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    • All HBS Web  (77)
      • Faculty Publications  (30)

      Causal InferenceRemove Causal Inference →

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      • 2025
      • Article

      Statistical Inference for Heterogeneous Treatment Effects Discovered by Generic Machine Learning in Randomized Experiments

      By: Kosuke Imai and Michael Lingzhi Li
      Researchers are increasingly turning to machine learning (ML) algorithms to investigate causal heterogeneity in randomized experiments. Despite their promise, ML algorithms may fail to accurately ascertain heterogeneous treatment effects under practical settings with... View Details
      Keywords: AI and Machine Learning; Mathematical Methods; Analytics and Data Science
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      Imai, Kosuke, and Michael Lingzhi Li. "Statistical Inference for Heterogeneous Treatment Effects Discovered by Generic Machine Learning in Randomized Experiments." Journal of Business & Economic Statistics 43, no. 1 (2025): 256–268.
      • 2024
      • Article

      Neyman Meets Causal Machine Learning: Experimental Evaluation of Individualized Treatment Rules

      By: Michael Lingzhi Li and Kosuke Imai
      A century ago, Neyman showed how to evaluate the efficacy of treatment using a randomized experiment under a minimal set of assumptions. This classical repeated sampling framework serves as a basis of routine experimental analyses conducted by today’s scientists across... View Details
      Keywords: AI and Machine Learning; Research
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      Li, Michael Lingzhi, and Kosuke Imai. "Neyman Meets Causal Machine Learning: Experimental Evaluation of Individualized Treatment Rules." Journal of Causal Inference 12, no. 1 (2024).
      • 2025
      • Working Paper

      Evaluations Amid Measurement Error: Determining the Optimal Timing for Workplace Interventions

      By: Matthew DosSantos DiSorbo, Iavor I. Bojinov and Fiammetta Menchetti
      Researchers have embraced factorial experiments to simultaneously evaluate multiple treatments, each with different levels. Typically, in large-scale factorial experiments, the primary objective is identifying the treatment with the largest causal effect, especially... View Details
      Keywords: Factorial Designs; Fisher Randomizations; Rank Estimators; Employer Interventions; Causal Inference; Mathematical Methods; Performance Improvement
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      DosSantos DiSorbo, Matthew, Iavor I. Bojinov, and Fiammetta Menchetti. "Evaluations Amid Measurement Error: Determining the Optimal Timing for Workplace Interventions." Harvard Business School Working Paper, No. 24-075, June 2024. (Revised May 2025.)
      • 2024
      • Working Paper

      Advancing Personalization: How to Experiment, Learn & Optimize

      By: Aurelie Lemmens, Jason M.T. Roos, Sebastian Gabel, Eva Ascarza, Hernan Bruno, Elea McDonnell Feit, Brett Gordon, Ayelet Israeli, Carl F. Mela and Oded Netzer
      Personalization has become the heartbeat of modern marketing. Advances in causal inference and machine learning enable companies to understand how the same marketing action can impact the choices of individual customers differently. This article provides an academic... View Details
      Keywords: Personalization; Targeting; Experiments; Observational Studies; Policy Implementation; Policy Evaluation; Customization and Personalization; Marketing Strategy; AI and Machine Learning
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      Lemmens, Aurelie, Jason M.T. Roos, Sebastian Gabel, Eva Ascarza, Hernan Bruno, Elea McDonnell Feit, Brett Gordon, Ayelet Israeli, Carl F. Mela, and Oded Netzer. "Advancing Personalization: How to Experiment, Learn & Optimize." Working Paper, July 2024. (Revised March 2025.)
      • 2023
      • Working Paper

      An Experimental Design for Anytime-Valid Causal Inference on Multi-Armed Bandits

      By: Biyonka Liang and Iavor I. Bojinov
      Typically, multi-armed bandit (MAB) experiments are analyzed at the end of the study and thus require the analyst to specify a fixed sample size in advance. However, in many online learning applications, it is advantageous to continuously produce inference on the... View Details
      Keywords: Analytics and Data Science; AI and Machine Learning; Mathematical Methods
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      Liang, Biyonka, and Iavor I. Bojinov. "An Experimental Design for Anytime-Valid Causal Inference on Multi-Armed Bandits." Harvard Business School Working Paper, No. 24-057, March 2024.
      • 2024
      • Working Paper

      Anytime-Valid Inference in Linear Models and Regression-Adjusted Causal Inference

      By: Michael Lindon, Dae Woong Ham, Martin Tingley and Iavor I. Bojinov
      Linear regression adjustment is commonly used to analyze randomized controlled experiments due to its efficiency and robustness against model misspecification. Current testing and interval estimation procedures leverage the asymptotic distribution of such estimators to... View Details
      Keywords: Mathematical Methods; Analytics and Data Science
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      Lindon, Michael, Dae Woong Ham, Martin Tingley, and Iavor I. Bojinov. "Anytime-Valid Inference in Linear Models and Regression-Adjusted Causal Inference." Harvard Business School Working Paper, No. 24-060, March 2024.
      • 2023
      • Article

      Estimating Causal Peer Influence in Homophilous Social Networks by Inferring Latent Locations.

      By: Edward McFowland III and Cosma Rohilla Shalizi
      Social influence cannot be identified from purely observational data on social networks, because such influence is generically confounded with latent homophily, that is, with a node’s network partners being informative about the node’s attributes and therefore its... View Details
      Keywords: Causal Inference; Homophily; Social Networks; Peer Influence; Social and Collaborative Networks; Power and Influence; Mathematical Methods
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      McFowland III, Edward, and Cosma Rohilla Shalizi. "Estimating Causal Peer Influence in Homophilous Social Networks by Inferring Latent Locations." Journal of the American Statistical Association 118, no. 541 (2023): 707–718.
      • March–April 2023
      • Article

      Pricing for Heterogeneous Products: Analytics for Ticket Reselling

      By: Michael Alley, Max Biggs, Rim Hariss, Charles Herrmann, Michael Lingzhi Li and Georgia Perakis
      Problem definition: We present a data-driven study of the secondary ticket market. In particular, we are primarily concerned with accurately estimating price sensitivity for listed tickets. In this setting, there are many issues including endogeneity, heterogeneity in... View Details
      Keywords: Price; Demand and Consumers; AI and Machine Learning; Investment Return; Entertainment and Recreation Industry; Sports Industry
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      Alley, Michael, Max Biggs, Rim Hariss, Charles Herrmann, Michael Lingzhi Li, and Georgia Perakis. "Pricing for Heterogeneous Products: Analytics for Ticket Reselling." Manufacturing & Service Operations Management 25, no. 2 (March–April 2023): 409–426.
      • 2023
      • Working Paper

      Distributionally Robust Causal Inference with Observational Data

      By: Dimitris Bertsimas, Kosuke Imai and Michael Lingzhi Li
      We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds in two steps. We first... View Details
      Keywords: AI and Machine Learning; Mathematical Methods
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      Bertsimas, Dimitris, Kosuke Imai, and Michael Lingzhi Li. "Distributionally Robust Causal Inference with Observational Data." Working Paper, February 2023.
      • 2023
      • Article

      Experimental Evaluation of Individualized Treatment Rules

      By: Kosuke Imai and Michael Lingzhi Li
      The increasing availability of individual-level data has led to numerous applications of individualized (or personalized) treatment rules (ITRs). Policy makers often wish to empirically evaluate ITRs and compare their relative performance before implementing them in a... View Details
      Keywords: Causal Inference; Heterogeneous Treatment Effects; Precision Medicine; Uplift Modeling; Analytics and Data Science; AI and Machine Learning
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      Imai, Kosuke, and Michael Lingzhi Li. "Experimental Evaluation of Individualized Treatment Rules." Journal of the American Statistical Association 118, no. 541 (2023): 242–256.
      • December 2022
      • Article

      Fostering Perceptions of Authenticity via Sensitive Self-Disclosure

      By: Li Jiang, Leslie K. John, Reihane Boghrati and Maryam Kouchaki
      Leaders’ perceived authenticity—the sense that leaders are acting in accordance with their “true self”—is associated with positive outcomes for both employees and organizations alike. How might leaders foster this impression? We show that sensitive self-disclosure, in... View Details
      Keywords: Authenticity; Weaknesses; Self-disclosure; Leaders; Impression Management; Leadership Style; Motivation and Incentives
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      Jiang, Li, Leslie K. John, Reihane Boghrati, and Maryam Kouchaki. "Fostering Perceptions of Authenticity via Sensitive Self-Disclosure." Journal of Experimental Psychology: Applied 28, no. 4 (December 2022): 898–915.
      • October–December 2022
      • Article

      Achieving Reliable Causal Inference with Data-Mined Variables: A Random Forest Approach to the Measurement Error Problem

      By: Mochen Yang, Edward McFowland III, Gordon Burtch and Gediminas Adomavicius
      Combining machine learning with econometric analysis is becoming increasingly prevalent in both research and practice. A common empirical strategy involves the application of predictive modeling techniques to "mine" variables of interest from available data, followed... View Details
      Keywords: Machine Learning; Econometric Analysis; Instrumental Variable; Random Forest; Causal Inference; AI and Machine Learning; Forecasting and Prediction
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      Yang, Mochen, Edward McFowland III, Gordon Burtch, and Gediminas Adomavicius. "Achieving Reliable Causal Inference with Data-Mined Variables: A Random Forest Approach to the Measurement Error Problem." INFORMS Journal on Data Science 1, no. 2 (October–December 2022): 138–155.
      • June 2022 (Revised January 2025)
      • Technical Note

      Causal Inference

      By: Iavor I Bojinov, Michael Parzen and Paul Hamilton
      This note provides an overview of causal inference for an introductory data science course. First, the note discusses observational studies and confounding variables. Next the note describes how randomized experiments can be used to account for the effect of... View Details
      Keywords: Causal Inference; Causality; Experiment; Experimental Design; Data Science; Analytics and Data Science
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      Bojinov, Iavor I., Michael Parzen, and Paul Hamilton. "Causal Inference." Harvard Business School Technical Note 622-111, June 2022. (Revised January 2025.)
      • 2022
      • Working Paper

      Causal Inference During A Pandemic: Evidence on the Effectiveness of Nebulized Ibuprofen as an Unproven Treatment for COVID-19 in Argentina

      By: Sebastian Calonico, Rafael Di Tella and Juan Cruz Lopez Del Valle
      Many medical decisions during the pandemic were made without the support of causal evidence obtained in clinical trials. We study the case of nebulized ibuprofen (NaIHS), a drug that was extensively used on COVID-19 patients in Argentina amidst wild claims about its... View Details
      Keywords: COVID-19; Drug Treatment; Health Pandemics; Health Care and Treatment; Decision Making; Outcome or Result; Argentina
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      Calonico, Sebastian, Rafael Di Tella, and Juan Cruz Lopez Del Valle. "Causal Inference During A Pandemic: Evidence on the Effectiveness of Nebulized Ibuprofen as an Unproven Treatment for COVID-19 in Argentina." NBER Working Paper Series, No. 30084, May 2022.
      • Article

      How Much Should We Trust Staggered Difference-In-Differences Estimates?

      By: Andrew C. Baker, David F. Larcker and Charles C.Y. Wang
      We explain when and how staggered difference-in-differences regression estimators, commonly applied to assess the impact of policy changes, are biased. These biases are likely to be relevant for a large portion of research settings in finance, accounting, and law that... View Details
      Keywords: Difference In Differences; Staggered Difference-in-differences Designs; Generalized Difference-in-differences; Dynamic Treatment Effects; Mathematical Methods
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      Baker, Andrew C., David F. Larcker, and Charles C.Y. Wang. "How Much Should We Trust Staggered Difference-In-Differences Estimates?" Journal of Financial Economics 144, no. 2 (May 2022): 370–395. (Editor's Choice, May 2022; Jensen Prize, First Place, June 2023.)
      • April–June 2022
      • Other Article

      Commentary on 'Causal Decision Making and Causal Effect Estimation Are Not the Same... and Why It Matters'

      By: Edward McFowland III
      There has been a substantial discussion in various methodological and applied literatures around causal inference; especially in the use of machine learning and statistical models to understand heterogeneity in treatment effects and to make optimal decision... View Details
      Keywords: Causal Inference; Treatment Effect Estimation; Treatment Assignment Policy; Human-in-the-loop; Decision Making; Fairness
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      McFowland III, Edward. "Commentary on 'Causal Decision Making and Causal Effect Estimation Are Not the Same... and Why It Matters'." INFORMS Journal on Data Science 1, no. 1 (April–June 2022): 21–22.
      • March 2022
      • Article

      Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models

      By: Fiammetta Menchetti and Iavor Bojinov
      Researchers regularly use synthetic control methods for estimating causal effects when a sub-set of units receive a single persistent treatment, and the rest are unaffected by the change. In many applications, however, units not assigned to treatment are nevertheless... View Details
      Keywords: Causal Inference; Partial Interference; Synthetic Controls; Bayesian Structural Time Series; Mathematical Methods
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      Menchetti, Fiammetta, and Iavor Bojinov. "Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models." Annals of Applied Statistics 16, no. 1 (March 2022): 414–435.
      • 2021
      • Working Paper

      Population Interference in Panel Experiments

      By: Iavor I Bojinov, Kevin Wu Han and Guillaume Basse
      The phenomenon of population interference, where a treatment assigned to one experimental unit affects another experimental unit's outcome, has received considerable attention in standard randomized experiments. The complications produced by population interference in... View Details
      Keywords: Finite Population; Potential Outcomes; Dynamic Causal Effects; Mathematical Methods
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      Bojinov, Iavor I., Kevin Wu Han, and Guillaume Basse. "Population Interference in Panel Experiments." Harvard Business School Working Paper, No. 21-100, March 2021.
      • 2020
      • Working Paper

      Fresh Fruit and Vegetable Consumption: The Impact of Access and Value

      By: Retsef Levi, Elisabeth Paulson and Georgia Perakis
      The goal of this paper is to leverage household-level data to improve food-related policies aimed at increasing the consumption of fruits and vegetables (FVs) among low-income households. Currently, several interventions target areas where residents have limited... View Details
      Keywords: Food Deserts; Food Access; Food Policy; Causal Inference; Food; Nutrition; Poverty; Government Administration
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      Levi, Retsef, Elisabeth Paulson, and Georgia Perakis. "Fresh Fruit and Vegetable Consumption: The Impact of Access and Value." MIT Sloan Research Paper, No. 5389-18, October 2020.
      • Article

      The Importance of Being Causal

      By: Iavor I Bojinov, Albert Chen and Min Liu
      Causal inference is the study of how actions, interventions, or treatments affect outcomes of interest. The methods that have received the lion’s share of attention in the data science literature for establishing causation are variations of randomized experiments.... View Details
      Keywords: Causal Inference; Observational Studies; Cross-sectional Studies; Panel Studies; Interrupted Time-series; Instrumental Variables
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      Bojinov, Iavor I., Albert Chen, and Min Liu. "The Importance of Being Causal." Harvard Data Science Review 2.3 (July 30, 2020).
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