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.

Turrell, A. (2018), Econometrics in Python part I - Double machine learning, Markov Wanderer: A blog on economics, science, coding and data. http://aeturrell.com/2018/02/10/econometrics-in-python-partI-ML/.