naive.gel {naivereg}

Estimete the parameters with gel after IV selecting

Description

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

Usage

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).

Details

See naivereg and gel

Value

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.

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

# 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))