causalQual (version 1.0.0)

causalQual_rd: Causal Inference for Qualitative Outcomes under Regression Discontinuity

Description

Fit local polynomial regression models for qualitative outcomes to estimate the probabilities of shift at the cutoff.

Usage

causalQual_rd(Y, running_variable, cutoff)

Value

An object of class causalQual.

Arguments

Y

Qualitative outcome. Must be labeled as \(\{1, 2, \dots\}\).

running_variable

Running variable determining treatment assignment.

cutoff

Cutoff or threshold. Units with running_variable < cutoff are considered controls, while units with running_variable >= cutoff are considered treated.

Author

Riccardo Di Francesco

Details

Under a regression discontinuity design, identification requires that the probability mass functions for class \(m\) of potential outcomes are continuous in the running variable (continuity). If this assumption holds, we can recover the probability shift at the cutoff for class \(m\):

$$\delta_{m, C} := P(Y_i (1) = m | Running_i = cutoff) - P(Y_i(0) = m | Running_i = cutoff).$$

causalQual_rd applies, for each class \(m\), standard local polynomial estimators to the binary variable \(1(Y_i = m)\). Specifically, the ruotine implements the robust bias-corrected inference procedure of Calonico et al. (2014) (see the rdrobust function).

References

• Di Francesco, R., and Mellace, G. (2025). Causal Inference for Qualitative Outcomes. arXiv preprint arXiv:2502.11691. tools:::Rd_expr_doi("10.48550/arXiv.2502.11691").

See Also

causalQual_soo causalQual_iv causalQual_did

Examples

## Generate synthetic data.
set.seed(1986)

data <- generate_qualitative_data_rd(100, outcome_type = "ordered")

Y <- data$Y
running_variable <- data$running_variable
cutoff <- data$cutoff

## Estimate probabilities of shift at the cutoff.
fit <- causalQual_rd(Y, running_variable, cutoff)

summary(fit)
plot(fit)