3.2.2. doubleml.irm.datasets.make_iivm_data

doubleml.irm.datasets.make_iivm_data(n_obs=500, dim_x=20, theta=1.0, alpha_x=0.2, return_type='DoubleMLData')

Generates data from a interactive IV regression (IIVM) model. The data generating process is defined as

\[ \begin{align}\begin{aligned}d_i &= 1\left\lbrace \alpha_x Z + v_i > 0 \right\rbrace,\\y_i &= \theta d_i + x_i' \beta + u_i,\end{aligned}\end{align} \]

with \(Z \sim \text{Bernoulli}(0.5)\) and

\[\begin{split}\left(\begin{matrix} u_i \\ v_i \end{matrix} \right) \sim \mathcal{N}\left(0, \left(\begin{matrix} 1 & 0.3 \\ 0.3 & 1 \end{matrix} \right) \right).\end{split}\]

The covariates \(x_i \sim \mathcal{N}(0, \Sigma)\), where \(\Sigma\) is a matrix with entries \(\Sigma_{kj} = 0.5^{|j-k|}\) and \(\beta\) is a dim_x-vector with entries \(\beta_j=\frac{1}{j^2}\).

The data generating process is inspired by a process used in the simulation experiment of Farbmacher, Gruber and Klaassen (2020).

Parameters:

• n_obs – The number of observations to simulate.

• dim_x – The number of covariates.

• theta – The value of the causal parameter.

• alpha_x – The value of the parameter \(\alpha_x\).

• return_type –

  If 'DoubleMLData' or DoubleMLData, returns a DoubleMLData object.

  If 'DataFrame', 'pd.DataFrame' or pd.DataFrame, returns a pd.DataFrame.

  If 'array', 'np.ndarray', 'np.array' or np.ndarray, returns np.ndarray’s (x, y, d, z).

References

Farbmacher, H., Guber, R. and Klaaßen, S. (2020). Instrument Validity Tests with Causal Forests. MEA Discussion Paper No. 13-2020. Available at SSRN: http://dx.doi.org/10.2139/ssrn.3619201.