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DMLパッケージで試してみる

Partially Linear Regression Model

Y=Dθ0+g0(X)+ζ,E(ζ∣D,X)=0,D=m0(X)+V,E(V∣X)=0,\begin{align}\begin{aligned}Y = D \theta_0 + g_0(X) + \zeta, & &\mathbb{E}(\zeta | D,X) = 0, \\ D = m_0(X) + V, & &\mathbb{E}(V | X) = 0,\end{aligned}\end{align}
(1)

doubleml.DoubleMLPLR — DoubleML documentation

class doubleml.DoubleMLPLR(obj_dml_data, ml_l, ml_m, ml_g=None, n_folds=5, n_rep=1, score='partialling out', draw_sample_splitting=True)

nuisance functions

  • ml_lは ℓ0(X)=E[Y∣X]\ell_0(X) = E[Y|X]

  • ml_mは m0(X)=E[D∣X]m_0(X) = E[D|X]

  • ml_gは g0(X)=E[Y−Dθ0∣X]g_0(X) = E[Y - D \theta_0|X]で、scoreが'IV-type'のときのみ使われる

デフォルトのscoreが'partialling out'で、これはRobinson (1988）の

ψ(W;θ,η):={Y−ℓ(X)−θ(D−m(X))}(D−m(X)),η=(ℓ,m)\psi(W ; \theta, \eta):=\{Y-\ell(X)-\theta(D-m(X))\}(D-m(X)), \quad \eta=(\ell, m)
(2)

というタイプのスコア関数であり、推定量としては

Y−E[Y∣X]⏟ℓ0(X)=θ0(D−E[D∣X]⏟m0(X))+UY - \underbrace{ E[Y|X] }_{\ell_0(X)} = \theta_0 (D - \underbrace{ E[D|X]}_{m_0(X)} ) + U
(3)

という、残差回帰タイプの推定量をもたらす。

import numpy as np
import doubleml as dml
from doubleml.datasets import make_plr_CCDDHNR2018
from sklearn.ensemble import RandomForestRegressor
from sklearn.base import clone
np.random.seed(0)
learner = RandomForestRegressor(n_estimators=100, max_features=20, max_depth=5, min_samples_leaf=2, random_state=0)
ml_g = learner
ml_m = learner
obj_dml_data = make_plr_CCDDHNR2018(alpha=0.5, n_obs=500, dim_x=20)
dml_plr_obj = dml.DoubleMLPLR(obj_dml_data, ml_g, ml_m)
dml_plr_obj.fit().summary
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計量経済学・因果推論
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計量経済学・因果推論
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