# A Semiparametric Instrumented Difference-in-Differences Approach to Policy Learning

arXiv: https://arxiv.org/abs/2310.09545 · HTML: https://mlsanity.com/paper/2310.09545/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 63 references that are in the map.
- First posted on arXiv 14 Oct 2023.

## Builds on (most cited first, 26 of 26)

- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Confidence Intervals for Policy Evaluation in Adaptive Experiments](https://mlsanity.com/paper/1911.02768/) (2019)
- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Sensitivity Analysis of Individual Treatment Effects: A Robust Conformal Inference Approach](https://mlsanity.com/paper/2111.12161/) (2021)
- [Semiparametric proximal causal inference](https://mlsanity.com/paper/2011.08411/) (2020)
- [Learning When-to-Treat Policies](https://mlsanity.com/paper/1905.09751/) (2019)
- [Fast Rates for Contextual Linear Optimization](https://mlsanity.com/paper/2011.03030/) (2020)
- [The State of Applied Econometrics - Causality and Policy Evaluation](https://mlsanity.com/paper/1607.00699/) (2016)
- [Doubly Robust Distributionally Robust Off-Policy Evaluation and Learning](https://mlsanity.com/paper/2202.09667/) (2022)
- [Off-Policy Confidence Interval Estimation with Confounded Markov Decision Process](https://mlsanity.com/paper/2202.10589/) (2022)
- [Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables](https://mlsanity.com/paper/1611.09925/) (2016)
- [A semiparametric instrumental variable approach to optimal treatment regimes under endogeneity](https://mlsanity.com/paper/1911.09260/) (2019)
- [Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding](https://mlsanity.com/paper/2105.01187/) (2021)
- [An Instrumental Variable Approach to Confounded Off-Policy Evaluation](https://mlsanity.com/paper/2212.14468/) (2022)
- [What's Trending in Difference-in-Differences? A Synthesis of the Recent Econometrics Literature](https://mlsanity.com/paper/2201.01194/) (2022)
- [Estimating Optimal Treatment Rules with an Instrumental Variable: A Partial Identification Learning Approach](https://mlsanity.com/paper/2002.02579/) (2020)
- [Learning from a Biased Sample](https://mlsanity.com/paper/2209.01754/) (2022)
- [Policy Targeting under Network Interference](https://mlsanity.com/paper/1906.10258/) (2019)
- [Using Decision Lists to Construct Interpretable and Parsimonious Treatment Regimes](https://mlsanity.com/paper/1504.07715/) (2015)
- [Efficient and robust transfer learning of optimal individualized treatment regimes with right-censored survival data](https://mlsanity.com/paper/2301.05491/) (2023)
- [Selecting and ranking individualized treatment rules with unmeasured confounding](https://mlsanity.com/paper/2002.10436/) (2020)
- [General Identification of Dynamic Treatment Regimes Under Interference](https://mlsanity.com/paper/2004.01218/) (2020)
- [Structural mean models for instrumented difference-in-differences](https://mlsanity.com/paper/2209.10339/) (2022)
- [A Negative Correlation Strategy for Bracketing in Difference-in-Differences](https://mlsanity.com/paper/2006.02423/) (2020)
- [Using negative controls to identify causal effects with invalid instrumental variables](https://mlsanity.com/paper/2204.04119/) (2022)
- [A Nonparametric Framework for Universal Difference-in-Differences](https://mlsanity.com/paper/2212.13641/) (2022)

## Abstract (arXiv)

Recently, there has been a surge in methodological development for the difference-in-differences (DiD) approach to evaluate causal effects. Standard methods in the literature rely on the parallel trends assumption to identify the average treatment effect on the treated. However, the parallel trends assumption may be violated in the presence of unmeasured confounding, and the average treatment effect on the treated may not be useful in learning a treatment assignment policy for the entire population. In this article, we propose a general instrumented DiD approach for learning the optimal treatment policy. Specifically, we establish identification results using a binary instrumental variable (IV) when the parallel trends assumption fails to hold. Additionally, we construct a Wald estimator, novel inverse probability weighting (IPW) estimators, and a class of semiparametric efficient and multiply robust estimators, with theoretical guarantees on consistency and asymptotic normality, even when relying on flexible machine learning algorithms for nuisance parameters estimation. Furthermore, we extend the instrumented DiD to the panel data setting. We evaluate our methods in extensive simulations and a real data application.