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Estimator for the Partially Linear Model.

Source: R/ddml_plm.R
ddml_plm.Rd

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.

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.

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.

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)
#> PLM estimation results: 
#>  
#> , , single base learner
#> 
#>                  Estimate  Std. Error     t value     Pr(>|t|)
#> (Intercept)  0.0007204734 0.006877341   0.1047605 9.165659e-01
#> D_r         -0.1483220220 0.014700193 -10.0898010 6.129365e-24
#> 

# 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)
#> PLM estimation results: 
#>  
#> , , nnls
#> 
#>                Estimate  Std. Error    t value     Pr(>|t|)
#> (Intercept)  0.00147421 0.006883107   0.214178 8.304082e-01
#> D_r         -0.14947020 0.014730261 -10.147152 3.411741e-24
#> 
#> , , mdl:ols
#> 
#>                 Estimate  Std. Error   t value     Pr(>|t|)
#> (Intercept)  0.003412073 0.006898066  0.494642 6.208528e-01
#> D_r         -0.141683435 0.014682123 -9.650064 4.912490e-22
#> 
#> , , mdl:lasso
#> 
#>                  Estimate  Std. Error      t value     Pr(>|t|)
#> (Intercept) -0.0002879934 0.006884257  -0.04183362 9.666313e-01
#> D_r         -0.1495940169 0.014729260 -10.15624781 3.108085e-24
#> 
#> , , mdl:ridge
#> 
#>                  Estimate  Std. Error      t value     Pr(>|t|)
#> (Intercept) -0.0002309068 0.006884361  -0.03354077 9.732434e-01
#> D_r         -0.1494407672 0.014732341 -10.14372166 3.533745e-24
#>