# make_pliv_CHS2015: Generates data from a partially linear IV regression model... In DoubleML: Double Machine Learning in R

## Description

Generates data from a partially linear IV regression model used in Chernozhukov, Hansen and Spindler (2015). The data generating process is defined as

z_i = Π x_i + ζ_i,

d_i = x_i'γ + z_i'δ + u_i,

y_i = α d_i + x_i'β + ε_i,

with

≤ft(\begin{array}{c} \varepsilon_i \\ u_i \\ ζ_i \\ x_i \end{array} \right) \sim \mathcal{N}≤ft(0, ≤ft(\begin{array}{cccc} 1 & 0.6 & 0 & 0 \\ 0.6 & 1 & 0 & 0 \\ 0 & 0 & 0.25 I_{p_n^z} & 0 \\ 0 & 0 & 0 & Σ \end{array} \right) \right)

where Σ is a p_n^x \times p_n^x matrix with entries Σ_{kj} = 0.5^{|j-k|} and I_{p_n^z} is the p^z_n \times p^z_n identity matrix. β=γ iis a p^x_n-vector with entries β_j = \frac{1}{j^2}, δ is a p^z_n-vector with entries δ_j = \frac{1}{j^2} and Π = (I_{p_n^z}, O_{p_n^z \times (p_n^x - p_n^z)}).

## Usage

 1 2 3 4 5 6 7 make_pliv_CHS2015( n_obs, alpha = 1, dim_x = 200, dim_z = 150, return_type = "DoubleMLData" ) 

## Arguments

 n_obs (integer(1)) The number of observations to simulate. alpha (numeric(1)) The value of the causal parameter. dim_x (integer(1)) The number of covariates. dim_z (integer(1)) The number of instruments. return_type (character(1)) If "DoubleMLData", returns a DoubleMLData object. If "data.frame" returns a data.frame(). If "data.table" returns a data.table(). If "matrix" a named list() with entries X, y, d and z is returned. Every entry in the list is a matrix() object. Default is "DoubleMLData".

## Value

A data object according to the choice of return_type.

## References

Chernozhukov, V., Hansen, C. and Spindler, M. (2015), Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments. American Economic Review: Papers and Proceedings, 105 (5): 486-90.

DoubleML documentation built on Oct. 26, 2021, 5:06 p.m.