# Constructor for `"momentModel"` classes It builds an object class `"momentModel"`, which is a union class for `"linearModel"`, `"nonlinearModel"`, `"formulaModel"` and `"functionModel"` classes. These are classes for moment based models. This is the first step before running any estimation algorithm. ```r momentModel(g, x=NULL, theta0=NULL,grad=NULL, vcov = c("iid", "HAC", "MDS", "CL"), vcovOptions=list(), centeredVcov = TRUE, data=parent.frame(), na.action="na.omit", survOptions=list(), smooth=FALSE) ``` ## Arguments - `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 (see detailsbelow). - `x`: The matrix or vector of data from which the function $g(\theta,x)$ is computed. If "g" is a formula, it is an c("$n\n$", "$ \\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 because only then a numerical algorithm is used to minimize the objective function. If the dimension of $\theta$ is one, see the argument "optfct". - `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). - `vcov`: Assumption on the properties of the moment conditions. By default, they are weakly dependant processes. For `MDS`, we assume that the conditions are martingale difference sequences, which implies they are serially uncorrelated, but may be heteroscedastic. There is a difference between `iid` and `MDS` only when `g` is a formula. In that case, residuals are assumed homoscedastic as well as serially uncorrelated. For type `CL`, clustered covariance matrix is computed. The options are then included in `vcovOptions` (see `meatCL`). - `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. - `data`: A data.frame or a matrix with column names (Optional). - `na.action`: Action to take for missing values. If missing values are present and the option is set to `"na.pass"`, the model won't be estimable. - `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"`. - `smooth`: If `TRUE`, the moment function is smoothed using a kernel method. ## Returns 'momentModel' returns an object of one of the subclasses of `"momentModel"`. ## References 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. ## Examples ```r data(simData) theta <- c(beta0=1,beta1=2) ## A linearModel model1 <- momentModel(y~x1, ~z1+z2, data=simData) ## A nonlinearModel g <- y~beta0+x1^beta1 h <- ~z1+z2 model2 <- momentModel(g, h, c(beta0=1, beta1=2), data=simData) ## A functionModel fct <- function(tet, x) { m1 <- (tet[1] - x) m2 <- (tet[2]^2 - (x - tet[1])^2) m3 <- x^3 - tet[1]*(tet[1]^2 + 3*tet[2]^2) f <- cbind(m1, m2, m3) return(f) } dfct <- function(tet, x) { jacobian <- matrix(c( 1, 2*(-tet[1]+mean(x)), -3*tet[1]^2-3*tet[2]^2,0, 2*tet[2], -6*tet[1]*tet[2]), nrow=3,ncol=2) return(jacobian) } model3 <- momentModel(fct, simData$x3, theta0=c(beta0=1, beta1=2), grad=dfct) ```

momentModel function