# Estimete the parameters with gel after IV selecting Hybrid gel estimator after selecting IVs in the reduced form equation. ```r naive.gel( g, x, z, max.degree = 10, criterion = c("BIC", "AIC", "GCV", "AICc", "EBIC"), df.method = c("default", "active"), penalty = c("grLasso", "grMCP", "grSCAD", "gel", "cMCP"), endogenous.index = c(), IV.intercept = FALSE, family = c("gaussian", "binomial", "poisson"), ... ) ``` ## 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 details gel). - `x`: The design matrix, without an intercept. - `z`: The instrument variables matrix. - `max.degree`: The upper limit value of degree of B-splines when using BIC/AIC to choose the tuning parameters, default is BIC. - `criterion`: The criterion by which to select the regularization parameter. One of "AIC", "BIC","EBIC", "GCV", "AICc"; default is "BIC". - `df.method`: How should effective model parameters be calculated? One of: "active", which counts the number of nonzero coefficients; or "default", which uses the calculated df returned by grpreg. default is "default". - `penalty`: The penalty to be applied to the model. For group selection, one of grLasso, grMCP, or grSCAD. For bi-level selection, one of gel or cMCP. Default is " grLasso". - `endogenous.index`: Specify which variables in design matrix are endogenous variables, the variable corresponds to the value 1 is endogenous variables, the variable corresponds to the value 0 is exogenous variable, the default is all endogenous variables. - `IV.intercept`: Intercept of instrument variables, default is “FALSE”. - `family`: Either "gaussian" or "binomial", depending on the response, default is "gaussian". - `...`: Arguments passed to gel (such as type,kernel...,detail see gel). ## Returns An object of type `naive.gel` which is a list with the following components: - **degree**: Degree of B-splines. - **criterion**: The criterion by which to select the regularization parameter. One of "AIC", "BIC", "GCV", "AICc","EBIC"; default is "BIC". - **ind**: The index of selected instrument variables. - **ind.b**: The index of selected instrument variables after B-splines. - **gel**: Gel object, detail see gel. ## Details See naivereg and gel ## Examples ```r # gel estimation after IV selection n = 200 phi<-c(.2,.7) thet <- 0.2 sd <- .2 set.seed(123) x <- matrix(arima.sim(n = n, list(order = c(2,0,1), ar = phi, ma = thet, sd = sd)), ncol = 1) y <- x[7:n] ym1 <- x[6:(n-1)] ym2 <- x[5:(n-2)] H <- cbind(x[4:(n-3)], x[3:(n-4)], x[2:(n-5)], x[1:(n-6)]) g <- y ~ ym1 + ym2 x <- H naive.gel(g, cbind(ym1,ym2),x, tet0 =c(0,.3,.6)) ``` ## References Q. Fan and W. Zhong (2018), “Nonparametric Additive Instrumental Variable Estimator: A Group Shrinkage Estimation Perspective,” Journal of Business & Economic Statistics, doi: 10.1080/07350015.2016.1180991. Caner, M. and Fan, Q. (2015), Hybrid GEL Estimators: Instrument Selection with Adaptive Lasso, Journal of Econometrics, Volume 187, 256–274. ## Author(s) Qingliang Fan, KongYu He, Wei Zhong

naive.gel function