# gel4: GEL estimation In gmm4: S4 Generalized Method of Moments

## Description

The main functions and methods to fit any model with GEL. As opposed to modelFit, models don't need to be created. It is all done by the functions. It is meant to be more user friendly.

## Usage

 1 2 3 4 5 6 7 8 9 gel4(g, x=NULL, theta0=NULL,lambda0=NULL, getVcov=FALSE, gelType = c("EL","ET","EEL","HD", "REEL","ETEL","ETHD"), vcov = c("MDS","iid","HAC"), grad=NULL, vcovOptions=list(), centeredVcov = TRUE, cstLHS=NULL, cstRHS=NULL, lamSlv=NULL, rhoFct=NULL, initTheta=c("gmm", "theta0"), data = parent.frame(), coefSlv=c("optim","nlminb","constrOptim"), lControl=list(), tControl=list()) 

## Arguments

 g A function of the form g(θ,x) and which returns a n \times q matrix with typical element g_i(θ,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 (see detailsbelow). x The matrix or vector of data from which the function g(θ,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, a formula or a list of formulas. For these cases, they are needed to create the "gelModels" object. lambda0 The q \times 1 vector of starting values for the Lagrange multipliers. By default a zero vector is used. getVcov Should the method computes the covariance matrices of the coefficients and Lagrange multipliers. gelType A character string specifying the type of GEL. vcov Assumption on the properties of the moment conditions. grad A function of the form G(θ,x) which returns a q\times k matrix of derivatives of \bar{g}(θ) with respect to θ. vcovOptions A list of options for the covariance matrix of the moment conditions. See vcovHAC for the default values. centeredVcov Should the moment function be centered when computing its covariance matrix. Doing so may improve inference. 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. lamSlv An alternative solver for the Lagrange multiplier. By default, either Wu_lam, EEL_lam, REEL_lam or getLambda is used. See the vignette for the required format. rhoFct An optional function that return ρ(v). This is for users who want a GEL model that is not built in the package. The four arguments of the function must be "gmat", the matrix of moments, "lambda", the vector of Lagrange multipliers, "derive", which specify the order of derivative to return, and k a numeric scale factor required for time series and kernel smoothed moments. initTheta Method to obtain the starting values for the coefficient vector. By default the GMM estimate with identity matrix is used. The second argument means that "theta0" is used instead. data A required data.frame, in which all variables in g and x can be found. coefSlv Minimization solver for the coefficient vector. lControl A list of controls for the Lagrange multiplier algorithm. tControl A list of controls for the coefficient algorithm.

## Value

It returns an object of class "gelfit"

## References

Anatolyev, S. (2005), GMM, GEL, Serial Correlation, and Asymptotic Bias. Econometrica, 73, 983-1002.

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

Kitamura, Yuichi (1997), Empirical Likelihood Methods With Weakly Dependent Processes. The Annals of Statistics, 25, 2084-2102.

Kitamura, Y. and Otsu, T. and Evdokimov, K. (2013), Robustness, Infinitesimal Neighborhoods and Moment Restrictions. Econometrica, 81, 1185-1201.

Newey, W.K. and Smith, R.J. (2004), Higher Order Properties of GMM and Generalized Empirical Likelihood Estimators. Econometrica, 72, 219-255.

Smith, R.J. (2004), GEL Criteria for Moment Condition Models. Working paper, CEMMAP.

modelFit, gelModel
 1 2 3 data(simData) res <- gel4(y~x1, ~z1+z2, vcov="MDS", gelType="ET", data=simData) res