R: Estimators of Average Treatment Effects.

ddml_ate {ddml}

R Documentation

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 = 2,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 5,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DX = custom_ensemble_weights,
  subsamples_D0 = NULL,
  subsamples_D1 = NULL,
  cv_subsamples_list_D0 = NULL,
  cv_subsamples_list_D1 = NULL,
  trim = 0.01,
  silent = FALSE
)

ddml_att(
  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_D0 = NULL,
  subsamples_D1 = NULL,
  cv_subsamples_list_D0 = NULL,
  cv_subsamples_list_D1 = NULL,
  trim = 0.01,
  silent = FALSE
)

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.
`subsamples_D0`, `subsamples_D1`	List of vectors with sample indices for cross-fitting, corresponding to untreated and treated observations, respectively.
`cv_subsamples_list_D0`, `cv_subsamples_list_D1`	List of lists, each corresponding to a subsample containing vectors with subsample indices for cross-validation. Arguments are separated for untreated and treated observations, respectively.
`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].

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, subsamples_D0,subsamples_D1, cv_subsamples_list_D0,cv_subsamples_list_D1, 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.

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 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)

[Package ddml version 0.2.2 Index]