Generates data from a partially linear regression model used in a blog article by Turrell (2018).

Generates data from a partially linear regression model used in a blog article by Turrell (2018). The data generating process is defined as

\(d_i = m_0(x_i' b) + v_i,\)

\(y_i = \theta d_i + g_0(x_i' b) + u_i,\)

with \(v_i \sim \mathcal{N}(0,1)\), \(u_i \sim \mathcal{N}(0,1)\), and covariates \(x_i \sim \mathcal{N}(0, \Sigma)\), where \(\Sigma\) is a random symmetric, positive-definite matrix generated with clusterGeneration::genPositiveDefMat(). \(b\) is a vector with entries \(b_j=\frac{1}{j}\) and the nuisance functions are given by

\(m_0(x_i) = \frac{1}{2 \pi} \frac{\sinh(\gamma)}{\cosh(\gamma) - \cos(x_i-\nu)},\)

\(g_0(x_i) = \sin(x_i)^2.\)

Usage

make_plr_turrell2018(
  n_obs = 100,
  dim_x = 20,
  theta = 0.5,
  return_type = "DoubleMLData",
  nu = 0,
  gamma = 1
)

Arguments

n_obs: (integer(1))
The number of observations to simulate.
dim_x: (integer(1))
The number of covariates.
theta: (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".
nu: (numeric(1))
The value of the parameter \(\nu\). Default is 0.
gamma: (numeric(1))
The value of the parameter \(\gamma\). Default is 1.

Value

A data object according to the choice of return_type.

References

Turrell, A. (2018), Econometrics in Python part I - Double machine learning, Markov Wanderer: A blog on economics, science, coding and data. https://aeturrell.com/blog/posts/econometrics-in-python-parti-ml/.