ddml_late: Estimator of the Local Average Treatment Effect.

In ddml: Double/Debiased Machine Learning

Estimator of the Local Average Treatment Effect.

Description

Estimator of the local average treatment effect.

Usage

ddml_late(
  y,
  D,
  Z,
  X,
  learners,
  learners_DXZ = learners,
  learners_ZX = learners,
  sample_folds = 10,
  ensemble_type = "nnls",
  shortstack = FALSE,
  cv_folds = 10,
  custom_ensemble_weights = NULL,
  custom_ensemble_weights_DXZ = custom_ensemble_weights,
  custom_ensemble_weights_ZX = custom_ensemble_weights,
  cluster_variable = seq_along(y),
  subsamples_byZ = NULL,
  cv_subsamples_byZ = NULL,
  trim = 0.01,
  silent = FALSE
)

Arguments

y	The outcome variable.
D	The binary endogenous variable of interest.
Z	Binary instrumental variable.
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_DXZ, learners_ZX	Optional arguments to allow for different estimators of E[D \vert X, Z], E[Z \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.
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_ZX	Optional arguments to allow for different custom ensemble weights for learners_DXZ,learners_ZX. Setup is identical to custom_ensemble_weights. Note: custom_ensemble_weights and custom_ensemble_weights_DXZ,custom_ensemble_weights_ZX must have the same number of columns.
cluster_variable	A vector of cluster indices.
subsamples_byZ	List of two lists corresponding to the two instrument levels. Each list contains vectors with sample indices for cross-fitting.
cv_subsamples_byZ	List of two lists, each corresponding to one of the two instrument 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_late provides a double/debiased machine learning estimator for the local average treatment effect in the interactive model given by

Y = g_0(D, X) + U,

where (Y, D, X, Z, U) is a random vector such that \operatorname{supp} D = \operatorname{supp} Z = \{0,1\}, E[U\vert X, Z] = 0, E[Var(E[D\vert X, Z]\vert X)] \neq 0, \Pr(Z=1\vert X) \in (0, 1) with probability 1, p_0(1, X) \geq p_0(0, X) with probability 1 where p_0(Z, X) \equiv \Pr(D=1\vert Z, X), and g_0 is an unknown nuisance function.

In this model, the local average treatment effect is defined as

\theta_0^{\textrm{LATE}} \equiv E[g_0(1, X) - g_0(0, X)\vert p_0(1, X) > p(0, X)].

Value

ddml_late returns an object of S3 class ddml_late. An object of class ddml_late is a list containing the following components:

late

A vector with the average treatment effect 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_late().

oos_pred

List of matrices, providing the reduced form predicted values.

learners,learners_DXZ,learners_ZX, cluster_variable,subsamples_Z0, subsamples_Z1,cv_subsamples_list_Z0, cv_subsamples_list_Z1,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.

Imbens G, Angrist J (1004). "Identification and Estimation of Local Average Treatment Effects." Econometrica, 62(2), 467-475.

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

See Also

summary.ddml_late()

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

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

# Estimate the local 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")
late_fit <- ddml_late(y, D, Z, 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(late_fit)

ddml documentation built on Oct. 3, 2024, 1:13 a.m.