opl_tb_c
In OPL: Optimal Policy Learning

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(OPL)

Introduction

The opl_tb_c function implements ex-ante treatment assignment using as policy class a threshold-based (or quadrant) approach at specific threshold values c1 and c2 for respectively the selection variables var1 and var2.

Usage

opl_tb_c(make_cate_result, z, w, c1 = NA, c2 = NA)

Arguments

make_cate_result: A data frame containing input data, including a column named my_cate, representing conditional average treatment effects (CATE).
z: A character vector of length 2 specifying the column names of the two selection variables.
w: A character string indicating the column name for treatment assignment (binary variable).
c1: User-defined or function-optimized threshold for the first selection variable (between 0 and 1).
c2: User-defined or function-optimized threshold for the second selection variable (between 0 and 1).

Output

The function returns the input data frame augmented with: - z[1]_std: Standardized first selection variable. - z[2]_std: Standardized second selection variable. - units_to_be_treated: Binary indicator for treatment assignment.

Additionally, the function: - Prints a summary of key results, including threshold values, constrained and unconstrained welfare, and treatment proportions. - Displays a scatter plot visualizing the policy assignment.

Details

The function follows these steps: 1. Standardizes the selection variables to a [0,1] range. 2. Identifies the optimal thresholds using grid search to maximize constrained welfare. 3. Computes and reports key statistics, including average welfare and percentage of treated units.

Example

# Load example data
set.seed(123)
data_example <- data.frame(
  my_cate = runif(100, -1, 1),
  var1 = runif(100, 0, 1),
  var2 = runif(100, 0, 1),
  treatment = sample(0:1, 100, replace = TRUE)
)

# Run threshold-based policy learning
result <- opl_tb_c(
  make_cate_result = data_example,
  z = c("var1", "var2"),
  w = "treatment"
)

Interpretation of Results

The printed summary provides insights into the optimal threshold values and the proportion of units assigned to treatment.
The scatter plot visualizes the treatment assignment based on the optimized thresholds.

References

Athey, S., & Wager, S. (2021). Policy Learning with Observational Data. Econometrica, 89(1), 133–161.
Cerulli, G. (2021). Improving econometric prediction by machine learning. Applied Economics Letters, 28(16), 1419-1425.
Cerulli, G. (2022). Optimal treatment assignment of a threshold-based policy: empirical protocol and related issues. Applied Economics Letters. DOI: 10.1080/13504851.2022.2032577.
Gareth, J., Witten, D., Hastie, D.T., & Tibshirani, R. (2013). An Introduction to Statistical Learning: with Applications in R. New York: Springer.
Kitagawa, T., & Tetenov, A. (2018). Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice. Econometrica, 86(2), 591–616.

This vignette provides an overview of the opl_tb_c function and demonstrates its usage for threshold-based policy learning. For further details, consult the package documentation.

Acknowledgment

The development of this software was supported by FOSSR (Fostering Open Science in Social Science Research), a project funded by the European Union - NextGenerationEU under the NPRR Grant agreement n. MURIR0000008.