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Author: Clement de Chaisemartin
Publisher:
ISBN:
Category :
Languages : en
Pages : 34
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Book Description
We study regressions with period and group fixed effects and several treatment variables. Under a parallel trends assumption, the coefficient on each treatment identifies the sum of two terms. The first term is a weighted sum of the effect of that treatment in each group and period, with weights that may be negative and sum to one. The second term is a sum of the effects of the other treatments, with weights summing to zero. Accordingly, coefficients in those regressions are not robust to heterogeneous effects, and may be contaminated by the effect of other treatments. We propose alternative differences-in-differences estimators. To estimate, say, the effect of the first treatment, our estimators compare the outcome evolution of a group whose first treatment changes while its other treatments remain unchanged, to control groups whose treatments all remain unchanged, and with the same baseline treatments or treatments' history as the switching group. Those carefully selected comparisons are robust to heterogeneous effects, and do not suffer from the contamination problem.
Author: Clement de Chaisemartin
Publisher:
ISBN:
Category :
Languages : en
Pages : 34
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Book Description
We study regressions with period and group fixed effects and several treatment variables. Under a parallel trends assumption, the coefficient on each treatment identifies the sum of two terms. The first term is a weighted sum of the effect of that treatment in each group and period, with weights that may be negative and sum to one. The second term is a sum of the effects of the other treatments, with weights summing to zero. Accordingly, coefficients in those regressions are not robust to heterogeneous effects, and may be contaminated by the effect of other treatments. We propose alternative differences-in-differences estimators. To estimate, say, the effect of the first treatment, our estimators compare the outcome evolution of a group whose first treatment changes while its other treatments remain unchanged, to control groups whose treatments all remain unchanged, and with the same baseline treatments or treatments' history as the switching group. Those carefully selected comparisons are robust to heterogeneous effects, and do not suffer from the contamination problem.
Author: Clément de Chaisemartin
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Two-way fixed effects (TWFE) regressions with period and group fixed effects are widely used to estimate policies' effects: 26 of the 100 most cited papers published by the American Economic Review from 2015 to 2019 estimate such regressions. Researchers have long thought that TWFE estimators are equivalent to differences-in-differences (DID) estimators, that rely on a partly testable parallel trends assumption. In two-groups two-periods designs where a treatment group is untreated at both dates and a treatment group becomes treated at the second period, the treatment coefficient in a TWFE is indeed equivalent to a DID. Motivated by this fact, researchers have also estimated TWFE regressions in more complicated designs with many groups and periods, variation in treatment timing, treatments switching on and off, and/or non-binary treatments, confident that there as well, TWFE was giving them an estimation method that only relied on a partly testable parallel trends assumption. Two recent strands of literature have shattered that confidence. First, it has recently been shown that even if parallel trends holds, TWFE may produce misleading estimates, if the policy's effect is heterogeneous between groups or over time, as is often the case. The realization that one of the most commonly used empirical methods in the quantitative social sciences relies on an often-implausible assumption has spurred a flurry of methodological papers. Some of them have diagnosed this issue and analyzed its origins. Other papers have proposed alternative estimators relying on parallel trends conditions, like TWFE estimators, but robust to heterogeneous effects, unlike TWFE estimators. Hereafter, those alternative estimators are referred to as heterogeneity-robust DID estimators. Second, in a recent paper, Roth (2022) has shown that tests of the parallel trends assumption often lack statistical power, and may fail to detect differential trends between treated and control locations that are often large enough to account for a significant share of the policy's estimated effect. This realization has spurred a growing interest among practitioners for a second strand of literature, that has proposed alternative estimation methods relying on weaker assumptions than parallel trends. Examples include estimators relying on a conditional parallel trends assumption (see, e.g., Abadie, 2005), estimators assuming bounded differential trends (see, e.g., Manski and Pepper, 2018; Rambachan and Roth, 2023), estimators assuming a factor model with interactive fixed effects (see, e.g., Bai, 2003) and synthetic control estimators (see, e.g., Abadie et al., 2010), and estimators assuming grouped patterns of heterogeneity (see,e.g., Bonhomme and Manresa, 2015).This textbook aims to provide an overview of these two strands of literature, as well as other panel data methods routinely used for causal inference by practitionners.
Author: Clément de Chaisemartin
Publisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 50
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Book Description
Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they identify weighted sums of the average treatment effects (ATE) in each group and period, with weights that may be negative. Due to the negative weights, the linear regression estimand may for instance be negative while all the ATEs are positive. In two articles that have used those regressions, half of the weights are negative. We propose another estimator that solves this issue. In one of the articles we revisit, it is of a different sign than the linear regression estimator.
Author: Michael Lechner
Publisher: Foundations and Trends(r) in E
ISBN: 9781601984982
Category : Business & Economics
Languages : en
Pages : 72
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Book Description
This monograph presents a brief overview of the literature on the difference-in-difference estimation strategy and discusses major issues mainly using a treatment effect perspective that allows more general considerations than the classical regression formulation that still dominates the applied work.
Author: Jeffrey M. Wooldridge
Publisher: MIT Press
ISBN: 0262232588
Category : Business & Economics
Languages : en
Pages : 1095
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Book Description
The second edition of a comprehensive state-of-the-art graduate level text on microeconometric methods, substantially revised and updated. The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis. Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.
Author: Anaïs Fabre
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Dmitry Arkhangelsky
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We present a new perspective on the Synthetic Control (SC) method as a weighted least squares regression estimator with time fixed effects and unit weights. This perspective suggests a generalization with two way (both unit and time) fixed effects, and both unit and time weights, which can be interpreted as a unit and time weighted version of the standard Difference In Differences (DID) estimator. We find that this new Synthetic Difference In Differences (SDID) estimator has attractive properties compared to the SC and DID estimators. Formally we show that our approach has double robustness properties: the SDID estimator is consistent under a wide variety of weighting schemes given a well-specified fixed effects model, and SDID is consistent with appropriately penalized SC weights when the basic fixed effects model is misspecified and instead the true data generating process involves a more general low-rank structure (e.g., a latent factor model). We also present results that justify standard inference based on weighted DID regression. Further generalizations include unit and time weighted factor models.
Author: Edward W. Frees
Publisher: Cambridge University Press
ISBN: 9780521535380
Category : Business & Economics
Languages : en
Pages : 492
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Book Description
An introduction to foundations and applications for quantitatively oriented graduate social-science students and individual researchers.
Author: Alvin E. Roth
Publisher: Houghton Mifflin Harcourt
ISBN: 0544291131
Category : Business & Economics
Languages : en
Pages : 275
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Book Description
A Nobel laureate reveals the often surprising rules that govern a vast array of activities -- both mundane and life-changing -- in which money may play little or no role. If you've ever sought a job or hired someone, applied to college or guided your child into a good kindergarten, asked someone out on a date or been asked out, you've participated in a kind of market. Most of the study of economics deals with commodity markets, where the price of a good connects sellers and buyers. But what about other kinds of "goods," like a spot in the Yale freshman class or a position at Google? This is the territory of matching markets, where "sellers" and "buyers" must choose each other, and price isn't the only factor determining who gets what. Alvin E. Roth is one of the world's leading experts on matching markets. He has even designed several of them, including the exchange that places medical students in residencies and the system that increases the number of kidney transplants by better matching donors to patients. In Who Gets What -- And Why, Roth reveals the matching markets hidden around us and shows how to recognize a good match and make smarter, more confident decisions.
Author: Yves Croissant
Publisher: John Wiley & Sons
ISBN: 1118949188
Category : Mathematics
Languages : en
Pages : 435
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Book Description
Panel Data Econometrics with R provides a tutorial for using R in the field of panel data econometrics. Illustrated throughout with examples in econometrics, political science, agriculture and epidemiology, this book presents classic methodology and applications as well as more advanced topics and recent developments in this field including error component models, spatial panels and dynamic models. They have developed the software programming in R and host replicable material on the book’s accompanying website.
