Description Usage Arguments Details Value Author(s) References Examples

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

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`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", "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). |

See naivereg and gmm.

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. |

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.

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```
$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
```

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