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Recent Developments in Applied Econometrics

Paper Session

Saturday, Jan. 4, 2025 10:15 AM - 12:15 PM (PST)

Hilton San Francisco Union Square, Union Square 14
Hosted By: Econometric Society
  • Chair: Daniel Wilhelm, Munich University

Sequential Synthetic Difference in Differences

Dmitry Arkhangelsky
,
CEMFI
Aleksei Samkov
,
CEMFI

Abstract

We study the estimation of treatment effects of a binary policy in environments with a staggered treatment rollout. We propose a new estimator -- Sequential Synthetic Difference in Difference (Sequential SDiD) -- and establish its theoretical properties in a linear model with interactive fixed effects. Our estimator is based on sequentially applying the original SDiD estimator proposed in Arkhangelsky et al. (2021) to appropriately aggregated data. To establish the theoretical properties of our method, we compare it to an infeasible OLS estimator based on the knowledge of the subspaces spanned by the interactive fixed effects. We show that this OLS estimator has a sequential representation and use this result to show that it is asymptotically equivalent to the Sequential SDiD estimator. This result implies the asymptotic normality of our estimator along with corresponding efficiency guarantees. The method developed in this paper presents a natural alternative to the conventional DiD strategies in staggered adoption designs.

Causal Duration Analysis with Diff-in-Diff

Ben Deaner
,
University College London
Hyejin Ku
,
University College London

Abstract

In economic program evaluation it is common to obtain panel data in which outcomes are indicators that an individual has reached an absorbing state. This may be an indicator that an individual has exited a period of unemployment, passed an exam, left a marriage, or had their parole revoked. The parallel trends assumption that underpins difference-in-differences generally fails in such settings. We suggest alternative identifying conditions that are analogous to those of diff-in-diff
but apply to hazard rates rather than mean outcomes.
These alternative assumptions motivate estimators that retain the simplicity and transparency of standard diff-in-diff, and we suggest analogous specification tests. Our approach can be adapted to general linear restrictions between the hazard rates of different groups, motivating duration analogues of the triple differences and synthetic control methods. We apply our procedures to examine the impact of a policy that increased the generosity of unemployment benefits using a cross-cohort comparison.

Inference for Rank-Rank Regressions

Denis Chetverikov
,
University of California-Los Angeles
Daniel Wilhelm
,
Munich University

Abstract

Slope coefficients in rank-rank regressions are popular measures of intergenerational mobility, for instance in regressions of a child's income rank on their parent's income rank. In this paper, we first point out that commonly used variance estimators such as the homoskedastic or robust variance estimators do not consistently estimate the asymptotic variance of the OLS estimator in a rank-rank regression. We show that the probability limits of these estimators may be too large or too small depending on the shape of the copula of child and parent incomes. Second, we derive a general asymptotic theory for rank-rank regressions and provide a consistent estimator of the OLS estimator's asymptotic variance. We then extend the asymptotic theory to other regressions involving ranks that have been used in empirical work. Finally, we apply our new inference methods to three empirical studies. We find that the confidence intervals based on estimators of the correct variance may sometimes be substantially shorter and sometimes substantially longer than those based on commonly used variance estimators. The differences in confidence intervals concern economically meaningful values of mobility and thus lead to different conclusions when comparing mobility in U.S. commuting zones with mobility in other countries.

Difference-in-Differences Estimators with Repeated Cross-Sections, Staggered Timing, and Heterogeneous Treatment Effects

Partha Deb
,
CUNY-Hunter College
Edward C. Norton
,
University of Michigan
Jeffrey M. Wooldridge
,
Michigan State University
Jeffrey Zabel
,
Tufts University

Abstract

This paper builds on the recent theoretical advances in the difference-in-differences literature
for the case in which the start of treatment is staggered over time across cohorts of treated
groups and treatment effects are heterogeneous over both cohorts and time. Specifically, in
the repeated cross-section context, we show that a linear regression with a sufficiently flexible
functional form consisting of parameters for cohort-by-time treatment effects, two-way
fixed effects, and interaction terms yields consistent estimates of heterogeneous treatment
effects when the treatment start time is staggered. Because this specification is estimated
using OLS, the estimates are efficient and aggregation of treatment effects and inference
are straightforward. We illustrate the use of this model and provide comparisons to other
recently derived estimators using two empirical examples.

Discussant(s)
Ben Deaner
,
University College London
Jeffrey Zabel
,
Tufts University
Ruohan Zhan
,
Hong Kong University of Science and Technology
Dmitry Arkhangelsky
,
CEMFI
Daniel Wilhelm
,
Munich University
JEL Classifications
  • C12 - Hypothesis Testing: General
  • C13 - Estimation: General