Differences-in-differences (DID) is one of the most widely used methods for impact-evaluation in economics and the social sciences. The key idea behind DiD is to compare outcomes trends for treated and control groups, allowing researchers to estimate the effects of policies or interventions when randomized experiments are not feasible. This book provides a clear and rigorous guide to modern DID methods, covering both classical approaches and newer estimators developed for complex real-world settings. Designed for advanced undergraduate students, graduate students, and applied researchers, it explains when standard methods are reliable, when they can mislead, and how alternative approaches can provide more credible results. Throughout, theoretical discussion is paired with empirical applications, exercises using real datasets, and practical recommendations for implementation.
The book offers:
鈥� Discussion of all designs in which DID apply: classical designs, staggered adoption designs, designs with variation in treatment dose, and staggered first switch designs
鈥� Study of standard estimators, estimators without parallel trends (e.g., synthetic controls), and heterogeneity-robust estimators
鈥� 5 lists of dos and don鈥檛s for practitioners
鈥� 150 exercises to understand the theory, and 50 practical exercises to apply it to real empirical examples in Stata and R
Cl茅ment de Chaisemartin is professor of economics at Sciences Po, Paris. Xavier D’Haultfoeuille is professor of economics at CREST-ENSAE.
- Preface
- I Introduction and Setup
- 1 Introduction
- 1.1 The classical DID design: Chapters 3 and 4
- 1.1.1 Definition of a classical DID design
- 1.1.2 Potential outcomes and target parameter
- 1.1.3 Three possible estimators: treated versus control, before鈥揳fter, and DID
- 1.1.4 The parallel-trends assumption
- 1.1.5 Parallel-trends is weaker than the assumptions underlying treated-versus-control and before鈥揳fter comparisons
- 1.1.6 The parallel-trends assumption remains a strong assumption, whose plausibility should be assessed
- 1.1.7 Relaxations of the parallel-trends assumption
- 1.1.8 Application to the effect of the 2009 VAT reduction in French restaurants on profits, prices, and wages
- 1.2 Beyond the classical DID design: Chapters 5 to 8
- 1.2.1 Two-way fixed effects regressions
- 1.2.2 What does a TWFER estimate outside of the classical DID design?
- 1.2.3 Heterogeneity-robust DID estimators
- 1.2.3.1 Staggered adoption designs
- 1.2.3.2 Heterogeneous adoption designs
- 1.2.3.3 Staggered first switch designs
- 2 Data, Notation, and Assumptions
- 2.1 Data requirements: group-level panel data
- 2.2 Treatment and potential outcomes
- 2.3 Identifying assumptions
- 2.3.1 Exclusion restrictions
- 2.3.2 Parallel trends
- 2.4 The book鈥檚 perspective on statistical inference
- 2.4.1 A 鈥渕odel-based鈥� perspective on statistical inference
- 2.4.2 Assuming independent outcomes between groups does not rule out common shocks*
- 2.4.3 At what level should we cluster standard errors?*
- II The Classical Design
- 3 The Classical DID Design
- 3.1 Target parameters
- 3.2 Two-way fixed effects regressions
- 3.2.1 Static two-way fixed effects regressions
- 3.2.1.1 Assuming randomized treatment rather than parallel-trends?
- 3.2.2 Event-study two-way fixed effects regressions
- 3.2.2.1 Estimating event-study effects
- 3.2.2.2 Pretrend tests
- 3.2.2.3 Application to the effect of compulsory licensing on innovation
- 3.3 Inference
- 3.3.1 Asymptotically valid CIs with many treated and control groups
- 3.3.2 When are G0 and G1 large enough to rely on CIs with HC2 standard errors and Bell and McCaffrey鈥檚 critical values? Some simulations
- 3.3.3 What can researchers do when HC2-BM CIs seem unreliable?*
- 3.3.3.1 Few treated groups but many control groups
- 3.3.3.2 Few treated and control groups
- 3.3.3.3 Recommendations for practitioners
- 3.4 Limitations of pretrend tests
- 3.4.1 We can test for parallel-trends before but not after treatment
- 3.4.1.1 Concomitant shocks
- 3.4.1.2 Other policies
- 3.4.2 Pretrend tests often lack power
- 3.4.3 Do pretrend tests lead to a pretesting problem?*
- 3.5 An alternative, imputation estimator
- 3.5.1 Imputation estimator
- 3.5.2 Three numerical equivalences
- 3.5.3 Comparing the properties of 尾虃鈩�fe and 尾虃鈩�imp
- 3.5.4 Application to the effect of compulsory licensing on innovation
- 3.6 Estimating heterogeneous effects
- 3.6.1 Estimating the correlation between treatment effects and some covariates
- 3.6.2 Estimating the variance of group-specific effects*
- 3.6.3 Estimating the distribution of group-specific effects*
- 3.7 Nonlinear DID
- 3.7.1 Limited dependent variables
- 3.7.2 Sensitivity to functional form*
- 3.7.2.1 The parallel-trends assumption may not be invariant to functional form
- 3.7.2.2 A necessary and sufficient condition to have parallel-trends for any functional form
- 3.7.2.3 When should researchers worry about sensitivity to functional form?
- 3.7.3 Estimating quantile treatment effects*
- 3.8 Instrumental-variable DID estimators
- 3.9 Further topics
- 3.9.1 Imbalanced panels
- 3.9.2 Weighting
- 3.9.3 Accounting for and estimating spillover effects
- 3.10 Practitioners鈥� do鈥檚 and don鈥檛s
- 3.11 Appendix*
- 3.11.1 The Frisch鈥揥augh鈥揕ovell theorem
- 3.11.2 Proof of (3.14)
- 4 Alternatives to parallel-trends
- 4.1 TWFE and DID estimators with control variables
- 4.1.1 Conditional parallel-trends
- 4.1.2 TWFERs with control variables
- 4.1.3 DID estimators with control variables
- 4.1.3.1 Parametric estimators
- 4.1.3.2 Nonparametric estimators
- 4.1.3.3 Matched DIDs
- 4.1.3.4 Controlling for group-specific linear trends
- 4.1.3.5 Triple-difference estimators*
- 4.1.3.6 When to include control variables in the estimation?
- 4.1.4 Controlling for the lagged outcome?
- 4.1.4.1 AR(1) model for the outcome without treatment*
- 4.1.4.2 Self-selection, and parallel-trends conditional on the baseline outcome
- 4.1.5 Computing DID estimators with controls in Stata and R
- 4.1.6 Application to the effect of compulsory licensing on innovation
- 4.2 Interactive fixed effects, synthetic controls, and synthetic DID
- 4.2.1 Interactive fixed effects
- 4.2.2 Synthetic control and synthetic DID
- 4.2.2.1 Synthetic control
- 4.2.2.2 Synthetic DID
- 4.2.3 Application to the effect of compulsory licensing on innovation
- 4.3 Bounded differential trends
- 4.4 Practitioners鈥� do鈥檚 and don鈥檛s
- 4.5 Appendix*
- 4.5.1 Proof of Theorem 4.1
- 4.5.2 Comparison of variances of DID estimators with and without covariates
- 4.5.3 Details on the computation of the TWFE-IFE estimator
- III Beyond the Classical Design
- 5 The pifalls of TWFE estimators
- 5.1 A decomposition of 尾虃fe
- 5.2 尾虃fe may be biased for ATT
- 5.3 尾虃fe may not estimate a convex combination of effects
- 5.4 Decompositions of related estimators
- 5.5 Stata and R commands to compute the implicit weights of TWFERs and first-difference regressions
- 5.6 Application to the effect of newspapers on turnout in US elections
- 5.6.1 Basic TWFER
- 5.6.2 TWFER with state鈥搚ear FEs
- 5.6.3 First-difference regression with state鈥搚ear FEs
- 5.7 Next steps
- 6 Staggered Adoption Designs
- 6.1 Target parameters
- 6.2 Two-way fixed effects estimators
- 6.2.1 Static two-way fixed effects estimator
- 6.2.1.1 Decomposition of 尾虃fe
- 6.2.1.2 Application to the effect of unilateral divorce laws on divorces
- 6.2.1.3 The origin of the negative weights
- 6.2.1.4 Assuming randomized treatment timing instead of parallel trends?*
- 6.2.2 Event-study TWFE regressions
- 6.2.2.1 Decomposition of ES-TWFERs
- 6.2.2.2 Application to the effect of unilateral divorce laws on divorces
- 6.2.3 Local projection regressions*
- 6.3 Heterogeneity-robust estimators
- 6.3.1 Target parameters
- 6.3.2 DID estimators
- 6.3.2.1 Estimators
- 6.3.2.2 Extensions
- 6.3.2.3 Inference
- 6.3.2.4 Numerical equivalences with regression coefficients
- 6.3.2.5 Computation in Stata, R, and Python
- 6.3.3 Imputation estimators
- 6.3.3.1 Some numerical equivalences
- 6.3.3.2 Extensions
- 6.3.3.3 Inference
- 6.3.3.4 Computation in Stata and R
- 6.3.4 A comparison of heterogeneity-robust estimators
- 6.3.4.1 Variance
- 6.3.4.2 Confidence intervals coverage
- 6.3.4.3 Bias
- 6.3.4.4 Implementation in Stata, R, and Python
- 6.3.5 Application to the effect of unilateral divorce laws on divorces
- 6.4 TWFE and HR estimators in 13 SADs in political science
- 6.5 Estimating heterogeneous treatment effects
- 6.6 Nonlinear DID
- 6.6.1 Limited dependent variables
- 6.6.1.1 Application to the effect of free-trade agreements on trade
- 6.6.2 Estimating quantile treatment effects*
- 6.7 Further topics*
- 6.7.1 Using always-treated groups as controls?
- 6.7.2 Imbalanced panels
- 6.7.3 Weighting
- 6.7.4 Accounting for and estimating spillover effects
- 6.8 Practitioners鈥� do鈥檚 and don鈥檛s
- 6.9 Appendix*
- 7 Heterogeneous Adoption Designs
- 7.1 Target parameters
- 7.1.1 The conditional-average-slope function
- 7.1.2 Two unconditional averages of slopes
- 7.2 TWFERs in heterogeneous-adoption designs
- 7.2.1 Parallel-trends assumption
- 7.2.2 尾虃fe may not identify a convex combination of slopes
- 7.2.3 The origin of the negative weights
- 7.2.4 Assuming randomized treatment dose rather than parallel trends*
- 7.3 Heterogeneity-robust estimators
- 7.3.1 Parallel-trends assumptions and a fundamental decomposition
- 7.3.2 Designs with stayers or quasi-stayers
- 7.3.2.1 Identification
- 7.3.2.2 Estimation with stayers
- 7.3.2.3 Estimation without stayers but with quasi-stayers
- 7.3.3 Designs without stayers or quasi-stayers
- 7.3.4 Testing the null that there are quasi-stayers
- 7.3.5 Application to the effect, on US employment, of eliminating a potential tariffs鈥� spike on Chinese imports
- 7.4 Practitioners鈥� do鈥檚 and don鈥檛s
- 7.5 Appendix*
- 7.5.1 Proof of Theorem 7.1
- 7.5.2 Proof of Theorem 7.2
- 7.5.3 Proof of Theorem 7.3
- 8 General Designs
- 8.1 Static TWFER
- 8.1.1 Decomposition of TWFERs under the usual parallel-trends assumption
- 8.1.2 Decomposition of TWFERs under a parallel-trends assumption in a counterfactual where groups鈥� treatment does not change
- 8.1.3 Decomposition of TWFERs with randomly assigned treatments*
- 8.1.4 Extensions
- 8.1.4.1 TWFERs with several treatments
- 8.1.4.2 Two-stage-least-squares TWFERs, and Bartik regressions*
- 8.2 Distributed-lag TWFER
- 8.3 HR estimators for staggered first switch designs
- 8.3.1 Staggered first switch designs
- 8.3.2 Parallel-trends assumption
- 8.3.3 Target parameters and estimators
- 8.3.3.1 Building blocks: the group-specific actual-versus-status-quo effects
- 8.3.3.2 A generalization of the ATT鈩� event-study effects to staggered first switch designs
- 8.3.3.3 Path-specific event-study effects
- 8.3.3.4 Normalized event-study effects
- 8.3.3.5 Distributed-lag regressions allowing for heterogeneous effects across groups
- 8.3.3.6 A generalization of ATT to staggered first switch designs
- 8.3.3.7 Pretrend estimators
- 8.3.3.8 Testing if lagged treatments affect the outcome
- 8.3.4 Inference
- 8.3.5 Extensions
- 8.3.5.1 Continuous treatment
- 8.3.5.2 Estimators with control variables
- 8.3.5.3 Estimating heterogeneous effects
- 8.3.5.4 Estimators with several treatments*
- 8.3.5.5 Instrumental-variable DID estimators*
- 8.3.5.6 The initial-conditions problem in designs where the treatment varies at period one*
- 8.3.6 Application to the effect of newspapers on turnout in US elections
- 8.4 Heterogeneity-robust estimators, without dynamic effects
- 8.4.1 Switchers and stayers designs
- 8.4.2 Parallel-trends assumption
- 8.4.3 Target parameters and estimators
- 8.4.3.1 Target parameters
- 8.4.3.2 Estimators
- 8.4.3.3 Pretrend estimators
- 8.4.3.4 Estimators robust to dynamic effects up to a prespecified number of lags
- 8.4.4 Imputation estimators
- 8.4.5 Extensions
- 8.4.5.1 Continuous treatment
- 8.4.5.2 Estimators with several treatments*
- 8.4.5.3 Instrumental-variable DID estimators*
- 8.4.6 Computation in Stata and R
- 8.4.7 Application to the effect of newspapers on turnout in US elections
- 8.5 Conclusion
- 8.5.1 TWFE and HR estimators in general designs
- 8.5.2 HR estimators in designs without stayers?
- 8.5.2.1 Using quasi-stayers
- 8.5.2.2 Changing the treatment鈥檚 definition
- 8.5.2.3 Functional-form assumptions
- 8.6 Practitioners鈥� do鈥檚 and don鈥檛s
- 8.7 Appendix*
- 8.7.1 Proof of Theorem 8.1
- 8.7.2 Proof of Theorem 8.2
- 8.7.3 Proof of Theorem 8.3
- 8.7.4 Proof of Theorem 8.4
- 8.7.5 Proof of Theorem 8.5
- 8.7.6 Proof of Theorem 8.6
- Bibliography
- Index
“This book will be a canonical reference for differences-in-differences-style designs (and beyond). It offers a unique perspective not currently covered by any book at a graduate level, but which is nevertheless a central part of the research landscape in applied microeconomics and econometrics.”—Damian Clarke, University of Exeter and University of Chile
“A highly ambitious, impressively comprehensive, and methodologically sophisticated book that fills a real gap in the DiD literature. The authors display a superior grasp of the literature and pair that with strong empirical illustrations of key points, encouraging readers to actively work through empirical examples while simultaneously checking their conceptual understanding.”—L. Jason Anastasopoulos, University of Georgia
“The main strength of this excellent book lies in the comprehensive and coherent coverage of a wide range of DID designs, all presented in a unified notation. Another major advantage is the set of ready-to-use empirical examples accompanied by software code, which makes the material very accessible for applied researchers.”—Martin Huber, University of Fribourg
“Two of the masters of modern differences-in-differences provide both a theoretical and practical guide to dealing with all the messy real-world issues that come up in many applications of this extremely popular method. Continuous or multivalued treatments, a small number of treated units, when to include control variables, treatments that switch on- and then off-again—this fantastic book provides theory, practical examples, and code to help you handle it all.”—David McKenzie, Development Research Group, World Bank
“Differences-in-differences is now an indispensable framework for quantitative social science research. Two of the field’s foremost experts, Cl茅ment de Chaisemartin and Xavier D’Haultfoeuille, take readers from the practical essentials all the way to the research frontier, making this book an invaluable resource for both newcomers and experienced researchers.”—Kosuke Imai, Harvard University
“A brilliant and insightful deep dive into causal inference with differences-in-differences written by two of the world’s leading researchers in this rapidly expanding field. This book provides a comprehensive exposition from the classical DID design through to the wealth of recent designs including those that address staggered and heterogeneous adoption. Assumptions are clearly explained, compelling examples are presented throughout, and extremely helpful code is provided. A must read for all those interested in causal inference.”—Richard Blundell, University College London
Accessibility Features
-
Inaccessible, or known limited accessibility
-
No known hazards or warnings
