Description Usage Arguments Details Value Author(s) References Examples

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

1 2 3 4 5 6 7 8 9 10 11 12 13 |

`g` |
A function of the form |

`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). |

See naivereg and gel

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. |

Qingliang Fan, KongYu He, Wei Zhong

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
# 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))
``` |

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