# make_pliv_multiway_cluster_CKMS2021: 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 with multiway cluster sample used in Chiang et al. (2021). The data generating process is defined as

Z_{ij} = X_{ij}' ξ_0 + V_{ij},

D_{ij} = Z_{ij}' π_{10} + X_{ij}' π_{20} + v_{ij},

Y_{ij} = D_{ij} θ + X_{ij}' ζ_0 + \varepsilon_{ij},

with

X_{ij} = (1 - ω_1^X - ω_2^X) α_{ij}^X + ω_1^X α_{i}^X + ω_2^X α_{j}^X,

\varepsilon_{ij} = (1 - ω_1^\varepsilon - ω_2^\varepsilon) α_{ij}^\varepsilon + ω_1^\varepsilon α_{i}^\varepsilon + ω_2^\varepsilon α_{j}^\varepsilon,

v_{ij} = (1 - ω_1^v - ω_2^v) α_{ij}^v + ω_1^v α_{i}^v + ω_2^v α_{j}^v,

V_{ij} = (1 - ω_1^V - ω_2^V) α_{ij}^V + ω_1^V α_{i}^V + ω_2^V α_{j}^V,

and α_{ij}^X, α_{i}^X, α_{j}^X \sim \mathcal{N}(0, Σ) where Σ is a p_x \times p_x matrix with entries Σ_{kj} = s_X^{|j-k|}.

Further

≤ft(\begin{array}{c} α_{ij}^\varepsilon \\ α_{ij}^v \end{array}\right), ≤ft(\begin{array}{c} α_{i}^\varepsilon \\ α_{i}^v \end{array}\right), ≤ft(\begin{array}{c} α_{j}^\varepsilon \\ α_{j}^v \end{array}\right) \sim \mathcal{N}≤ft(0, ≤ft(\begin{array}{cc} 1 & s_{\varepsilon v} \\ s_{\varepsilon v} & 1 \end{array}\right) \right)

and α_{ij}^V, α_{i}^V, α_{j}^V \sim \mathcal{N}(0, 1).

## Usage

 1 2 3 4 5 6 7 8 make_pliv_multiway_cluster_CKMS2021( N = 25, M = 25, dim_X = 100, theta = 1, return_type = "DoubleMLClusterData", ... ) 

## Arguments

 N (integer(1)) The number of observations (first dimension). M (integer(1)) The number of observations (second dimension). dim_X (integer(1)) The number of covariates. theta (numeric(1)) The value of the causal parameter. return_type (character(1)) If "DoubleMLClusterData", returns a DoubleMLClusterData 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, z and cluster_vars is returned. Every entry in the list is a matrix() object. Default is "DoubleMLClusterData". ... Additional keyword arguments to set non-default values for the parameters π_{10}=1.0, ω_X = ω_{\varepsilon} = ω_V = ω_v = (0.25, 0.25), s_X = s_{\varepsilon v} = 0.25, or the p_x-vectors ζ_0 = π_{20} = ξ_0 with default entries ζ_{0})_j = 0.5^j.

## Value

A data object according to the choice of return_type.

## References

Chiang, H. D., Kato K., Ma, Y. and Sasaki, Y. (2021), Multiway Cluster Robust Double/Debiased Machine Learning, Journal of Business & Economic Statistics, doi: 10.1080/07350015.2021.1895815, https://arxiv.org/abs/1909.03489.

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