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

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. (integer(1)) The number of covariates. (numeric(1)) The value of the causal parameter. (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 .