make_pliv_multiway_cluster_CKMS2021 {DoubleML}R Documentation

Generates data from a partially linear IV regression model with multiway cluster sample used in Chiang et al. (2021).

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

Zij=Xijξ0+Vij,Z_{ij} = X_{ij}' \xi_0 + V_{ij},

Dij=Zijπ10+Xijπ20+vij,D_{ij} = Z_{ij}' \pi_{10} + X_{ij}' \pi_{20} + v_{ij},

Yij=Dijθ+Xijζ0+εij,Y_{ij} = D_{ij} \theta + X_{ij}' \zeta_0 + \varepsilon_{ij},

with

Xij=(1ω1Xω2X)αijX+ω1XαiX+ω2XαjX,X_{ij} = (1 - \omega_1^X - \omega_2^X) \alpha_{ij}^X + \omega_1^X \alpha_{i}^X + \omega_2^X \alpha_{j}^X,

εij=(1ω1εω2ε)αijε+ω1εαiε+ω2εαjε,\varepsilon_{ij} = (1 - \omega_1^\varepsilon - \omega_2^\varepsilon) \alpha_{ij}^\varepsilon + \omega_1^\varepsilon \alpha_{i}^\varepsilon + \omega_2^\varepsilon \alpha_{j}^\varepsilon,

vij=(1ω1vω2v)αijv+ω1vαiv+ω2vαjv,v_{ij} = (1 - \omega_1^v - \omega_2^v) \alpha_{ij}^v + \omega_1^v \alpha_{i}^v + \omega_2^v \alpha_{j}^v,

Vij=(1ω1Vω2V)αijV+ω1VαiV+ω2VαjV,V_{ij} = (1 - \omega_1^V - \omega_2^V) \alpha_{ij}^V + \omega_1^V \alpha_{i}^V + \omega_2^V \alpha_{j}^V,

and αijX,αiX,αjXN(0,Σ)\alpha_{ij}^X, \alpha_{i}^X, \alpha_{j}^X \sim \mathcal{N}(0, \Sigma) where Σ\Sigma is a px×pxp_x \times p_x matrix with entries Σkj=sXjk\Sigma_{kj} = s_X^{|j-k|}.

Further

(αijεαijv),(αiεαiv),(αjεαjv)N(0,(1sεvsεv1))\left(\begin{array}{c} \alpha_{ij}^\varepsilon \\ \alpha_{ij}^v \end{array}\right), \left(\begin{array}{c} \alpha_{i}^\varepsilon \\ \alpha_{i}^v \end{array}\right), \left(\begin{array}{c} \alpha_{j}^\varepsilon \\ \alpha_{j}^v \end{array}\right) \sim \mathcal{N}\left(0, \left(\begin{array}{cc} 1 & s_{\varepsilon v} \\ s_{\varepsilon v} & 1 \end{array}\right) \right)

and αijV,αiV,αjVN(0,1)\alpha_{ij}^V, \alpha_{i}^V, \alpha_{j}^V \sim \mathcal{N}(0, 1).

Usage

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 π10=1.0\pi_{10}=1.0, ωX=ωε=ωV=ωv=(0.25,0.25)\omega_X = \omega_{\varepsilon} = \omega_V = \omega_v = (0.25, 0.25), sX=sεv=0.25s_X = s_{\varepsilon v} = 0.25, or the pxp_x-vectors ζ0=π20=ξ0\zeta_0 = \pi_{20} = \xi_0 with default entries ζ0)j=0.5j\zeta_{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.


[Package DoubleML version 1.0.1 Index]