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 \(a_0=1\), \(a_1=0.25\), \(s_1=1\), \(b_0=1\), \(b_1=0.25\), \(s_2=1\).

  n_obs = 500,
  dim_x = 20,
  alpha = 0.5,
  return_type = "DoubleMLData"



The number of observations to simulate.


The number of covariates.


The value of the causal parameter.


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".


A data object according to the choice of return_type.


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 .