Causal Inference with a Continuous Treatment: Addressing Positivity Constraints, Nonlinearity, and Effect Heterogeneity

Abstract

Causal inference approaches often emphasize binary treatments. But in many applications, the underlying constructs are continuous. In the potential outcomes framework, a continuous treatment can take on numerous values, each corresponding to a potential outcome that may be realized. In this setting, common estimands may be intractable because of a common issue in social research, particularly research on social inequality: the exposure is highly stratified by confounders. The authors show how to avoid drawing inferences about counterfactuals where data are unlikely to exist by carefully selecting the causal estimand. The authors adopt an additive shift estimand that adds a small, fixed amount to each unit’s income. This approach is preferable to population-average dose-response curves in settings in which some treatment values rarely occur in some subgroups. The authors also show how to estimate and summarize patterns of nonlinearity and effect heterogeneity with continuous treatments. As a motivating example, the authors consider the causal effect of parental income on college attendance, a setting in which the exposure is highly stratified by confounders (e.g., parental education). This approach applies to a wide range of possible treatment conditions in sociology.