Implementation of sample selection estimators

doubleml/__init__.py

@@ -13,6 +13,7 @@
 from .double_ml_lpq import DoubleMLLPQ
 from .double_ml_cvar import DoubleMLCVAR
 from .double_ml_policytree import DoubleMLPolicyTree
+from .double_ml_ssm import DoubleMLSSM
 
 __all__ = ['DoubleMLPLR',
            'DoubleMLPLIV',
@@ -27,6 +28,7 @@
            'DoubleMLQTE',
            'DoubleMLLPQ',
            'DoubleMLCVAR',
-           'DoubleMLPolicyTree']
+           'DoubleMLPolicyTree',
+           'DoubleMLSSM']
 
 __version__ = get_distribution('doubleml').version

doubleml/datasets.py

@@ -1345,3 +1345,91 @@ def treatment_effect(x):
         'effects': te,
         'treatment_effect': treatment_effect}
     return res_dict
+
+
+def make_ssm_data(n_obs=8000, dim_x=100, theta=1, mar=True, return_type='DoubleMLData'):
+    """
+    Generates data from a sample selection model (SSM).
+    The data generating process is defined as
+
+    .. math::
+
+        y_i &= \\theta d_i + x_i' \\beta d_i + u_i, & with Y being observed if s = 1,
+
+        s_i &= 1\\left\\lbrace d_i + \\gamma z_i + x_i' \\beta + v_i > 0 \\right\\rbrace, & &d_i
+        = 1\\left\\lbrace x_i' \\beta + w_i > 0 \\right\\rbrace,
+
+
+    with covariates :math:`x_i \\sim \\mathcal{N}(0, \\Sigma^2_x)`, where
+    :math:`\\Sigma^2_x` is a matrix with entries
+    :math:`\\Sigma_{kj} = 0.5^{|j-k|}`.
+    :math:`\\beta` is a `dim_x`-vector with entries :math:`\\beta_j=\\frac{0.4}{j^2}`
+    :math:`z_i \\sim \\mathcal{N}(0, 1)`,
+    :math:`(u_i,v_i) \\sim \\mathcal{N}(0, \\Sigma^2_{u,v})`,
+    :math:`w_i \\sim \\mathcal{N}(0, 1)`
+
+
+    The data generating process is inspired by a process used in the simulation study (see Appendix E) of Bia,
+    Huber and Lafférs (2023).
+
+    Parameters
+    ----------
+    n_obs :
+        The number of observations to simulate.
+    dim_x :
+        The number of covariates.
+    theta :
+        The value of the causal parameter.
+    mar:
+        Boolean. Indicates whether missingness at random holds.
+    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, s)``.
+
+    References
+    ----------
+    Michela Bia, Martin Huber & Lukáš Lafférs (2023) Double Machine Learning for Sample Selection Models,
+    Journal of Business & Economic Statistics, DOI: 10.1080/07350015.2023.2271071
+    """
+    if mar:
+        sigma = np.array([[1, 0], [0, 1]])
+        gamma = 0
+    else:
+        sigma = np.array([[1, 0.8], [0.8, 1]])
+        gamma = 1
+
+    e = np.random.multivariate_normal(mean=[0, 0], cov=sigma, size=n_obs).T
+
+    cov_mat = toeplitz([np.power(0.5, k) for k in range(dim_x)])
+    x = np.random.multivariate_normal(np.zeros(dim_x), cov_mat, size=[n_obs, ])
+
+    beta = [0.4 / (k**2) for k in range(1, dim_x + 1)]
+
+    d = np.where(np.dot(x, beta) + np.random.randn(n_obs) > 0, 1, 0)
+    z = np.random.randn(n_obs)
+    s = np.where(np.dot(x, beta) + d + gamma * z + e[0] > 0, 1, 0)
+
+    y = np.dot(x, beta) + theta * d + e[1]
+    y[s == 0] = 0
+
+    if return_type in _array_alias:
+        return x, y, d, z, s
+    elif return_type in _data_frame_alias + _dml_data_alias:
+        x_cols = [f'X{i + 1}' for i in np.arange(dim_x)]
+        if mar:
+            data = pd.DataFrame(np.column_stack((x, y, d, s)),
+                                columns=x_cols + ['y', 'd', 's'])
+        else:
+            data = pd.DataFrame(np.column_stack((x, y, d, z, s)),
+                                columns=x_cols + ['y', 'd', 'z', 's'])
+        if return_type in _data_frame_alias:
+            return data
+        else:
+            if mar:
+                return DoubleMLData(data, 'y', 'd', x_cols, None, 's')
+            return DoubleMLData(data, 'y', 'd', x_cols, 'z', 's')
+    else:
+        raise ValueError('Invalid return_type.')