Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies

2011/10/17 by Jens Hainmueller · 151 citations
Mathematics · #Advanced Causal Inference Techniques #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · doi:10.1093/pan/mpr025

openalex publication_date 2011/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

This paper proposes entropy balancing, a data preprocessing method to achieve covariate balance in observational studies with binary treatments. Entropy balancing relies on a maximum entropy reweighting scheme that calibrates unit weights so that the reweighted treatment and control group satisfy a potentially large set of prespecified balance conditions that incorporate information about known sample moments. Entropy balancing thereby exactly adjusts inequalities in representation with respect to the first, second, and possibly higher moments of the covariate distributions. These balance improvements can reduce model dependence for the subsequent estimation of treatment effects. The method assures that balance improves on all covariate moments included in the reweighting. It also obviates the need for continual balance checking and iterative searching over propensity score models that may stochastically balance the covariate moments. We demonstrate the use of entropy balancing with Monte Carlo simulations and empirical applications.

Citations

• Large Sample Properties of Generalized Method of Moments Estimators
• The central role of the propensity score in observational studies for causal effects
• Variable Selection for Propensity Score Models
• Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score

Cited by

• The green dividend of digital finance: The impact of mobile money on solar adoption in Kenya
• The role of networked governance for local climate policy output. Evidence from Europe
• Generalizing Graph Neural Networks on Out-Of-Distribution Graphs
• Climate change exposure and corporate culture: A text-based approach
• Institutional investor distraction and corporate fraud: Evidence from China
• Retrospective Orthogonal Design: Response-Surface Reconstruction from Observational Data
• The Effects of Mandatory ESG Disclosure Around the World
• Optimal Estimation of Generalized Average Treatment Effects using Kernel Optimal Matching
• Balance-Subsampled Stable Prediction
• Tracking Pupils Into Adulthood: Selective Schools and Long-Term Human Capital
• Long-Run Career Outcomes of Multiple Job Holding
• The relative and joint effects of gunshot detection technology and video surveillance cameras on case clearance in Chicago
• Learning density ratios in causal inference using Bregman-Riesz regression
• Causal mediation analysis: From simple to more robust strategies for estimation of marginal natural (in)direct effects
• Unexpected Event during Survey Design: Promise and Pitfalls for Causal Inference
• Only one-third of protected areas in the Chaco effectively curb woodland loss, but their impact extends beyond their boundaries
• "Papai ou mamãe pode me dar uma mesada?" Uma análise sobre alfabetização financeira no PISA 2018 a partir do efeito da mesada
• Minimax Linear Estimation of the Retargeted Mean
• The impact of political risks on carbon emissions
• The demand for elections under autocracy: Regime approval and the elimination of local elections in Russia
• Numbers and Narratives: The Effect of a Combined Information and Role Model Intervention in Reducing Inequalities in Access to Higher Education in Denmark
• A study on the impact of open doors: investigating the influence of short leave and open prison on recidivism rates
• Marshall Lecture 2025: Political Information and Network Effects
• Learning loss due to school closures during the COVID-19 pandemic
• Marginalization of Regression-Adjusted Treatment Effects in Indirect Comparisons with Limited Patient-Level Data
• Polygenic and developmental profiles of autism differ by age at diagnosis
• Recent Developments in Causal Inference and Machine Learning
• Reversion to the Mean, or Their Version of the Dream? Latino Voting in an Age of Populism
• The prosecutor's cut: Body‐worn camera evidence and criminal case dispositions
• Migrant Deaths at Borders and Immigration Attitudes: Evidence from the 2013 Lampedusa Shipwreck
• The Null Impact of Parenthood on Technical Risk Preferences
• When Governments Deliver: Migrant Remittances and the Willingness to Pay Higher Local Taxes
• Environmental disasters and ecomodernist beliefs: Insights from a quasi‐natural experiment
• Excess costs of post-traumatic stress disorder related to child maltreatment in Germany
• Exit, voice and loyalty in the family: findings from a basic income experiment
• Entropy balancing is doubly robust
• The impact of ETS on productivity in developing economies: A micro-econometric evaluation with Chinese firm-level data
• Direct Bias-Correction Term Estimation for Propensity Scores and Average Treatment Effect Estimation
• Achieving Statistical Significance with Control Variables and Without Transparency
• Every person has their price? Political corruption and CEO compensation
• Enabling patient–physician continuity in Swedish primary care: the importance of a named GP. A registry-based observational study
• Does Open Government Data Alleviate the Burden on Government Employees? Evidence From a Quasi‐Experiment in China
• Urban mobility and learning: analyzing the influence of commuting time on students' GPA at Politecnico di Milano
• Cross-national evidence for political philosophers’ civic behavior
• Gender Promotion Gaps and Career Aspirations
• From Bow to Brain: Reducing Educational Inequalities through Music Education? Evidence from a Quasi-Experiment on a Violin Program for Young, Disadvantaged Children
• Economic Sanctions and Taxation of Natural Resource Rent: Evidence From Spatial Analysis
• Fog or smog? The impact of uncensored reporting on pollution on individuals’ environmental preferences
• Counting Race, Miscounting Identity: The Census and Hispanic Racial Self-Identification
• Kernel-Distance-Based Covariate Balancing
• Balancing vs modeling approaches to weighting in practice
• When international meets domestic: The interactive effect of domestic and international election observers
• Long-Term Consequences of Early Access to Educational Opportunity
• The reverberations of British Brexit politics abroad
• Employment Responses to a Partner’s Disability Onset (“Care Shocks”): Do Working Conditions Matter?
• Do managerial incentives facilitate anti-competitive behavior? Evidence from collusion
• Populist electoral success and party system concentration: A cross-national analysis
• How deceptive online networks reached millions in the US 2020 elections
• End-to-End Balancing for Causal Continuous Treatment-Effect Estimation
• How to Measure Your App: A Couple of Pitfalls and Remedies in Measuring App Performance in Online Controlled Experiments
• FairTune: A Bias-Aware Fine-Tuning Framework Towards Fair Heart Rate Prediction from PPG
• Effects of international sanctions on age-specific mortality: a cross-national panel data analysis
• Estimating quantile-specific rental yields for residential housing in Sydney
• Household responses to trade shocks
• Transfer learning of individualized treatment rules from experimental to real-world data
• The impact of immunotherapy on reductions in cancer mortality: Evidence from Medicare
• Environmental Performance, Financial Constraint and Tax Avoidance Practices: Insights from FTSE All-Share Companies
• Targeted digital voter suppression efforts likely decrease voter turnout
• Treatment Effects Estimation by Uniform Transformer
• Just the right amount of caution? Remote instruction and student performance in Sweden during the COVID-19 pandemic
• Towards Out-Of-Distribution Generalization: A Survey
• Generalized full matching and extrapolation of the results from a large-scale voter mobilization experiment
• Stable Prediction across Unknown Environments
• The Statistical Performance of Matching-Adjusted Indirect Comparisons
• Policy preferences in response to large forced migration inflows
• Negotiating Difficult Issues with Little Fervour? Why Peace Processes in Territorial Conflicts Tend to Produce Incomplete Outcomes
• Hit by the Silk Road: how wage coordination in Europe mitigates the China shock*
• A framework for causal estimand selection under positivity violations
• Health shocks and earnings trajectories: A comparative study of migrants and natives in Finland
• Do Socially Responsible Firms Walk the Talk?
• Fueling discontent: the politics of carbon taxation in Canada
• Invited Commentary: Does Chronic Immunosuppression Have a Negative Impact on Patients Who Require Emergency General Surgery?
• Democratizing corporate governance: How retail investors’ ESG attention reduces ESG-washing
• What to Observe When Assuming Selection on Observables
• Does Social Trust Travel? Comparing Resident and Non‐resident Citizens from a High‐Trusting Country
• Who Does the Caring? Gender Disparities in COVID-19 Attitudes and Behaviors
• From local to global: How foreign acquisitions reshape job mobility
• Why are corporations terminated? A century of evidence from the Netherlands
• Climate change and corporate cash holdings: Global evidence
• Estimating Average Treatment Effects: Supplementary Analyses and Remaining Challenges
• Optimal transport weights for causal inference
• Prevalence and correlates of loneliness and social isolation in the oldest old: a systematic review, meta-analysis and meta-regression
• Fairness in Rankings and Recommendations: An Overview
• Labor market sorting and the gender pay gap revisited
• Evidence for the irrelevance of irrelevant events
• Permutation Weighting
• Estimating Average Treatment Effects with Support Vector Machines
• Navigated Weighting to Improve Inverse Probability Weighting for Missing Data Problems and Causal Inference
• Robust Estimation of Propensity Score Weights via Subclassification
• Regulatory avoidance responses to private Country-by-Country Reporting
• The impact of suspension on participation in school-based extracurricular activities and out-of-school community service
• Consequences of Corruption for Political System Support: Evidence From a Brazilian Scandal
• Certification effect of R&D subsidies on debt financing: do institutional forces matter?
• How to Reform Without Reforming: School District Racial Composition and Pennsylvania’s “Fair” Funding Formula
• Do solar panels increase housing rents in Australia?
• Randomized Controlled Trial of Counseling Approach for Long-Term Welfare Recipients in Switzerland
• Corruption and Default Risk: Global Evidence
• The role of corporate social responsibility (CSR) information in supply-chain contracting: Evidence from the expansion of CSR rating coverage
• Learning Decomposed Representation for Counterfactual Inference
• Using Balancing Weights to Target the Treatment Effect on the Treated when Overlap is Poor
• How balance and sample size impact bias in the estimation of causal treatment effects: A simulation study
• The Finite Sample Performance of Treatment Effects Estimators based on the Lasso
• Misinformation and Motivated Reasoning: Responses to Economic News in a Politicized Environment
• Reducing bias in difference-in-differences models using entropy balancing
• Residual Balancing: A Method of Constructing Weights for Marginal Structural Models
• The effects of school shootings on risky behavior, health, and human capital
• Counterfactual Representation Learning with Balancing Weights
• Propensity score weighting for causal inference with multi-stage clustered data
• Synthetic Area Weighting for Measuring Public Opinion in Small Areas
• The Impact of Executives’ IT Expertise on Reported Data Security Breaches
• Decriminalizing or reassembling schools? Implications of removing police from schools for racial and ethnic disparities in criminal justice system contact
• Can norm‐based information campaigns reduce corruption?
• Political practitioners poorly predict which messages persuade the public
• Influence of different endodontic treatment protocols on tooth survival: A retrospective cohort study with multistate analysis and group balancing
• Varying impacts of letters of recommendation on college admissions: Approximate balancing weights for subgroup effects in observational studies
• Do candidates’ policy positions matter in regional elections? Evidence from the 2021 elections to the Welsh Senedd
• Augmented Inverse Hybrid Weighting: Robust Inference under Deterministic and Random Distribution Shifts
• When the Rich Get Richer: Class, Globalization, and the Sociotropic Determinants of Populism
• Sparsity Double Robust Inference of Average Treatment Effects
• Optimal Covariate Balancing Conditions in Propensity Score Estimation
• A Python Library For Empirical Calibration
• Balanced off-policy evaluation in general action spaces
• Seven deadly sins of contemporary quantitative political analysis
• Impact of the Family Doctor Contracting System on unmet healthcare needs in Shandong Province, China
• How Voters Respond to Currency Crises: Evidence From Turkey
• Entropy-balanced accruals
• Populist Persuasion in Electoral Campaigns: Evidence from Bryan's Unique Whistle-Stop Tour
• Does mandatory disclosure of firm’s tax avoidance position affect corporate investment efficiency?
• Strategic Violence during Democratization: Evidence from Myanmar
• Earlier Surgery Reduces Complications in Acute Traumatic Thoracolumbar Spinal Cord Injury: Analysis of a Multi-Center Cohort of 4108 Patients
• Reality of Accomplishing Surgery within 24 Hours for Complete Cervical Spinal Cord Injury: Clinical Practices and Safety
• Methods for population adjustment with limited access to individual patient data: A review and simulation study
• Electoral Backlash against Climate Policy: A Natural Experiment on Retrospective Voting and Local Resistance to Public Policy
• On variance estimation for generalizing from a trial to a target population
• The benefits of a virtual emergency department observation unit for hospital observation patients
• Spanking and children's social competence: Evidence from a US kindergarten cohort study
• Spanking and children's early academic skills: Strengthening causal estimates
• WITHDRAWN: Corporate culture and carbon emission performance
• Did increasing the UK’s Universal Credit and working tax credits by £20 per week in 2020–2021 reduce food insecurity?
• CEO Narcissism and Repetitive Language in MD&A Disclosures: Informative Reinforcement or Opportunistic Obfuscation?
• The Effects of Structural Conditions on Sectoral Productivity in South, East and South East Asia

Related

• Entropy balancing is doubly robust
• Large Sample Properties of Entropy Balancing Estimators of Average Causal Effects
• Balancing Higher Moments Matters for Causal Estimation: Further Context for the Results of Setodji et al. (2017)
• Kernel-Distance-Based Covariate Balancing
• Balancing Approach for Causal Inference at Scale