# sysGmm: Generalized method of moment estimation for system of... In gmm: Generalized Method of Moments and Generalized Empirical Likelihood

## Description

Functions to estimate a system of equations based on GMM.

## Usage

  1 2 3 4 5 6 7 8 9 10 sysGmm(g, h, wmatrix = c("optimal","ident"), vcov=c("MDS", "HAC", "CondHom", "TrueFixed"), kernel=c("Quadratic Spectral","Truncated", "Bartlett", "Parzen", "Tukey-Hanning"), crit=10e-7,bw = bwAndrews, prewhite = FALSE, ar.method = "ols", approx="AR(1)", tol = 1e-7, model=TRUE, X=FALSE, Y=FALSE, centeredVcov = TRUE, weightsMatrix = NULL, data, crossEquConst = NULL, commonCoef = FALSE) five(g, h, commonCoef = FALSE, data = NULL) threeSLS(g, h, commonCoef = FALSE, data = NULL) sur(g, commonCoef = FALSE, data = NULL) randEffect(g, data = NULL) 

## Arguments

 g A possibly named list of formulas h A formula if the same instruments are used in each equation or a list of formulas. wmatrix Which weighting matrix should be used in the objective function. By default, it is the inverse of the covariance matrix of g(θ,x). The other choice is the identity matrix. vcov Assumption on the properties of the moment vector. By default, it is a martingale difference sequence. "HAC" is for weakly dependent processes and "CondHom" implies conditional homoscedasticity. The option "TrueFixed" is used only when the matrix of weights is provided and it is the optimal one. kernel type of kernel used to compute the covariance matrix of the vector of sample moment conditions (see kernHAC for more details) crit The stopping rule for the iterative GMM. It can be reduce to increase the precision. bw The method to compute the bandwidth parameter. By default it is bwAndrews which is proposed by Andrews (1991). The alternative is bwNeweyWest of Newey-West(1994). prewhite logical or integer. Should the estimating functions be prewhitened? If TRUE or greater than 0 a VAR model of order as.integer(prewhite) is fitted via ar with method "ols" and demean = FALSE. ar.method character. The method argument passed to ar for prewhitening. approx A character specifying the approximation method if the bandwidth has to be chosen by bwAndrews. tol Weights that exceed tol are used for computing the covariance matrix, all other weights are treated as 0. model, X, Y logical. If TRUE the corresponding components of the fit (the model frame, the model matrix, the response) are returned if g is a formula. centeredVcov Should the moment function be centered when computing its covariance matrix. Doing so may improve inference. weightsMatrix It allows users to provide gmm with a fixed weighting matrix. This matrix must be q \times q, symmetric and strictly positive definite. When provided, the type option becomes irrelevant. data A data.frame or a matrix with column names (Optional). commonCoef If true, coefficients accross equations are the same crossEquConst Only used if the number of regressors are the same in each equation. It is a vector which indicates which coefficient are constant across equations. The order is 1 for Intercept and 2 to k as it is formulated in the formulas g. Setting it to 1:k is equivalent to setting commonCoef to TRUE.

## Details

This set of functions implement the estimation of system of equations as presented in Hayashi (2000)

## Value

'sysGmm' returns an object of 'class' '"sysGmm"'

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 "sysGmm" is a list containing at least:

 coefficients list of vectors of coefficients for each equation residuals list of the residuals for each equation. fitted.values list of the fitted values for each equation. vcov the covariance matrix of the stacked coefficients objective the value of the objective function \| var(\bar{g})^{-1/2}\bar{g}\|^2 terms The list of terms objects for each equation call the matched call. y If requested, a list of response variables. x if requested, a list of the model matrices. model if requested (the default), a list of the model frames.

## 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.

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.

Hayashi, F. (2000), Econometrics. Princeton University Press.

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 data(wage) eq1 <- LW~S+IQ+EXPR eq2 <- LW80~S80+IQ+EXPR80 g2 <- list(Wage69=eq1, WAGE80=eq2) h2 <- list(~S+EXPR+MED+KWW, ~S80+EXPR80+MED+KWW) res <- sysGmm(g2, h2, data=wage, commonCoef=TRUE) summary(res) res2 <- sysGmm(g2, h2, data=wage) summary(res2) five(g2, h2, data=wage) threeSLS(g2, h2[[1]], data=wage) sur(g2, data=wage) randEffect(g2, data=wage) ## Cross-Equation restrictions ## All but the intercept are assumed to be the same res <- sysGmm(g2, h2, data=wage, crossEquConst = 2:4) summary(res) 

gmm documentation built on June 20, 2017, 3:01 p.m.