Estimator for the flexible partially linear IV model.
ddml_fpliv(
y,
D,
Z,
X,
learners,
learners_DXZ = learners,
learners_DX = learners,
sample_folds = 10,
ensemble_type = "nnls",
shortstack = FALSE,
cv_folds = 10,
enforce_LIE = TRUE,
custom_ensemble_weights = NULL,
custom_ensemble_weights_DXZ = custom_ensemble_weights,
custom_ensemble_weights_DX = custom_ensemble_weights,
cluster_variable = seq_along(y),
subsamples = NULL,
cv_subsamples_list = NULL,
silent = FALSE
)ddml_fpliv returns an object of S3 class
ddml_fpliv. An object of class ddml_fpliv is a list
containing the following components:
coefA vector with the \(\theta_0\) estimates.
weightsA list of matrices, providing the weight assigned to each base learner (in chronological order) by the ensemble procedure.
mspeA list of matrices, providing the MSPE of each base learner (in chronological order) computed by the cross-validation step in the ensemble construction.
iv_fitObject of class ivreg from the IV
regression of \(Y - \hat{E}[Y\vert X]\) on
\(D - \hat{E}[D\vert X]\) using
\(\hat{E}[D\vert X,Z] - \hat{E}[D\vert X]\) as the instrument.
learners,learners_DX,learners_DXZ,
cluster_variable,subsamples,
cv_subsamples_list,ensemble_typePass-through of selected user-provided arguments. See above.
The outcome variable.
A matrix of endogenous variables.
A (sparse) matrix of instruments.
A (sparse) matrix of control variables.
May take one of two forms, depending on whether a single
learner or stacking with multiple learners is used for estimation of the
conditional expectation functions.
If a single learner is used, learners is a list with two named
elements:
what The base learner function. The function must be
such that it predicts a named input y using a named input
X.
args Optional arguments to be passed to what.
If stacking with multiple learners is used, learners is a list of
lists, each containing four named elements:
fun The base learner function. The function must be
such that it predicts a named input y using a named input
X.
args Optional arguments to be passed to fun.
assign_X An optional vector of column indices
corresponding to control variables in X that are passed to
the base learner.
assign_Z An optional vector of column indices
corresponding to instruments in Z that are passed to the
base learner.
Omission of the args element results in default arguments being
used in fun. Omission of assign_X (and/or assign_Z)
results in inclusion of all variables in X (and/or Z).
Optional arguments to allow for different
estimators of \(E[D \vert X, Z]\), \(E[D \vert X]\). Setup is
identical to learners.
Number of cross-fitting folds.
Ensemble method to combine base learners into final estimate of the conditional expectation functions. Possible values are:
"nnls" Non-negative least squares.
"nnls1" Non-negative least squares with the constraint
that all weights sum to one.
"singlebest" Select base learner with minimum MSPE.
"ols" Ordinary least squares.
"average" Simple average over base learners.
Multiple ensemble types may be passed as a vector of strings.
Boolean to use short-stacking.
Number of folds used for cross-validation in ensemble construction.
Indicator equal to 1 if the law of iterated expectations is enforced in the first stage.
A numerical matrix with user-specified
ensemble weights. Each column corresponds to a custom ensemble
specification, each row corresponds to a base learner in learners
(in chronological order). Optional column names are used to name the
estimation results corresponding the custom ensemble specification.
Optional
arguments to allow for different
custom ensemble weights for learners_DXZ,learners_DX. Setup
is identical to custom_ensemble_weights. Note:
custom_ensemble_weights and
custom_ensemble_weights_DXZ,custom_ensemble_weights_DX must
have the same number of columns.
A vector of cluster indices.
List of vectors with sample indices for cross-fitting.
List of lists, each corresponding to a subsample containing vectors with subsample indices for cross-validation.
Boolean to silence estimation updates.
ddml_fpliv provides a double/debiased machine learning
estimator for the parameter of interest \(\theta_0\) in the partially
linear IV model given by
\(Y = \theta_0D + g_0(X) + U,\)
where \((Y, D, X, Z, U)\) is a random vector such that \(E[U\vert X, Z] = 0\) and \(E[Var(E[D\vert X, Z]\vert X)] \neq 0\), and \(g_0\) is an unknown nuisance function.
Ahrens A, Hansen C B, Schaffer M E, Wiemann T (2023). "ddml: Double/debiased machine learning in Stata." https://arxiv.org/abs/2301.09397
Chernozhukov V, Chetverikov D, Demirer M, Duflo E, Hansen C B, Newey W, Robins J (2018). "Double/debiased machine learning for treatment and structural parameters." The Econometrics Journal, 21(1), C1-C68.
Wolpert D H (1992). "Stacked generalization." Neural Networks, 5(2), 241-259.
summary.ddml_fpliv(), AER::ivreg()
Other ddml:
ddml_ate(),
ddml_late(),
ddml_pliv(),
ddml_plm()
# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
D = AE98[, "morekids"]
Z = AE98[, "samesex", drop = FALSE]
X = AE98[, c("age","agefst","black","hisp","othrace","educ")]
# Estimate the partially linear IV model using a single base learner: Ridge.
fpliv_fit <- ddml_fpliv(y, D, Z, X,
learners = list(what = mdl_glmnet,
args = list(alpha = 0)),
sample_folds = 2,
silent = TRUE)
summary(fpliv_fit)
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