Estimation of treatment effects on ordinal variables in multivariate ordered choice models

The current study examines the estimation of treatment effects on ordinal variables when the conditional independence assumption between the treatment variable and the outcome variable is violated. An extension of existing approaches is proposed through a parametric method based on a hierarchical system of ordered choice equations. The key methodological contribution involves deriving analytical formulas for calculating average treatment effects and average marginal effects of explanatory variables within multivariate ordered probit models that account for endogenous treatment and non-random selection in ordinal outcomes. Using NSDUH survey data (2020–2023), we empirically analyze stress effects on addictive goods consumption. The analysis demonstrates a significant impact of stress on the propensity for addictive behavior. It also assesses the treatment effects of different levels of stress on the probability and frequency of substance use. A comparative analysis with models that ignore endogeneity confirms the necessity of an estimation hierarchical system for exact measurement of the stress effect. Substance use probability increases consistently with stress levels, with women exhibiting greater vulnerability to these effects. The study shows that stress impact varies across socioeconomic groups, identifying specific high-risk populations for substance use initiation.