Estimator for the flexible partially linear IV model.
Usage
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
)
Arguments
- y
The outcome variable.
- D
A matrix of endogenous variables.
- Z
A (sparse) matrix of instruments.
- X
A (sparse) matrix of control variables.
- learners
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 inputy
using a named inputX
.args
Optional arguments to be passed towhat
.
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 inputy
using a named inputX
.args
Optional arguments to be passed tofun
.assign_X
An optional vector of column indices corresponding to control variables inX
that are passed to the base learner.assign_Z
An optional vector of column indices corresponding to instruments inZ
that are passed to the base learner.
Omission of the
args
element results in default arguments being used infun
. Omission ofassign_X
(and/orassign_Z
) results in inclusion of all variables inX
(and/orZ
).- learners_DXZ, learners_DX
Optional arguments to allow for different estimators of \(E[D \vert X, Z]\), \(E[D \vert X]\). Setup is identical to
learners
.- sample_folds
Number of cross-fitting folds.
- ensemble_type
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.
- shortstack
Boolean to use short-stacking.
- cv_folds
Number of folds used for cross-validation in ensemble construction.
- enforce_LIE
Indicator equal to 1 if the law of iterated expectations is enforced in the first stage.
- custom_ensemble_weights
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.- custom_ensemble_weights_DXZ, custom_ensemble_weights_DX
Optional arguments to allow for different custom ensemble weights for
learners_DXZ
,learners_DX
. Setup is identical tocustom_ensemble_weights
. Note:custom_ensemble_weights
andcustom_ensemble_weights_DXZ
,custom_ensemble_weights_DX
must have the same number of columns.- cluster_variable
A vector of cluster indices.
- subsamples
List of vectors with sample indices for cross-fitting.
- cv_subsamples_list
List of lists, each corresponding to a subsample containing vectors with subsample indices for cross-validation.
- silent
Boolean to silence estimation updates.
Value
ddml_fpliv
returns an object of S3 class
ddml_fpliv
. An object of class ddml_fpliv
is a list
containing the following components:
coef
A vector with the \(\theta_0\) estimates.
weights
A list of matrices, providing the weight assigned to each base learner (in chronological order) by the ensemble procedure.
mspe
A list of matrices, providing the MSPE of each base learner (in chronological order) computed by the cross-validation step in the ensemble construction.
iv_fit
Object 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_type
Pass-through of selected user-provided arguments. See above.
Details
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.
References
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.
See also
summary.ddml_fpliv()
, AER::ivreg()
Other ddml:
ddml_ate()
,
ddml_late()
,
ddml_pliv()
,
ddml_plm()
Examples
# 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)
#> FPLIV estimation results:
#>
#> , , single base learner
#>
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -6.75e-05 0.0069 -0.00979 0.992
#> D_r -1.40e-01 0.1818 -0.77195 0.440
#>