Primary Submission Category: Heterogeneous Treatment Effects
Causal Inference for Distributional Treatments
Authors: Andrej Srakar,
Presenting Author: Andrej Srakar*
Symbolic data analysis proposes that a distribution or an interval of the individual records’ values is associated with each unit considering new variable types named symbolic variables. Wo build on contributions by Athey and Imbens (2006), Gunsilius (2020) and Pollmann (2022) to develop concept of a distributional treatment, i.e. causal variable which is of distributional nature. Different to previous authors we transform the problem in a general regression context for empirical distributional data, in particular Dias-Brito (2011) two-quantile and Irpino-Verde (2012) two-component regressions which more adequately solve the problem of negative coefficients in the regression of quantile functions. We develop explicit formulas for average treatment effect, average treatment effect for compliers and local average treatment effect in a linear regression framework. We study the performance of our approach in asymptotic and simulation context. We demonstrate that in the Dias-Brito case it transforms in a constrained OLS optimization problem with well defined optimal solutions. In Irpino-Verde case we derive an explicit form for the ATE estimator and show it is consistent and asymptotically normal. We apply this to causal relationship between health indicators and decision to retire using pooled panel dataset of Health and Retirement Study (HRS). Our analysis can be generalized to other causal approaches in econometrics and statistics.