Generates data from a partially linear IV regression model used in Chernozhukov, Hansen and Spindler (2015). The data generating process is defined as

\(z_i = \Pi x_i + \zeta_i,\)

\(d_i = x_i'\gamma + z_i'\delta + u_i,\)

\(y_i = \alpha d_i + x_i'\beta + \epsilon_i,\)

with

\(\left(\begin{array}{c} \varepsilon_i \\ u_i \\ \zeta_i \\ x_i \end{array} \right) \sim \mathcal{N}\left(0, \left(\begin{array}{cccc} 1 & 0.6 & 0 & 0 \\ 0.6 & 1 & 0 & 0 \\ 0 & 0 & 0.25 I_{p_n^z} & 0 \\ 0 & 0 & 0 & \Sigma \end{array} \right) \right)\)

where \(\Sigma\) is a \(p_n^x \times p_n^x\) matrix with entries \(\Sigma_{kj} = 0.5^{|j-k|}\) and \(I_{p_n^z}\) is the \(p^z_n \times p^z_n\) identity matrix. \(\beta=\gamma\) iis a \(p^x_n\)-vector with entries \(\beta_j = \frac{1}{j^2}\), \(\delta\) is a \(p^z_n\)-vector with entries \(\delta_j = \frac{1}{j^2}\) and \(\Pi = (I_{p_n^z}, O_{p_n^z \times (p_n^x - p_n^z)})\).

make_pliv_CHS2015(
  n_obs,
  alpha = 1,
  dim_x = 200,
  dim_z = 150,
  return_type = "DoubleMLData"
)

Arguments

n_obs

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

alpha

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

dim_x

(integer(1))
The number of covariates.

dim_z

(integer(1))
The number of instruments.

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, d and z 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., Hansen, C. and Spindler, M. (2015), Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments. American Economic Review: Papers and Proceedings, 105 (5): 486-90.