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Estimating endogenous treatments effects under long-range dependency without untreated controls.

Shiming Hao1

  • 1Law School, Yunnan University, Chenggong, Kunming, Yunnan, P. R. China.

Plos One
|June 3, 2026
PubMed
Summary

This study introduces a new econometric method for analyzing staggered social policy effects using time-series data. The approach addresses complex treatment heterogeneities and endogeneities, offering robust estimation without traditional instruments.

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Area of Science:

  • Econometrics
  • Social Policy Analysis
  • Time-Series Analysis

Background:

  • Estimating social policy impacts using natural experiments is crucial but challenged by staggered treatment adoptions and omitted variable endogeneity.
  • Existing methods often require suitable untreated units or instrument variables, which are not always available.

Purpose of the Study:

  • To develop a novel method for identifying and estimating treatment effects with multiple, staggered, and endogenous treatments.
  • To address scenarios lacking untreated units or suitable instrument variables.

Main Methods:

  • Proposes a conditional mean symmetry condition using a common proximal variable to eliminate confounding biases.
  • Introduces a weak index restriction with Bernstein expansions for consistent estimation of multiple heterogeneous treatment effects, robust to weak proximal variables.
  • Develops a bootstrap procedure to handle inference challenges arising from time-series dependencies.

Main Results:

  • The proposed method can identify and estimate staggered endogenous treatment effects under novel conditions.
  • Asymptotic distribution of the estimator is characterized as a fractional Brownian motion process.
  • Monte Carlo simulations demonstrate the estimator's effectiveness in small samples.

Conclusions:

  • The novel econometric framework successfully addresses identification and estimation challenges in staggered endogenous treatment effect analysis.
  • The method provides a viable alternative when traditional identification strategies are unavailable.
  • Empirical application to unilateral divorce law reforms illustrates the practical utility of the proposed approach.