Estimator for the Partially Linear IV Model.

Estimator for the partially linear IV model.

Usage

ddml_pliv(
  y,
  D,
  Z,
  X,
  learners,
  learners_DX = learners,
  learners_ZX = learners,
  sample_folds = 10,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 10,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DX = custom_ensemble_weights,
  custom_ensemble_weights_ZX = 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 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 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).

learners_DX, learners_ZX

Optional arguments to allow for different base learners for estimation of \(E[D|X]\), \(E[Z|X]\). 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.

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_DX, custom_ensemble_weights_ZX

Optional arguments to allow for different custom ensemble weights for learners_DX,learners_ZX. Setup is identical to custom_ensemble_weights. Note: custom_ensemble_weights and custom_ensemble_weights_DX,custom_ensemble_weights_ZX 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_pliv returns an object of S3 class ddml_pliv. An object of class ddml_pliv 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 \(Z - \hat{E}[Z\vert X]\) as the instrument. See also AER::ivreg() for details.
learners,learners_DX,learners_ZX, cluster_variable, subsamples, cv_subsamples_list,ensemble_type: Pass-through of selected user-provided arguments. See above.

Details

ddml_pliv 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 \(E[Cov(U, Z\vert X)] = 0\) and \(E[Cov(D, Z\vert X)] \neq 0\), 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.

Kleiber C, Zeileis A (2008). Applied Econometrics with R. Springer-Verlag, New York.

Wolpert D H (1992). "Stacked generalization." Neural Networks, 5(2), 241-259.

Examples

# Construct variables from the included Angrist & Evans (1998) data
y = AE98[, "worked"]
D = AE98[, "morekids"]
Z = AE98[, "samesex"]
X = AE98[, c("age","agefst","black","hisp","othrace","educ")]

# Estimate the partially linear IV model using a single base learner, ridge.
pliv_fit <- ddml_pliv(y, D, Z, X,
                      learners = list(what = mdl_glmnet,
                                      args = list(alpha = 0)),
                      sample_folds = 2,
                      silent = TRUE)
summary(pliv_fit)
#> PLIV estimation results: 
#>  
#> , , single base learner
#> 
#>              Estimate Std. Error   t value Pr(>|t|)
#> (Intercept) -3.44e-07     0.0069 -4.99e-05    1.000
#> D_r         -2.35e-01     0.1893 -1.24e+00    0.214
#>