns an object of class "gmmfit"

References

Zeileis A (2006), Object-oriented Computation of Sandwich Estimators. Journal of Statistical Software, 16(9), 1–16. URL doi: 10.18637/jss.v016.i09.

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

Newey WK & West KD (1987), A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix. Econometrica, 55, 703–708.

Newey WK & West KD (1994), Automatic Lag Selection in Covariance Matrix Estimation. Review of Economic Studies, 61, 631-653.

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), Finite-Sample Properties of Some Alternative GMM Estimators. Journal of Business and Economic Statistics, 14 262-280.

See Also

gmmFit, momentModel

Examples

data(simData)

res <- gmm4(y~x1, ~z1+z2, vcov="MDS", type="iter", data=simData)
res