Beyond Interaction Effects: Two Logics for Studying Population Inequalities

TL;DR

Addressing how causal effects of college vary across subpopulations, the paper contrasts deductive interaction models with inductive causal learning methods, and clarifies estimands including $ATE$, $CATE$, and $ITE$ within a unified framework. It uses simulations to show that linear heterogeneity is well captured by traditional models, while complex, high-order heterogeneity benefits from causal forests and meta-learners. A two-stage discovery-then-confirmation strategy is recommended to harness the strengths of both approaches. The work guides inequality research and policy targeting under high-dimensional covariates, emphasizing careful specification of estimands, methodological alignment with goals, and transparency in reporting.

Abstract

When sociologists and other social scientist ask whether the return to college differs by race and gender, they face a choice between two fundamentally different modes of inquiry. Traditional interaction models follow deductive logic: the researcher specifies which variables moderate effects and tests these hypotheses. Machine learning methods follow inductive logic: algorithms search across vast combinatorial spaces to discover patterns of heterogeneity. This article develops a framework for navigating between these approaches. We show that the choice between deduction and induction reflects a tradeoff between interpretability and flexibility, and we demonstrate through simulation when each approach excels. Our framework is particularly relevant for inequality research, where understanding how treatment effects vary across intersecting social subpopulation is substantively central.

Figures (6)

• Figure 1: Structural causal model distinguishing CATE from ITE. Observed confounders $X$ affect both treatment $W$ and outcome $Y$. Unobserved factors $U$ (shown greyed) also influence outcomes. CATE can be identified by adjusting for $X$; ITE would require knowledge of individual-specific values of $U$, which we do not observe.
• Figure 2: Causal structure of the simulation. Income (Inc) is a confounder that also modifies the treatment effect. Minority status (Min) and gender (Fem) modify effects but do not affect treatment assignment---they are pure moderators. Neighborhood quality (Nbh) affects outcomes only and does not moderate effects. The unobserved noise term $U$ represents individual-specific factors that affect outcomes; recovering $U$ through abduction is essential for counterfactual inference at the individual level.
• Figure 3: Causal forest estimates versus true conditional average treatment effects across three simulation scenarios. Points falling along the diagonal indicate accurate estimation.
• Figure 4: Variable importance from causal forest in the complex nonlinear scenario, showing which covariates drive treatment effect heterogeneity.
• Figure 5: True versus estimated CATE by subgroup in the complex nonlinear scenario. The causal forest (green) tracks true effects (gray) more closely than OLS (blue) across most subgroups, with the largest discrepancy for minority women where OLS cannot distinguish between high and low income (see rows 1 and 3 of Table \ref{['tab:subgroup']}). The causal forest achieves over four times lower mean absolute bias than OLS (0.17 vs. 0.74).

Theorems & Definitions (3)

• Definition 1: Average Treatment Effect
• Definition 2: Conditional Average Treatment Effect
• Definition 3: Individual Treatment Effect