ddml_plm {ddml}

Estimator for the Partially Linear Model.

Description

Estimator for the partially linear model.

Usage

ddml_plm(
  y,
  D,
  X,
  learners,
  learners_DX = learners,
  sample_folds = 2,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 5,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DX = custom_ensemble_weights,
  subsamples = NULL,
  cv_subsamples_list = NULL,
  silent = FALSE
)

Arguments

y

The outcome variable.

D

A matrix of endogenous variables.

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.

Omission of the args element results in default arguments being used in fun. Omission of assign_X results in inclusion of all variables in X.

learners_DX

Optional argument to allow for different estimators of E[D|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

Optional argument to allow for different custom ensemble weights for learners_DX. Setup is identical to custom_ensemble_weights. Note: custom_ensemble_weights and custom_ensemble_weights_DX must have the same number of columns.

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.

Details

ddml_plm provides a double/debiased machine learning estimator for the parameter of interest \theta_0 in the partially linear model given by

Y = \theta_0D + g_0(X) + U,

where (Y, D, X, U) is a random vector such that E[Cov(U, D\vert X)] = 0 and E[Var(D\vert X)] \neq 0, and g_0 is an unknown nuisance function.

Value

ddml_plm returns an object of S3 class ddml_plm. An object of class ddml_plm 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.

ols_fit

Object of class lm from the second stage regression of Y - \hat{E}[Y|X] on D - \hat{E}[D|X].

learners,learners_DX,subsamples, cv_subsamples_list,ensemble_type

Pass-through of selected user-provided arguments. See above.

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_plm()

Other ddml: ddml_ate(), ddml_fpliv(), ddml_late(), ddml_pliv()

Examples

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

# Estimate the partially linear model using a single base learner, ridge.
plm_fit <- ddml_plm(y, D, X,
                    learners = list(what = mdl_glmnet,
                                    args = list(alpha = 0)),
                    sample_folds = 2,
                    silent = TRUE)
summary(plm_fit)

# Estimate the partially linear model using short-stacking with base learners
#     ols, lasso, and ridge. We can also use custom_ensemble_weights
#     to estimate the ATE using every individual base learner.
weights_everylearner <- diag(1, 3)
colnames(weights_everylearner) <- c("mdl:ols", "mdl:lasso", "mdl:ridge")
plm_fit <- ddml_plm(y, D, X,
                    learners = list(list(fun = ols),
                                    list(fun = mdl_glmnet),
                                    list(fun = mdl_glmnet,
                                         args = list(alpha = 0))),
                    ensemble_type = 'nnls',
                    custom_ensemble_weights = weights_everylearner,
                    shortstack = TRUE,
                    sample_folds = 2,
                    silent = TRUE)
summary(plm_fit)