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Best Linear Predictor (BLP) Analysis for Conditional Average Treatment Effects

blp_analysis.Rd

Runs the Best Linear Predictor (BLP) analysis proposed by Chernozhukov, Demirer, Duflo, and Fernandez-Val (2020) to summarize heterogeneous treatment effects (HTEs) estimated by a causal forest or any CATE estimator. Tests whether HTEs are significantly driven by observed covariates.

Usage

blp_analysis(
  cate_hat,
  Y,
  W,
  Y_hat = NULL,
  W_hat = NULL,
  data = NULL,
  run_gates = TRUE,
  n_groups = 5,
  debiased = TRUE,
  conf_level = 0.95
)

Arguments

cate_hat

Numeric vector of estimated CATEs (e.g., from grf::causal_forest()).

Y

Numeric vector. Observed outcomes.

W

Numeric vector. Binary treatment assignment (0/1).

Y_hat

Numeric vector. Cross-fitted \(E[Y \mid X]\) estimates.

W_hat

Numeric vector. Cross-fitted \(E[W \mid X]\) (propensity score).

data

Data frame or matrix of raw covariates. Used for GATES subgroup analysis if run_gates = TRUE.

run_gates

Logical. Whether to also run GATES analysis. Default TRUE.

n_groups

Integer. Number of quantile groups for GATES. Default 5.

debiased

Logical. Use debiased estimates with cross-fitting if TRUE (default). Requires Y_hat and W_hat.

conf_level

Numeric. Confidence level. Default 0.95.

Value

A list with:

blp

Data frame with BLP coefficients \(\beta_1\) (average treatment effect) and \(\beta_2\) (HTE loading). A significant \(\beta_2\) indicates meaningful heterogeneity.

gates

Data frame of Group Average Treatment Effects by quantile group, or NULL if run_gates = FALSE.

blp_plot

ggplot2 coefficient plot of BLP results.

gates_plot

ggplot2 GATES plot, or NULL.

Details

The BLP is estimated from the regression: $$Y_i - \hat{Y}_i = \beta_1 (\hat{W}_i - \hat{e}_i) + \beta_2 (\hat{\tau}_i - \bar{\hat{\tau}})(\hat{W}_i - \hat{e}_i) + \varepsilon_i$$ Key tests:

  • \(\beta_1 \neq 0\): Overall ATE different from zero.

  • \(\beta_2 \neq 0\): CATE varies with \(\hat{\tau}\) (HTE present).

References

Chernozhukov, V., Demirer, M., Duflo, E., & Fernandez-Val, I. (2020). Generic machine learning inference on heterogeneous treatment effects in randomized experiments. NBER Working Paper 24678.

Examples

if (FALSE) { # \dontrun{
library(grf)
n <- 2000; p <- 10
X <- matrix(rnorm(n * p), n, p)
W <- rbinom(n, 1, 0.5)
tau <- pmax(X[, 1], 0)
Y <- tau * W + rnorm(n)

cf <- causal_forest(X, Y, W)
tau_hat <- predict(cf)$predictions
blp_analysis(
  cate_hat = tau_hat, Y = Y, W = W,
  Y_hat = cf$Y.hat, W_hat = cf$W.hat
)
} # }