make_plr_CCDDHNR2018 {DoubleML}

Generates data from a partially linear regression model used in Chernozhukov et al. (2018)

Description

Generates data from a partially linear regression model used in Chernozhukov et al. (2018) for Figure 1. The data generating process is defined as

d_i = m_0(x_i) + s_1 v_i,

y_i = \alpha d_i + g_0(x_i) + s_2 \zeta_i,

with v_i \sim \mathcal{N}(0,1) and \zeta_i \sim \mathcal{N}(0,1),. The covariates are distributed as x_i \sim \mathcal{N}(0, \Sigma), where \Sigma is a matrix with entries \Sigma_{kj} = 0.7^{|j-k|}. The nuisance functions are given by

m_0(x_i) = a_0 x_{i,1} + a_1 \frac{\exp(x_{i,3})}{1+\exp(x_{i,3})},

g_0(x_i) = b_0 \frac{\exp(x_{i,1})}{1+\exp(x_{i,1})} + b_1 x_{i,3},

with a_0=1, a_1=0.25, s_1=1, b_0=1, b_1=0.25, s_2=1.

Usage

make_plr_CCDDHNR2018(
  n_obs = 500,
  dim_x = 20,
  alpha = 0.5,
  return_type = "DoubleMLData"
)

Arguments

n_obs

(integer(1))
The number of observations to simulate.

dim_x

(integer(1))
The number of covariates.

alpha

(numeric(1))
The value of the causal parameter.

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 and d 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., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W. and Robins, J. (2018), Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21: C1-C68. doi:10.1111/ectj.12097.