ddml_ate: Estimators of Average Treatment Effects.

Description

Estimators of the average treatment effect and the average treatment effect on the treated.

Usage

ddml_ate(
  y,
  D,
  X,
  learners,
  learners_DX = learners,
  sample_folds = 10,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 10,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DX = custom_ensemble_weights,
  cluster_variable = seq_along(y),
  subsamples_byD = NULL,
  cv_subsamples_byD = NULL,
  trim = 0.01,
  silent = FALSE
)
ddml_att(
  y,
  D,
  X,
  learners,
  learners_DX = learners,
  sample_folds = 10,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 10,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DX = custom_ensemble_weights,
  cluster_variable = seq_along(y),
  subsamples_byD = NULL,
  cv_subsamples_byD = NULL,
  trim = 0.01,
  silent = FALSE
)

Value

ddml_ate and ddml_att return an object of S3 class ddml_ate and ddml_att, respectively. An object of class ddml_ate or ddml_att is a list containing the following components:

ate / att: A vector with the average treatment effect / average treatment effect on the treated 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.
psi_a, psi_b: Matrices needed for the computation of scores. Used in summary.ddml_ate() or summary.ddml_att().
oos_pred: List of matrices, providing the reduced form predicted values.
learners,learners_DX,cluster_variable, subsamples_D0,subsamples_D1, cv_subsamples_list_D0,cv_subsamples_list_D1, ensemble_type: Pass-through of selected user-provided arguments. See above.

Arguments

y

The outcome variable.

D

The binary endogenous variable of interest.

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.

cluster_variable

A vector of cluster indices.

subsamples_byD

List of two lists corresponding to the two treatment levels. Each list contains vectors with sample indices for cross-fitting.

cv_subsamples_byD

List of two lists, each corresponding to one of the two treatment levels. Each of the two lists contains lists, each corresponding to a subsample and contains vectors with subsample indices for cross-validation.

trim

Number in (0, 1) for trimming the estimated propensity scores at trim and 1-trim.

silent

Boolean to silence estimation updates.

Details

ddml_ate and ddml_att provide double/debiased machine learning estimators for the average treatment effect and the average treatment effect on the treated, respectively, in the interactive model given by

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

where \((Y, D, X, U)\) is a random vector such that \(\operatorname{supp} D = \{0,1\}\), \(E[U\vert D, X] = 0\), and \(\Pr(D=1\vert X) \in (0, 1)\) with probability 1, and \(g_0\) is an unknown nuisance function.

In this model, the average treatment effect is defined as

\(\theta_0^{\textrm{ATE}} \equiv E[g_0(1, X) - g_0(0, X)]\).

and the average treatment effect on the treated is defined as

\(\theta_0^{\textrm{ATT}} \equiv E[g_0(1, X) - g_0(0, X)\vert D = 1]\).

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.

Examples

Run this code

# 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 average treatment effect using a single base learner, ridge.
ate_fit <- ddml_ate(y, D, X,
                    learners = list(what = mdl_glmnet,
                                    args = list(alpha = 0)),
                    sample_folds = 2,
                    silent = TRUE)
summary(ate_fit)

# Estimate the average treatment effect 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")
ate_fit <- ddml_ate(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(ate_fit)

Run the code above in your browser using DataLab