# naive.gmm: Estimete the parameters with gmm after IV selecting In naivereg: Nonparametric Additive Instrumental Variable Estimator and Related IV Methods

## Description

Hybrid gmm estimator after selecting IVs in the reduced form equation.

## Usage

  1 2 3 4 5 6 7 8 9 10 11 12 13 naive.gmm( 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(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 details gmm). 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", "GCV", "AICc","EBIC", 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 gmm (such as type,kernel...,detail see gmm).

## Details

See naivereg and gmm.

## Value

An object of type naive.gmm 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. gmm Gmm object, detail see gmm.

## Author(s)

Qingliang Fan, KongYu He, Wei Zhong

## 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.

## Examples

 1 2 3 4 5 6 # gmm estimation after IV selection data("naivedata") x=naivedata[,1] y=naivedata[,2] z=naivedata[,3:22] naive.gmm(y~x+x^2,cbind(x,x^2),z) 

### Example output

$degree [1] 3$criterion
[1] "BIC"

$ind [1] 1 4 5 15 19$ind.b
[1]  1  2  3 10 11 12 13 14 15 43 44 45 55 56 57

\$gel
Method
twoStep

Objective function value:  0.01845174

(Intercept)            x
-0.055811     0.505174


naivereg documentation built on March 18, 2020, 5:09 p.m.