Monotonic Path-Specific Effects: Application to Estimating Educational Returns

TL;DR

The paper develops a Monotonic Path-Specific Effects (MPSE) framework to dissect educational returns along sequential transitions. By leveraging mediator monotonicity and sequential ignorability, it identifies a decomposition of the average treatment effect into a direct component and monotonic continuation effects through ordered educational stages, enabling unique path-specific inferences. The author proposes two estimators—a semiparametric efficient EIF-based Debiased Machine Learning (DML) method and a parametric Regression-With-Residuals (RWR) approach—and validates them via simulations and an empirical study using the NLSY97, finding that high school graduation largely affects earnings directly, with modest indirect effects through subsequent education. The framework relaxes cross-world assumptions relative to standard mediation, accommodates observed mediator confounding with separate covariate sets, and offers bias-sensitivity tools for unobserved confounding, with extensions to categorical mediators and applications beyond education acknowledged. Overall, MPSE provides a principled, identifiable, and practically estimable way to quantify how different educational transitions contribute to outcomes such as earnings.

Abstract

Conventional research on educational effects typically either employs a "years of schooling" measure of education, or dichotomizes attainment as a point-in-time treatment. Yet, such a conceptualization of education is misaligned with the sequential process by which individuals make educational transitions. In this paper, I propose a causal mediation framework for the study of educational effects on outcomes such as earnings. The framework considers the effect of a given educational transition as operating indirectly, via progression through subsequent transitions, as well as directly, net of these transitions. I demonstrate that the average treatment effect (ATE) of education can be additively decomposed into mutually exclusive components that capture these direct and indirect effects. The decomposition has several special properties which distinguish it from conventional mediation decompositions of the ATE, properties which facilitate less restrictive identification assumptions as well as identification of all causal paths in the decomposition. An analysis of the returns to high school completion in the NLSY97 cohort suggests that the payoff to a high school degree stems overwhelmingly from its direct labor market returns. Mediation via college attendance, completion and graduate school attendance is small because of individuals' low counterfactual progression rates through these subsequent transitions.

Figures (12)

• Figure 1: Causal Relationships with Two Monotonic Mediators Shown in a Directed Acyclic Graph (DAG) and the 3 Monotonic Path Specific Effects (MPSEs). $A$ denotes an initial transition of interest, $Y$, an outcome, and $M_{1}$ and $M_{2}$ are two causally ordered, monotonic mediators. The set $(X,Z_{1},Z_{2})$ captures pre-treatment and intermediate confounders.
• Figure 2: Decomposition of the Average Total Effect (ATE) of High School Graduation on Logged Earnings via Debiased Machine-Learning (DML) and Regression-With-Residuals (RWR).
• Figure 3: Bias, RMSE, and coverage of DML and RWR estimators for $n=1000,1500,2000$. The red dots show the performance of the DML and RWR estimators when the correct feature matrix is supplied to the estimators; the blue dots show the performance of the two estimators when an incorrect feature matrix is supplied to the estimators.
• Figure 4: Sensitivity Analysis for the "gross effect" $(\tau_{k})$ and "direct effect" $(\Delta_{k})$ terms in decomposition. Each row corresponds to a different set of ($\alpha_{k},\beta_{k})$ terms, where $\alpha_{k}=\mathbb{E}[Y|x,\overline{z}_{k},\overline{1}_{k},m_{k},U_{k}=1]-\mathbb{E}[Y|x,\overline{z}_{k},\overline{1}_{k},m_{k},U_{k}=0]$ parameterizes the effect of $U_{k}$ on Y, and $\beta_{k}=\text{Pr}[U_{k}=1|x,\overline{z}_{k},\overline{1}_{k},m_{k}]-\text{Pr}[U_{k}=1|x,\overline{z}_{k},\overline{1}_{k}])$ parameterizes the effect of $M_{k}$ on $U_{k}$. Each row corresponds to a different set of $(\alpha_{k},\beta_{k})$ terms. For example, the top row corresponds to $(\alpha_{0},\beta_{0})$, while the second row corresponds to $(\alpha_{1},\beta_{1})$, and so on.
• Figure 5: Distribution of the estimated graduate-school propensity score $\Pr(M_3 = 1 \mid X, Z, A = 1, M_1 = 1, M_2 = 1)$ among BA completers. The distribution shows substantial overlap without concentration near 0 or 1, supporting the plausibility of the positivity assumption for the graduate-school transition.

Theorems & Definitions (4)

• Theorem 3.1
• Theorem 3.2: Semiparametric efficiency
• Lemma J.1
• proof